FATE AND TRACKING OF ENGINEERED
NANOMATERIALS IN AQUEOUS ENVIRONMENTS
by Julie Lynn Bitter
A dissertation submitted to Johns Hopkins University in conformity with the requirements for the degree of Doctor of Philosophy
Department of Chemistry Johns Hopkins University
Baltimore, Maryland March 2014
© 2014 Julie L. Bitter All Rights Reserved
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Abstract
Engineered nanomaterials are incorporated into over 1600 commercially available
products on the market today, increasing the likelihood of nanoparticle release during a
nano-containing product’s life cycle. To determine any potential risks associated with
nanoparticle release, it is important to develop a detailed understanding of their behavior
in different aquatic systems. Towards this goal, this thesis focuses on the use of various
microscopic and spectroscopic techniques to study how the physical and chemical
properties of different nanoparticles affect their behavior in bulk aquatic media and near
environmental surfaces under a variety of conditions.
Suspensions of oxidized multiwalled and single walled carbon nanotubes (O-
MWCNTs/O-SWCNTs) were used to examine nanoparticles in bulk aquatic
environments. The effect of ultraviolet (UV) radiation on their colloidal stability was
investigated because UV light is used in drinking and waste water treatment to destroy
harmful pathogens; however, its effect on engineered nanomaterials remains unclear.
Results have shown that absorption of 254nm light causes colloidal O-MWCNTs to
become unstable and aggregate from a loss of surface oxygen by a photodecarboxylation
mechanism. There were observed removal and changes in functional group densities at
the O-MWCNT surface. The same mechanism was exhibited by O-SWCNTs; however,
whereas this transformation proceeds in the absence of any significant mass loss or
changes to the O-MWCNT structure, O-SWCNTs were effectively mineralized by the
UV radiation.
To examine nanoparticles near environmental surfaces, video microscopy was
used to track individual and ensemble averages of silica microspheres and micron-sized
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gold rods under various aquatic conditions above silicate surfaces. Using image analysis
algorithms and theoretical calculations, accurate and quantitative measurements of weak
(kT-scale) particle-surface interactions, diffusion behavior, and stability were obtained.
Hydrodynamic interactions provided evidence that silica “gel-layers”, which decrease in
thickness with increasing ionic strength, gave rise to anomalous colloidal stability of
silica microspheres seen over a range of solution conditions. These interactions were also
probed by examining the position dependent translational and rotational diffusion of gold
rods through slit pores and model 2-dimensional porous media. Theoretical calculations
were found to fit experimental rod trajectories well, exhibiting an ionic strength mediated
particle-surface separation dependence of the translational diffusion.
Advisor: Dr. D. Howard Fairbrother
Co-Advisor: Dr. Michael A. Bevan
Reader: Dr. John P. Toscano
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Acknowledgements
First I need to thank my advisor, Dr. Howard Fairbrother, for taking me into his
group six years ago. He gave me the opportunity to study chemistry in the environment,
which has been an interest to me since I was a child. Though difficult at times, he
encouraged me to pursue the most quality results possible in each project I undertook. I
thank him for the passion he tackled every obstacle, and for opening doors of
opportunity.
I also need to thank my co-advisor, Dr. Michael Bevan, for taking me under his
tutelage even though I was not an engineer by training. I am grateful for his patience with
my questions and ability to deconstruct difficult concepts. I would not have been able to
achieve what I have without his help.
My journey would not have been as fulfilling without the people who have gone
through it with me, and I need to thank the former and current lab members of both the
Fairbrother group: Dr. Justin Gorham, Dr. Joshua Wnuk, Dr. Billy Smith, Dr. Kevin
Wepasnick, Dr. Samantha Rosenberg, Jin Yang, Michael Barclay, David Goodwin,
Miranda Gallagher, Ronald Lankone, and Julie Spencer; and Bevan group: Dr. Daniel
Beltran, Dr. Tara Edwards, Gregg Duncan, Julia Swavola, Brad Rupp, Yuguang Yang,
Xiaoqing Hua, and Anna Coughlan. Without their assistance and guidance I would not
have been successful.
I owe great thanks to my undergraduate research advisor, Dr. Michael Sigman,
without whose support I never would have pursued graduate school in the first place. His
constant encouragement and support from academia was much appreciated.
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Lastly, to my parents, Ralph and Annette Bitter; my brother and sister-in-law,
Ralph and Jennifer Bitter; and my boyfriend, Timothy Tivvis. I want to thank them for
their undying love and support, especially in this last year when it has definitely been the
most trying. Be it the late phone calls after a bad day or sharing the happiness associated
with publishing my first paper, they stuck next to me through it all and I am forever
grateful for the hugs and the tears.
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Table of Contents
Page
ABSTRACT ...................................................................................................................... ii
ACKNOWLEDGMENTS ................................................................................................ iv
TABLE OF CONTENTS .................................................................................................. vi
LIST OF TABLES ...........................................................................................................xiv
LIST OF FIGURES .........................................................................................................xvi
LIST OF SCHEMES...................................................................................................... xxii
1. INTRODUCTION........................................................................................ ................1
1.1 Background........................... ..........................................................................1
1.1.1 Natural and Engineered Nanomaterials ...........................................1
1.1.2 Importance of Nanoparticle Size and Shape ....................................2
1.1.3 Engineered Nanoparticles in Consumer Products ............................4
1.1.4 Release and Transformation of Engineered Nanoparticles in the Environment ..........................................................................................5
1.1.5 Toxicity of Engineered Nanoparticles .............................................7
1.1.6 Methods to Characterize and Study Nanoparticles ........................ 10
1.2 Significance and Objectives .......................................................................... 11
1.3 Summary and Dissertation Outline ............................................................... 12
1.4 References ..................................................................................................... 14
PART I: INTERACTIONS OF COLLOIDAL PARTICLES IN AQUEOUS SUSPENSIONS
2. EXPERIMENTAL SET-UP AND PARAMETERS FOR UV STUDIES ................. 21
2.1 Chemicals and Materials ............................................................................... 21
2.1.1 Chemicals ....................................................................................... 21
2.1.2 Materials ........................................................................................ 22
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2.2 Carbon Nanotubes ......................................................................................... 23
2.2.1 Oxidized Multiwalled Carbon Nanotubes (O-MWCNTs) ............. 23
2.2.2 Oxidized Single Walled Carbon Nanotubes (O-SWCNTs) .......... 24
2.3 UV Irradiation Apparatus ............................................................................. 25
2.3.1 Rayonet Photochemical Reaction Chamber ................................... 25
2.3.2 Calibration of the Light Intensity ................................................... 26
2.4 Instrumentation ............................................................................................. 29
2.4.1 UV-Visible Spectroscopy .............................................................. 29
2.4.2 Dynamic Light Scattering (DLS) .................................................. 30
2.4.3 Zeta Potential ................................................................................. 31
2.4.4 X-ray Photoelectron Spectroscopy (XPS) .................................... 32
2.4.5 Chemical Derivatization (CD) ...................................................... 33
2.4.6 Transmission Electron Microscopy (TEM) .................................. 37
2.4.7 Raman Spectroscopy ...................................................................... 37
2.4.8 Total Inorganic Carbon (TIC) ....................................................... 39
2.4.9 Near-Infrared Fluorescence Spectroscopy (NIRF) ....................... 40
2.5 Oxidized CNT (O-CNT) Suspensions .......................................................... 44
2.5.1 Preparation of Stock O-CNT Suspensions ..................................... 44
2.5.2 Preparation of Experimental O-CNT Suspensions ........................ 45
2.6 UV Irradiation of O-CNT Suspensions......................................................... 46
2.6.1 Large Batch Volumes .................................................................... 46
2.6.2 Small Sample Volumes .................................................................. 48
2.7 References ..................................................................................................... 49
3. PHOTOCHEMICAL TRANSFORMATIONS OF OXIDIZED CARBON NANOTUBES AS A RESULT OF EXPOSURE TO UVC IRRADIATION ................. 51
3.1 Introduction ................................................................................................... 52
3.2 Experimental ................................................................................................. 56
3.2.1 O-CNTs .......................................................................................... 56
3.2.2 Chemicals ....................................................................................... 57
3.2.3 Preparation of O-CNT Suspensions ............................................... 58
3.2.4 UVC Irradiation ............................................................................. 59
3.2.4.1 Large Batch Volumes ..................................................... 60
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3.2.4.2 Small Sample Volumes ................................................... 61
3.2.5 Calibration of UVC Light Intensity ............................................... 62
3.2.6 Characterization of O-MWCNT Powders ..................................... 63
3.2.6.1 Chemical Characterization .............................................. 63
3.2.6.2 Structural Characterization ............................................. 64
3.3 Results and Discussion of O-MWCNTs ....................................................... 65
3.3.1 Visual Effect of UVC Irradiation ................................................... 65
3.3.2 Effects of Water Quality Parameters ............................................. 67
3.3.3 Chemical Transformations to O-MWCNTs Caused by UVC Irradiation .................................................................................................. 69
3.3.4 Structural Transformations to O-MWCNTs .................................. 78
3.3.5 Phototransformations of Oxidized Carbon Based Nanomaterials ........................................................................................... 82
3.3.6 Environmental Implications ........................................................... 84
3.4 Results and Discussion of O-SWCNTs ........................................................ 85
3.4.1 Visual Effect of UVC Irradiation ................................................... 85
3.4.2 Chemical Transformations to O-MWCNTs Caused by UVC Irradiation .................................................................................................. 87
3.4.3 Structural Transformations to O-SWCNTs ................................... 88
3.5 Conclusions ................................................................................................... 91
3.6 Acknowledgements ....................................................................................... 92
3.7 Supplemental Information ............................................................................ 92
3.7.1 UV-Visible Spectroscopy of O-MWCNT Suspensions ................. 92
3.7.2 Choosing a Suitable Buffer ............................................................ 94
3.7.3 Calibration of Light Intensity via Actinometry ............................. 96
3.7.4 Water Quality Parameters .............................................................. 99
3.7.5 Chemical Characterization of Large Volume Irradiation Experiments .............................................................................................100
3.7.6 Measurement of Total Inorganic Carbon (TIC) and Calculation of CO2 Evolved .......................................................................................101
3.7.7 Oxic versus Anoxic Conditions ....................................................104
3.8 References ....................................................................................................105
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PART II: INTERACTIONS OF PARTICLES AND SURFACES IN AQUATIC ENVRIRONMENTS
4. THEORY ...................................................................................................................112
4.1 Solution and Surface Chemistry ..................................................................112
4.1.1 Solution Chemistry .......................................................................112
4.1.2 Surface Chemistry .........................................................................114
4.2 Colloidal and Surface Interactions of Spherical Particles ............................115
4.2.1 Net Potential Energy Interactions .................................................115
4.2.2 Gravitational Body Forces ............................................................116
4.2.3 Electrostatic Repulsion .................................................................116
4.2.4 The Derjaguin Approximation ......................................................118
4.2.5 van der Waals Attraction ..............................................................120
4.2.6 Steric Repulsion ............................................................................123
4.3 Diffusion Modes of Spherical Particles .......................................................124
4.3.1 Diffusion of Spheres near a Flat Surface ......................................124
4.3.2 Diffusion of Spheres through Obstacles .......................................126
4.4 Colloidal and Surface Interactions of Rod-Shaped Particles .......................128
4.4.1 Net Potential Energy Interactions .................................................128
4.4.2 Gravitational Body Forces ............................................................128
4.4.3 Electrostatic Repulsion derived from the Derjaguin Approximation .........................................................................................129
4.4.4 Electrostatic Repulsion from the Linear Superposition Approximation .........................................................................................130
4.5 Diffusion Modes of Rod-Shaped Particles ....................................................131
4.5.1 Diffusion of Rods in the Bulk .........................................................131
4.5.2 Diffusion of Rods near a Flat Surface .............................................133
4.5.3 Diffusion of Rods between Two Parallel Surfaces .......................134
4.5.4 Diffusion of Rods through Obstacles ............................................136
4.6 References ....................................................................................................137
5. EXPERIMENTAL SET-UPS AND PARAMETERS FOR MICROSCOPY STUDIES .........................................................................................................................138
5.1 Chemicals and Materials ..............................................................................138
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5.1.1 Chemicals ......................................................................................138
5.1.2 Materials .......................................................................................138
5.2 Colloids ........................................................................................................140
5.2.1 Silica Microspheres .......................................................................140
5.2.2 Gold Rods .....................................................................................141
5.2.2.1 Estimation of Surface Potential .....................................142
5.3 Preparation of Samples ................................................................................142
5.3.1 One-wall Cells ..............................................................................142
5.3.2 Confined Cells ..............................................................................143
5.3.3 Porous Media ................................................................................144
5.4 Microscopy Techniques ...............................................................................145
5.4.1 Bright Field ...................................................................................145
5.4.2 Dark Field .....................................................................................147
5.4.3 Total Internal Reflection ...............................................................148
5.5 Image and Data Analysis .............................................................................152
5.6 References ....................................................................................................153
6. ANAMOLOUS SILICA COLLOID STABILITY AND GEL LAYER MEDIATED INTERACTIONS.......................................................................................154
6.1 Introduction ..................................................................................................154
6.2 Theory ..........................................................................................................156
6.2.1 Potential Energy Profiles ..............................................................156
6.2.2 Diffusivity Profiles........................................................................160
6.3 Materials and Methods .................................................................................161
6.3.1 Colloids and Surfaces ...................................................................161
6.3.2 Ensemble Total Internal Reflection Microscopy ..........................161
6.3.3 Diffusivity Landscape Analysis ....................................................162
6.4 Results and Discussion ................................................................................163
6.4.1 Example Deviation from DLVO Theory ......................................163
6.4.2 Interaction Potentials vs. Ionic Strength (at fixed pH = 10) .........164
6.4.3 Hydrodynamic Interactions vs. Ionic Strength (at fixed pH = 10) ..................................................................................................167
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6.4.4 Role of “Gel” Layer in van der Waals, Electrostatic, and Steric Potentials ..................................................................................................168
6.4.5 Fitting DLVO and Steric Interactions in the presence of a “Gel” Layer ..............................................................................................171
6.4.6 Do Inferred Gel Layer Properties Make Sense? ...........................173
6.4.7 Potentials and Stability vs. Ionic Strength and pH .......................176
6.5 Conclusions ..................................................................................................180
6.6 Appendix ......................................................................................................181
6.7 Acknowledgements ......................................................................................182
6.8 Supplemental Information ...........................................................................183
6.8.1 Solution Chemistry .........................................................................183
6.8.2 pH and Ionic Strength Dependent Surface Potentials .....................185
6.8.3 Potential Energy Profiles at Various Solution Conditions ..............186
6.8.4 Comparison of hm Derived from Different Gel Layer Scenarios ..................................................................................................188
6.9 References ....................................................................................................189
7. DIFFUSION OF MICRON-SIZED GOLD RODS ACROSS SILICATE SURFACES AND THROUGH SLIT PORES ................................................................193
7.1 Introduction ..................................................................................................193
7.2 Theory ..........................................................................................................198
7.2.1 Potential Energy Profiles ..............................................................198
7.2.2 Bulk Diffusion Modes...................................................................201
7.2.2.1 Bulk Translational Diffusion Coefficients .....................202
7.2.2.2 Bulk Rotational Diffusion Coefficients .........................202
7.2.3 Interfacial Diffusion Modes ..........................................................203
7.2.3.1 Interfacial Translational Diffusion Coefficients ............204
7.2.3.2 Interfacial Rotational Diffusion Coefficients .................204
7.3 Materials and Methods .................................................................................205
7.3.1 Colloids and Surfaces ...................................................................205
7.3.2 Ensemble Video Microscopy ........................................................207
7.3.3 Image Analysis..............................................................................207
7.3.4 Measuring System Noise ..............................................................210
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7.3.5 Calculations of Position-Dependent Diffusivities ........................210
7.4 Results and Discussion ................................................................................212
7.4.1 Measuring the Mean Squared Displacement for Translational and Rotational Diffusion ..........................................................................212
7.4.2 Effects of Ionic Strength on Diffusion Coefficients .....................215
7.4.3 Comparing Diffusion Coefficients from Experiment and Theory ......................................................................................................218
7.5 Conclusions ..................................................................................................220
7.6 Acknowledgements ......................................................................................221
7.7 Supplemental Information ...........................................................................221
7.7.1 Numerical Calculation of the Electrostatic Repulsion between a Rod in a Parallel Configuration and a Wall ..........................................221
7.7.2 Stokesian Dynamics Simulations ..................................................223
7.7.2.1 Approximate diffusivities for cylindrical rod above wall ...............................................................................................224
7.7.3 Evaluating Stuck Particle Behavior ..............................................225
7.8 References ....................................................................................................226
8. COLLOIDAL ROD DIFFUSION THORUGH MODEL 2-DIMENSIONAL POROUS MEDIA ............................................................................................................231
8.1 Introduction ..................................................................................................231
8.2 Theory ..........................................................................................................236
8.2.1 Diffusion of Spheres through Obstacles .......................................237
8.2.2 Diffusion of Rod-Shaped Particles ...............................................238
8.2.3 Diffusion of Rods through Obstacles ............................................238
8.3 Materials and Methods .................................................................................239
8.3.1 Colloids and Surfaces ...................................................................239
8.3.2 Dark Field Microscopy .................................................................241
8.3.3 Image Analysis..............................................................................241
8.4 Results and Discussion ................................................................................243
8.4.1 Tracking Rod-Shaped Particles through Porous Media ................243
8.4.2 Deciphering Calculated Mean Squared Displacements ................244
8.4.3 Comparing the Effect of Silica Area Fraction ..............................245
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8.5 Conclusions ..................................................................................................247
8.6 Acknowledgements ......................................................................................247
8.7 References ....................................................................................................246
CURRICULA VITA ........................................................................................................251
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List of Tables
Page Chapter 3
Table 3.1 – Mass loss experienced by O-MWCNTs from NanoLab Inc. and Cheaptubes as a result of UVC induced aggregation under different solution conditions .......................................................................................................................... 81
Table 3.2 – Mass loss experienced by O-SWCNTs from Southwest Nanotechnologies as a result of UVC induced aggregation at pH 7 ................................. 88
Table S3.1 – Calculation of the quantum flux for 16, 8, 6, 4, 2, and 0 lamps. Flux is determined by actinometric measurements performed with potassium ferrioxalate. The quantum flux listed for 16 lamps appears twice to indicate that which was actually measured during the actinometry experiment, and what the likely flux is based on extrapolation via linear regression of the data from 0 – 8 lamps ....................... 98
Table S3.2 – XPS measurements performed on various O-MWCNTs before and after irradiation with 254nm UVC light for various O-MWCNTs under oxic or anoxic conditions at pH 10. Only the total oxygen percent is shown, the percent carbon is neglected, but the %C + %O = 100%. For example, if the %O = 7.5%, the carbon peak result was 92.5%. The numbers in parentheses show the percentage of carboxylic acid groups that were measured before and after irradiation. The asterisk (*) indicates that the experiment was performed at pH 7 instead of pH 10 .....................101
Chapter 6
Table 6.1 – Constants used in theoretical fits..................................................................160
Table 6.2 – Experimental parameters for each pH and ionic strength condition examined. The column labeled as “-1 (#3)” is the steric decay length from a net potential fit based on Case 3 in Fig. 3, and “-1 (#4)” is the steric decay length from a net potential fit based on Case 4. The columns labeled as hm-U are most probable particle-wall separations obtained from potential energy profile fits, and hm-D is the most probable height from diffusivity profile fits. Dashes indicate cases without a steric contribution, and “x”s indicate irreversibly deposited particles where potential energy and diffusivity profiles could not be measured ....................................................179
Table 6.3 – Constants used in to fit the Hamaker function from Lifshitz theory ............182
Table S6.1 – Constants used in theoretical fits ...............................................................184
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Chapter 7
Table 7.1 – Constants used in theoretical fits..................................................................205
Table 7.2 – Measured values used in the fitting of one-wall experimental data .............217
Table 7.3 – Measured values used in the fitting of two-wall experimental data .............217
Table 7.4 – Calculated values of the most probable and average heights from the Derjaguin and linear superposition approximations (Derjaguin/LSA) used to find diffusion coefficients .......................................................................................................219
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List of Figures
Page Chapter 2
Figure 2.1 – Chemical derivatization reactions using fluorinated reagents to tag carbonyl, hydroxyl, and carboxyl functional groups ........................................................ 35
Figure 2.2 – Fluorescence emission spectra for pristine SWCNTs from South West Nano Technologies with excitation wavelength 638nm ................................................... 42
Figure 2.3 – Fluorescence emission spectra for pristine SWCNTs from South West Nano Technologies with excitation wavelength 691nm ................................................... 43
Figure 2.4 – Fluorescence emission spectra for pristine SWCNTs from South West Nano Technologies with excitation wavelength 782nm ................................................... 43
Figure 2.5 – Diagram of different roll up vectors/chiralities (m,n) for SWCNTs describing the different configurations that exist (armchair vs. zigzag). The more blue that is filled in each hexagon equates to a more abundant that species, therefore the (6,5) species is the most abundant and is completely blue ......................................... 44
Chapter 3
Figure 3.1 – Visual effects of UVC irradiation on oxidized multiwalled CNTs from NanoLab, Inc. under anoxic conditions at pH 10 and 3mM Na+. No observable change is apparent over the first 18 hours; afterwards aggregation and settling are observed. Starting O-MWCNT concentration is approximately 5mg/L ........................... 65
Figure 3.2 – Change in absorbance (filled red circles) and particle size (open blue squares) plotted as a function of UVC irradiation time for oxidized multiwalled CNTs under anoxic conditions at pH 7 and 3mM Na+ under radiation with 8 UVC lamps. The shaded region indicates the time where visible aggregation of CNTs was observed ............................................................................................................................ 67
Figure 3.3 – Absorbance profiles for oxidized multiwalled CNTs under anoxic conditions as a function of ionic strength at constant pH 7 (A) and pH at constant ionic strength 3mM Na+ (B) plotted as a function of UV irradiation time ....................... 68
Figure 3.4 – XPS results for oxidized multiwalled CNTs in absence of any irradiation (solid red line) and after UVC-induced aggregation and settling had occurred (dashed blue line). The solution conditions in these experiments were 3mM NaCl and pH 10. Figures 4A and 4B show the C(1s) and O(1s) envelopes before and after irradiation. The distribution of oxygen-containing functional groups (C) determined by chemical derivatization illustrates how UVC irradiation changes the concentration of different oxygen-containing functional groups .................. 69
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Figure 3.5 – Absorbance (A) and particle size (B) profiles for oxidized multiwalled CNTs at pH 7 and 12mM NaCl exposed to different light intensities, plotted as a function of irradiation time. The dashed lines indicate t1/2 (A) where the absorbance reaches half of its initial value, and t630nm (B) where the particle size reached ~630nm. Kinetic data is plotted as a log-log function of t1/2 (C) or t630nm (D) versus light intensity (I) ............................................................................................................... 73
Figure 3.6 – Absorbance (A) and particle size (B) profiles for oxidized multiwalled CNTs at pH 7 and 12mM NaCl. plotted as a function of UVC irradiation time, conducted under anoxic (nitrogen purged) or oxic (oxygen purged) conditions .............. 75
Figure 3.7 – Low (top row) and high (bottom row) resolution TEM micrographs of O-MWCNTs before and after UVC irradiation at pH 7 under anoxic conditions ............ 79
Figure 3.8 – Raman spectroscopy showing the effects of UVC irradiation on O-MWCNTs purchased from NanoLab, Inc. and Cheaptubes. Results are shown for O-MWCNTs before irradiation and after UVC-induced aggregation under oxic and anoxic conditions at pH 10 ............................................................................................... 80
Figure 3.9 – Visual effects of UVC irradiation on single walled CNTs from Southwest Nanotechnologies oxidized with 40% nitric acid. Irradiation was performed under ambient conditions at pH 7. No observable aggregation is observed for the first 10 days, as only the color of the suspension lightens over the course of this time. Starting O-SWCNT concentration is approximately 13.6mg/L ........ 86
Figure 3.10 – Change in absorbance (filled red circles) and particle size (open blue squares) plotted as a function of UVC irradiation time for oxidized single walled CNTs under ambient conditions at pH 7 under radiation with 16 UVC lamps ................ 87
Figure 3.11 – NIRF signal for pristine SWCNTS compared to differently oxidized SWCNT under excitation wavelengths (A) 638nm, (B) 691nm, and (C) 782nm. Suspension concentration was slightly varied as a result of centrifugation to remove bundling ............................................................................................................................ 90
Figure 3.12 – NIRF results for lightly oxidized SWCNT control suspension versus exposures to 8 UVC lamps for 10, 30, and 60min under excitation wavelengths (A) 638nm, (B) 691nm, and (C) 782nm. Suspension concentration was 10mg/L at pH 10....................................................................................................................................... 91
Figure S3.1 – UV-Vis absorbance spectra from 200 – 450nm of oxidized multiwalled CNTs at pH 7 and 12mM NaCl, purged with nitrogen and measured as a function of irradiation time. Absorption maximum (λ = 264nm) corresponds to the π→ π* transition in the conjugated sidewall ring structure. The dashed line indicates the irradiation wavelength of 254nm, and the solid line indicates the wavelength at which measurements were taken (350nm). Inset shows the full spectra ranging from 200 – 900nm ................................................................................... 93
Figure S3.2 – UV-Vis absorbance spectra from 200 – 900nm for the individual constituents that make up an O-MWCNT suspension. The inset shows the region from 200 – 220nm to show the increase displayed in the absorbance profiles of the 3mM phosphate buffered water and the 12mM NaCl solution. These contributions
xviii
can be seen in the profiles of the experimental O-MWCNT suspension from Figure S1 ...................................................................................................................................... 94
Figure S3.3 – Absorbance measurements for O-MWCNTs from NanoLab, Inc. under anoxic conditions using two common buffers to keep the suspension stable at pH 4 ................................................................................................................................... 95
Figure S3.4 – Calibration curves (A) and the calculated quantum flux (B) for various lamp intensities measured with the ferrioxalate actinometry experiments .......... 97
Figure S3.5 – Comparison of absorbance measurements for a control/dark sample and a sample exposed to UVC radiation at pH 7 and 3mM Na+ ...................................... 99
Figure S3.6. – Particle size measurement profiles for oxidized multiwalled CNTs under anoxic conditions as a function of ionic strength (A) and pH (B) plotted as a function of UV irradiation time .......................................................................................100
Figure S3.7 – CO2 measurements from irradiated and dark control samples performed at pH 7 ............................................................................................................103
Figure S3.8 – The change in total dissolved oxygen plotted as a function of irradiation time measured from the same experiment as shown in Figure 6 ...................105
Chapter 5
Figure 5.1 – Schematic representation of dark field set-up. Adapted from Hu et. al.5 ....................................................................................................................................148
Figure 5.2 – Internal reflection of a laser as predicted by Snell’s Law ..........................149
Figure 5.3 – Schematic representation of TIRM set-up, inset shows exponential decay of evanescent wave with a spherical particle scattering light. Adapted from Wu and Bevan.7 ...............................................................................................................151
Chapter 6
Figure 6.1 – Example of disagreement between ensemble TIRM measured particle-wall potential energy profile (points) and DLVO theory (red solid line) for 2μm SiO2 in [NaCl]=20mM at pH=10. Addition of a steric potential to the DLVO potentials produces a net potential prediction (blue dashed line) in better agreement with the depth of the secondary minimum and produces an energy barrier consistent with the particles’ observed stability ...............................................................................164
Figure 6.2 – Ensemble TIRM measurements of (A) potential energy profiles, U(h), and (B) diffusivity profiles, D(h), for 2.1μm SiO2 at pH = 10 with [NaCl] = 0.1 – 100mM. The color scheme for lines and points indicates [NaCl] given in the legend in (A). In (A), the points are measured data from an equilibrium analysis of particle
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trajectories using Equation 6.1, solid lines indicate DLVO potentials only (Equation 6.3 with UE+UV), and dashed lines indicate DLVO plus a short range steric contribution (Equation 6.3 with UE+UV+US). In (B), the points are measured data from a non-equilibrium analysis of particle trajectories using Equation 6.13, solid lines are fits to theoretical predictions from Equation 6.14, and error bars are explained in the Methods section .....................................................................................166
Figure 6.3 – Schematics and predicted potentials (for pH = 10, [NaCl] = 80mM in Figure 6.2A) based on various cases for including SiO2 gel layers. In the schematics and predictions, h is the separation between the outer edges of the SiO2 gel layers (i.e. the H2O/SiO2 gel interfaces), and L is the separation between the inner edges of the SiO2 gel layers (i.e. the SiO2 gel/bulk interface). See text for detailed explanation of each case, but in brief: (top-to-bottom) (1) the typical configuration with no gel layers considered in the DLVO theory, (2) gel layers of mostly SiO2 composition, (3) gel layers of mostly H2O composition that are permeable to fluid flow, (4) gel layers of mostly H2O composition that are impermeable to fluid flow. The potentials are color coded as: electrostatics (red), van der Waals (blue), steric (yellow), and net (green) ..................................................................................................170
Figure 6.4 – Steric decay length, γ-1, (left) and gel layer thickness, Δ, (right) vs. [NaCl]/mM at pH=10 from fits in Figure 6.2A based on models for Cases 3 (red triangles) and 4 (blue circles) in Figure 6.3 .....................................................................172
Figure 6.5 – Summary of whether DLVO theory fit measured potentials and the degree of particle stability vs. solution pH and [NaCl]. Points indicate: (1) robust levitation, accurately modeled by DLVO theory (green circles), (2) robust levitation, modeled by DLVO + steric repulsion (green triangles), (3) slow deposition of particles, levitated particles are modeled by DLVO + steric repulsion (yellow inverted triangles), and (4) irreversible deposition (red squares) .......................176
Figure 6.6 – Hamaker functions for two silica half spaces vs. separation and medium ionic strength. Points were computed from the Lifshitz theory in Eq. 6.9 for salt concentrations of 0.01 mM (blue), 0.1 mM (pink), 1 mM (green), 10 mM (red), 100 mM (black), as well as an infinite salt case computed by neglecting the n=0 term in Eq. 6.9 (black triangles). The infinite salt case was fit by Eq. 6.18 (solid black line), which was used in Eq. 6.17 to capture all other salt concentrations (dashed lines) ...................................................................................................................182
Figure S6.1 – Empirical fit to literature data33 and model34 for quartz surface potential vs. pH and ionic strengths of 1mM (green squares), 10mM (red triangles), and 100mM (black circles). The lines are fits to the data given by Eq. (S6.8) ................185
Figures S6.2 – Ensemble TIRM measurements of potential energy profiles, U(h), at pH 7 with same format as pH = 10 data and fits in Fig. 6.2A. The ionic strengths range from [NaCl] = 0.1 – 20mM with exact values reported in Table 6.2 .....................186
Figures S6.3 – Ensemble TIRM measurements of potential energy profiles, U(h), at pH 5.5 with same format as pH = 10 data and fits in Fig. 6.2A. The ionic strengths range from [NaCl] = 0.1 – 20mM with exact values reported in Table 6.2 .....................187
xx
Figures S6.4 – Ensemble TIRM measurements of potential energy profiles, U(h), at pH 4 with same format as pH = 10 data and fits in Fig. 6.2A. The ionic strengths range from [NaCl] = 0.1 – 5mM with exact values reported in Table 6.2.......................187
Figure S6.5 – The most probable separation at the potential energy minimum, and where the sum of the forces equal zero, for the potential energy profiles at pH = 10 in Fig. 6.2A. The x-axis shows estimates of hm from DLVO (closed symbols) and non-DLVO (open symbols) fits of Eq. 6.3 to the U(h) data in Fig. 6.2A for both Cases 3 (red triangles) and 4 (blue circles), and the y-axis shows estimates of hm from fits of Eq. 6.14 to the D(h) data in Fig. 6.2B. The x-axis is labeled as Lm and hm since L is the hydrodynamic separation scale in Case 3 and h is the hydrodynamic separation scale in Case 4. A 1:1 line shows when the two measurements are equivalent ...........................................................................................188
Chapter 7
Figure 7.1 – Cropped (120 pixel x 120 pixel) and scaled 2x: the original experimental image (A), an inverted version of the same image (B), the result after the thresholding algorithm has been performed on the inverted version of the image (C), and the original image now with marked centers and end points (D). Also included are plots of the center of mass position (E) and angular rotation (F) as a function of time to illustrate how the tracking algorithm works .....................................208
Figure 7.2 – Comparison of the schematics used for experiments and calculations, including all pertinent scales and variables .....................................................................211
Figure 7.3 – Mean squared displacement data plotted as a function of time for the translational (A and C) and rotational (B and D) trajectories of varying length colloidal rods in an open system (top) and confined system (bottom). Closed and open symbols represent actual experimental data acquired from the tracking algorithms and solid lines represent the best fit linear regression to the first five data points in each set ..............................................................................................................213
Figure 7.4 – Translational (A and C) and rotational (B and D) diffusion coefficients determined from the fits to mean squared displacement data for each ionic strength condition examined is plotted as a function of rod aspect ratio for colloidal rods in an open system (top) and confined system (bottom). The highest (hmax, dash), lowest (hmin, dot-dot-dash), and best fit (hm, solid) lines are plotted for each data set ....216
Figure 7.5 – Measured diffusion coefficients from one-wall experiments ratioed to the calculated diffusion coefficients from values of hm obtained from Derjaguin and linear superposition approximations at various ionic strength conditions ................219
Figure S7.1 – Histograms of the various length (A) and theta (B and C) values tracked for a rod that was irreversibly bound to the surface. These measurements help to inform on the extent of noise originating from the system as well as the tracking algorithms used ..................................................................................................226 Chapter 8
xxi
Figure 8.1 – Different concentrations of porous media resulting in increasing area fractions of (A) 0.048, (B) 0.085, (C) 0.114, (D) 0.156, (E) 0.210, and (F) 0.245 ..........242
Figure 8.2 – Plotted trajectories of three differently sized gold rods maneuvering through porous media with an area fraction 0.085. Green = 3.9μm, Blue = 3.4μm, and Pink = 4.5μm .............................................................................................................244
Figure 8.3 – Mean squared displacement calculations at (A) 600ms, (B) 60sec, and (C) 600sec for the three gold rods maneuvering through porous media with an area fraction 0.085. Green = 3.9μm, Blue = 3.4μm, and Pink = 4.5μm ..................................245
Figure 8.4 – Mean squared displacement calculations at (A) 600ms, (B) 60sec, and (C) 600sec for the gold rods of similar sizes (4.5 – 4.9μm) maneuvering through porous media with area fractions 0.0 (black filled circles), 0.048 (red open squares), 0.085 (yellow filled triangles), 0.114 (green open upside down triangles), and 0.156 (blue filled diamonds) ......................................................................................................246
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List of Schemes
Page Chapter 3
Scheme 3.1 – Mechanism for the photodecarboxylation of 5H-dibenzo[a,d] cyclohepten-5-carboxylic acid in water proceeding through a carbanion intermediate upon irradiation with 254nm light based on work by McAuley et. al.47 ............................................................................................................................... 76 Scheme 3.2 – Proposed pathway for photodecarboxylation and subsequent aggregation of O-MWCNTs through the removal of carboxylic acid functional groups ................................................................................................................................ 77
1
Chapter 1:
Introduction
1.1 Background
1.1.1 Natural and Engineered Nanomaterials
A colloid is defined as one substance microscopically dispersed throughout
another substance, and includes examples such as blood cells in plasma or soot particles
in air to create smoke. Colloids are made up of particles in sizes of up to 1μm in
diameter, thereby automatically encompassing the separate group of nanoparticles. A
nanoparticle (NP) is defined as a particle having at least one dimension between 1 and
100nm. Natural forms of NPs have existed in the environment for as long as the Earth
has, and are generated by a wide variety of geological and biological processes. Natural
sources of NPs include volcanic dust, natural waters, soils, and sediments.1 These
colloids exist in a variety of forms, most noticeably as inorganic species such as clays,
mica, iron oxides (hematite, magnetite), manganese, and silicates, and additionally as
dissolved organic species like humic and fulvic acids, as well as biopolymer materials
excreted by bacteria.2 Organisms living in an ecosystem have evolved in an environment
that contains any number of these natural NPs, and have adapted to live among them and
clear them from their organ systems. While there is evidence that some natural NPs can
be toxic (e.g., volcanic ash), a new problem is posed by the introduction of unfamiliar
engineered NPs to an ecosystem.1
Engineered NPs are synthesized in a laboratory using a variety of methods and a
myriad of chemical precursors to make particles that contain transition metals that are
2
wholly metallic (gold, Au; silver, Ag; platinum, Pt) or oxidized (titanium, TiO2; iron,
Fe2O3; zinc, ZnO), semiconductors (silicon, SiO2), organic (fullerenes (C60), nanotubes
(CNTs), polymers), or any combinations of these groups. These methods have been
developed and fine-tuned so that NPs can be specifically created to yield a particular size
or shape. Interestingly, the hydrophobicity/hydrophilicity or electronic charge of a NP
can be tailored by adhering layers of additional chemicals. Such a high interest in NPs is
garnered by the vast assortment of particles that can be created by varying the
composition of cores, shells, and layers used during synthesis. However, some
engineered NPs contain chemicals in concentrations toxic to most organisms or exist in
forms that do not occur naturally. They also possess the ability to persist long after
disposal depending on how the surface has been artificially modified.
1.1.2 Importance of Nanoparticle Size and Shape
The size and shape of a NP can greatly influence its properties. This is very
important because depending on the field of study different properties are necessary to
achieve a desired outcome. For example, all types of NPs, in a variety of sizes and
shapes, have been used in polymer composites for energy and optics applications.
Polymer films made into composite materials can be prepared using graphene oxide (GO)
nanosheets,3 AuNPs,4 CNTs,5 fullerenes, and a host of semiconducting and metal oxide
nanoparticles6 for micro and nanoelectronic devices ranging from light emitting diodes to
transistors and photovoltaics. Depending on the particle, sometimes the tensile strength of
polymer nanocomposites can be increased by larger particles better than smaller ones, or
strength through alignment can be provided by elongated rods better than better than
spheres and triangles.7
3
Alignment is very important in optics research when creating devices that use
liquid crystals, where the alignment of metallic or semiconducting NPs is controlled
using electric fields. Acharya et. al. showed that anisotropic particles clearly displayed a
greater advantage over spheres because their inherent dipole allows them to more easily
align with the field, enhancing ordering and performance by tuning the aspect ratio of the
anisotropic particles in the liquid crystals.8 Conversely, a variety of available NP shapes
have been taken advantage of in the field of nonlinear optics where NPs have become
attractive for use as chemical and biological sensors. Depending on the type of sensor,
NPs made of Au, Ag, copper (Cu), metal oxides, and quantum dots can be grown and
modified at their surfaces to tailor the desired properties to a target cell.9 A cornucopia of
nanomaterials can also be found in the field of energy research. Energy storage and
conversion have been the two main goals of energy research, and groups have been able
to use a variety of semiconductors,10, 11 metals,12 and organic NPs13 to create
supercapacitors, dye-sensitized solar cells, electrodes, and filters for remediation.
Two important fields of research where shape has been key are biology/medicine
and electronics. Research has found that certain types of anisotropic particles have given
better results over spheres. For example, Roohani-Esfahani et. al. found that the use of
needle shaped hydroxyapatite nanoparticles improved the strength, interconnectivity, and
porosity of biphasic calcium phosphate scaffolds to most closely simulate natural bone.
The second and third best choices, showing about 2/3 and 1/2 the strength of the needle
composites, were spheres and rod-shaped particles respectively.14 CNTs have been one of
the most commonly studied anisotropic nanoparticles in research for the past 20 years.
Outside of their use to increase the structural integrity of thin films15-17, CNTs have been
4
of special interest to researchers in the electronics field. Single walled CNTs (SWCNTs)
can have metallic or semiconducting properties depending on the orientation of their
sidewall structure. Therefore, electrons and ion species can be carried by these NPs,
which makes them effective field effect transistors, electrical switches, and sensors.18-21
1.1.3 Engineered Nanoparticles in Consumer Products
Currently, nanomaterials are found in more than 1600 products on the market.22
Evaluation of that list back in 2009 by Hansen et. al. showed that the majority of
nanomaterial-containing products are found in the health and fitness industry. Those
products can be broken down into different categories based on how the NP is used
within the product, such as whether the nanomaterial is in the bulk (i.e. nanocrystalline
copper), on the surface (as in films), or as particles (bound, suspended, or airborne). The
majority of these commercial products are using nanomaterials that are found in particle
form, where 19% have NPs bound to the surfaces, 37% use them suspended in liquids,
and 13% are suspended in solids. Products with NPs suspended in liquids or airborne
were further classified as “expected to cause exposure” based on the fact they are in
products that require contact with and application to human skin (e.g., sunscreen or
cosmetics). Surface-bound nanoparticles in consumer products were placed into the lesser
category of “may cause exposure,” due to the fact that though contact would occur,
removing the NPs from the surface would require much more force.23
One of the large unknowns when it comes to NP-containing consumer products is
what happens to the NPs during and after use? Different longevities are expected
depending on the type of consumer products they are used in, the concentration of the NP
within the product and how it is incorporated, as well as the predicted lifetime of the
5
product, frequency of its use, and how well it degrades. Life cycle analysis of three
common nanomaterials (nano-Ag, nano-TiO2, and CNTs) was performed by Mueller and
Nowack24 to estimate the predicted environmental concentrations (PEC) of highly
commercialized NPs that will likely be released from NP-containing consumer products.
By ratioing these PEC values to what are considered predicted no effect concentrations
(PNEC) the authors calculated a risk quotient (RQ) for each NP. Their analysis revealed
that nano-TiO2 showed a very high RQ (between 1 and 16 depending on if the realistic or
high-exposure model was used) because of its prolific use in sunscreen, paints, and
cosmetics. Meanwhile, nano-Ag and CNTs were predicted to have very low risks of
release associated with them, about 100 to 1000 times less than TiO2, most likely due to
the amount of products currently containing these nanoparticles. However, it is believed
that their RQs will increase with cheaper production and increasing incorporation in the
coming years. Though these results were calculated using some estimations and did not
include emission from production sites, it still speaks to the need to be critical of how
products incorporate NPs.
1.1.4 Release and Transformation of Engineered Nanoparticles in the Environment
The prolific use of nanomaterials in consumer products has substantiated the
growing concerns about NP release into the environment. It is believed that the most
common entry points for NPs to our waterways will be from industrial point sources, run-
off from farms and sewers, or the decomposition of NP-containing products in landfills.
There is concern that the natural process of NP removal, which has already been achieved
by organisms in a given ecosystem, will be disrupted by the introduction of engineered
species. This becomes a large problem when there are no natural analogues to the
6
manufactured/engineered NPs that are being released, or if they are being released in
quantities that are beyond the organism’s capability to recover from. For example,
quantum dots contain specific heavy metals (e.g., cadmium) that are not abundant in
nature, or some of the surface coatings created to increase hydrophilicity or
biocompatibility may not have a natural analogue.25 Currently, expectations are that low
NP concentrations (on the ng/L to pg/L scale) are the concentrations we would have to be
concerned about actually reaching an aquatic environment. Also, when mixing small
quantities of engineered NPs with those already existing in an ecosystem, it is believed
that heteroaggregation of these two types of colloids should be the dominant mechanism
of removal from aquatic systems.26
However, once released, NPs will have the potential to undergo transformations
within their environment including interactions with concomitant chemicals,
biotransformations within cells, mechanical force alterations, and photochemical induced
changes. A NP’s behavior can then be influenced by these transformations in some way,
whether it is their ultimate fate, how they are able to transport through the environment,
or how toxic they become. Lowry et. al’s review categorizes transformations into four
common types including chemical, physical, biological, or interactions with
macromolecules.27
Chemical transformations include, but are not limited to, the degradation of
surface coatings, dissolution by oxidation, or the adsorption/desorption of chemical
species to and from the surface. Studies on Ag28, 29, Cu30, and Fe31 NPs have seen these
chemical transformations which in turn affect their aggregation states, toxicity, and even
caused the formation of new particles from dissolved ions. Physical transformations are
7
most commonly associated with homo- and heteroaggregation of nanoparticles, usually
brought on by changes to the surface chemistry. Photolysis has also been shown to
change the surface chemistry of various particles, thereby inducing aggregation32 or
reduction33-35 of particle size.
Transformations within biological organisms are often caused by reduction or
oxidation mediated processes. These processes allow cells to break down biodegradable
polymers and proteins, or induce the dissolution of quantum dots and metal oxide NPs
depending on the compartment and cellular conditions when the NP is engulfed.36 Studies
using fungi show the foreign material, such as fullerols37 and quantum dots,38 are
degraded by these organisms through oxidation processes. When cerium oxide NPs were
introduced to cucumber plants, the NPs were reduced by biogenic reducing substances
and organic acids.39 Upon entering different environments NPs can become coated with
different proteins40, 41 and macromolecules42, 43 that exist within that particular
environment. These coatings change the inherent chemical and physical properties of the
NP, and thereby alter the way the particle transports and interacts with surfaces of
varying compositions.
1.1.5 Toxicity of Engineered Nanoparticles
The transformation processes discussed above can impose drastic changes in NP
toxicity to various cells and organisms. Key issues being investigated include: (i) is the
nature of a given material important, (ii) how does the NP change once it enters the body,
(iii) can the NP penetrate different mucosal barriers, (iv) can the NP be transported within
the body, (v) how does the NP change upon transport from organ to organ, and (vi) what
is the cellular response to these particles? These issues are all interrelated, which
8
complicates effective studies and results. A review of the toxicity literature by Elder et.
al. states that the two most common routes of exposure are estimated to be through the
skin or the respiratory tract. However, it is well documented that upon entering the body
nanomaterials will acquire a protein coating from the adsorption of biomolecules. This
protein corona can greatly influence the fate of a particle that is internalized. However,
this coating is not fixed, but will change as the particle moves to different areas of a cell
or the body, equilibrating with the surrounding media.44 For example, one study on silica
microspheres found that particle size and surface functionalization were key factors in
determining what proteins are adsorbed, though there were many proteins found to bind
to the particle surface in all circumstances.40
Size and composition are important factors when determining a NP’s toxicity.
This is because in ecological systems a variety of trophic levels exist, each corresponding
to a different feeding mechanism of the organisms there. The ability of an organism to
ingest or absorb the particles from their surroundings will be determined by the size and
shape of a given NP. Studies by Jeng et. al. and Karlsson et. al. showed that ZnO and
CuO were found to be much more toxic as a nanoparticle than a microparticle, where the
opposite was seen for TiO2. Meanwhile, iron oxides (Fe2O3, Fe3O4) showed very low
toxicity regardless of size.45, 46 One thing to notice is that metal oxides of both Ti and Fe
are found naturally, which may influence how toxic they are to different organisms.
Metal NPs are a slightly different story from metal oxides. A large concern is if
metallic NPs are able to dissolve into ions, which may turn out to be potentially toxic
themselves. When the toxicity of metallic NPs were examined for three different aquatic
species, Griffitt et. al.47 found that of Ag, Cu, aluminum (Al), nickel (Ni), and cobalt (Co)
9
NPs, Ag and Cu were the most toxic. As a comparison, no death was observed when the
same organisms were exposed to TiO2 NPs. However, review of the literature has shown
that Ag and Fe-Pt NPs are the most cytotoxic because they induce DNA damage in a
variety of bacterial species.48 In plant species (algae, fungi, seed-bearing plants), cell
porosity is disrupted by Ag, allowing more engineered NPs to pass through to the cytosol.
Indirect toxicity occurs when the amount of light that the leaf absorbs, and thus
photosynthesis, is inhibited by NP accumulation on plant surfaces. Toxicity was found to
be enhanced upon exposure to sunlight, potentially by generating reactive oxygen species
(ROS) and causing metal dissolution into ions.49
Johnston et. al.50 published a critical review of the available literature on the
toxicity of different carbonaceous NPs, examining studies conducted both in vivo and in
vitro. The largest percentage of these studies examined pulmonary cells due to the
likelihood that CNT powders, or suspensions aspirated into the air, may be inhaled.
Though the literature covers a broad range of topics, the authors propose that the CNT
toxicity is most likely determined by their length, metal content, tendency to aggregate,
and their surface chemistry. With the large aspect ratios of CNTs, a reasonable theory for
toxicity would be that a macrophage would not be able to engulf the CNT particle,
thereby inducing a persistent inflammatory response including the release of ROS.
Genotoxic and cytotoxic consequences are derived from this oxidative response. Of
course there are discrepancies between studies based on lack of characterization of
materials, differences in experimental set up, and appropriate controls studied, but overall
a decrease in toxicity appeared to correspond with multiwalled CNTs (MWCNTs),
functionalized CNTs, and lower metal impurity content.
10
1.1.6 Methods to Characterize and Study Nanoparticles
Operating on the assumption that exposure and release of nanomaterials into
different natural environments, accidental or otherwise, is a possibility then adequate risk
assessment will need to be designed around particle detection in complex matrices. One
of the biggest problems is that unreasonably high concentrations of NPs are used in
toxicity and release studies. Now using these concentrations can be important to define
limits of exposure or to enable more accurate quantification, but in fact the challenge is to
examine NPs at environmentally relevant concentrations (ng/L – pg/L). Unfortunately,
sufficiently low and environmentally relevant concentrations of NPs cannot adequately
be measured with the analytical techniques used by the majority of researchers due to
their limits of detection. The second challenge is that high backgrounds are often found in
natural environmental samples due to the presence of natural colloidal particles and other
chemicals.
The best strategy for coping with these challenges, according to the review by
Hassellöv et. al., may be to combine existing analytical techniques with new
methodology that simultaneously allows for screening capability and a highly selective
detection.51 Different methods give us complementary pieces of the puzzle: microscopy
enables researchers to image particles with atomic resolution; light scattering can give us
insights into the aggregation state and concentration of colloidal suspensions;
ultrafiltration, chromatography, and mass spectrometry allows for tunable size or charge
selection and separation; and a multitude of spectroscopy techniques, which take
advantage of the electromagnetic spectrum, can be used to evaluate everything from
chemical composition to electronic character. However, with all of this information, very
11
few of these techniques can actually reach down to the ng/L range of detection. With that
in mind, suggestions have been provided to improve environmental sampling for NP
species which include: careful extraction and pre-fractionation, knowing the aggregation
state of the sample, and using a combination of techniques that allows for good
separation with high resolution down to the single particle level (e.g., field flow
fractionation (FFF); inductively coupled plasma with mass spectrometry (ICP-MS) or
atomic emission spectroscopy (ICP-AES); and atomic force, scanning electron, or
transmission electron microscopy (AFM, SEM, TEM).
1.2 Significance and Objective
The probability of engineered nanomaterials entering the environment increases
every year as production of NPs intensifies with every new use for different areas of our
lives. It is for this reason that many researchers are focused on the environmental, health,
and safety concerns of this growing body of nanotechnology. As mentioned above, many
studies lack plausible scenarios to study NPs in the environment, for reasons such as the
concentration or dosage that is used is too high or very clean laboratory samples are used
instead of complex samples. Oftentimes, these are necessary steps to take to gain a
fundamental understanding of how colloids interact with their surroundings. Eventually,
better technology will be utilized to isolate and analyze samples on the nanogram or
picogram scale to give us a much more reliable look at the type of reality we face when
nanoparticles are released.
The objective of this dissertation is to form a bridge between different science and
engineering fields of study to provide the best interpretation of these studies’ results.
12
Merging the fields of analytical, physical, and surface chemistries with environmental
engineering and traditional colloid science, I hope to bring new insights into the nature of
colloidal and surface interactions. Two specific approaches were taken: (i) analytical
approaches are combined with mechanistic insights from the organic photochemistry
community to study the effects of ultraviolet (UV) light on the surface chemistry of
oxidized multiwalled carbon nanotubes (O-MWCNTs); and (ii) state-of-the-art
microscopy and colloidal theory are applied to examine individual anisotropic particles
diffusing across environmentally relevant surfaces. Though there has been significant
literature on both the transformations of carbon nanomaterials and the photochemistry of
small molecules, the two have remained exclusive from one another. Similarly,
traditional colloidal theory has been applied to environmental engineering problems in a
plethora of studies; however, these studies tend to examine the bulk diffusion of high
concentrations of particles and do not attempt to extract detailed information from an
individual particle. The work presented in this thesis takes a comprehensive analytical
approach to the study of colloidal particles in the environment while striving for common
language among different fields of study.
1.3 Summary and Dissertation Outline
This dissertation is organized to frame a discussion regarding various colloidal
particles and their interactions with the surrounding aquatic environment. Part I describes
a more qualitative understanding of colloidal particles in solution. Using O-MWCNT
suspensions, numerous spectroscopic and microscopic techniques are employed to
explain how UV light affects changes to the colloidal stability of these NPs. Chapter 2
13
outlines the experimental details for sample preparation and characterization, as well as
background information and parameters for each analytical technique used. Chapter 3
then discusses the results from studies examining the effects of high energy UV light (λ =
254nm) on the colloidal stability of O-MWCNT suspensions. Changes seen in the surface
chemistry of the CNTs before and after irradiation, as monitored by x-ray photoelectron
spectroscopy, Raman spectroscopy, and transmission electron microscopy, are arguably
similar to the photodecarboxylation process seen so prevalently in the organic
photochemistry literature on small molecules.
Part II takes a more quantitative approach to the analysis of colloidal suspensions
by delving into the colloidal theory of particle-surface interactions. Chapter 4 discusses
in depth the theoretical aspects of (i) the colloid and surface forces that exist between
spherical particles diffusing across planar surfaces, (ii) the colloid and surface forces that
exist between anisotropic particles diffusing across planar surfaces, and (iii) the colloid
and surface forces that dictate spherical particles diffusing across planar surfaces with
spherical asperities. The theories regarding anisotropic particles and diffusion of spheres
around asperities are then used to provide estimates of anisotropic particles navigating
asperity-covered planar surfaces. The complete experimental details for the studies in
Part II can be found in Chapter 5, including procedures for sample preparation,
background information and parameters for the various forms of microscopy used to
examine the colloidal particles, and details regarding data analysis.
The results for the studies investigating colloidal diffusion are found in Chapters
6 – 8. Chapter 6 takes advantage of newer and more sensitive technology to tackle an old
problem. Deviations of experimental results involving silica microspheres over silicate
14
surfaces from theoretical potentials predicted using traditional electrostatic repulsion and
van der Waals attraction (DLVO theory) are investigated. Sensitive measurements of
particle heights using total internal reflection microscopy (TIRM) enabled calculation of
gel-layer mediated interactions that introduced steric repulsion to the system. Two new
models were developed, both fitting experimental data very well, allowing for estimation
of the gel layer thickness at various solution conditions to be calculated and an
accompanying discussion of gel layer properties. Chapters 7 & 8 investigate the diffusion
of anisotropic colloidal particles and how they are influenced by solution chemistry and
surfaces. In Chapter 7, new algorithms were developed to track the diffusion of gold rods
over smooth silicate surfaces. The geometry of the sample cell and increasing ionic
strength conditions were found to profoundly impact the translational diffusion of these
particles, whereas rotational diffusion was almost insensitive to these factors. It was
found that the particle-wall surface separations decreased with increasing ionic strength
and the addition of a second wall. Chapter 8 discusses increasing the complexity of the
system by introducing a confined geometry filled with spherical asperities that the rods
must diffuse around.
1.4 References
1. Handy, R.; Owen, R.; Valsami-Jones, E., The ecotoxicology of nanoparticles and nanomaterials: current status, knowledge gaps, challenges, and future needs. Ecotoxicology 2008, 17, (5), 315-325.
2. Baalousha, M.; Lead, J. R.; von der Kammer, F.; Hofmann, T., Natural Colloids and Nanoparticles in Aquatic and Terrestrial Environments. In Environmental and Human Health Impacts of Nanotechnology, John Wiley & Sons, Ltd: 2009; pp 109-161.
15
3. Eda, G.; Fanchini, G.; Chhowalla, M., Large-area ultrathin films of reduced graphene oxide as a transparent and flexible electronic material. Nature Nanotechnology 2008, 3, (5), 270-274.
4. Park, J. H.; Lim, Y. T.; Park, O. O.; Kim, J. K.; Yu, J.-W.; Kim, Y. C., Polymer/Gold Nanoparticle Nanocomposite Light-Emitting Diodes:  Enhancement of Electroluminescence Stability and Quantum Efficiency of Blue-Light-Emitting Polymers. Chemistry of Materials 2004, 16, (4), 688-692.
5. Cao, Q.; Rogers, J. A., Ultrathin Films of Single-Walled Carbon Nanotubes for Electronics and Sensors: A Review of Fundamental and Applied Aspects. Advanced Materials 2009, 21, (1), 29-53.
6. Godovsky, D. Y., Device Applications of Polymer-Nanocomposites. In Biopolymers · PVA Hydrogels, Anionic Polymerisation Nanocomposites, Springer Berlin Heidelberg: 2000; Vol. 153, pp 163-205.
7. Kutvonen, A.; Rossi, G.; Puisto, S. R.; Rostedt, N. K. J.; Ala-Nissila, T., Influence of nanoparticle size, loading, and shape on the mechanical properties of polymer nanocomposites. The Journal of Chemical Physics 2012, 137, (21), -.
8. Acharya, S.; Kundu, S.; Hill, J. P.; Richards, G. J.; Ariga, K., Nanorod-Driven Orientational Control of Liquid Crystal for Polarization-Tailored Electro-Optic Devices. Advanced Materials 2009, 21, (9), 989-993.
9. Ray, P. C., Size and Shape Dependent Second Order Nonlinear Optical Properties of Nanomaterials and Their Application in Biological and Chemical Sensing. Chemical Reviews 2010, 110, (9), 5332-5365.
10. Selvan, R. K.; Perelshtein, I.; Perkas, N.; Gedanken, A., Synthesis of Hexagonal-Shaped SnO2 Nanocrystals and SnO2@C Nanocomposites for Electrochemical Redox Supercapacitors. The Journal of Physical Chemistry C 2008, 112, (6), 1825-1830.
11. Nair, A. S.; Peining, Z.; Babu, V. J.; Shengyuan, Y.; Ramakrishna, S., Anisotropic TiO2 nanomaterials in dye-sensitized solar cells. Physical Chemistry Chemical Physics 2011, 13, (48), 21248-21261.
12. Meng, H.; Wang, C.; Shen, P. K.; Wu, G., Palladium thorn clusters as catalysts for electrooxidation of formic acid. Energy & Environmental Science 2011, 4, (4), 1522-1526.
13. Thavasi, V.; Singh, G.; Ramakrishna, S., Electrospun nanofibers in energy and environmental applications. Energy & Environmental Science 2008, 1, (2), 205-221.
14. Roohani-Esfahani, S.-I.; Nouri-Khorasani, S.; Lu, Z.; Appleyard, R.; Zreiqat, H., The influence hydroxyapatite nanoparticle shape and size on the properties of
16
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20. Javey, A.; Guo, J.; Wang, Q.; Lundstrom, M.; Dai, H. J., Ballistic carbon nanotube field-effect transistors. Nature 2003, 424, (6949), 654-657.
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27. Lowry, G. V.; Gregory, K. B.; Apte, S. C.; Lead, J. R., Transformations of Nanomaterials in the Environment. Environmental Science & Technology 2012, 46, (13), 6893-6899.
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33. Hou, W.-C.; Jafvert, C. T., Photochemical Transformation of Aqueous C60 Clusters in Sunlight. Environmental Science & Technology 2009, 43, (2), 362-367.
34. Gorham, J.; MacCuspie, R.; Klein, K.; Fairbrother, D. H.; Holbrook, R. D., UV-induced photochemical transformations of citrate-capped silver nanoparticle suspensions. Journal of Nanoparticle Research C7 - 1139 2012, 14, (10), 1-16.
35. Lee, J.; Cho, M.; Fortner, J. D.; Hughes, J. B.; Kim, J.-H., Transformation of Aggregated C60 in the Aqueous Phase by UV Irradiation. Environmental Science & Technology 2009, 43, (13), 4878-4883.
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37. Schreiner, K. M.; Filley, T. R.; Blanchette, R. A.; Bowen, B. B.; Bolskar, R. D.; Hockaday, W. C.; Masiello, C. A.; Raebiger, J. W., White-Rot Basidiomycete-Mediated Decomposition of C60 Fullerol. Environmental Science & Technology 2009, 43, (9), 3162-3168.
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40. Lundqvist, M.; Stigler, J.; Elia, G.; Lynch, I.; Cedervall, T.; Dawson, K. A., Nanoparticle size and surface properties determine the protein corona with possible implications for biological impacts. Proceedings of the National Academy of Sciences 2008, 105, (38), 14265-14270.
41. Ravindran, A.; Singh, A.; Raichur, A. M.; Chandrasekaran, N.; Mukherjee, A., Studies on interaction of colloidal Ag nanoparticles with Bovine Serum Albumin (BSA). Colloids and Surfaces B: Biointerfaces 2010, 76, (1), 32-37.
42. Wilkinson, K. J.; Negre, J. C.; Buffle, J., Coagulation of colloidal material in surface waters: the role of natural organic matter. Journal of Contaminant Hydrology 1997, 26, (1–4), 229-243.
43. Smith, B.; Yang, J.; Bitter, J. L.; Ball, W. P.; Fairbrother, D. H., Influence of Surface Oxygen on the Interactions of Carbon Nanotubes with Natural Organic Matter. Environmental Science & Technology 2012, 46, (23), 12839-12847.
44. Elder, A.; Lynch, I.; Grieger, K.; Chan-Remillard, S.; Gatti, A.; Gnewuch, H.; Kenawy, E.; Korenstein, R.; Kuhlbusch, T.; Linker, F.; Matias, S.; Monteiro-Riviere, N.; Pinto, V. R. S.; Rudnitsky, R.; Savolainen, K.; Shvedova, A., Human Health Risks of Engineered Nanomaterials. In Nanomaterials: Risks and Benefits, Linkov, I.; Steevens, J., Eds. Springer Netherlands: 2009; pp 3-29.
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20
PART I: INTERACTIONS OF COLLOIDAL PARTICLES IN AQUEOUS SUSPENSIONS
21
Chapter 2:
Experimental Set-Up and Parameters for UV Studies
2.1 Chemicals and Materials
2.1.1 Chemicals
Sodium salts were all purchased from Fisher Scientific (Pittsburgh, PA, USA) and
used without purification. Sodium dihydrogen phosphate and sodium hydrogen phosphate
were used to prepare buffer solutions that stabilized carbon nanotube (CNT) suspensions
at various pH values during UV irradiation. Phosphate buffers were chosen because the
concentrations of dissolved ion species were not affected by changes in the dissolved
oxygen or dissolved carbon dioxide levels. Sodium chloride and sodium hydroxide were
used to increase the ionic strength and pH conditions of the CNT suspensions for
different UV irradiation experiments. Sodium hydroxide was also used in the cleaning
procedures for both CNTs and experimental glassware. Sodium deoxycholate was
purchased from Sigma-Aldrich (St. Louis, MO, USA) and used without further
purification to aid in the suspension of single-walled carbon nanotubes.
Nitric acid (70% w/w) and hydrochloric acid (9M) were purchased from Sigma-
Aldrich and used without further purification. Nitric acid was used solely for oxidizing
CNTs, whereas hydrochloric acid had a variety of purposes including setting low pH
values of CNT suspensions, expediting the aggregation of CNT suspensions, and
cleaning CNT powders and experimental glassware.
HPLC-grade ultrapure water purchased from VWR International (Philadelphia,
PA, USA) was used as received to prepare CNT stock suspensions and to dilute stocks to
22
experimental concentrations, as well as prepare solutions for actinometry chemical
measurements. This type of water was chosen because it helped reduce variability
between water samples when compared to lower purity samples obtained using
traditional filtered water systems. Ultra-high purity oxygen and nitrogen gas were
purchased from Air Gas (Salem, NH, USA). These gases were used to purge CNT
suspensions to change the levels of dissolved oxygen and dissolved carbon dioxide in an
experimental system. Standards to calibrate the meter reading for pH and conductivity
were purchased from Ricca Chemical Company (Arlington, TX, USA) and Oakton
(Vernon Hills, IL, USA), respectively.
Three fluorinated derivatizing agents were used in conjunction with x-ray
photoelectron spectroscopy to measure the level of oxidation imparted to CNT samples
(see section 2.4.5). 2,2,2-trifluoroacetic anhydride (TFAA), 2,2,2-trifluoroethanol (TFE)
with N,N’-di-tert-butyl-carbodiimide (DTBC) and pyridine, and 2,2,2-
trifluoroethylhydrazine (TFH) were all purchased from Sigma-Aldrich and used without
further purification.
Potassium ferrioxalate (K3[Fe(C2O4)3]), o-phenanthroline, sulfuric acid (18M),
and sodium acetate were the chemicals used for the calibration of light intensity. They
were purchased from Alfa Aesar (Ward Hill, MA, USA) and Fisher Scientific and used
without further purification to perform actinometric chemical measurements on the UV
lamps in the Rayonet photochemical reactor used in these studies. Actinometry
measurements will be discussed in section 2.3.2.
2.1.2 Materials
Pyrex glassware from Corning (Corning, NY, USA) was used to prepare and store
23
CNT stock suspensions. Each vessel underwent a rigorous cleaning procedure involving
sonication for 30min in 4M NaOH, then sonication in 4M HCl for 30min, and lastly
sonication in deionized (DI) water for 30min. Between each sonication the glassware was
rinsed thoroughly with DI water. Special quartz glassware was purchased for UV
irradiation experiments. Two quartz beakers (600mL and 1000mL volumes) and 25
quartz test tubes (15mL volume) were acquired from Technical Glass Products
(Painesville Twp., OH, USA). A rigorous but less harsh cleaning procedure was carried
out on the quartz vessels, using a diluted base and acid without sonication to avoid
scratching or etching the delicate quartz sidewalls.
2.2 Carbon Nanotubes
2.2.1 Oxidized Multiwalled Carbon Nanotubes (O-MWCNTs)
Two different commercially available O-MWCNTs were used. The first
CNT powder, which was used in the majority of the experiments discussed in the
following chapter, was purchased from NanoLab, Inc. (Newton, MA, USA) and had been
oxidized by the manufacturer using a 3:1 sulfuric:nitric mixture (PD15L5-20-COOH,
Outer diameter: 15+/-5nm, Length: 5-20μm, Purity: >95%). The second O-MWCNTs
were purchased from Cheaptubes (Brattleboro, VT, USA) and had also been oxidized
using a 3:1 sulfuric:nitric mixture (MWCNT-OH, Outer diameter: 10-20nm, Length: 10-
30μm, Ash: <1.5%, Purity: >95%). Two similar CNTs were purchased from different
manufacturers principally to compare the behavior of two common commercially
available O-MWCNTs. The O-MWCNTs from NanoLab, Inc. were subject to a rigorous
cleaning procedure outlined in Smith et. al.1 and others2, 3 to remove any amorphous
24
carbon or residual metals leftover from the manufacturer’s oxidation process. These O-
MWCNTs first underwent repeated rinsing/centrifugation cycles (4000rpm, 10min) with
deionized water, then 4M NaOH was used to remove any amorphous or graphitic carbon
byproducts remaining from oxidation that were adsorbed to the CNT surface through pi-
pi interactions. A 4M HCl solution was added next to neutralize the solution and help
dissolve any residual metal nanoparticles, and finally repeated rinses with DI water were
performed to significantly lower the electrolyte concentration in the supernatant. Samples
were considered clean when a low enough electrolyte concentration was reached. This
was measured by testing the resistivity of the supernatant, reaching >0.5MΩ upon
completion. Post cleaning, the O-MWCNTs were pipetted onto a cleaned glass
microscope slide and dried overnight at 70°C. Once dry, the powder was scraped off
using a razorblade and ball-milled for homogeneity. Cleaned and dried O-MWCNTs
were stored in small clean screw-cap vials prior to use. The oxidized CNTs purchased
from Cheaptubes did not undergo the same cleaning procedure, and were used as
received to compare how the cleaning and removal of amorphous carbon impacted the
overall effects of UVC irradiation. Characterization of these powders prior to use in
irradiation experiments was performed using a variety of methods discussed below.
2.2.2 Oxidized Single Walled Carbon Nanotubes (O-SWCNTs)
Commercially available pristine SWCNTs (SG-65, outer diameter: 0.93nm,
specific surface are: 800m2/g, carbon content: >90%) from Southwest Nanotechnologies
(Norman, OK, USA). were acquired from collaborators at Duke University (Durham,
NC, USA) and oxidized in our lab using various weight to weight (w/w) percentages of
nitric acid. The purpose of using different concentrations of nitric acid solution was to
25
increase the total surface concentration of oxygen grafted onto the CNT surface. Previous
studies in our lab have shown that this method can impart increasing levels of oxygen
with increasing nitric acid concentration.4 The analytical balance, a spatula, the sample
vial, and aluminum foil sheets were deionized before weighing out SWCNT powders.
Aluminum foil sheets were used to minimize loss of powders to traditional weigh paper.
100mg of pristine SWCNTs were dispersed by sonication in 250mL of either 10%, 40%,
or 70% w/w nitric acid solution for one hour. The mixture was then refluxed at 140°C for
1.5hrs with stirring. After cooling to room temperature, the acid-CNT mixture was
decanted into small test tubes and then repeatedly centrifuged to collect the newly
oxidized SWCNTs. The same cleaning procedure described above for the NanoLab, Inc.
O-MWCNTs was used to remove excess amorphous carbon and metal nanoparticles from
the O-SWCNTs. Once clean, the O-SWCNTs were dried, ball-milled, and stored before
use.
2.3 UV Irradiation Apparatus
2.3.1 Rayonet Photochemical Reaction Chamber
The quartz vessels described above were used to contain suspensions of oxidized
CNTs during irradiation in the Rayonet photochemical reaction chamber. An RPR-100
photochemical reactor unit equipped with 16, 35W (RPR-2537A) low pressure – low
intensity mercury lamps (90% 254nm emission, intensity = 12.5mW/cm2 two inches from
lamps) was purchased from Southern New England Ultraviolet (Branford, CT, USA).
The inside of the Rayonet chamber contained a smooth mirrored surface to reflect all of
the light output by the lamps. A cooling fan inside the bottom of the chamber was always
26
turned on while the lamps were on, which kept the photochemical reactor at 35°C.
Oftentimes an additional box fan was used externally to help cool the reactor when the
lamps were turned on for long periods of time (in excess of 12 hours). How the
irradiation experiments were performed is discussed in section 2.6.
2.3.2 Calibration of the Light Intensity
Knowing the intensity of light being produced by the experimental system is
necessary if one is ever to compare results between studies. Calibration can occur in one
of two ways: using an electronic photometer or by chemical actinometric measurements.
Chemical actinometry uses a compound that absorbs some quanta of radiation, promoting
it to an excited state. Once excited, the compound decomposes, yielding a colored
product whose concentration can be measured by UV-Visible spectroscopy. With more
intense radiation incident upon the solution, more molecules are excited and subsequently
decompose. Thus, a more intense color resulting from a higher concentration of the final
product is generated with longer exposures. In this case, the intensity of the radiation
corresponds to how many photons are being absorbed by the actinometric compound. For
the purpose of this investigation, actinometric measurements were performed at various
light intensities by changing the number of UV lamps that were turned on inside the
chamber. Actinometry experiments were performed in the dark because these chemical
compounds can decompose under ambient lighting conditions.
For this study, actinometry was performed using the chemical indicator,
potassium ferrioxalate. Irradiation with UV light causes the decomposition of the
ferrioxalate anion to form free Fe2+ ions. The addition of o-phenanthroline, a bidentate
ligand which strongly binds to most metal ions, to this solution causes the coordination of
27
Fe2+ ions following irradiation and forms a red colored complex with an absorption
maximum at λ = 510nm. The absorbance of this complex is measured as a function of the
length of time that the ferrioxalate has been exposed to the radiation. From these
absorbance measurements, it is possible to determine the concentration of Fe2+ ions and
thereby derive the quanta of light absorbed.
As described in the method by Hatchard and Parker,5 147.5mg of potassium
ferrioxalate were dissolved in 50mL of acidic water (45mL water + 5mL 1N H2SO4) to
form a 0.006M ferrioxalate solution. 3mL of this solution were put into the 15mL quartz
test tubes and irradiated for different prescribed periods of time (t). The test tubes were
irradiated while the carousel was turned on and rotating to achieve uniform exposure.
Once removed from the reaction chamber, each test tube was slid into an aluminum foil
sleeve to prevent extraneous light from continuing to decompose the ferrioxalate. After
all of the irradiation points had been completed, 2mL of the irradiated solution were
removed and placed into a clean glass screw cap vial that was also covered by an
aluminum foil sleeve. Here, 2mL of a 0.0055M o-phenanthroline solution and 1mL of a
pH 3.5 acetate solution were added to the vial to complex the Fe2+ ions and quench the
reaction. This 5mL volume was then diluted to a 20mL total volume and stored for at
least 1hr in the dark to ensure that all of the Fe2+ produced by the UVC light had
complexed with the o-phenanthroline. Afterwards, the optical density (D) of the solution
for each time point was measured at 510nm by UV-Vis to determine the concentration of
the colored complex. A plot of D vs. t was constructed and the slope of the linear region
was found by fitting the data points using a simple linear regression. Until the supply of
ferrioxalate has been consumed, D varies linearly with t. In this regime, Eq. 1 can be used
28
to determine the quantum flux (QF);5
3
1 3
2
10DVV NQF
t dV
(2.1)
where V1 is the volume of ferrioxalate solution irradiated (3mL), V3 is the total end
volume of solution (20mL), N is Avogadro’s number, Φ is the quantum yield at the
irradiation wavelength (for 254nm, Φ = 1.25), ε is the molar extinction coefficient of the
ferrioxalate-phenanthroline complex at 510nm (1.11 x 104 L/mol·cm), d is the path length
of the cuvette (1cm), and V2 is the volume of irradiated solution used for complexation
(2mL). It is important to note that once all available ferrioxalate has been consumed, the
plot of D vs. t will plateau. This plateaued region is not useful in the calculation of the
quantum yield, so time points were carefully chosen to ensure that six to eight data points
fell in the linear regime.
Actinometry was performed for all lamp arrangements used for various
experiments of light intensity. These experiments were conducted with different numbers
of symmetrically distributed UVC lamps in the Rayonet reaction chamber. An
experiment was also performed where the ferrioxalate solution was placed inside the
rotating carousel, but the lamps were not turned on. Time points were taken and analyzed
in the same fashion as mentioned above to account for any residual radiation that may be
produced by the lamps despite them being turned off. Results from these experiments can
be found in the following chapter.
29
2.4 Instrumentation
2.4.1 UV-Visible Spectroscopy
UV-Visible spectroscopy measures the electronic transitions of molecules
containing π-electrons or non-bonding (n) electrons (σ-electrons can be measured if the
spectrophotometer used can measure below 200nm). This includes transition metal ions,
highly conjugated organic compounds, and biological macromolecules. When a molecule
absorbs electromagnetic radiation it promotes these electrons to higher anti-bonding
states. The wavelength at which these molecules absorb corresponds to the size of the
HOMO-LUMO gap, which is associated with the types of functional groups present in
the molecule of interest. The resulting absorption spectrum can therefore aid in structure
determination. The Beer-Lambert law is the most common method used for the
measurement of either the concentration (c) or molar absorptivity (ε) of a molecule when
one or the other is known, where the absorbance (A) of a sample is related to the intensity
of light transmitted through the sample (I) by,
0log( / )A I I bc (2.2)
where I0 is the intensity of incoming radiation and b is the path length of the cuvette.6
This law maintains a linear relationship from A = 0 – 1.0 absorbance units.
For the purpose of these studies, the molar absorptivity of O-CNT samples was
estimated by preparing suspensions of varying concentrations and measuring the resulting
absorbance. However, since CNTs are not small, well-defined molecules with uniform
molecular weights, ε did vary with the O-CNT used. For that reason, a selected value of
optical density (A) was used as the main metric to establish O-CNT density rather than
30
attempting to use concentration or molarity. A Varian Cary 50 UV-Visible
spectrophotometer (Agilent Technologies) was used to set the absorbance of all O-CNT
suspensions in a 1cm path length quartz cuvette. Measurements consisted of five scans
taken over the range λ = 200 – 900nm, and the value at 350nm averaged and recorded.
The wavelength λ = 350nm was chosen because it allowed for strong signal without
interference from salts, acids, or bases. Further discussion is included in the supplemental
information section in Chapter 3.
2.4.2 Dynamic Light Scattering (DLS)
DLS is a technique used to determine the size of particles in solution by
measuring the intensity and fluctuations of scattered light. A laser is used to probe a
suspension of particles as they undergo Brownian motion. The intensity fluctuations are
measured as a function of time, which can then reveal information about the size of the
particles (i.e., smaller particles will move more quickly, thereby resulting in a shorter
amount of time between interference of the incoming light). An autocorrelation function
is used to calculate the size of the particles in the suspension. This correlates how quickly
a particle diffuses, which is directly related to a particle’s size by the Stokes-Einstein
relationship,
6
Bk TD
a (2.3)
where D is the particle diffusion coefficient, kB is Boltzmann’s constant, T is the
temperature, η is the solution viscosity, and a is the particle radius.7
O-CNTs are not spherical particles so the Stokes-Einstein equation is not
completely accurate, but it can be used to provide an estimation of their effective
31
hydrodynamic diameter, D(h). Particle size measurements were carried out in disposable
plastic cuvettes at 24°C using a Malvern ZetaSizer Nano-ZS. This instrument uses a He-
Ne laser (633nm) operating at 5mW as the optical probe, and non-invasive backscatter
measurements were taken at 173° from the incident beam. Five separate measurements
were taken per sample, each measurement consisting of 10 – 15 scans, with the average
and standard deviation calculated and recorded.
2.4.3 Zeta Potential
Zeta potential is a quantity used to describe the electric potential at the shear plane
of a particle’s electric double layer (EDL), and is often used as a measure of how stable a
suspension is. Particles with measured zeta potentials of greater than ±40mV are
considered to have good colloidal stability. Zeta potential (ζ) is related to the
experimentally determined electrophoretic mobility (μe) given by Smoluchowski’s model,
0re
(2.4)
where εr is the dielectric constant of medium, ε0 is the permittivity of free space, and η is
the viscosity of the medium.8 Electrophoretic mobility (EM) is an electrophoresis
method, so it measures the migration and velocity of charged particles under an electric
field. This is a dynamic method where the ions in the EDL are constantly moving with
and around the particle as it flows through the medium towards the charged endplate.
Therefore EM can only be an estimation of the electric potential and not an absolute
result.
The same Malvern ZetaSizer Nano-ZS used for DLS is equipped with zeta
potential capabilities. O-CNT suspensions were injected via syringe into a clear
32
disposable folded capillary zeta cell. Laser Doppler Micro-electrophoresis was used to
measure the zeta potential of a given particle suspension. An interferometric technique
measured the velocity of a particle, enabling the calculation of EM and then the zeta
potential using the Smoluchowski model described above. Five separate measurements
were taken per sample, each measurement consisting of 10 – 15 scans, with the average
and standard deviation calculated and recorded.
2.4.4 X-ray Photoelectron Spectroscopy (XPS)
XPS is an analytical surface sensitive technique used to determine a material’s
chemical composition. Under ultra-high vacuum, x-rays are directed at a sample and
penetrate to a depth of about 10nm. These x-rays eject core level electrons from surface
atoms, and these electrons carry kinetic energies corresponding to the energy levels they
were ejected from. A hemispherical analyzer is set to only allow electrons of specific
kinetic energies to pass through, where all others are deflected, resulting in a destructive
collision with the side of the analyzer. The electrons are counted as they pass through to
the detector, and their binding energy is calculated using the equation,
KE BEh (2.5)
where hν is the energy of the x-ray, KE and BE are the kinetic energy and binding energy
respectively, and ϕ is the work function, which is the minimum energy required to
remove an electron from a solid.9 The binding energy of an electron is specific for a
particular element, as well as the energy level from which it was ejected. This allows for
determination and quantification of the elements (except hydrogen) composing the
surface. Quantification is accomplished by taking the area under each curve ratioed by a
sensitivity factor for each element. In addition to composition, XPS can also give
33
information on the oxidation states or chemical environment of an atom (e.g., C-F vs C-
O, NO3 vs NH2) based on detailed analysis of the specific binding energy of ejected
photoelectron spectral envelopes.
This technique was used to analyze O-CNT samples prior to and after irradiation
with UVC light to measure any chemical changes that may have been imparted to the O-
CNT particles by irradiation. XPS analysis of O-CNT samples was performed on a PHI
5400 XPS system using Mg Kα x-ray (1253.6eV) radiation. A small (~5mg) sample of
powdered O-CNTs was pressed onto a 1cm x 1cm piece of double sided copper tape that
was adhered to an XPS sample stub. Enough powdered sample was used to ensure no
copper tape was visible. The high energy electron analyzer was operated at a constant
pass energy to measure the ejected photoelectrons. A survey scan of the sample was
performed using AugerScan software at a pass energy of 178.95eV at a scan rate of
0.25eV/step for binding energies ranging from 1200eV to 0eV. Elemental quantification
was then performed on regions of interest using a pass energy of 58.7eV for general
purposes, and at 5.85eV for more detailed information on the envelope features. All O-
CNT samples were analyzed for total oxygen content in commercial software (CasaXPS)
to establish the carbon:oxygen ratio before and after irradiation with 254nm UVC light.
Oxygen functional group distributions were determined using wet chemical derivatization
techniques previously used in our lab to study CNTs.10, 11
2.4.5 Chemical Derivatization (CD)
Chemical derivatization is one of two common ways to determine the oxidation
state of an atom. Peak fitting of the XPS elemental spectral envelopes is the other method
and is more frequently used. However, the peak fitting method is often fraught with
34
ambiguity when attempting to deconvolute the spectral envelope. Deconvolution involves
assigning a peak position for a particular functional group within the overall peak of the
elemental region. Ambiguity arises due to discrepancies in the literature regarding peak
positions, which may encompass a small range rather than a specific value, and multiple
options for the full-width-half-max (FWHM) values of different chemical species.
Instead of arbitrarily assigning peaks to the spectral envelope, CD uses a chemical
tag for a particular functional group of interest. The method used in this study takes
advantage of fluorine-containing reagents to selectively and quantitatively tag specific
functional groups (hydroxyl, carboxyl, and carbonyl). Each O-CNT sample of interest
was derivatized for all three functional groups that can be quantified. Three small
separate aliquots (~5mg) of each O-CNT sample were added to three individual tiny
Pyrex cups. These cups were then placed inside three separate vacuum flasks, which
contain a cup holder suspended above the bottom of the flask. At the very bottom of each
flask beneath the cup holder, a particular derivatizing reagent was added (2,2,2-
trifluoroacetic anhydride (TFAA) for tagging hydroxyl groups; 2,2,2-trifluoroethanol
(TFE) for tagging carboxyl groups; and 2,2,2-trifluoroethylhydrazine (TFH) for tagging
carbonyl groups). Each flask was then attached to a vacuum line and inserted halfway
into liquid nitrogen so as to cover the bottom of the flask and freeze the liquid reagent.
Once frozen, the flask was opened to the vacuum line and allowed to pump away the
atmosphere inside. Upon closing the flask to the vacuum line, it was allowed to thaw
back to room temperature and the gas-phase reactions were allowed to proceed in the
vacuum flasks overnight. While thawing, the derivatizing reagent would create a gaseous
atmosphere that the functional group of interest would react with, labeling it with a
35
fluorine molecule. Figure 2.1 shows the derivatization schemes for each reaction to tag
the three functional groups of interest.
Figure 2.1 – Chemical derivatization reactions using fluorinated reagents to tag carbonyl, hydroxyl, and carboxyl functional groups.
Hydroxyl:
OHO
+
O
OH
F3C O
O
CF3
O+
O
F3C OH
O
CF3
O
Carbonyl:
+ +CF3HN
H2N
N
H2O
HN
CF3
Carboxyl:
+
CF3HO
C NN
N
OOCF3
+NH
NH
O
NO O
HN
Primary Product
Secondary Product
36
XPS analysis was performed on derivatized O-CNT samples from dark and
exposed UVC samples to monitor changes in the oxygen functional groups densities that
occurred as a result of exposure to UV light. Commercial software (CasaXPS) was used
to quantify the elemental regions of interest by integrating the area under the C(1s),
O(1s), N(1s), and F(1s) peaks.
Using the XPS results for the changes in oxygen-containing functional groups,
one can find an estimate of the amount of a given functional group by converting the
atomic percentages to weight percentages for the carbon and oxygen before and after
irradiation. This is accomplished by multiplying the atomic signal generated by the XPS
by the molecular weight of carbon or oxygen,
% %
% %
16
12wt atom
wt atom
O O
C C
(2.6)
Totaling the carbon and oxygen separately for before and after irradiation, one can then
divide the amount of carbon from the desired functional group to find the weight
percentage of carbon using the equation,
( ) %
( ) %% %
12X atom
X wtwt wt
CC
C O
(2.7)
where, X is the functional group of interest. Multiplying this percentage by the
concentration and volume of CNTs used in the study, one can estimate the mass of
carbon expected to be contained within each functional group before and after irradiation.
This can be useful when attempting to determine the amount of a given functional group
lost or gained during a particular experiment (see Section 2.4.8).
37
2.4.6 Transmission Electron Microscopy (TEM)
Electron microscopy takes advantage of an electron’s very small de Broglie
wavelength, which allows for imaging in much higher resolution than with traditional
optical microscopes. TEM is a technique that uses a focused beam of electrons passing
through a thin sample to image at the nanometer level. The electrons generated from a
high voltage source are focused by a series of special lenses and mirrors and are then sent
through the sample. The electron waves transmitted through the sample can be used to
create an image at very high magnifications, capable of observing individual atoms (and
in the case of larger atoms, resolving them).
TEM was not used to image individual atoms of O-CNTs, as increased
magnification requires increased energy, which using runs the risk of damaging the
sample from the high intensity electron beam. Instead, TEM was used to check for
structural changes on the CNTs imparted by UV light exposure, as high resolution
imaging can provide a view of the number of sidewalls present in a MWCNT, as well as
any amorphous carbon or defects in the sidewalls that may be present. Samples were
prepared for TEM analysis by dipping a holey-carbon TEM grid into suspensions of pre
and post exposure O-CNTs and allowing them to dry in air. The grids were then imaged
using a Philips CM 300 field emission gun TEM operating at 297kV. A CCD camera
mounted on a GIF 200 electron energy loss spectrometer was used for image collection.
2.4.7 Raman Spectroscopy
Raman spectroscopy is a light scattering technique often used to examine
complementary vibrational modes of molecules that are not IR-active. Effects are only
observed for molecules that can be polarized, and the extent of polarizability is directly
38
reflected in how intense the Raman scattering signal is; a stronger signal is generated for
molecules that are more polarizable. A laser is used to excite the molecule to a virtual
energy state, which is a state of higher energy that does not actually correspond to a
discrete energy level. Upon relaxation, the molecule will emit a photon of energy and
return to a different rotational or vibrational state from the one it originally began. This
difference between the starting and ending energy states of the molecule is what is
measured, appearing as a shift in frequency from the original excitation wavelength.
There are two different types of Raman effects: a Stokes shift is when the molecule
returns to a higher energy state than it began, and an anti-Stokes shift is when the final
energy state is lower than the initial state.
Carbon allotropes are often characterized with Raman spectroscopy because it is a
technique that is very sensitive to “highly symmetric covalent bonds with little or no
natural dipole moment.”12 This technique was used in this study to measure the amount
of damage imparted to the physical structure of the O-CNTs as a result of exposure to UV
irradiation in oxic and anoxic aquatic environments. Dried O-CNT samples from before
and after exposure were sent to Purdue University (West Lafayette, IN, USA) for
analysis. The powder was mounted onto a clean glass microscopic slide and a 100x
objective was used to focus on a specific sample area, then that area was analyzed over
10 second exposure times with three spectral averages using an XploRA ONE Raman
system from Horiba Scientific (Edison, NJ, USA). A solid state Nd:YAG laser (50mW)
was used as the excitation source, emitting a wavelength of 532nm. Instrument
parameters include: slit = 200 µm, hold= 300, grating = 1800, filter = 10%. Samples were
then scanned over the range of 500 – 3000 cm-1 to acquire the D and G band intensities of
39
each sample, then allowing for comparison of the ID:IG band ratio as a measure of
structural integrity.
2.4.8 Total Inorganic Carbon (TIC)
Measurements of the total inorganic carbon of an aquatic system are used to
determine the level of dissolved carbon dioxide and carbonate salts. This is often used as
an important metric to measure the health of an aquatic system, where increased levels of
CO2 in the atmosphere allows more CO2 to dissolve in water, forming carbonic acid
species that decrease the pH. To measure TIC a sample is acidified, which forces all
species towards the formation of CO2, and passed through an infrared/mass spectrum
analyzer. For the purpose of this study, TIC measurements were performed to test the
evolution of CO2 believed to arise from O-CNTs through photodecarboxylation as a
function of UV irradiation time. They were compared to dark controls (test tubes
wrapped in aluminum foil to prevent the suspension from being exposed to the UV light)
to eliminate the amount of CO2 already present in the system.
The concentration of CO2 expected to be produced by the irradiation of O-CNTs
is small, even if we assume that all of the carboxylic acid functional groups are removed,
so O-CNTs were prepared as a more concentrated stock for these experiments (25mg/L)
to achieve a measurable amount of CO2. Suspensions were set to pH 7 with the addition
of 3mM phosphate buffer and sent to Purdue University for analysis. Quartz test tubes
were filled with 8mL of O-CNT suspension, leaving 9mL of headspace. A stainless steel
syringe needle was inserted through a rubber septa capped onto each test tube and used to
sparge the CNT suspension with nitrogen gas for 30 minutes at a flow rate of 2.5mL/sec.
Half of the sample tubes were irradiated using a Rayonet RPR-100 photochemical reactor
40
(Southern New England Ultraviolet (SNEU), Branford, CT) with 16 RPR-2537A lamps
(24W). In the reactor, sample tubes were placed within a carousel at the center of the
reactor and rotated at 5 rpm to ensure uniform exposure.
After a specified period of irradiation, test tubes were removed and acidified with
85% phosphoric acid to pH < 3. Test tubes were shaken vigorously for 5min and allowed
to equilibrate overnight, after which 3mL aliquots from the headspace of each tube were
withdrawn for CO2 analysis. Dark controls were acidified and treated the same way for
analysis. The gas phase CO2 concentration was measured with a PDZ-Europa Elemental
Analyzer interfaced to a Sercon 20-20 Isotope Ratio Mass Spectrometer (Crewe,
England). Once this concentration had been determined, the amount of CO2 in the
aqueous phase could be calculated using the equation,
2
2
[ ]
[ ]g
Haq
COk
CO (2.8)
where kH is the Henry’s constant for CO2 dissolved in water, which is dimensionalized by
multiplying the constant by RT.13 The TIC can then be calculated from these two
concentrations by,
312 10g g aq aqTIC C V C V (2.9)
to calculate the total inorganic carbon content in milligrams.
2.4.9 Near-Infrared Fluorescence Spectroscopy (NIRF)
The near-infrared region of the electromagnetic spectrum (800 – 2500nm)
measures vibrational overtones (vibrational modes from the ground state that are excited
to the second or higher vibrational state) and combination bands (when two or more
41
fundamental vibrations (0 → 1) are excited simultaneously). A sample is probed by
irradiating with either a broadband visible-NIR source or specific wavelength laser
source. The resulting fluorescence spectra is often complex and requires deconvolution
for evaluation.
SWCNTs have been found to exhibit distinct fluorescence bands in the NIR
region corresponding to specific chiralities, the intensity of which is directly related to the
concentration of that chirality of CNT as seen in Figures 2.2 – 2.5. However,
fluorescence of SWCNTs can be quickly quenched by bundling or aggregation, so to
achieve individual tubes a surfactant is often added to the suspension and then
ultrasonicated. MWCNTs suffer from quenching by the multiple graphene sidewalls that
make up their structure, so they cannot be successfully quantified using this technique.
For this study, suspensions of pristine SWCNTs, O-SWCNTs at various oxidation
levels, and UV irradiated samples were sent to Duke University (Durham, NC, USA) to
be analyzed for NIRF. A Nanospectralyzer NS1 from Applied Nanofluorescence
(Houston, TX, USA) was used to evaluate suspensions made in a neutral 2% w/v SDC
solution. In some cases, ultracentrifugation was necessary to either concentrate the
volume of sample or remove bundled SWCNTs that would quench the fluorescence
signal. The supernatant was removed after centrifugation for 5.5hr at 60,000rpm and
22°C on a Beckman SW 60 rotor. The pelleted SWCNTs were resuspended by dissolving
a mass of sodium deoxycholate (SDC) into a volume of O-SWCNTs to produce a final
2%w/v suspension of SDC. Samples were then sonicated for 10min using a sonic horn
probe at 50% amplitude while immersed in a salt water ice bath. Three excitation
wavelengths were used: 638 nm at 32 mW (Figure 2.2), 691 nm at 31 mW (Figure 2.3),
an
6
pr
h
th
b
Fiw
nd 782 nm
000 – 11,50
ristine SG6
exagon com
hat the domi
atch of CNT
igure 2.2 – Fluwith excitation w
at 74 mW (
00cm-1.14 Th
5 SWCNTs
mpletely filled
inant SWCN
Ts its name.
uorescence emiwavelength 63
(Figure 2.4)
e diagram in
discussed
d in with blu
NT compone
ission spectra f8nm.
42
and fluores
ndicating th
in Section
ue correspon
nt in this ba
for pristine SW
scence emis
he different r
2.2.2 can b
nds to the ro
atch exhibits
WCNTs from So
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roll-up vecto
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oll-up vector
s that vector.
outh West Nan
ed over the r
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Figure 2.5.
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. The
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Fiw
Fiw
igure 2.3 – Fluwith excitation w
igure 2.4 – Fluwith excitation w
uorescence emiwavelength 69
uorescence emiwavelength 78
ission spectra f1nm.
ission spectra f2nm.
43
for pristine SW
for pristine SW
WCNTs from So
WCNTs from So
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outh West Nan
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44
ensions
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45
characterized by UV-Vis absorbance measurements, dynamic light scattering (DLS), and
zeta potential for consistency before being diluted for UV irradiation experiments.
2.5.2 Preparation of Experimental O-CNT Suspensions
Stock suspensions of O-CNTs were diluted to the same optical density of A = 0.34
at λ = 350nm (this corresponds to approximately 5mg/L for oxidized NanoLab CNTs, ε ~
0.065) using the ultrapure HPLC water. This ensured uniformity in experimental
suspensions regardless of type of manufacturer. Phosphate buffer was added to achieve a
final concentration of 3mM, and a small aliquot of HCl or NaOH was then added to
adjust the pH to ±0.1 unit with an Accumet Excel XL20 pH and conductivity meter from
Fisher Scientific. Depending on the conditions being examined, additional aliquots of 4M
NaCl were added to the suspension to bring the concentration of Na+ between 4.5 –
12mM. Once the suspension was appropriately set, a final scan consisting of five runs
was taken of the suspension from λ = 200 – 900nm, and then averaged to determine the
starting experimental concentration. 350nm was chosen as the wavelength for analysis
because it had a high absorbance without interference from buffer or salt.
For initial particle size measurements, a 0.5mL sample was removed from the
experimental suspension and diluted to a concentration of 1.25mg/L with ultrapure water
that had been buffered and pH balanced to identical solution conditions. Five separate
DLS measurements were taken per sample, each measurement consisting of 10-15 scans,
with the average and standard deviation calculated and recorded.
Initial zeta potential measurements were carried out on the samples used for DLS
analysis, having been diluted 1:10. Five separate measurements were taken per sample,
each measurement consisting of 10-15 scans, with the average and standard deviation
46
calculated and recorded.
Once initial absorbance and particle size measurements confirmed that a stable
and appropriately concentrated experimental suspension of O-CNTs had been prepared,
samples were transferred to the appropriate quartz vessel and purged with ultra-high
purity oxygen or nitrogen before being sealed first with Parafilm and then with aluminum
foil. The outside surface of the quartz glassware was wiped down with acetone to remove
dust and oils before being put into the Rayonet chamber.
2.6 UV Irradiation of O-CNT Suspensions
For the majority of UV studies, irradiation was performed with all 16 35W
RPR-2537A lamps in the chamber. Other experiments intended to test the effects of light
intensity were performed with 8, 4, or 2 lamps. To accomplish this, some of the lamps
were either symmetrically removed from the chamber or wrapped with aluminum foil to
ensure uniform light distribution around the entire chamber at experimental conditions
that tested lower intensities of UVC light. Experiments were performed by exposing
colloidal suspensions of O-CNTs to the effects of UVC irradiation in one of two
configurations: large batches or small sample volumes.
2.6.1 Large Batch Volumes
The 600mL or 1000mL quartz beaker was used to contain large volumes of O-
CNTs. The purpose of these experiments was to produce enough residual powdered
CNTs after irradiation for surface characterization and mass loss measurements. These
experiments were performed exclusively with 16 lamps and without the addition of extra
47
NaCl. The CNT sample was prepared as described above, and then the beaker was set on
a stand inside the chamber so that the sides of the glassware sat at a height equal to the
midpoint of the lamps so as to achieve the most intense exposure. O-CNT suspensions
were then irradiated in a static configuration until the UVC light was able to induce
aggregation and settling of O-CNT particles. The reactor was then shut down and the
beaker was removed.
At this point a small amount of 9M HCl was added to the beaker and the contents
stirred. This addition of strong acid was to help remove any small particles from
suspension that were too small to visually observe. The aggregated suspension of O-
CNTs was then centrifuged (4000rpm for 10min) to collect O-CNTs for analysis. The
supernatant was decanted and collected in a clean 1L Pyrex bottle after each
centrifugation cycle. Once all of the acidic supernatant had been removed, the O-CNTs
underwent a thorough rinsing cycle where DI water was added, the O-CNTs mixed, then
centrifuged and decanted until the resistivity of the supernatant was >0.5MΩ. The
remaining sample was dried on a cleaned glass microscope slide overnight at 70°C, then
scraped off and weighed on aluminum foil that had been deionized to remove static
charge.
UVC irradiated O-CNT samples were compared to a separate set of O-CNTs from
the same batch. These control studies were prepared in the same manner as those for
irradiation. However, the control suspensions were prepared and then destabilized by
stirring in a sufficient amount of 9M HCl to cause particle destabilization. Control and
UVC irradiated O-CNTs were used to examine any chemical and physical changes that
may have been imparted due to UVC irradiation.
48
2.6.2 Small Sample Volumes
A dozen 15mL quartz test tubes were used for small sample volume experiments.
The purpose of these experiments was to measure the changes in particle concentration
(absorbance) and size as a function of irradiation time and light intensity leading up to
visible aggregation. The light intensity was varied by removing or shielding lamps,
always decreasing the light intensity in half. Measurements were taken at 16, 8, 4, and 2
lamps turned on the chamber. In these experiments the test tubes were placed into a
rotating 12-slot carousel set to a height within the photochemical reaction chamber at the
lamp midpoint to ensure that each test tube received uniform exposure.
A time zero measurement was recorded where the sample had been prepared but
not yet exposed to UV irradiation. Quartz test tubes were then removed at discrete time
intervals over the course of irradiation. These samples were monitored for changes in the
solution chemistry using the pH and conductivity meter at each time point. For specific
experiments testing the effects of dissolved oxygen (DO) concentration, a Thermo
Electron Corporation Orion 5 Star DO meter (Thermo Fisher Scientific) was also used at
this stage. Each time a test tube was removed a replacement (containing already sampled
O-CNTs) was inserted into the vacated spot to maintain uniform light intensity. A 0.5mL
aliquot was taken first from the top of each test tube removed from the carousel (taking
care not to shake or disturb the contents) and placed into a clean 5mL screw cap vial and
set aside for particle size analysis. The rest of the suspension was gently centrifuged
(1000rpm) for 3 minutes to remove any large aggregates that would compromise
absorbance measurements by excessive scattering.
For absorbance measurements, an aliquot of the centrifuged O-MWCNT
49
suspension was pipetted into a 1cm path length quartz cuvette and the UV-Vis spectra
measured from 200 – 900nm. Absorbance readings were taken five times and the average
signal at 350nm was recorded and used as a measure of the particle concentration. These
concentrations were plotted as a function of irradiation time to track the progress of
UVC-induced aggregation. For particle size measurements, the 0.5mL sample placed in
the screw cap vial was diluted to 1.25mg/L with ultrapure buffered water and analyzed.
2.7 References
1. Smith, B.; Yang, J.; Bitter, J. L.; Ball, W. P.; Fairbrother, D. H., Influence of Surface Oxygen on the Interactions of Carbon Nanotubes with Natural Organic Matter. Environmental Science & Technology 2012, 46, (23), 12839-12847.
2. Salzmann, C. G.; Llewellyn, S. A.; Tobias, G.; Ward, M. A. H.; Huh, Y.; Green, M. L. H., The Role of Carboxylated Carbonaceous Fragments in the Functionalization and Spectroscopy of a Single-Walled Carbon-Nanotube Material. Advanced Materials 2007, 19, (6), 883-887.
3. Fogden, S. n.; Verdejo, R.; Cottam, B.; Shaffer, M., Purification of single walled carbon nanotubes: The problem with oxidation debris. Chemical Physics Letters 2008, 460, (1-3), 162-167.
4. Smith, B.; Wepasnick, K.; Schrote, K. E.; Cho, H.-H.; Ball, W. P.; Fairbrother, D. H., Influence of Surface Oxides on the Colloidal Stability of Multi-Walled Carbon Nanotubes: A Structure-Property Relationship. Langmuir 2009, 25, (17), 9767-9776.
5. Hatchard, C. G.; Parker, C. A., A New Sensitive Chemical Actinometer. II. Potassium Ferrioxalate as a Standard Chemical Actinometer. Proc. R. Soc. Lond. A. 1956, 235, (1203), 518-536.
6. Skoog, D. A.; Holler, F. J.; Nieman, T. A., Principles of Instrumental Analysis. 5th ed.; Saunders College Publishing: Philadelphia, 1998.
7. Berne, B. J.; Pecora, R., Dynamic Light Scattering: With Applications to Chemistry, Biology, and Physics. Wiley: New York, 2000.
8. Smulochowski, M., Contribution to the theory of electric endosmosis and some correlative phenomena. In Bulletin International de L'Académie Des Sciences de
50
Cracovie, Classe Des Sciences Mathématiques Et Naturelles, Imprimerie de l'Université: Krakow, 1903; pp 182-199.
9. Attard, G.; Barnes, C., Surfaces. Oxford University Press: New York, 2007.
10. Langley, L. A.; Villanueva, D. E.; Fairbrother, D. H., Quantification of Surface Oxides on Carbonaceous Materials. Chemistry of Materials 2005, 18, (1), 169-178.
11. Wepasnick, K. A.; Smith, B. A.; Schrote, K. E.; Wilson, H. K.; Diegelmann, S. R.; Fairbrother, D. H., Surface and structural characterization of multi-walled carbon nanotubes following different oxidative treatments. Carbon 2011, 49, (1), 24-36.
12. Hodkiewicz, J., Characterizing Carbon Materials with Raman Spectroscopy. In Scientific, T., Ed. Madison, 2010; Vol. 51901.
13. Stumm, W.; Morgan, J. J., Aquatic Chemistry: Chemical Equilibria and Rates in Natural Waters. 3rd ed.; Wiley-Interscience: New York, 1996.
14. Schierz, A.; Parks, A. N.; Washburn, K. M.; Chandler, G. T.; Ferguson, P. L., Characterization and Quantitative Analysis of Single-Walled Carbon Nanotubes in the Aquatic Environment Using Near-Infrared Fluorescence Spectroscopy. Environmental Science & Technology 2012, 46, (22), 12262-12271.
51
Chapter 3:
Photochemical Transformations of Oxidized Carbon Nanotubes as a Result of Exposure to UVC Irradiation
Motivated by the use of UVC radiation in drinking and waste water treatment
plants to destroy harmful pathogens, we have investigated the effect of 254nm (UVC)
radiation on the physical and chemical properties of oxidized multiwalled carbon
nanotube (O-MWCNT) suspensions. Absorbance and particle size measurements were
employed to monitor suspension stability, while x-ray photoelectron spectroscopy (XPS),
transmission electron microscopy (TEM), and Raman spectroscopy were used to
characterize any chemical and structural transformations imparted to the O-MWCNTs as
a result of irradiation. After an initial period of irradiation where suspensions appeared to
remain stable, exposure to 254nm light caused O-MWCNT particles to aggregate. The
length of this initially stable period increased as a function of increasing pH and
decreasing ionic strength. Photo-induced aggregation was found to be the result of a loss
of negatively charged carboxylic acid functional groups. Experiments performed in
solutions containing different levels of dissolved oxygen, used to increase the amount of
reactive oxygen species (ROS) generated upon irradiation, suggest that although ROS can
react with the graphenic sidewalls they are not directly involved in the
photodecarboxylation process. However, our results are consistent with a single photon
excitation process, previously identified in organic photochemistry literature as the
mechanism for removal of CO2 from small organics molecules. The pronounced changes
in the surface chemistry of O-MWCNTs that accompany UVC exposure, however,
proceed in the absence of any significant mass loss or changes in the O-MWCNT
52
structure. UVC irradiation is therefore incapable of mineralizing O-MWCNTs, although
it can transform the physical state and surface chemical properties of O-MWCNTs.
Preliminary studies on oxidized single walled carbon nanotubes (O-SWCNTs) showed
different behavior under similar conditions, but can be ascribed to the same mechanism
as the O-MWCNTs.
3.1 Introduction
The rapidly expanding use of nanoparticles (NPs), such as carbon nanotubes
(CNTs), nano-silver, and nano-scale metal oxides in consumer products has prompted
research into the potential health and safety effects of these NPs when they are released
into the environment.1-9 NPs could enter the environment from various point sources
during industrial manufacturing, as a result of spills that occur during transport, or from
the degradation of NP-containing products (e.g. polymer nanocomposites) at various
stages of their life cycle.2 Once NPs enter the environment they can undergo physical
and/or chemical transformations. Possible chemical transformations include degradation
of surface coatings, oxidation/reduction as a result of exposure to concomitant chemicals
such as hydroxyl radicals, ozone, or sulfides, or biotransformations when NPs are
exposed to cellular enzymes and proteins. All of these transformation processes could
modify a NP’s environmental behavior (e.g. transport, aggregation state, toxicity) with
direct relevance to their environmental health and safety effects.10 Consequently, it is
important to understand the nature and kinetics of transformations that occur to NPs.
Photolysis of carbon based nanomaterials, such as fullerenes, graphene oxide
nanosheets, and carbon nanotubes, is one of the most widely studied processes for
53
transformation. Depending on the original state of the carbon surface, the overall effect of
photolysis appears to fall into one of two categories, oxidation or reduction. Previous
studies have shown that when the surface is pristine or unfunctionalized, photolysis often
results in oxidation of the surface through the introduction of oxygen containing
functional groups. For example, in the case of fullerene clusters (nC60) exposed to UV
light in water, oxidation of the surface under either anoxic 11 and oxic12 conditions
reduces aggregate size, which is postulated to be a result of the surfaces becoming more
hydrophilic.11, 13 This oxidative process also occurs in the presence of natural organic
matter, with UV-induced oxidation enhancing the colloidal stability of humic acid coated
nC60.14 Similarly, when unfunctionalized (pristine) CNTs are irradiated with UV light,
photo-induced oxidation has been observed. For example, Savage et.al. studied pristine
MWCNT films in air exposed to both ambient light and 240nm UV irradiation.15 Using
thermoelectric power (TEP) as their gauge, TEP values became more positive the longer
the films were photolyzed in an oxygen-containing environment. The authors argued that
MWCNTs were being oxidized under these conditions, and that oxidation was occurring
preferentially at defects in the CNT sidewalls. Alvarez et. al.16 and Lee et. al.17 exposed
pristine single walled CNTs (SWCNTs) to UV irradiation, and showed with X-ray
photoelectron spectroscopy (XPS) that an increase in the surface oxygen content after UV
exposure. These findings were supported with attenuated total reflection-Fourier
transform infrared spectroscopy (ATR-FTIR) data which suggested that the oxygen
introduced was predominantly in the form of hydroxyl groups.
In contrast, photoreduction occurs when the carbon surface is already oxidized
prior to photolysis. For example, suspensions of graphene oxide (GO) nanosheets
54
exposed to UVA-visible irradiation (310 – 450nm)18-23 have shown a decrease in epoxide
and hydroxyl groups, as measured by XPS and IR. Obvious differences in the physical
structure of irradiated and unexposed GO nanosheets were also observed by AFM and
TEM, with large defect areas present after irradiation. This effect has been attributed to
the photo-induced removal of oxygen-containing carbon, which Stroyuk et. al.
determined that UVA irradiation (λ = 350nm, 3.54eV) was of sufficient energy to remove
C-O from epoxide (2.1eV) and hydroxyl (0.7eV) functionalities to induce the
photoelimination of peripheral carbonyl and hydroxyl groups.23 This is consistent with
data from Smirnov et. al., who used mass spectrometry to detect the evolution of H2O,
CO, O2, and CO2 from the surface of GO films.19 Matsumoto et. al. proposed
mechanisms for the evolution of these gases involving the excitation of the π-π* band to
produce holes and electrons that would facilitate the removal of CO2 and H2O from the
GO nanosheets.18
Similar photochemical transformations have been observed when oxidized CNTs
are photolyzed. For example, Chen and Jafvert examined carboxylated SWCNTs in water
under both sunlight irradiation and 350nm lamp light.24, 25 The oxidized SWCNTs (O-
SWCNTs) aggregated after irradiation at a variety of pH conditions compared to dark
controls, in which O-SWCNTs are normally known to be stable. They also monitored the
ROS production of singlet oxygen, superoxide radicals, and hydroxyl radicals from as-
received carboxylated SWCNTs and compared those results to heat treated/acid washed
SWCNTs. The singlet oxygen (1O2) and hydroxyl radical (•OH) production decreased for
the treated CNTs compared to the as-received. The authors suggested that this could be a
function of: (1) the decrease in amorphous carbon content, (2) the decrease in metal
55
content, (3) a decrease in –COOH functionalization, and (4) the change in the
aggregation state, which has been shown to occur for the thermal/acid treated CNTs. In a
related study, Hwang et. al. used 300-400nm (UVA) irradiation to study carboxylated
MWCNT suspensions in water with mono and divalent salts.26 A loss of surface oxygen
content was observed by XPS when oxidized MWCNTs were irradiated with UVA light.
This loss in oxygen resulted in destabilization and aggregation of MWCNTs as measured
by time resolved dynamic light scattering (TR-DLS) and quartz crystal microbalance
(QCM-D), respectively. A related study by the same researchers, also conducted with
UVA light saw a loss of oxygen in the form of carboxylic acid functional groups and an
increase in the structural disorder, monitored by XPS and Raman, respectively. The
addition of hydrogen peroxide was observed to enhance the rate of CNT aggregation, an
effect that was attributed to reactions of reactive oxygen species (ROS) with carboxylic
acid groups on the CNT surfaces.27
To date, studies on the photolysis of CNTs have focused on the effect of visible
light and lower energy UVA light. In contrast, comparatively little is known about the
effects of the more aggressive UVC irradiation, used in drinking and waste water
treatment plants, on its ability to degrade nanoparticles. With its potential to directly
excite electronic transitions and thereby open up new transformation pathways, the
known UVC-induced transformations of nanomaterials are limited. This has motivated us
to study the effects of UVC light on oxidized multi-walled carbon nanotubes (O-
MWCNTs) under various solution conditions (e.g. pH, ionic strength, dissolved oxygen)
as a function of irradiation time and light intensity. The concentration and size of
suspended particles were measured with UV-Vis and DLS respectively as a function of
56
irradiation time, while chemical and physical transformations were evaluated using
complementary analytical techniques including mass loss, TEM, Raman, and XPS with
chemical derivatization. Questions we sought to address included, (1) what are the
fundamental physical and chemical transformations of oxidized MWCNTs when they are
exposed to UVC irradiation, (2) how do water quality parameters affect the rate of
transformation, (3) can UVC degrade or mineralize oxidized MWCNTs, and (4) can we
provide mechanistic insights into the fundamental transformation processes.
3.2 Experimental
3.2.1 O-CNTs
Commercially available O-MWCNTs and O-SWCNTs were used for this study.
MWCNTs were purchased from NanoLab, Inc. (Newton, MA) that had been oxidized by
the manufacturer using a 3:1 sulfuric:nitric mixture (PD15L5-20-COOH, outer diameter:
15+/-5nm, Length: 5-20μm, Purity: >95%). Oxidized MWCNTs (MWCNT-OH, outer
diameter: 10-20nm, Length: 10-30μm, Ash: <1.5%, Purity: >95%) were also purchased
from Cheaptubes (Brattleboro, VT) and used as received, principally as a point of
comparison to the behavior of the NanoLab O-MWCNTs.
Pristine SWCNTs (SG-65, outer diameter: 0.93nm, specific surface are: 800m2/g,
carbon content: >90%) from Southwest Nanotechnologies (Norman, OK, USA) were
oxidized in our own laboratory using 10% w/w, 40% w/w, and 70% w/w nitric acid to
impart a systematically increasing amount of oxygen to the CNT surface used as a
mechanistic comparison to the two multiwall CNTs. In brief, the mixture was refluxed in
57
nitric acid at 140°C for 1.5hrs with stirring. After cooling to room temperature, the acid-
CNT mixture was decanted into small test tubes and then repeatedly centrifuged to
collect the newly oxidized SWCNTs (O-SWCNTs).
O-CNTs were subject to a rigorous cleaning procedure outlined in Smith et. al.28-
30 Briefly, the O-CNTs first underwent repeated rinsing/centrifugation cycles with
deionized water to remove as much of the nitric acid as possible. Then 4M NaOH was
used to remove amorphous carbon and excess carbon products remaining from oxidation.
4M HCl was added next to neutralize the solution, and finally repeated rinses with DI
water were performed to remove the electrolytes from the supernatant. The sample was
judged free of electrolyte when the resistivity of the supernatant reached >0.5MΩ. Post
cleaning, the CNTs were dried on a microscope slide, scraped off, and ball-milled for
homogeneity. Cleaned and dried CNTs were stored in small clean screw cap vials prior to
preparing colloidal suspensions and subsequent photolysis experiments. This cleaning
procedure was used for the oxidized CNTs purchased from NanoLab, Inc. and Southwest
Nanotechnologies, but not for the CNTs purchased from Cheaptubes. The purpose of
cleaning one MWCNT and not the other was to compare the effects, if any, of residual
metal and amorphous carbon on the CNT colloidal stability during UV irradiation.
3.2.2 Chemicals
Sodium chloride, sodium hydroxide, sodium dihydrogen phosphate, and sodium
hydrogen phosphate were purchased from Fisher Scientific and used without purification.
Nitric acid, hydrochloric acid, and derivatizing agents 2,2,2-trifluoroacetic anhydride
(TFAA), 2,2,2-trifluoroethanol (TFE), N,N’-di-tert-butyl-carbodiimide (DTBC), and
2,2,2-trifluoroethylhydrazine (TFH) were all purchased from Sigma-Aldrich and used
58
without further purification. HPLC-grade ultrapure water was purchased from VWR
International and used as received. Ultra-high purity oxygen and nitrogen were purchased
from Air Gas (Malvern, PA).
3.2.3 Preparation of O-CNTs Suspensions
Stock suspensions of O-CNTs were prepared by adding a known mass (4 – 6mg)
of the desired CNTs to 200mL of HPLC-grade ultrapure water. Samples were then
sonicated for 20hrs (Branson 1510, 70W). After sonication, suspensions were centrifuged
at 1000rpms for 5min to remove any glass that was etched from the walls of the flask,
and any CNTs that were not taken up into suspension (i.e., CNT bundles, amorphous
carbon, very lowly oxidized CNTs). This stock suspension was then transferred to clean
200mL Pyrex containers for storage.
A Varian Cary 50 UV-Vis was used to determine the absorbance of stock O-CNT
suspensions, and to set the absorbance of the final experimental suspensions to 0.34 at
350nm (this corresponds to approximately 5mg/L for oxidized NanoLab MWCNTs). A
typical UV-Vis spectra of the O-MWCNT suspension is shown in Figure S3.1. The
desired ionic strength was obtained by adding appropriate volumes of a 4M NaCl stock
solution. Suspensions of O-CNTs were set to the desired pH (±0.1) by adding phosphate
buffer (3mM final concentration) and HCl or NaOH as needed. The triprotic phosphate
buffer was chosen because it did not impact the absorption profile in the region being
examined, allowed stability over a range of pH values to be studied (4 – 10), and was not
negatively impacted by the removal of carbon dioxide, unlike carbonate buffers. Separate
control studies conducted with phosphate and acetate buffers revealed that the nature of
the phosphate buffer also did not influence the effect or kinetics of UVC exposure
59
(Figure S2). In the absence of a buffer, the pH of the suspension would undergo a drastic
decrease during irradiation, artificially destabilizing the O-CNTs before the UV radiation
had a chance to induce aggregation. The use of a buffer was therefore necessary to
stabilize the pH throughout an experiment, enabling us to isolate the effect of different
variables (pH, ionic strength, light intensity) on particle stability.
For initial particle size measurements prior to UVC photolysis, a 0.5mL aliquot
was removed and diluted to 1.25mg/L with buffered and pH balanced ultrapure water.
Particle size measurements were carried out on this sample in disposable plastic cuvettes
at 24°C with a Malvern ZetaSizer Nano-ZS using a 5mW He-Ne laser (633nm) to probe
CNTs. A non-invasive backscattering configuration (detection angle 173° with respect to
the incident laser light) was used to collect measurements. Effective hydrodynamic
diameter results were modeled by the Stokes-Einstein relationship and represent the
average of five separate measurements, each measurement consisting of 10-15 scans.
Once initial absorbance and particle size measurements confirmed that a stable
and appropriately concentrated experimental O-CNT suspension had been prepared,
samples were transferred to a quartz vessel. These vessels were then purged with ultra-
high purity oxygen or nitrogen before the vessel was sealed first with Parafilm and then
with aluminum foil. The outside surface of the quartz glassware was wiped down with
acetone before being exposed to UVC irradiation.
3.2.4 UVC Irradiation
Irradiation was performed on colloidal suspensions of O-CNTs in an RPR-100
Rayonet UV photochemical reaction chamber equipped with 16, 35W low pressure
mercury lamps (90% 254nm emission, irradiance with all 16 lamps = 15.4 – 16.0
60
mW/cm2), purchased from Southern New England Ultraviolet (Branford, CT). Most
experiments were performed with 16 lamps (photon flux ~ 1.32 x 1017 quanta/sec as
measured by actinometry). For experiments performed with less than 16 lamps, some
lamps were symmetrically wrapped with aluminum foil to ensure uniform light
distribution around the entire chamber. Photon flux measurements for experiments
performed with less than 16 lamps can be found in Figure S3 and Table S1.
Experiments were performed by exposing colloidal suspensions of O-MWCNTs
to UVC irradiation in one of two configurations:
3.2.4.1 Large Batch Volumes
A 600mL or 1000mL quartz beaker was used to contain large volumes of
O-MWCNTs during irradiation to produce enough sample for surface
characterization and mass loss measurements following UVC irradiation. In these
experiments a beaker was set on a stand inside the chamber so that the sides of the
glassware sat at a height equal to the midpoint of the lamps for maximum
exposure. O-MWCNT suspensions were irradiated in this static configuration
until UVC-induced aggregation and settling had occurred. At this point a small
amount of concentrated HCl was added to the beaker to aid in the removal of any
remaining suspended CNTs. The contents of the beaker were then centrifuged
(4000rpms for 10min), and the supernatant was decanted and collected in a clean
1L Pyrex bottle. The O-MWCNTs collected in the test tubes were then rinsed
thoroughly with DI water until the resistivity of the supernatant was >0.5MΩ and
dried on a cleaned glass microscope slide overnight at 70°C. The mass of O-
MWCNTs remaining after irradiation was determined by scraping the dried O-
61
MWCNTs off the glass and weighing them on aluminum foil that had been
deionized to remove static charge. Mass loss was determined by comparing the
values obtained from UVC irradiated O-MWCNT samples to control studies,
where suspensions of O-MWCNTs had been prepared and then crashed out of
solution by adding sufficient acid to cause particle destabilization without any
UVC exposure. O-MWCNTs generated from control and irradiation studies were
also used for surface characterization. O-SWCNTs were also irradiated in this
manner.
3.2.4.2 Small Sample Volumes
A dozen 15mL quartz test tubes were used to measure changes in particle
concentration (absorbance) and size as a function of irradiation time. In these
experiments the test tubes were placed into a rotating 12-slot carousel set to a
height at the midpoint of the UVC lamps to ensure that each test tube received
uniform exposure. Quartz test tubes were removed at discrete time intervals
during UVC exposure for sampling, and monitored for changes in the solution
chemistry using a pH meter and conductivity probe at each time point. Each time
a test tube was removed a replacement (containing an already sampled suspension
of O-MWCNTs) was inserted into its place to maintain uniform light intensity
within the carousel. Variations in solution conditions and light intensity were
studied with this method, so the absolute light intensity was calibrated for these
experiments (see below).
For each O-MWCNT suspension removed from the carousel, a 0.5mL
aliquot was extracted from the top of the test tube (taking care not to shake or
62
disturb the contents) and placed into a clean 5mL screw cap vial and set aside for
particle size analysis. For particle size measurements, the 0.5mL sample placed in
the screw cap vial was diluted to 1.25mg/L with ultrapure buffered water and
analyzed using a Malvern ZetaSizer Nano-ZS The suspension remaining in the
quartz test tube was gently centrifuged (1000rpms) for 3 minutes to remove any
large aggregates that would compromise absorbance measurements by excessive
scattering. For absorbance measurements, an aliquot of the centrifuged O-
MWCNT suspension was pipetted into a 1cm path length quartz cuvette and the
UV-Vis spectra measured from 200 – 900nm in a Varian Cary 50 UV-Vis
spectrophotometer. Five separate absorbance readings were taken and the average
signal at 350nm was used as a measure of the O-MWCNT particle concentration.
These concentrations were plotted as a function of irradiation time to track the
progress of UVC-induced aggregation.
3.2.5 Calibration of UVC Light Intensity
To determine the intensity of UVC light experienced by the O-MWCNTs during
irradiation, actinometry was performed using potassium ferrioxalate as a colorimetric
indicator. UV light causes the decomposition of ferrioxalate to Fe2+ ions. The addition of
o-phenanthroline to this solution causes the Fe2+ ions to form a red colored complex with
an absorption maximum at 510nm. By measuring the absorbance of this complex it is
possible to determine the concentration of Fe2+ ions and thereby derive the quanta of light
absorbed for all light intensities studied.31 More comprehensive details regarding the
calibration of the photochemical reactor can be found in the Supporting Information.
63
3.2.6 Characterization of O-MWCNT Powders
O-CNTs were analyzed before and after UVC induced aggregation to determine
the effect of irradiation on both the chemical and structural characteristics of the NPs.
3.2.6.1 Chemical characterization
To determine surface composition, a small sample of powdered O-CNTs
was pressed onto a 1cm x 1cm piece of double sided copper tape that was adhered
to an XPS sample stub, ensuring no copper was visible. A PHI 5400 XPS system
using Mg Kα x-ray (1253.6eV) irradiation was used to analyze O-MWCNT
samples. A high energy electron analyzer operating at a constant pass energy was
used to measure the ejected photoelectrons. Elemental quantification was
performed using a pass energy of 178.95eV at a scan rate of 0.25eV/step. O-
MWCNT samples were analyzed for total oxygen content as well as oxygen
functional group distribution using wet chemical derivatization techniques
previously used to study CNTs in our lab.32, 33 In brief this method uses fluorine-
containing reagents (2,2,2-trifluoroacetic anhydride (TFAA), 2,2,2-
trifluoroethanol (TFE), and 2,2,2-trifluoroethylhydrazine (TFH)) to selectively
and quantitatively tag specific functional groups. Commercial software
(CasaXPS) was used to quantify elemental regions by integrating the area under
the C(1s), O(1s), N(1s), and F(1s) peaks. O-SWCNTs did not produce enough
residual sample to perform chemical derivatization and total oxygen analysis.
64
3.2.6.2 Structural characterization
(i) TEM: O-MWCNTs were prepared for TEM analysis by dipping a
holey-carbon TEM grid into O-MWCNT-containing suspensions and allowing
them to dry in air. The grids were then imaged using a Philips CM 300 field
emission gun TEM operating at 297kV. A CCD camera mounted on a GIF 200
electron energy loss spectrometer was used for image collection.
(ii) Raman: Dried O-MWCNT samples were mounted onto a microscopic
slide and analyzed by Raman spectroscopy over 10 second exposure times with 3
spectral averages using an XploRA ONE Raman system from Horiba Scientific
(Edison, NJ). A solid state Nd:YAG laser (50mW) emitting an excitation
wavelength of 532 nm was used with 100x objective. Samples were scanned over
the range of 500 – 3000 cm-1. Instrument parameters include: slit = 200 µm, hold=
300, grating = 1800, filter = 10%.
(iii) Near Infrared Fluorescence (NIRF): Dried powders or suspensions of
O-SWCNTs were analyzed by NIRF using a Nanospectralyzer NS1 from Applied
Nanofluorescence (Houston, TX, USA). Suspensions were created in a 2% w/v
sodium deoxycholate (SDC) solution and analyzed over the range 6000 –
11,500cm-1 using excitation wavelengths of 638nm, 691nm, and 782nm.
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66
strictly a result of UVC exposure (see Figure S3.5). The CNT aggregation and settling
observed in this study are qualitatively consistent with previous findings that studied
carboxylated single walled CNTs,24 as well as the decreased stability seen when
carboxylated multiwalled CNTs26 were exposed to UVA irradiation.
Phototransformations induced by UVC irradiation were examined more
quantitatively by acquiring absorbance and particle size measurements as a function of
irradiation times using UV-Vis and DLS, respectively. The UV-Vis absorbance profile
for suspensions of O-MWCNTs (Figure S3.1) are similar to previous studies26 with a
broad peak at λ = 264nm, corresponding to the π→π* transition in the conjugated
sidewall ring structure.34, 35 Although the intensity of the profile decreases with increasing
wavelength, scattering from O-MWCNT particles prevents the baseline from reaching an
absorbance value equal to zero. The sharp increase seen at wavelengths approaching λ =
200nm is due to the absorption of the phosphate buffer and NaCl added to each O-
MWCNT suspension (see Figure S3.2).36 As the UVC irradiation time increases, Figure
S3.1 shows that the intensity of the profile decreases without any significant changes in
shape. An example of the data acquired on the particle concentration and particle size
measured as a function of UVC irradiation time is shown in Figure 3.2. During the initial
stages of irradiation (up to approximately 18 hours in this case) absorbance
measurements illustrate that the concentration of O-MWCNTs in suspension remains
relatively unchanged, and the average particle size only increases slightly. However, for
irradiation times in excess of 24 hours a rapid increase in particle size (> 400nm) is
observed and the colloidal O-MWCNT concentration drops sharply. It is during this time
67
(shaded region of Figure 3.2) that small particulates are observed, and large settleable
aggregates start to form.
3.3.2 Effects of Water Quality Parameters
The effects of water quality were investigated at a variety of solution conditions,
defined by a specific pH and ionic strength. Figure 3.3 and Figure S3.6 illustrate that the
resistance of the O-MWCNTs to UVC-induced aggregation increases at lower ionic
strength and higher pH conditions. Thus, for NaCl concentrations of 4 – 5mM, the O-
MWCNT absorbance and particle size remains roughly unchanged for irradiation times
less than 18hrs. In contrast, for NaCl concentrations of 12mM the particles reach their
critical size after less than 6hrs and settleable aggregates are observed. In terms of pH
Figure 3.2 – Change in absorbance (filled red circles) and particle size (open blue squares) plotted as afunction of UVC irradiation time for oxidized multiwalled CNTs under anoxic conditions at pH 7 and3mM Na+ under radiation with 8 UVC lamps. The shaded region indicates the time where visibleaggregation of CNTs was observed.
Irradiation Time (hrs)
0 6 12 18 24 30
Ab
sorb
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at
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0.10
0.15
0.20
0.25
0.30
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200
300
400
500
600
68
effects, when the ionic strength is held constant, at pH 4 (black triangles) the O-
MWCNTs are quickly destabilized by UV irradiation, having almost completely
aggregated in less than two hours. In contrast, at pH 10 (green circles) the same particles
resisted the effects of UV-induced aggregation for over 48 hours. It should be noted that
these trends in increased resistance to UVC irradiation correspond to the same conditions
(low ionic strength, high pH) that increase the stability of negatively charged colloids
towards aggregation. The stability of pH and conductivity readings maintained with the
use of the phosphate buffer indicated that the pH and ionic strength of the suspension
were not the cause of the observed aggregation and settling. These results suggested to us
that the cause of CNT instability was due to a loss of surface oxygen.37, 38
Figure 3.3 – Absorbance profiles for oxidized multiwalled CNTs under anoxic conditions as a function of ionic strength at constant pH 7 (A) and pH at constant ionic strength 3mM Na+ (B) plotted as a function of UV irradiation time.
Irradiation Time (hrs)
0 6 12 18 24 30 36
Ab
sorb
ance
at
350n
m
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
4.5mM4.7mM 6mM12mM 12mM
A
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Irradiation Time (hrs)
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Ab
sorb
ance at 350n
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0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
4 7 10
pH
B
69
3.3.3 Chemical Transformations to O-MWCNTs caused by UVC Irradiation
XPS was used to examine any chemical changes that occurred to the surface of O-
MWCNTs as a result of UVC-induced aggregation. Figures 3.4A and 3.4B show a
comparison of the C(1s) and O(1s) spectral envelopes obtained from a suspension of O-
MWCNTs that were not exposed to UV light (solid red line) and a suspension of the
same O-MWCNTs after UVC-induced aggregation (dashed blue line). Although the
C(1s) spectral envelope remains virtually unchanged after UVC irradiation, the O(1s)
envelope exhibits a noticeable decrease in intensity (from 9%O to 5.9%O). A similar
decrease in oxygen was observed for a number of O-MWCNTs under different solution
conditions (see Table S3.2) as a result of UVC-induced aggregation. The decrease in the
oxygen signal intensity in the absence of any marked changed to the carbon region is a
consequence of the fact that all of the oxygen functional groups are located at the surface
Figure 3.4 – XPS results for oxidized multiwalled CNTs in absence of any irradiation (solid red line) andafter UVC-induced aggregation and settling had occurred (dashed blue line). The solution conditions inthese experiments were 3mM NaCl and pH 10. Figures 4A and 4B show the C(1s) and O(1s) envelopesbefore and after irradiation. The distribution of oxygen-containing functional groups (C) determined bychemical derivatization illustrates how UVC irradiation changes the concentration of different oxygen-containing functional groups.
Binding Energy (eV)
526528530532534536538540542
Co
un
ts
beforeafter
O(1s) B
Total%
O
%O(C
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%O(C
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Per
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2
3
4
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6
7
8
9 before after
C
Binding Energy (eV)
280282284286288290292294296
Co
un
ts
beforeafter
C(1s) A
70
of the O-MWCNTs, while approximately 68% of the C(1s) signal comes from the pure
carbon core of the O-MWCNTs. This calculation is based on a NanoLab, Inc. O-
MWCNT which has a manufacturer specified average of 10 walls with an interlayer
spacing of 0.34nm.39
To provide more detailed information on the effect that UVC irradiation has on
the surface chemistry of O-MWCNTs we used chemical derivatization to quantify
changes in hydroxyl, carboxyl, and carbonyl group densities.32, 33 Figure 3.4C shows an
example of the results from this analysis applied to O-MWCNTs before and after UVC-
induced aggregation. The data reveals that the carboxyl groups, as well as residual
(%Oother) oxygen functionalities such as ethers or esters that could also be present on the
O-MWCNT surface but cannot be tagged by chemical derivatization, exhibited a
measurable decrease in concentration. The loss of carboxylic acid groups was observed in
all of the UVC irradiated O-MWCNTs where chemical derivatization was performed,
indicative of a photodecarboxylation (PDC) process. Although there is some variability in
the results, chemical derivatization analysis showed that UVC-induced aggregation
produced a slight increase in the concentration of hydroxyl and carbonyl functionalities,
in contrast to the decrease in carboxyl group density.
The results shown in Figure 3.4 and Table S3.2 provide compelling evidence that
the UVC-induced aggregation of O-MWCNTs is caused by a PDC process, since the
negatively charged carboxylic acid groups are principally responsible for the colloidal
stability of O-MWCNTs. Previous studies have revealed that O-MWCNT stability is
strongly dependent on the concentration of surface bound carboxylic acid groups.38 As
UVC irradiation proceeds, the concentration of carboxylic acid groups decreases
71
systematically until a sufficient number of these groups, and thus the negative charge on
the O-MWCNTs, have been removed. This process results in a point where the O-
MWCNTs are no longer colloidally stable and consequently begin to aggregate (see
Figure 3.1). The extent of decarboxylation necessary to induce aggregation will depend
on the solution conditions. This provides a rationale for the data shown in Figure 3.3,
where the stability of O-MWCNTs towards UVC irradiation increases under solution
conditions that favor the stability of negatively charged colloids (i.e. low ionic strength
and high pH). As a consequence, the length of time necessary to induce aggregation also
increases under these same conditions. The increasing loss of carboxylic acid groups that
occurs as the irradiation time increases also rationalizes the changes in particle
concentration and size observed in Figure 3.2.
Separate experiments were conducted in an attempt to probe the evolution of CO2
during UVC irradiation. Results from these experiments (Figure S3.7) show slightly
higher levels of CO2 evolution for UVC irradiated samples, as compared to the
background levels measured in dark controls. Although the amount of CO2 evolved
during irradiation is comparable to the background CO2 levels from the dark controls, the
data shown in Figure S3.7 is qualitatively consistent with the idea of small (μg) quantities
of CO2 being evolved during the irradiation process. Based on the mass of O-MWCNTs
used in these experiments and the average percentage of carboxylic acid groups present
on these O-MWCNTs, the loss of all of the surface carboxylic acid groups would
correspond to a mass of CO2 evolved on the order of 1 – 2μg, which is qualitatively
consistent with our observations. More experimental detail on these studies can be found
in the Supplemental Information.
72
To better understand the mechanism of PDC, a kinetic study of UVC-induced
aggregation was performed as a function of light intensity by varying the number of
lamps in the Rayonet photoreactor. Figure 5 shows that the irradiation time needed to
affect UVC-induced aggregation increases systematically as the number of lamps
decreases, approximately doubling as the number of lamps is decreased by a factor of two
(16 to 8, 8 to 4, 4 to 2), except for a smaller relative change in going from 4 to 2 lamps.
Although the measurements of particle concentration by UV-Vis or particle size by DLS
provide only an indirect measure of the extent of reaction, we can take advantage of the
fact that if the fundamental nature of the transformation process remains invariant to the
light intensity, then the rate of the reaction will be directly proportional to the effective
rate constant (keff). We ensure this invariance occurs by keeping the initial particle
concentration and solution conditions constant between different light intensity
experiments, as is the case in Figure 3.5.
Under these conditions, the time taken to reach a common point in the
decarboxylation process will be inversely proportional to keff. In Figure 3.5 we choose the
irradiation time taken for the O-MWCNT suspension to decrease to half of its initial
absorbance value (A.U. = 0.17; Figure 3.5C) and for the particle size to increase in
effective hydrodynamic diameter to 630nm (Figure 3.5D) as examples of common points
in the reaction profile that can be measured with reasonable degrees of accuracy. More
importantly, since keff In, where I is the intensity of light (which is directly proportional
to the number of UV lamps) and n is the number of photons involved in the rate
determining step associated with PDC we can write;
73
0.17 630
1 1 or nm n
eff
t tk I
(3.1)
0.17 630log or log log log(# UV bulbs)nmt t n I n (3.2)
Figure 3.5 – Absorbance (A) and particle size (B) profiles for oxidized multiwalled CNTs at pH 7 and12mM NaCl exposed to different light intensities, plotted as a function of irradiation time. The dashed linesindicate t1/2 (A) where the absorbance reaches half of its initial value, and t630nm (B) where the particle sizereached ~630nm. Kinetic data is plotted as a log-log function of t1/2 (C) or t630nm (D) versus light intensity(I).
Irradiation Time (hrs)
0 8 16 24 32 40 48 56
Ab
sorb
ance
at
350n
m
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
16 bulbs8 bulbs4 bulbs 2 bulbs
A
Irradiation Time (hrs)
0 4 8 12 16 20 24 28 32 36
Par
ticl
e S
ize
Ave
rag
e, D
(h)
(nm
)
200
400
600
800
1000
1200
1400
1600
180016 bulbs8 bulbs 4 bulbs 2 bulbs
B
log(I)0.2 0.4 0.6 0.8 1.0 1.2 1.4
log
(t63
0nm
)
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
D
log (I)0.2 0.4 0.6 0.8 1.0 1.2 1.4
log
(t 1
/2)
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
C
74
where, t0.17 and t630nm represent the irradiation time required for the particle concentration
to decrease to 0.17 absorbance units or the particle size to increase to 630nm,
respectively. Thus, a plot of log (t0.17) or log (t630nm) as a function of log (# UV lamps)
should be linear with a gradient of –n. Analysis of Figures 3.5C and 3.5D shows these
two log-log relationships are close to linear (R2 = 0.9475 for 3.5C and 0.9623 for 3.5D)
with slopes of -0.89 and -0.92 respectively. Since photon induced processes require an
integral number of photons our results indicate that UVC photoinduced decarboxylation
is initiated by a single photon process.
Additional mechanistic insights into the PDC process were obtained by examining
the effect of dissolved oxygen on the stability of O-MWCNT suspensions towards UVC-
induced aggregation. Figure 3.6 shows the absorbance and particle size measurements
taken for experiments performed at the same pH and ionic strength, but under oxic (open
squares) and anoxic (filled circles) conditions. A comparison of the effect of UVC
irradiation on O-MWCNTs in nitrogen purged and oxygen saturated solutions revealed
essentially identical behaviors at the pH and ionic strength condition examined. Both
systems exhibited a decrease in colloidal O-MWCNT concentration (Fig. 3.6A) with a
corresponding increase in particle size (Fig. 3.6B) after approximately 5hrs of UVC
irradiation. Separate measurements (Figure S3.8) revealed that the concentration of DO
in the oxygen saturated solutions was ~3.5 times greater than the level in the nitrogen
purged solutions. These results combined indicate that the rate of photo-induced
aggregation is independent of the dissolved oxygen content. This in turn suggests that the
PDC process does not involve intermediate radicals of reactive oxygen species (such as
•OH), which should increase as the dissolved oxygen concentration increases.40-42 This is
75
validated by very short lifetimes of •OH in water43 and that decreasing concentrations of
•OH are generated from O-CNTs over the course of irradiation.24
Collectively, results from the light intensity and dissolved oxygen experiments
suggest a PDC mechanism that involves a direct single photon excitation of the
carboxylic acid group that triggers the expulsion of CO2. This mechanism is the same as
that which has been proposed and experimentally verified using laser flash photolysis,44
UV irradiation in a Rayonet photochemical reactor,45 and DFT calculations46 for PDC of
aliphatic or aromatic acids and esters such as ketoprofen, acetyl phenyl acetic acid, and
their derivatives. Photoexcitation promotes the molecule to an excited singlet state, which
expels CO2 as it undergoes a rapid intersystem crossing to a triplet state. Before relaxing
Irradiation Time (hrs)
0 2 4 6 8 10 12 14
Ab
so
rban
ce a
t 35
0nm
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
N2 purged
O2 purged
A
Irradiation Time (hrs)
0 1 2 3 4 5 6 7
Par
tic
le S
ize
Ave
rag
e, D
(h)
(nm
)
200
400
600
800
1000 N2 purged
O2 purgedB
Figure 3.6 – Absorbance (A) and particle size (B) profiles for oxidized multiwalled CNTs at pH 7 and12mM NaCl. plotted as a function of UVC irradiation time, conducted under anoxic (nitrogen purged) oroxic (oxygen purged) conditions.
76
back to a ground state configuration, the available radical or ionic species will extract a
hydrogen from a neighboring carbon atom or the surrounding medium.
Scheme 3.1 shows an example from the organic photochemistry literature of PDC
from 5H-dibenzo[a,d]cyclohepten-5-carboxylic acid,47 a reasonable representation of the
local chemical environment for carboxylic acids attached to CNT sidewalls. In this study,
the authors concluded that benzannelated acetic acids undergo PDC rapidly from a singlet
excited state, proceeding through a carbanion intermediate. They confirmed it was a
singlet state by probing the triplet excited state, which gave no PDC reaction, and the
carbanion intermediate with EPR measurements. Experiments performed in D2O proved
that the hydrogen captured upon returning to the ground state was from the surrounding
medium because the carbanion incorporated deuterium at the position vacated by CO2. A
review of the organic photochemistry literature on other small acid molecules shows that
PDC can occur when the acid is protonated or deprotonated, as well as in both aqueous
and organic solvents. Depending on the conditions (pH, oxic vs. anoxic) and solvent type,
PDC proceeds through either ionic (heterolytic cleavage)44, 45 or radical (mesolytic
cleavage)44, 46 intermediates, which are monitored by analytical techniques such as
Scheme 3.1 – Mechanism for the photodecarboxylation of 5H-dibenzo[a,d]cyclohepten-5-carboxylic acidin water proceeding through a carbanion intermediate upon irradiation with 254nm light based on work byMcAuley et. al.47
77
transient absorption, fluorescence, mass spectrometry, and NMR. A more detailed
explanation of carboxylic acid and ester PDC can be found in the review article by Budac
and Wan.48 Models from the organic photochemistry literature led us to propose the
following process (Scheme 3.2) for PDC and subsequent aggregation of O-MWCNTs.
The diversity of chemical environments under which PDC can occur suggests that
reactive oxygen species are not responsible for the photoreduction process exhibited by
O-MWCNTs. The idea that strongly oxidizing ROS, such as hydroxyl radicals, are
responsible for a net reduction process such as PDC is hard to rationalize from an
intuitive chemical perspective. Moreover, such a mechanism is inconsistent not only with
our experimental observations at different concentrations of dissolved oxygen, but also
the extensive body of already existing but seemingly overlooked organic photochemistry
literature which has identified the mechanism, including the fact that PDC can occur in
organic solvents where ROS should not exist.
In more general terms it should be noted, however, that although the changes in
particle size and absorbance values can be ascribed to PDC, the effects of UV irradiation
are not restricted to the carboxylic acid groups. For example, photo-induced
Scheme 3.2 – Proposed pathway for photodecarboxylation and subsequent aggregation of O-MWCNTsthrough the removal of carboxylic acid functional groups.
Aggregation
78
decarboxylation of ester groups48 and the photoreduction of ethers23 (the later
demonstrated in the photochemistry of graphene oxide) would be consistent with the
significant decrease in the concentration of “other” oxides (not hydroxyl, carbonyl or
carboxyl) that chemical derivatization cannot assay (see Figure 3.4). In this respect, a
potential role for reactive oxygen species (such as hydroxyl radicals) that are produced as
a result of UV exposure to oxidized CNTs24, 25 could be the cause of the increase seen in
hydroxyl group density, and also the slight increase in structural disorder observed by
Raman (Figure 3.8). Thus, it seems that the UVC-induced chemical transformations to O-
MWCNTs are likely a result of more than one process, though PDC is the dominant
process that directly influences particle stability and governs the fate and transport
properties of the O-MWCNTs.
3.3.4 Structural Transformations to O-MWCNTs
To determine if there were any structural transformations imparted to the O-
MWCNTs as a consequence of UVC irradiation, TEM and Raman were both performed
on O-MWCNTs before and after UVC-induced aggregation. TEM images (Figure 3.7)
revealed an absence of any obvious structural changes to the O-MWCNTs after UVC
exposure, with the shape, size, and number of sidewalls remaining constant based on
visual observations of different O-MWCNTs. Some amorphous carbon can be seen
attached to the outer walls of the individual CNTs in both sets of micrographs, with
perhaps slightly more on the outer walls of the tubes after UVC irradiation. TEM analysis
was performed on a number of O-MWCNTs before and after UVC irradiation under
different solution conditions (pH, dissolved gas) with the same qualitative finding. The
lack of physical transformations to the surface of O-MWCNTs in our irradiation
79
experiments is similar to the observations of Hwang et. al. when they irradiated
carboxylated MWCNTs for seven days under UVA light.26
Raman spectroscopy was performed on O-MWCNTs that had not been exposed to
UVC irradiation (control), as well as suspensions that had been irradiated under oxic and
anoxic conditions for sufficient times to induce aggregation. In Raman experiments, O-
MWCNTs from two different manufacturers, NanoLab, Inc. and Cheaptubes (Figure 3.8),
were studied. Prior to irradiation, O-MWCNTs from both manufacturers exhibited
significant D-band intensities indicative of a large amount of disordered (sp2) carbon
atoms, presumably as a result of the aggressive oxidizing conditions needed to introduce
surface oxides into the graphenic sidewalls.49 The NanoLab, Inc. CNTs exhibited
Figure 3.7 – Low (top row) and high (bottom row) resolution TEM micrographs of O-MWCNTs beforeand after UVC irradiation at pH 7 under anoxic conditions.
80
identical ID:IG band ratios of 0.94 for the control samples and for O-MWCNTs which had
aggregated under the influence of UVC irradiation in a nitrogen purged suspension. In
contrast, the ID:IG band ratio increased slightly to 1.01 when O-MWCNTs were subjected
to UVC irradiation in a solution saturated with dissolved oxygen. In comparison, the
Cheaptubes O-MWCNTs ID:IG band ratio increased slightly from 1.17 in the control, to
1.22 after UVC-induced aggregation in either oxic or anoxic conditions. These Raman
results indicate that UVC induced aggregation proceeds in the absence of any significant
structural changes, consistent with the TEM data shown in Figure 7. The very modest
increases in ID:IG band ratio observed upon UVC irradiation could potentially be the
result of reactions between small quantities of ROS generated from irradiation of the
suspension and the graphenic portions of CNT sidewalls, or from the removal of surface
functional groups and damage imparted to the sidewalls by the high energy UVC light.
However, if ROS, such as hydroxyl radicals, played any appreciable role in the
photochemical transformation process we would expect to see a significantly larger
Cheaptubes
Raman Shift (cm-1)
500 1000 1500 2000 2500 3000
Control Irradiated, N2Irradiated, O2
NanoLab, Inc.
Raman Shift (cm-1)
500 1000 1500 2000 2500 3000
No
rmal
ized
Inte
nsi
ty (
a.u
.)
ControlIrradiated, N2Irradiated, O2
Figure 3.8 – Raman spectroscopy showing the effects of UVC irradiation on O-MWCNTs purchased fromNanoLab, Inc. and Cheaptubes. Results are shown for O-MWCNTs before irradiation and after UVC-induced aggregation under oxic and anoxic conditions at pH 10.
81
increase in the degree of structural disorder to have occurred.42, 50 Thus, results from
TEM and Raman indicate that the significant changes in the O-MWCNT surface
chemistry caused by UVC irradiation are not accompanied by any measurable changes to
the physical structure of O-MWCNTs.
This absence of any significant structural changes to the O-MWCNTs is also
consistent with the lack of mineralization. In large batch studies greater than 90% of the
initial mass was recovered after aggregation, regardless of the solution conditions, time of
irradiation, source of O-MWCNTs, or whether the CNTs were cleaned before use (Table
1). The small amount of mass loss could potentially be ascribed to the CO2 evolution that
accompanies PDC and the concomitant release of a small amount of dissolved organic
carbon that arises from destruction of the O-MWCNT sidewalls. It should be noted that
upon comparing the recovery of O-MWCNTs from experiments performed with CNTs
that were base cleaned to remove excess amorphous carbon (NanoLab, Inc.) and those
that were not (Cheaptubes), the results are similar and therefore we can say that this
cleaning step did not influence the fundamental PDC process. Recoveries also suggest
that irradiation causes almost negligible destruction, and that UVC irradiation is unable to
achieve any appreciable mineralization of the O-MWCNT particle structure.
Table 3.1 – Mass loss experienced by O-MWCNTs from NanoLab Inc. and Cheaptubes as a result of UVCinduced aggregation under different solution conditions.
CNT Manufacturer pH Purged With Percent Remaining NanoLab, Inc. 10 Nitrogen 91% NanoLab, Inc. 10 Nitrogen 92% NanoLab, Inc. 10 Oxygen 94% NanoLab, Inc. 7 Nitrogen 97%
Cheaptubes 10 Oxygen 93%
82
3.3.5 Phototransformations of Oxidized Carbon Based Nanomaterials
Our results showed similar chemical changes to studies from Hwang et. al.26 and
Qu et. al.,27 who irradiated the same O-MWCNTs used in this study with UVA light.
Specifically, the three studies saw a photoreduction process that lacked change to the
physical structure. A significant difference, however, comes from the mechanism used to
explain the PDC process. Qu et. al. postulate that hydroxyl radicals were responsible for
the decarboxylation via a reaction where a carboxylic acid combines with a hydroxyl
radical to produce a molecule of CO2 and water. Meanwhile, results from our study and
from existing organic photochemistry studies indicate that PDC occurs in both oxic and
anoxic conditions, as well as in organic solvents where hydroxyl radicals could not exist.
Together, these results are inconsistent with a PDC mechanism that involves ROS
species.44-48
In addition to O-MWCNTs, a variety of complementary UV irradiation studies
have been performed on fullerols, graphene oxide (GO) nanosheets, and O-SWCNTs.
Collectively, these results point to a common phototransformation process that occurs
across a range of different excitation wavelengths. For O-MWCNTs, we have seen a
process dominated by transformations that occur exclusively at the surface, meaning that
the bulk of the carbon atoms in the central core of the O-MWCNT remain unaffected by
the UV radiation. However, if we were to consider that process in the context of O-
SWCNTs or fullerols then we would predict that irradiation would have a much greater
relative effect since all of the atoms are at the surface of these nanomaterials. Consistent
with this assertion, previous studies have reported decreases in the particle size of O-
SWCNTs and fullerols by DLS and TEM as a result of UV irradiation,51, 52 with
83
measurable amounts of CO2 released from fullerols that indicate almost 50%
mineralization of the fullerol molecule.52
Therefore, we can distinguish two subgroups of oxidized carbon based
nanomaterials: 1) when all of the carbon atoms are at the surface of the nanomaterial (O-
SWCNTs, fullerols, graphene oxide nanosheets), and 2) when a surface layer exists but
the majority of carbon atoms are contained below the surface (O-MWCNTs). We can
examine the different effects seen for each subgroup as a result of photolysis by
comparing the data obtained for O-MWCNTs in the present investigation to studies on
GO nanosheets. In terms of the chemical transformations, data from studies using GO
nanosheet suspensions18, 20-22 show a similar reduction in surface oxygen concentration to
O-MWCNTs. However, the type and amount of oxygen-containing functional groups are
different between these two carbon allotropes, where GO possesses a much higher
percentage of epoxides due to the oxidation method used.53, 54 Peak fitting of the XPS
carbon envelopes by Matsumoto, Guardia, and Koinuma showed almost complete loss of
the C-O peak, whereas the carbon envelope showed little change for O-MWCNTs. In
contrast to the qualitatively similar chemical changes imparted by photolysis,
comparisons of the physical transformations exhibit a much more measurable difference
between O-MWCNTs and GO nanosheets. Minimal structural damage was observed for
O-MWCNTs in all three above-mentioned studies, but AFM micrographs and TEM
images of GO nanosheets show distinct holes created by the removal of oxygen. Raman
results from the GO nanosheets actually saw a decrease in the ID:IG band ratio, indicating
a less disordered surface, whereas Raman showed an increase in the disorder with O-
MWCNTs.
84
Therefore, the main difference between these two subgroups lies in the physical
transformations photolysis produces, and the resulting structural integrity of the
nanomaterial. Photoreduction and the subsequent loss of volatile carbon atoms create
noticeable defect areas in nanomaterials consisting of a single sheet of graphene.
Removal of portions of the sheet simultaneously degrades the material but lowers the
overall defect density by creating a smooth graphene-like structure with large defect
areas.18 This eventually leads to large scale disruption of the nanomaterial, including
mineralization and fragmentation.17, 51 When the same size portion of graphene is
removed from the outermost wall of an O-MWCNT, the remaining walls beneath this
hole show a defect site in the carbon layers, but do not impact the overall integrity of the
nanomaterial. Removal of oxygen functional groups simply causes the particle to become
unstable in aqueous solution. The magnitude of the van der Waals attraction between the
carbon cores causes aggregation once enough carboxylic acid groups are removed. Thus,
UVC light is unable to effect mineralization of O-MWCNTs.
3.3.6 Environmental Implications
Results from our study have shown that UVC irradiation can destabilize a
colloidal suspension of O-MWCNTs regardless of solution conditions. Many facilities
across the country have implemented UVC irradiation to disinfect their water resources.
However, these municipal drinking and wastewater treatment plants operate at a
multitude of volumes, ranging from 1 – 450 million gallons per day.55 Though the EPA
has issued standard dosages for water treatment plants to enact specific log kills of
various waterborne bacteria and viruses,56 there are not yet standards for nanoparticles.
To complicate matters, any number of variables including the concentration of
85
nanoparticles in the water being treated, the dissolved organic matter content, the output
wattage of lamps used, the water contact time, reactor depth, and flow rate of a given
plant differ between facilities. Even if the UV light intensity in a commercial water
treatment plant is an order of magnitude higher than the experiments described in this
study (photon flux ~ 1.32 x 1017 quanta/sec with all lamps operational), if we consider the
volumes of water disinfected each day in one of these plants it seems unlikely that UVC
treatment will transform O-MWCNTs to an appreciable extent given the timescales
(hours) required for PDC.
3.4 Results and Discussion of O-SWCNTs
3.4.1 Visual Effect of UVC Irradiation
Large batch experiments, like those performed on the O-MWCNTs, were used to
study colloidal suspensions of 40% w/w nitric acid treated O-SWCNTs to see if the
effects from UV radiation were similar. Upon irradiation with 254nm light, a drastically
different mechanism governing the MW and SW CNT suspensions was observed. Where
the O-MWCNTs took just over two days to aggregate and settle out of suspension, the O-
SWCNTs took over two weeks before the supernatant became noticeably clear to the eye.
However, the most significant difference was in the aggregation state of the CNTs. The
O-MWCNT suspension exhibited an initial period of stability where there were no
observable changes to the suspension, after which aggregates began to form and settle to
the bottom of the vessel. This was not the case for the O-SWCNTs. The color slowly
began to fade from the suspension of O-SWCNTs after the first few time points, and over
the course of irradiation no visible aggregates could be seen floating in the supernatant.
86
Eventually, fine black flecks began to appear at the bottom of the quartz beaker, and the
supernatant cleared completely. Figure 3.9 shows the progression of O-SWCNTs under
irradiation.
Absorbance and particle size measurements of the O-SWCNT suspensions
confirmed that a different process was occurring, validating the visual difference
observed between the two types of oxidized CNTs. Absorbance measurements in Figure
3.10 showed a profile that almost instantaneously begins to decline at the onset of
irradiation, and throughout there were regions of leveling where the absorbance value did
not change between tested samples. This was almost directly opposite to the profile
generated by the O-MWCNTs, where absorbance remained steady at the onset and then
declined sharply after a critical particle size was reached. Corresponding particle size
measurements for the O-SWCNT suspension showed very steady hydrodynamic diameter
readings for the first four days while the absorbance was rapidly decreasing. In
0 days 6 days 10 days 12 days 17 days
Figure 3.9 – Visual effects of UVC irradiation on single walled CNTs from Southwest Nanotechnologiesoxidized with 40% nitric acid. Irradiation was performed under ambient conditions at pH 7. No observableaggregation is observed for the first 10 days, as only the color of the suspension lightens over the course of this time. Starting O-SWCNT concentration is approximately 13.6mg/L. Photos by Miranda Gallagher.
87
the regions where the absorbance measurements reached a brief plateau a rise in particle
size was seen. As the decrease in absorbance became more linear, the particle size
continued to grow, eventually reaching far larger measurable particle sizes than the O-
MWCNTs. Once the threshold of 1000nm was reached, the absorbance began rapidly
decreasing. This decline eventually slowed until an absorbance value was eventually
reached corresponding to an estimated concentration of the supernatant that was less than
5% of the initial starting concentration. These changes occurred within ±0.1 of pH 7 and
relatively steady conductivity measurements (conductivity measurements showed much
higher recorded values for O-SWCNTs than O-MWCNTs).
3.4.2 Chemical Transformations to O-SWCNTs caused by UVC Irradiation
The large volume samples used for the absorbance and particle size measurements
above were cleaned and dried in the same fashion as the O-MWCNTs from Section 3.2.1.
Irradiation Time (days)0 3 6 9 12 15 18
Ab
sorb
ance
at
350n
m
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Particle S
ize Ave
rage, D
(h) (n
m)
0
500
1000
1500
2000
2500
3000
Figure 3.10 – Change in absorbance (filled red circles) and particle size (open blue squares) plotted as afunction of UVC irradiation time for oxidized single walled CNTs under ambient conditions at pH 7 underradiation with 16 UVC lamps.
88
However, mass recovery proved difficult as there was little residual powdered sample
remaining after irradiation. Weighing the remaining sample on the analytical balance
indicated that greater than 90% of the starting mass was lost during the course of UVC
irradiation, as is illustrated for two examples in Table 3.2. XPS analysis on the remaining
powder indicated a loss of surface oxygen, indicating a decrease from 16% on the starting
material to 10 – 12% on the powder remaining post irradiation. Chemical derivatization
for oxygen-containing functional groups was unable to be performed on O-SWCNT
samples exposed to UVC light due to the small quantity recovered. However, it is
believed that a similar photodecarboxylation (PDC) mechanism is responsible for the loss
of oxygen, as well as the mineralization observed.
3.4.3 Structural Transformations to O-SWCNTs
Fullerenes are similar analogues to SWCNTs, consisting of only a single layer of
carbon. Studies examining the effects of UV radiation on fullerenes and SWCNTs have
shown decreases in particle size, as well as slow loss of supernatant intensity over the
course of irradiation.13, 51 Hou and Jafvert suggested that the fullerenes were in fact being
either mineralized to CO2 or converted to another product like volatile organic
compounds.13 One needs to take into consideration that oxidation, especially more
Mass to Start (mg) Mass Recovered (mg) Percent Remaining 13.6 0.63 4.6% 13.6 0.55 4%
Table 3.2 – Mass loss experienced by O-SWCNTs from Southwest Nanotechnologies as a result of UVCinduced aggregation at pH 7.
89
aggressive methods of oxidation (i.e., nitric acid, 3:1 sulfuric:nitric acids) already imparts
large structural defects to the CNT surface. When these treatment methods are performed
on SWCNTs, it destroys the structural integrity of the material by punching holes into the
sidewall and breaking longer tubes into smaller pieces. Having the sidewall already
compromised by introducing 16% surface oxygen, it seems likely that the energy
absorbed by the O-SWCNTs during irradiation is enough to not only remove and alter
surface functionalization through UV-induced PDC, but also to fragment the tube into
smaller and smaller pieces.
Suspensions were created with small samples of powdered SWCNTs to
compare pristine SG65s to O-SWCNTs with different levels of surface oxygen present.
These varying surface oxygen levels were created by refluxing the pristine CNTs in
different w/w concentrations of nitric acid. These powders were suspended in a 2%w/v
SDC solution before being analyzed by near infrared fluorescence spectroscopy (NIRF).
It was discovered that the more aggressive treatments with nitric acid (i.e., 40% and 70%
HNO3) destroyed the fluorescence signal of the SWCNTs even before any exposure to
irradiation (Figure 3.11). Those O-SWCNTs that still showed some fluorescence
character after oxidation (10% HNO3) displayed selective removal of the main (6,5)
diameter tube peak at about 10,200cm-1. This result suggests that the oxidation process
may selectively oxidize smaller tubes first, destroying the sidewall structure and reducing
the fluorescence signature. Figure 3.11 illustrates this selective reduction by comparing a
sample from pristine SG65 SWCNTs versus the 10%, 40%, and 70% nitric acid treated
sample.
One suspension of O-SWCNTs that still showed some fluorescence after
90
oxidation was selected to test the effects of UV radiation. Several small volume samples
of the O-SWCNT suspensions were exposed to UV radiation and subsequently analyzed
by NIRF to mark any changes in the fluorescence signal as a result of UV light exposure.
Figure 3.12 shows a comparison of the control which was kept wrapped in aluminum foil,
to samples that were exposed to UVC radiation for 10, 30, and 60min. Though oxidation
removed the majority of the signal contribution from the (6,5) SWCNTs, as was seen in
Figure 3.11, UVC radiation seemed to destroy the electronic signature of the larger
diameter tubes ((7,5) and (8,4) tubes at approximately 9650cm-1 and 8950cm-1,
respectively) sooner as the time progression shows. The exposed samples lost all
fluorescence signal after just 60min of UV irradiation.
Wavenumber (cm-1)
7000 8000 9000 10000 11000
Flu
ore
scen
ce E
mis
sio
n I
nte
nsi
ty (
nW
/cm
-1)
0
2e-6
4e-6
6e-6
8e-6
1e-5
Pristine10% HNO340% HNO370% HNO3
A
Wavenumber (cm-1)7000 8000 9000 10000 11000
Flu
ore
sce
nce
Em
issi
on
In
ten
sity
(n
W/c
m-1
)
0
1e-6
2e-6
3e-6
4e-6
5e-6
6e-6
Pristine10% HNO340% HNO370% HNO3
B
Wavenumber (cm-1)
7000 8000 9000 10000 11000
Flu
ore
scen
ce E
mis
sio
n I
nte
nsi
ty (
nW
/cm
-1)
0
5e-6
1e-5
1e-5
2e-5
Pristine10% HNO340% HNO370% HNO3
C
Figure 3.11 – NIRF signal for pristine SWCNTS compared to differently oxidized SWCNT under excitation wavelengths (A) 638nm, (B) 691nm, and (C) 782nm. Suspension concentration was slightly varied as a result of centrifugation to remove bundling..
91
3.5 Conclusions
UVC irradiation performed using a Rayonet photochemical reaction chamber
resulted in transformations of O-MWCNTs principally through a photodecarboxylation
process. This process was found to be mediated by a one photon, direct excitation
mechanism consistent with existing literature in the organic photochemistry community,
and inconsistent with a process mediated by reactive oxygen species. During the initial
stages of irradiation the extent of carboxylic acid group removal from the surface of the
O-MWCNTs leads to a slow increase in particle size, but is not sufficient to cause
settleable aggregates to form. During this time, the particle concentration remains
constant and the suspension remains visibly unchanged to the naked eye. However, once
a sufficient number of carboxylic acid groups have been removed, a critical point is
reached where the electrostatic repulsion between O-MWCNTs is no longer sufficient to
prevent the CNTs from rapidly aggregating. UVC-induced aggregation occurs at all light
intensities studied and under both oxic and anoxic conditions where the resistance of
Wavenumber (cm-1)
7000 8000 9000 10000 11000
Flu
ore
scen
ce E
mis
sio
n I
nte
nsi
ty (
nW
/cm
-1)
0
1e-6
2e-6
3e-6
4e-6
5e-6
6e-6
Control10min Exposure 30min Exposure60min Exposure
C
Wavenumber (cm-1)
7000 8000 9000 10000 11000
Flu
ore
scen
ce E
mis
sio
n I
nte
nsi
ty (
nW
/cm
-1)
-1e-6
0
1e-6
2e-6
3e-6
4e-6
5e-6
Control10min Exposure30min Exposure60min Exposure
B
Wavenumber (cm-1)
7000 8000 9000 10000 11000
Flu
ore
scen
ce E
mis
sio
n I
nte
nsi
ty (
nW
/cm
-1)
0
2e-6
4e-6
6e-6
8e-6Control10min Exposure30min Exposure60min Exposure
A
Figure 3.12 – NIRF results for lightly oxidized SWCNT control suspension versus exposures to 8 UVC lamps for 10, 30, and 60min under excitation wavelengths (A) 638nm, (B) 691nm, and (C) 782nm. Suspension concentration was 10mg/L at pH 10.
92
O-MWCNTs towards photo-induced aggregation is enhanced in solution conditions that
favor the stabilization of negatively charged colloids (high pH and low ionic strength).
XPS, Raman, and TEM show significant changes in surface chemistry and aggregation
state induced by UVC exposure, but in the absence of any discernible structural
transformations or mineralization.
3.6 Acknowledgements
We acknowledge financial support by the Environmental Protection Agency
(R834858). The authors would also like to thank Dr. Ken Livi of the Earth and Planetary
Sciences Department at JHU for the TEM imaging, and the Materials Science
Department at JHU for use of the surface analysis laboratory. JLB would also like to
thank Miranda Gallagher and Ronald Lankone for their help with cleaning and processing
CNT samples.
3.7 Supplemental Information
3.7.1 UV-Visible Spectroscopy of O-MWCNT Suspensions
Absorbance of O-MWCNT suspensions was an easy way to monitor the colloidal
stability of CNTs during UVC irradiation. Figure S3.1 shows a representative example of
a typical UV exposure experiment, where the absorbance profile did not change
significantly over the course of the experiment. The dashed line indicates the wavelength
of UVC light being emitted from the lamps in the Rayonet reaction chamber, which
coincides with where the O-MWCNTs absorb most strongly (λ = 264nm). This peak is
93
due to the π→ π* transition in the conjugated ring structures. The sharp rise in
absorbance close to 200nm is due to the presence of ions in the suspension from the
added buffer and salt added to the O-MWCNT suspension. Figure S3.2 illustrates the
contribution of the various suspension components to the UV-Vis absorbance spectra.
Wavelength (nm)
200 300 400
Ab
sorb
ance
(a
.u.)
0.0
0.2
0.4
0.6
0hrs 2hrs 3hrs 4hrs 5hrs 6hrs 7hrs 8hrs 9hrs 10hrs 11hrs 12hrs
200 300 400 500 600 700 800 9000.0
0.1
0.2
0.3
0.4
0.5
Figure S3.1 – UV-Vis absorbance spectra from 200 – 450nm of oxidized multiwalled CNTs at pH 7 and 12mM NaCl, purged with nitrogen and measured as a function of irradiation time. Absorption maximum (λ = 264nm) corresponds to the π→ π* transition in the conjugated sidewall ring structure. The dashed line indicates the irradiation wavelength of 254nm, and the solid line indicates the wavelength at which measurements were taken (350nm). Inset shows the full spectra ranging from 200 – 900nm.
94
3.7.2 Choosing a Suitable Buffer
Choosing an appropriate buffer that will not degrade or influence the O-
MWCNTs while under irradiation with 254nm light was key in having reproducible and
reliable results. We avoided the use of buffers that contained conjugated ring structures
because those would be degraded by the UV light, and we avoided the use of buffers that
could potentially produce electrons or reactive oxygen species that could influence the
transformation of O-MWCNTs in suspension. It was decided that the buffer needed to be
polyprotic so it could be used over a range of pH values we wished to study. Carbonate is
a typical buffer used in previous experiments with O-MWCNTs,28, 37, 38 but upon purging
with nitrogen the carbonate is not stable due to the reduction of oxygen and carbon
Wavelength (nm)200 400 600 800
Ab
sorb
ance
(A
.U.)
0.0
0.1
0.2
0.3
0.4
0.5
HPLC water O-MWCNT suspension
Wavelength (nm)200 205 210 215 220
Ab
so
rban
ce
(A.U
.)
0.0
0.1
0.2
0.3
0.4HPLC blank 3mM phosphate buffer12mM NaClbuffer + NaCl
Figure S3.2 – UV-Vis absorbance spectra from 200 – 900nm for the individual constituents that make up an O-MWCNT suspension. The inset shows the region from 200 – 220nm to show the increase displayed in the absorbance profiles of the 3mM phosphate buffered water and the 12mM NaCl solution. These contributions can be seen in the profiles of the experimental O-MWCNT suspension from Figure S1.
95
dioxide dissolved in the medium. Therefore, we chose phosphate salts as the buffer of
choice for our experiments because it allowed the flexibility necessary with the pH range,
was unaffected by the UV light, and did not influence transformation.
Figure S3.3 shows two common buffers used for experiments performed at pH 4.
Suspensions were prepared as in the experimental section, buffered using either acetate or
phosphate, and purged with nitrogen. The two quartz vessels were put into the Rayonet
chamber and run simultaneously, monitoring the absorbance and pH as a function of
irradiation time. Results indicate that the phosphate behaved similarly to the acetate,
confirming our choice of using phosphate salts as a stable buffer for the remainder of our
experiments.
Irradiation Time (hrs)
0.0 0.5 1.0 1.5
Ab
sorb
ance
at
350n
m
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Acetate Phosphate
Figure S3.3 – Absorbance measurements for O-MWCNTs from NanoLab, Inc. under anoxic conditions using two common buffers to keep the suspension stable at pH 4.
96
3.7.3 Calibration of Light Intensity via Actinometry
To determine the quantum flux we used a colorimetric actinometry experiment to
measure the radiation of our UV lamps. As described in the experimental section of this
paper, potassium ferrioxalate decomposes to form Fe2+ ions under irradiation, which we
can then complex with o-phenanthroline to form a red solution. The intensity of this red
solution can be measured as a function of irradiation time to gauge the conversion to
Fe2+, thus measuring the intensity of light being emitted from our lamps.
Actinometry experiments are performed in the dark to eliminate light from the
windows and overhead lights contributing to the decomposition of the ferrioxalate.
Experimentally, 3mL of 0.006M ferrioxalate solution were put into the same 15mL
quartz test tubes used to irradiate O-MWCNTs and exposed to irradiation for different
prescribed periods of time (t). After each exposure period, 2mL of the irradiated solution
was removed and mixed with 2mL of 0.0055M o-phenanthroline and 1mL of a pH 3.5
acetate solution to quench the reaction. This 5mL volume was then diluted to a 20mL
total volume and stored for at least 1hr in the dark. This ensured that all of the Fe2+
produced by the UVC light had complexed with the o-phenanthroline. The optical density
(D) of the solution was then measured at 510nm by UV-Vis to determine the
concentration of the Fe2+:o-phenanthroline complex and a plot of D vs. t was constructed.
Until the supply of ferrioxalate has been consumed, D varies linearly with t, and in this
regime Eq. S3.1 can be used to determine the quantum flux (QF);31
3
1 3
2
10DVV NQF
t dV
Eq. S3.1
97
where V1 is the volume of ferrioxalate solution irradiated, V3 is the total end volume of
solution, N is Avogadro’s number, Φ is the quantum yield at the irradiation wavelength
(for 254nm, Φ = 1.25), ε is the molar extinction coefficient of the ferrioxalate-
phenanthroline complex at 510nm (1.11 x 104 L/mol·cm), d is the thickness of the
cuvette, and V2 is the volume of irradiated solution used for complexation.
Part A of Figure S3.4 illustrates the linear portion of our actinometry curves for
experiments performed with 16, 8, 6, 4, 2, and 0 lamps. A minimum of six data points
were collected and fit using a linear regression to determine the absorbance versus time
dependence for each set of exposures. What the results suggest is that when the lamps are
off, there is no residual light or photons being emitted from the lamps to induce any
degradation of the ferrioxalate compound. As the number of lamps in the Rayonet
chamber increases, it was found that intensity varied linearly as a function of the number
Ferrioxalate Exposure Time (sec)
0 20 40 60 80 100 120
Ab
sorb
ance
at
510n
m
0.0
0.5
1.0
1.5
2.0
1686420
A
Number of Lamps
0 2 4 6 8 10 12 14 16
Qu
an
tum
Flu
x (
qu
an
ta/s
ec
)
0.0
2.0e+16
4.0e+16
6.0e+16
8.0e+16
1.0e+17
1.2e+17
1.4e+17
B
Figure S3.4 – Calibration curves (A) and the calculated quantum flux (B) for various lamp intensities measured with the ferrioxalate actinometry experiments.
98
of lamps, except for experiments conducted with 16 lamps. By the time the maximum
number of lamps is reached, there is no real difference in the slope from 8 to 16 lamps.
This effect is most likely due to the light intensity at both 8 and 16 lamps being
sufficiently high to cause the ferrioxalate solution (0.006M, A254nm = 3.6) to convert
completely to Fe2+. Part B of Figure S3.4 shows the quantum flux calculated for each set
of exposures using Eq. S3.1. A linear regression was used to extrapolate what the likely
quantum flux for 16 lamps would be. In this instance the flux would be expected to reach
approximately 1.32 x 1017 quanta/sec, as opposed to the measured flux of 7.73 x 1016
quanta/sec. The values for all lamp intensities measured with actinometry can be found in
Table S3.1.
For experiments performed with O-MWCNTs, the optical density of the O-
MWCNT suspensions (5mg/L, A254nm = 0.34) is an order of magnitude lower than that of
the ferrioxalate. Consequently, the absorbance of the suspension in the quartz test tubes is
expected to follow a Beer-Lambert law regardless of the number of lamps used. Under
Number of Lamps Quantum Flux (quanta/sec)
0 3.07 x 1011 2 1.94 x 1016
4 2.59 x 1016 6 5.82 x 1016 8 6.30 x 1016
16 (measured) 7.73 x 1016 16 (extrapolated) 1.32 x 1017
Table S3.1 – Calculation of the quantum flux for 16, 8, 6, 4, 2, and 0 lamps. Flux is determined by actinometric measurements performed with potassium ferrioxalate. The quantum flux listed for 16 lamps appears twice to indicate that which was actually measured during the actinometry experiment, and what the likely flux is based on extrapolation via linear regression of the data from 0 – 8 lamps.
99
these conditions the effective light intensity within each test tube will be directly
proportional to the number of lamps.
3.7.4 Water Quality Parameters
An important factor in examining the effect of UVC radiation on suspensions of
O-MWCNTs is that they remain stable while not under the influence of light. To test this,
suspensions were run simultaneously, where half were being exposed to the UVC lamps
and the other half were wrapped in aluminum foil to prevent exposure. Figure S3.5 shows
that the O-MWCNT suspensions were in fact stable over the course of a given
experiment and showed no change in absorbance from start to finish.
Irradiance Time (hrs)0 3 6 9 12 15
Ab
sorb
an
ce a
t 35
0nm
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
ControlIrradiated
Figure S3.5 – Comparison of absorbance measurements for a control/dark sample and a sample exposed to UVC radiation at pH 7 and 3mM Na+.
100
As was discussed in Section 3.3.2, absorbance and particle size was measured as a
function of time for various solution conditions. Figure S3.6 illustrates the particle size
measurements corresponding to the absorbance readings from Figure 3.3.
3.7.5 Chemical Characterization of Large Volume Irradiation Experiments
XPS and chemical derivatization was performed on a series of large volume
experiments performed with O-MWCNT suspensions at various solution conditions.
Large volumes were used to ensure enough sample remained after exposure to text for
total percent surface oxygen and carboxylic acid functional groups. Table S3.2 lists the
measured atomic percentages of oxygen from control and irradiated samples. All samples
showed a decrease in carboxylic acid group density, even if there was no real change in
the total percent oxygen.
Irradiation Time (hrs)0 8 16 24 32 40 48
Particle S
ize, D(h
) (nm
)
200
300
400
500
600
B
pH4 7 10
Irradiation Time (hrs)
0 6 12 18 24 30 36
Par
ticl
e S
ize,
D(h
) (n
m)
200
300
400
500
600
4.5mM4.7mM6mM12mM 12mM
[NaCl]
A
Figure S3.6. – Particle size measurement profiles for oxidized multiwalled CNTs under anoxic conditions as a function of ionic strength (A) and pH (B) plotted as a function of UV irradiation time.
101
3.7.6 Measurement of Total Inorganic Carbon (TIC) and Calculation of CO2 Evolved
O-MWCNTs were prepared as a 25mg/L stock suspension and set to pH 7 with
3mM phosphate buffer. This stock suspension was sent to Purdue University for total
inorganic carbon analysis to determine the amount of CO2 evolved over the course of
irradiation. Quartz test tubes were filled with 8mL CNT suspension and contained 9mL
headspace. A stainless steel syringe needle was inserted through a rubber septa capped
onto each test tube and used to sparge the CNT suspension with nitrogen gas for 30
minutes at 2.5mL/sec flow rate. Sample tubes were irradiated using Rayonet RPR-100
merry-go-round photochemical reactor (Southern New England Ultraviolet (SNEU),
Branford, CT) with 16 RPR-2537A lamps (24 watts). In the reactor, sample tubes are
placed within the merry-go-round at the center of the reactor and rotated at 5 rpm to
ensure uniform exposure.
Table S3.2 – XPS measurements performed on various O-MWCNTs before and after irradiation with 254nm UVC light for various O-MWCNTs under oxic or anoxic conditions at pH 10. Only the total oxygen percent is shown, the percent carbon is neglected, but the %C + %O = 100%. For example, if the %O = 7.5%, the carbon peak result was 92.5%. The numbers in parentheses show the percentage of carboxylic acid groups that were measured before and after irradiation. The asterisk (*) indicates that the experiment was performed at pH 7 instead of pH 10.
Manufacturer Gas Purge %Oxygen Before
Irradiation %Oxygen After UV-Induced
Aggregation NanoLabs, Inc. Nitrogen 7.5 (1.7) 5.1 (0.6) NanoLabs, Inc. Oxygen 7.5 (1.7) 6.1 (1.3)
Cheaptubes Nitrogen 9.0 (0.7) 7.2 (0.5) Cheaptubes Oxygen 9.0 (0.7) 5.1 (0.4)
NanoLabs, Inc. Nitrogen 9.0 (3.2) 5.9 (2.2) Cheaptubes Oxygen 6.9 (0.9) 6.8 (0.3)
NanoLabs, Inc. Nitrogen 9.5 (1.7) 6.5 (0.8) NanoLabs, Inc.* Nitrogen 7.9 (1.8) 6.3 (0.4)
102
After a specified period of irradiation, test tubes were removed and acidified with
85% phosphoric acid to pH < 3. Test tubes were shaken vigorously for 5min and allowed
to equilibrate overnight, after which 3mL aliquots from the headspace of each tube were
withdrawn for CO2 analysis. Controls, test tubes wrapped in aluminum foil to prevent the
suspension from being exposed to the UV light while in the Rayonet chamber, were
acidified and treated the same way for analysis. The gas phase CO2 concentration was
measured with a PDZ-Europa Elemental Analyzer interfaced to a Sercon 20-20 Isotope
Ratio Mass Spectrometer (Crewe, England). The amount of CO2 in the aqueous phase
can be calculated using the equation,
2
2
[ ]
[ ]g
Haq
COk
CO Eq. S2
where kH is the Henry’s constant for CO2 dissolved in water, which is dimensionalized by
multiplying the constant by RT.57 The TIC can then be calculated from these two
concentrations by,
312 10g g aq aqTIC C V C V Eq. S3
to get the total carbon in milligrams. Results from the TIC analysis are shown in Figure
S3.7.
The XPS results for the changes in oxygen-containing functional groups can be
used to estimate of the amount of carboxylic acid groups removed during
photodecarboxylation. This is accomplished by converting the atomic percentage of
carboxylic acids determined by XPS to the expected weight percentage before and after
irradiation. First, the total carbon and oxygen signal before and after irradiation is
103
determined by multiplying the atomic signal by the molecular weight of carbon or
oxygen,
% %
% %
16
12wt atom
wt atom
O O
C C
Eq. S4
The total carbon and oxygen results can be combined, then the amount of carbon from the
carboxylic acid groups is divided by this total to find the weight percentage of carbon
using the equation,
( ) %
( ) %% %
12COOH atom
COOH wtwt wt
CC
C O
Eq. S5
Multiplying this percentage by the concentration and volume of CNTs used in the study,
we can estimate the mass of CO2 expected to be evolved as a result of irradiation. For
example, if all 10 atom% of the surface oxygen detected on the control sample by XPS
Irradiation Time (hrs)0 3 6 9 12 15 18
To
tal I
no
rgan
ic C
arb
on
(g
)
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
dark controlirradiated
Figure S3.7 – CO2 measurements from irradiated and dark control samples performed at pH 7.
104
were carboxylic acid groups, that would correspond to 12.9 wt% of carbon from
carboxylic acids. If all of the carboxylic acid groups were lost due to
photodecarboxylation during irradiation, in the above experiment performed with 8mL of
a 5mg/L concentration O-MWCNT suspension that would translate into production of
5.2μg of CO2.
3.7.7 Oxic versus Anoxic Conditions
The amount of dissolved oxygen (DO) water can hold varies by temperature,
where oxygen saturated water is usually between 8-9mg/L between 20-25°C (EPA).Our
experiments were performed using nitrogen or oxygen as the primary dissolved gas
species. Besides absorbance and particle size measurements shown in Figure 3.4 of this
manuscript, the DO of the suspensions was monitored when comparing two experiments
at the same solution conditions. Plotted in Figure S3.8 we can see how at time zero, the
DO level is at its lowest point for nitrogen purged samples, and its highest point for
oxygen purged samples. As irradiation occurs the DO level changes, presumably due to
the generation of hydrogen ions and oxygen species as they are cleaved from the CNT
surface. The fits to both curves in Figure S3.8 illustrate that the DO level increases or
decreases to a certain point, approximately half the irradiation time it takes to reach the
final aggregation state (around 6hrs). From that point on, the DO level then remains
around an equilibrium point, ending around 3.3mg/L and 6.2mg/L for the nitrogen and
oxygen purged experiments respectively.
105
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31. Hatchard, C. G.; Parker, C. A., A New Sensitive Chemical Actinometer. II. Potassium Ferrioxalate as a Standard Chemical Actinometer. Proc. R. Soc. Lond. A. 1956, 235, (1203), 518-536.
32. Langley, L. A.; Villanueva, D. E.; Fairbrother, D. H., Quantification of Surface Oxides on Carbonaceous Materials. Chemistry of Materials 2005, 18, (1), 169-178.
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34. Wang, X. S.; Liu, P.; Zheng, H. T.; Hu, H.; Zheng, W. J.; Suye, S. I., Preparation of Nicotinamide Adenine Dinucleotide Functionalized Multi-Walled Carbon Nanotube and its Application to Dehydrogenase Biosensor. Advanced Matieral Research 2011, 298, 121-127.
35. Anslyn, E. V.; Dougherty, D. A., Modern Physical Organic Chemistry. University Science Books: Sausalito, CA, 2006.
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57. Stumm, W.; Morgan, J. J., Aquatic Chemistry: Chemical Equilibria and Rates in Natural Waters. 3rd ed.; Wiley-Interscience: New York, 1996.
111
PART II: INTERACTIONS OF PARTICLES AND SURFACES IN AQUATIC ENVRIRONMENTS
112
Chapter 4:
Theory
4.1 Solution and Surface Chemistry
4.1.1 Solution Chemistry
Accurately determining the pH and ionic strength of the solution for each
experiment is necessary to properly understand how colloidal forces of the target particle
are affected by the medium. Knowing the concentration of each ion present in each
experimental solution allows for the calculation of a more accurate ionic strength, and
therefore a more correct estimate of the magnitude of forces acting on a particle. The
concentration and pH of the solution are directly related to the inverse Debye length, κ-1,
and surface potentials, ψ. CO2 saturated water has an equilibrium pH value of 5.8 at
25°C. One can determine the concentration of [H+] using the definition of pH as,
pHH 10 (4.1)
This can then be used to find [OH-] based on the dissociation equilibrium for H2O as,
OH HWk (4.2)
From here, the partial pressure of CO2, the pKa values for the different carbonic acid
species, and Henry’s law can be employed to determine the concentrations of all carbonic
acid species in water given by,
2
2
2
COCO
CO
PC
kh (4.3)
113
2 3 2 2H CO CO COC Kh C (4.4)
2 3
3
1a H CO
HCOH
K CC
C
(4.5)
3
23
2a HCO
COH
K CC
C
(4.6)
22 3 3 3
T H CO HCO COA C C C (4.7)
where PCO2 and khCO2 are the partial pressure and Henry’s law constant of CO2 at 25°C
respectively, KhCO2 is the hydration equilibrium constant for carbonic acid at 25°C, Ka1
and Ka2 are the dissociation constants for the diprotic carbonic acid species, and Cx are
the concentrations of the various ions in water.
Knowing the amount of salt, acid, or base added (in mol/L) and the total working
volume allows then for the calculation of the concentrations of K+, Na+, and Cl- in
solution by measuring the pH and conductivity of the newly made solution. One can then
establish the total concentration of the ions in solution by measuring the conductivity,
KM, and then using a salt dependent equation for conductivity given as,
Mall
T
KC
(4.8)
23 3
2 30 0
0
( , )
( , )
H HCO CO K OHT H CO KOH KOH
T T
Na ClNaCl NaCl
T
C C C C CC
C C
C CC
C
(4.9)
0.50 0 0( , ) ( )i iC A B C (4.10)
114
0 c c a az z (4.11)
where c and a stand for cation and anion respectively, Λ0 is the molar ionic conductivity
at infinite dilution for a given salt, z is the valence charge of the ion, λ is the molar ionic
conductivity for a specific ion, Λ(Ci, Λ0) is the concentration dependent molar ionic
conductivity of a particular species, A and B are constants determined by the ratio of
cations to anions, ΛT is the total calculated molar ionic conductivity for the given
solution, Ci indicates the concentrations of ionic species present in the solution, and Call is
the actual ionic strength of the solution determined from the measured value of KM. From
the total concentration of dissolved ions in solution we can determine the Debye
screening length (κ) for all experiments using,
0.5220 ( )
1...7
Ai i
m B
e Nz C
k T
i
(4.12)
where e0 is the elementary charge, NA is Avogadro’s number, εm is the dielectric
permittivity of the medium, kB is Boltzmann's constant, T is absolute temperature, zi is the
valence of a given ion, and Ci are the calculated concentrations of those ions.
4.1.2. Surface Chemistry
To accurately predict the net potentials for a given experiment, knowing the
solution chemistry is important, but one also needs to know how the prepared solution
affects the surface chemistry of the particles and surfaces of interest. Using a streaming
potential apparatus or measuring the zeta potential of a surface or particle, respectively, is
a traditional method for determining its surface chemistry. However, those have been
found to only be reliable as an estimate of the Stern layer potential. To model pH and
115
ionic strength dependent SiO2 surface potentials, literature measurements on quartz and
an associated amphoteric site binding model were found to accurately capture surface
potential values (ψ). By fitting these results with a convenient expression as,
( , ) ( ) ( ) exp[ ( ) ]pH C I C x C y C pH (4.13)
where the units on all constants are either mV, pH, or M where appropriate. The
measured pH and conductivity of the experimental solutions allows the derivation of a
pH and concentration dependent surface potential for silica particles and surfaces.
4.2 Colloidal and Surface Interactions of Spherical Particles
4.2.1 Net Potential Energy Interactions
The net particle-surface interaction potential for spherical colloidal particles of
diameter 2a is equal to the sum of gravitational body forces, colloidal, and surface forces
in aqueous solutions as given by,
( , ) ( , ) ( ) ( , ) ( )NETpw Epw G VDWpw Spwu h C u h C u h u h C u h (4.14)
where h is the surface-to-surface separation between a given particle and the wall and C
is the total ionic concentration of the solution. The subscripts E, G, VDW, and S stand for
electrostatic repulsion, gravitational body force, van der Waals attraction, and steric
repulsion, respectfully. This net potential is obtained by measuring a statistically
significant number of height excursions and creating a normalized equilibrium height
histogram, p(h). This histogram can be related to the height-dependent net particle-
surface interaction potential, uNETpw(h), via Boltzmann’s equation as,
116
lnNETpw Bu h k T p h (4.15)
where kB is Boltzmann's constant and T is absolute temperature.
The net potential, as well as the diffusivity landscape, D(h), can also be obtained
by measuring the time-dependent probability of heights, p(h,t), and using these to solve
the Smoluchowski equation given by,1
, , ,p h t p h t p h t dU h
D ht h h kT dh
(4.16)
This equation reduces to Boltzmann’s equation at steady state conditions. The diffusion
of spherical particles will be discussed in later sections.
4.2.2 Gravitational Body Force
Gravitational body effects are a result of a given particle’s buoyant weight, G,
multiplied by its relative height above the wall given by
( )Gu h Gh mgh (4.17)
34( )
3 p mG a g (4.18)
where a is the particle radius, ρp and ρm are the densities of the particle and medium
respectively, and g is acceleration due to gravity.
4.2.3 Electrostatic Repulsion
Electrostatic interactions result from the overlapping of electric double layers
(EDLs), which are defined as charged regions of ion density at or near a surface. In this
work, these double layers are present when a system contains ions in solution, consisting
117
of the intrinsic charge on a surface and a diffuse layer of counterions in the medium that
interact with the ions present on the surface. The resulting EDL is a direct result of a
particle or wall’s surface charge (σ) and surface potential (ψ), and they induce
electrostatic repulsion as the two surfaces approach one another. This repulsive
electrostatic interaction between the EDLs for a constant potential (ψ) can be well
modeled as an exponential function, and is expressed as
( , ) exp[ ( ) ]Epw pwu h C B C h (4.19)
2
0 00
( , )64 tanh tanh
4 4p wB
pw mB B
pH Ck TB a ze ze
ze k T k T
(4.20)
where κ is the Debye screening length, and B takes into account the pH and ionic strength
dependent surface potentials (ψp and ψw), which were discussed in Section 4.1.1.
The two surface potentials are considered to be equal in the case of individual
silica spheres interacting with silica surfaces as discussed in Chapter 6, but may in fact be
different when the particle and the surface are not composed of the same material (as in
Chapters 7 and 8).
The expression for electrostatic repulsion between a spherical particle and a flat
surface in Eq. 4.19 is actually based off of the work by Russian scientist Boris Derjaguin
published in 1934.2 The actual expression listed above is the result from the linearization
of a more complicated differential equation, but it is well suited for situations where the
particle-surface separation is small compared to the radius of the sphere.3 However, under
different circumstances, the linearized Poisson-Boltzmann theory (or linear superposition
approximation, LSA) is better suited. Scenarios detailing when LSA would be more
118
appropriate can be found in the Section 4.4.
4.2.4 The Derjaguin Approximation
Derjaguin’s work2 related the interaction of finite sized spherical bodies to the
overlapping double layers on semi-infinite planar surfaces. This geometric calculation
simplified the curved surface of a sphere into a series of ring-shaped flat discs. This series
of “stepped” surfaces with planar geometries can then be integrated over the series to
determine the potential over the entire curved surface area of interaction. This
approximation is useful for determining the interaction of two spherical bodies, as well as
a spherical body interacting with a flat surface. However, the Derjaguin approximation is
limited to the regime where the radius of the particle is far larger than the particle-surface
separation. In the case of interest here, a sphere greater than 1μm interacts with a flat
plate, where the plate is modeled as a sphere with a diameter much greater than the first
sphere (on the order of 106μm) so that it appears infinitely large in comparison.
The Derjaguin approximation states that the interaction potential between two
spherical particles of equal radii, or between a particle and surface (wall), can be obtained
from the energy per unit area of interaction between two flat plates, EXww(l), at a function
of separation, l. For our purpose we will examine only the particle-wall interaction,
uXpw(z), which is given by4
2pw wwX X
z
u z a E l dl
(4.21)
The electrostatic potential for the interaction of two charged surfaces is related to
the force between a charged spherical particle and a charged flat wall as,
119
2pw wwE EF z aE z (4.22)
where FEpw is the electrostatic force experienced between the particle and the wall,
respectively, and EEww is the electrostatic potential between two planar walls. EE
ww is
given by,
1 1 264 tanh tanh exp4 4
wwE B b
ze zeE l k Tn l
kT kT
(4.23)
where is given as,
1 22 22 b m Be Z n k T (4.24)
Force and potential energy are related by,
pw pwE E
dF z u z
dz (4.25)
where uEpw is the electrostatic interaction between a charged particle and wall surfaces,
given by,
2 exppwEu z B z a (4.26)
where B is a constant that takes into account the particle radius (a) and the surface
potentials (ψ) on the particle and wall. From here, we can write
exppw pwE E
du z B z a u z
dz (4.27)
This now allows us to relate our original equation for the electrostatic potential defining
the interaction of two charged surfaces with our definition for the force between a particle
and a wall in terms of potentials as,
120
2pw wwE E
du z aE z
dz (4.28)
We can insert Equations 4.23 and 4.27 into the equation above since we have the
definitions for each side. This yields,
2 1 2128 tanh tanh exp4 4
pwE B b
B B
ze zeu z ak Tn z a
k T k T
(4.29)
If we were to now substitute the equation for in and simplify, we obtain,
2
1 264 tanh tanh exp4 4
pw BE m
B B
k T ze zeu z a z a
ez k T k T
(4.30)
Using our expression for uEpw, we can pull out the definition of B as,
2
1 232 tanh tanh4 4
Bm
B B
k T ze zeB a
ez k T k T
(4.31)
The Derjaguin equation is used to describe the electrostatic repulsion in the
system discussed in Chapter 6 because it follows the parameters for applicability: the
range of interaction (surface to surface separation) is far less than the radii of the sphere.
The silica particles used were 2.1μm in diameter, whereas the separation distance was on
the order of zero to 0.4μm.
4.2.5 van der Waals Attraction
The attractive forces resulting from van der Waals forces arise from quantum
electrodynamics. Every molecule carries either a dipole moment or has the ability to
spontaneously form an instantaneous dipole, which results from the position of electrons
in an atom or molecule at a given moment in time. Two dipoles can induce an attractive
121
force between the two atoms or molecules. These attractive forces between atoms can be
extrapolated to explain the long-range interactions between a particle and a wall through
Lifshitz theory.
Lifshitz theory ignores the effects of individual atoms composing a material and
instead examines the material as a continuum. This takes into consideration how the
intrinsic bulk properties of a material and the medium comprising the system, such as the
dielectric constant, affect the overall charge or potential of a given surface, thereby
making the interaction attractive or repulsive. The distance that separates two objects in a
medium governs how strong or weak this force will be. For a spherical particle
interacting with a planar surface we use Lifshitz theory with a Derjaguin geometric
correction, as was discussed in Section 4.2.4. Application of Lifshitz theory enables us to
take into account retardation (reduction of attractive energy from slowed propagation of
radiation through a material or medium)5 and screening (effect of ions that emerge with
increasing ionic strengths) on the Hamaker constant.
The Hamaker constant is a proportionality constant that is related to the number
of atoms in the interacting bodies. This constant represents the strength of van der Waals
interactions. However, when we are talking about macroscopic surfaces and media, the
constant becomes defined by an analytical expression for the Hamaker function, Avdw, for
two half spaces with a distance h in separation. This function can be broken into two
terms,
inf 0( , ) ( ) ( , )VDW salt nA h C A h A h C (4.32)
122
The first term is the Hamaker function at infinite salt concentration, Ainfsalt that is
calculated as,6
inf1
3( ) [1 ] ln[1 ]
2 n
x xpm wmsalt B r pm wm
n
A h k T x e e dx
(4.33)
j k k jjk
j k k j
s s
s s
(4.34)
j k k jjk
j k k j
s s
s s
(4.35)
2 2 22
2( ) ( )n
k k
ls x
c
(4.36)
22 nn
lr
c
(4.37)
( )k k ni (4.38)
n
nkT
(4.38)
where jk is a function of the dielectric properties of the materials composing the particle
(p), wall (w), and medium (m). The analytical solution for the Hamaker function at
infinite salt concentration can then be fit with a rational expression. The second term that
accounts for screening effects is the zero frequency term of the Hamaker function, An=0,
which is calculated as,
0 0( , ) 0.5 [1 2 ( ) ]exp[ 2 ( ) ]nA h C A C h C h (4.39)
123
which uses the concentration dependent Debye screening length, , and Hamaker
constant, A0. The particle-wall van der Waals interaction potential then becomes a
function of separation and ionic strength that is calculated as,
610
2
( , )( , )
6
mp w VDWBVDWpw h
p w
a a A l Ck Tu h C dl
a a l
(4.40)
where ap and aw are the radii of the particle and wall respectively, and aw>>ap.
4.2.6 Steric Repulsion
Steric potentials are oftentimes used to describe repulsive forces caused by
polymers, polyelectrolytes, or macromolecules that are adhered or absorbed to a surface.
These polymers often form what is called a brush architecture, where at high enough
concentrations, the attractive portion of the polymer pack around the surface and
repulsive portions are forced to extend out into the surrounding medium, forming a
brush-like structure. Steric repulsive forces are very short-ranged, and arise only as the
two macromolecular coated surfaces approach one another and the outer edges of the
layers begin to overlap. The interaction of these surfaces depends on the change in free
energy of the two macromolecular layers under compression and penetration. The brush
architecture of a polymer is defined by two important variables: its thickness and free
energy. These variables will change in value depending on the type and chemical
structure of a polymer. For a polymer layer with a brush architecture on a planar surface
of an uncompressed thickness, δ0, and free energy per area, f0, the compressed free
energy per area, f(δ), for 1/2<δ/δ0<1 can be captured accurately by,7
0 0( ) 1 expB Bf f (4.41)
124
where ΓB and γB are dimensionless constants specific to the brush architecture of a
particular polymeric material. Using this expression in the Derjaguin approximation (see
Section 4.2.4), the steric potential between two symmetric macromolecular brush layers
as can be obtained as,
, 0 0 0( ) 16 exp 2S B B Bu h af h (4.42)
This equation is versatile because it can be used to obtain the steric repulsive
force for a variety of materials that exhibit different interfacial macromolecular
architectures with different decaying density profiles at their periphery, by applying
different values of Γ and γ in Eq. 4.41. Eq. 4.42 can be used to accurately model
macromolecular layer repulsion for a broad range of δ0, f0, Γ, and γ using a general
repulsive steric potential of the form,
( ) expSpwu h h (4.43)
This equation should be broadly applicable by lumping unknown constants together. This
expression is particularly useful when the uncompressed layer properties and architecture
being studied are not well characterized.
4.3 Diffusion Modes of Spherical Particles
4.3.1 Diffusion of Spheres near a Flat Surface
The Stokes-Einstein equation is used to explain the Brownian diffusion of an
unbounded spherical particle in a bulk viscous fluid which extends out infinitely in all
directions. The diffusion (D) is the inverse of the drag coefficient given by,
125
0 6Bk T
Da
(4.44)
where is the fluid medium viscosity. A sphere would be modeled simply with Stokes-
Einstein in ideal circumstances. However, when a spherical particle diffuses close to a
wall the diffusion slows as it approaches the surface. This occurs because as a particle
approaches a wall, the liquid separating the two objects must be removed from between
them for the surfaces to come into contact. This takes energy and induces a drag force on
the particle. Now the particle diffusion becomes a function of the sphere’s height above a
planar surface as,
0( ) ( )D h D f h
(4.45)
where f(h) is a factor used to account for the particle-wall hydrodynamic interactions as
described by Brenner.8 His expression describes how the motion of the sphere is slowed
as it approaches a surface, which can be accurately captured by the more simple
expression,
2
2 2
6 2( )
6 9 2
h ahf h
h ah a
(4.46)
from Bevan and Prieve.9
The translational diffusion of a sphere through the bulk medium can be captured
by the mean squared displacement (MSD), X2. For a particle moving in one dimension (x
or y directions) the MSD is given by,
2 22X D t x t
(4.47)
where Δx is simply the change in the sphere’s position during an increment of time as,
126
2
02
0
i
i
x xx t
t t
(4.48)
For spheres that may sample a variety of heights while diffusing, D(h) can be
used in the equation for MSD by obtaining an average height that a given particle
samples over a course of time. This average can be calculated by integrating over a height
range such as,
0
0
( ) ( )
( )
( )
n
avg n
D h p h dh
D h
p h dh
(4.49)
where p(h) is the probability distribution of heights sampled and is obtained from the net
potential energy defined as,
( )
( ) exp NETpw
B
u hp h
k T
(4.50)
which is simply the inverse of Eq. 4.15.
4.3.2 Diffusion of Spheres through Obstacles
Calculation of the diffusion of spheres over a flat surface hindered by spherical
obstacles can take advantage of the translational diffusion equations discussed in Section
4.3.1. However, to be accurate they must include factors that account for the size and
number of asperities in the field that the diffusing sphere may come into contact with.
Saxton10 suggested that the MSD for the lateral diffusion of a sphere through obstacles in
two dimensions follows the form,
127
2 2
0
4 2 ( , )x t Dt xdxC x t x
(4.51)
for a given point in time, t, where D is a function of the concentration of obstacles at a
particular position and time, C(x,t). These two variables are related by,
21( , ) exp
4 4
xC x t
Dt Dt
(4.52)
Kim and Torquato11 took a similar approach using an “exclusion” probability
function, Eυ(r), and a “void” nearest-neighbor probability density, Hυ(r). These two
variables are defined as the fraction of space available for exploration in a field of
spherical obstacles of density, ρ, by a particle, and the probability that an arbitrary point
in the system lies near a spherical obstacle between r and r + dr, respectively where r is
the radius of a spherical empty space in the grid. Eυ(r) and Hυ(r) are used in the
calculation of the volume fraction, ϕ, and specific surface, s, respectively. From here they
suggest a calculation for the effective diffusion coefficient, De, for a Brownian particle of
radius b in a system with spherical obstacles of radius a as De[ϕ(ρ,a);b]. They relate the
De in fluid saturated porous media to the MSD by,
2
26 ( )e
XD
X
(4.53)
where X2 is the MSD and τ(X2) is the average time for a Brownian particle to hit a surface
for the first time.
128
4.4 Colloidal and Surface Interactions of Rod-Shaped Particles
4.4.1 Net Potential Energy Interactions
At relatively low ionic strength conditions where the particle sits at a height above
the surface sufficiently far away so that van der Waals attraction is not contributing to the
net potential (>10nm), the net particle-surface interaction potential for a rod-shaped
particle over a planar surface, u(h), is the sum of the gravitational attractive forces and
electrostatic repulsion. Theoretical models of this potential energy can be calculated by
the addition of the above mentioned contributing potentials as,
( ) ( ) ( )NETpw G Epwu h u h u h (4.54)
where the subscripts G and E refer to the gravitational and electrostatic interactions
respectively, and h is the particle surface to planar surface separation distance. The
gravitational potential is associated with a body force governed by the size and shape of
the particle, whereas the electrostatic potential is associated with colloidal surface forces.
However, both forces are intimately dependent on the length of the rod. This differs from
spherical particles where all colloidal interactions of rod-shaped particles are derived per
unit length.
4.4.2 Gravitational Body Forces
The gravitational potential energy of each rod depends on its separation from the
wall, h, multiplied by its buoyant weight, G, as given by,
( )Gu h Gh mgh (4.55)
2 ( )p fG a L g (4.56)
129
where m is buoyant mass, g is acceleration due to gravity, a is the particle radius, L is the
particle length, and ρp and ρf are particle and fluid densities respectively. The geometric
parameter (πa2L) corresponds to a rectangular cylinder.
4.4.3 Electrostatic Repulsion derived from the Derjaguin Approximation
As mentioned above in Section 4.2.3, the Derjaguin approximation is most
applicable when the radius of the particle is far greater than the particle-surface
separation. It is also used to describe the electrostatic potential when double layers on a
rod and planar surface are sufficiently thin (κa>>1), corresponding to higher ionic
strength conditions. Therefore, the Derjaguin approximation can be used in conjunction
with the superposition, non-linear Poisson-Boltzmann equation for a 1:1 monovalent
electrolyte3 to give the rod-wall potential as,4
exp ( )2E
au h LB h
(4.57)
2
64 tanh tanh4 4
p wBm
B B
e ek TB
e k T k T
(4.58)
1 22
2( )Ai i
im B
e Nz C
k T
(4.59)
where κ is the Debye screening length, εm is the solvent dielectric constant which is the
product of permittivity in a vacuum (ε0) and the relative permittivity of water (εw), e is the
elemental charge, ψp and ψw are the surface potentials of the particle and the wall,
respectively, NA is Avogadro's number, Ci is the electrolyte molarity of species i, and zi is
the ion valence.
130
The height of a rod-shaped particle above a planar surface can be determined by
taking the derivative of the net potential and solving for h, as
1 lnABL
hG
(4.60)
where L is the length, G is the prefactor from the equation for the gravitational potential,
B is the prefactor from electrostatic repulsion, and A is a constant that contains geometric
corrections. This would predict the most ideal height of the particle. However, if the
particle samples many heights, an average height can be derived by integrating over the
probability distribution of heights sampled from Equation 4.50, similar to the average
diffusion coefficient,
0
0
( )
( )
n
avg n
hp h dh
h
p h dh
(4.61)
4.4.4 Electrostatic Repulsion from the Linear Superposition Approximation
For thick double layers (κa~1) the above expression will generally over-estimate
the interaction since the Derjaguin approximation no longer holds. We instead model the
rod as a rigid chain of touching spheres and approximate the electrostatic interaction
between the rod and wall by summing up all sphere-wall interactions based on the linear
superposition approximation (LSA) for thick double layers,
3,
1
4(z) ( )
3
p
G sphere s f ii
U a gz
(4.62)
and the electrostatic repulsion contribution given as,
131
,
1
(z) exp( ( ))p
E sphere ii
U B z a
(4.63)
where zi is the mass center for ith particle composing the rod, and B is the prefactor for the
electrostatic repulsive interactions based on the linear superposition approximation
(LSA), which can be used for thick double layers, given as,
2 22
42 4
kT a eB
e h a kT
(4.64)
4.5 Diffusion Modes of Rod-Shaped Particles
4.5.1 Diffusion of Rods in the Bulk
The same string of beads model that was used to determine the electrostatic
repulsion from LSA was used to calculate theoretical equations for the free diffusion of a
rod-shaped particle in the bulk, DB(p). These diffusion equations were calculated for rods
of varying aspect ratios (p), which is the length (L) divided by the radius (a), by adding
beads of radius, a, to the model. These equations consist of a Stokes-Einstein type
diffusion coefficient, D0, multiplied by a factor dependent on the aspect ratio of the
particle, f(p), where the bulk translational diffusion coefficient parallel to the long axis is
given by,
|| 0|| ||( ) ( )BD p D f p (4.65)
0|| 2Bk T
Dpd
(4.66)
2
|| 2
0.4536 1.772 41.5( ) ln( )
34.38 18.96
p pf p p
p p
(4.67)
132
and the translational bulk diffusion coefficient perpendicular to the long axis is given by,
0( ) ( )BD p D f p (4.68)
0 4Bk T
Dpd (4.69)
2
2
0.3604 28.36 72.63( ) ln( )
36.29 34.9
p pf p p
p p
(4.70)
where η is the fluid medium viscosity, and p is the particle aspect ratio where L is the
length and d the diameter.
A 2-dimensional (2-D) translational diffusion coefficient for the motion of a rod
in bulk medium can be established by combining the parallel and perpendicular modes to
achieve,
|| ( ) ( )( )
2B B
T
D p D pD p
(4.71)
A set of theoretical equations can be similarly derived for the rotational motion of
a rod-shaped particle freely diffusing in the bulk, DB(p), as given by,
0( ) ( )BR R RD p D f p (4.72)
0 3
3
( )B
R
k TD
pd (4.73)
3 2
3 2
1.373 19.39 148.1 265.2( ) ln( )
56.43 54.35 268.4R
p p pf p p
p p p
(4.74)
133
4.5.2 Diffusion of Rods near a Flat Surface
When a rod diffuses in the bulk it is only dependent on the rod length determined
by p. However, when a rod diffuses near a surface, the surface can influence the rod
diffusion depending on how close the two objects are to one another. This in turn makes
the diffusion coefficient for a rod diffusing near a surface dependent on the distance or
height between the rod and the surface, where the particle would be expected to slow as it
approaches the surface, similar to Brenner’s theory from Section 4.2.7.
Translational diffusion coefficient can be obtained for the motion of a rod of
aspect ratio, p, as a function of its particle surface-wall separation, h, above a planar
surface by multiplying the bulk diffusion coefficient, DB(p), by a correction factor
dependent on h and another correction factor dependent on p. The motion parallel to its
long axis takes the form,
|| || || ||( , ) ( ) ( )BD p h D f h g p (4.75)
3 2
|| 3 2
0.9909 0.3907 0.1832 0.001815( )
2.03 0.3874 0.07533
z a z a z af h
z a z a z a
(4.76)
|| ( ) 1.1669 0.0091g p p (4.77)
and the translational diffusion coefficient for the motion perpendicular to its long axis is,
( , ) ( ) ( )BD p h D f h g p (4.78)
3 2
3 2
0.9888 0.788 0.207 0.004766( )
3.195 0.09612 0.1523
z a z a z af h
z a z a z a
(4.79)
134
|| ( ) 1.2239 0.0120g p p (4.80)
Similar to the translational motion in the bulk, a 2-dimensional translational
diffusion coefficient for the motion of a rod near a flat surface can be established by
combining the parallel and perpendicular modes to achieve,
|| ( , ) ( , )( , )
2T
D p h D p hD p h
(4.81)
Subsequently, the rotational diffusion coefficient for a given rod-shaped particle
as function of its aspect ratio and height above the planar surface can be obtained the
same way and is given by,
( , ) ( ) ( )R BR R RD p h D f h g p (4.82)
3 2
3 2
0.998 131.1 21.25 0.01275( )
128.7 121.1 2.897R
z a z a z af h
z a z a z a
(4.83)
( ) 1.154 0.0096Rg p p (4.84)
4.5.3 Diffusion of Rods between Two Parallel Surfaces
A second set of translational diffusion coefficients can be obtained for a scenario
where a rod of aspect ratio, p, is diffusing between two parallel plates with separation, Δ.
An approximate solution for these diffusion coefficients can be calculated from the linear
superposition approximation12 in the form,
11 1
|| || || || ||( , ) ( ) ( ) (( ) 2 ) 1BD p h D f h g p f a z a
(4.85)
11 1
( , ) ( ) ( ) (( ) 2 ) 1BD p h D f h g p f a z a
(4.86)
135
for the parallel and perpendicular translational diffusion coefficients, respectively. This
can also be applied to the rotational diffusion a rod of between two parallel plates given
as,
11 1
( , ) ( ) ( ) (( ) 2 ) 1R BR R R RD p h D f h g p f a z a (4.87)
This approximation takes into account the hydrodynamic effects from the top and bottom
walls.
Just as was discussed in the second half of Section 4.3.1, the mean squared
displacement (MSD) is a useful tool for tracking the translational diffusion of rods.
Equations 4.47 and 4.48 from Section 4.2.7 can be applied to track the center of mass
position of a rod to help understand the translational motion as a function of time.
Another useful metric is the mean squared angular displacement (MSθ), which tracks the
total rotation of a particle as a function of time. This can be calculated by monitoring the
position of the end points of the rod in relation to the center of mass. The angular position
of each end point on the rod with respect to the center of mass, i, can be calculated as,
arctan( )cm ii
cm i
y y
x x
(4.88)
where xcm/ycm is the x or y center of mass position, and xi/yi is the position of one end of
the rod at some time point i. Values of θ can be implemented into Eq. 4.47 in place of
steps in the x or y direction to obtain the MSθ as,
2MS 2D t t
(4.89)
136
4.5.4 Diffusion of Rods through Obstacles
As discussed in Section 4.3.2, the theoretical expressions for the diffusion of
spheres through spherical obstacles can be extrapolated to the movement of rod-shaped
particles through a field of obstructions. Similar variables will be necessary to describe
the field including a volume or area fraction of spherical obstacles, ϕ, which can be used
as a dimensionalized variable in place of a concentration in Saxton’s equation. A factor
that would replace the spherical geometry with a cylindrical shape would be the first step
in the calculation. The next step would be to know the center of mass and rod end point
coordinates at a given point in time to allow for the calculation of the MSD or MSθ,
which can then be directly related to an effective diffusion coefficient. This De can also
be compared to the diffusion coefficient calculated for rod-shaped particles under the
same conditions without the presence of physical obstacles that may induce
hydrodynamic hindrances. With these pieces, one could produce a reliable estimation of
the diffusion of rods through obstacles of varying concentration densities.
However, like Saxton discusses, the volume or area fraction of the obstacles is
important for explaining the MSD. Above a given ϕ, called the percolation threshold, a
particle can become trapped in a small space between clusters of obstacles. In this
instance the diffusion of the particle may appear faster than a particle that is diffusing
more freely; this can be the result of the trapped particle’s diffusion appearing more one
dimensional (1-D) in nature as opposed to 2-D. In that case, analyzing the particle’s
trajectory as 2-D motion would falsely give the particle a faster displacement. In these
cases, one must consider that as the area fraction of obstacles increases, there is the
likelihood that a particle’s motion is not strictly 1-D or 2-D, but a fractal dimension
137
between these two. Thus, a parameter indicating the dimension describing the particle
motion may also be employed to accurately capture the diffusion of rods through spheres.
4.6 References
1. Murphy, T. J.; Aguirre, J. L., Brownian Motion of N Interacting Particles.1. Extension of Einstein Diffusion Relation to N-Particle Case. J. Chem. Phys. 1972, 57, (5), 2098.
2. Derjaguin, B., Untersuchungen über die Reibung und Adhäsion, IV. Kolloid-Zeitschrift 1934, 69, (2), 155-164.
3. Russel, W. B.; Saville, D. A.; Schowalter, W. R., Colloidal Dispersions. Cambridge University Press: New York, 1989.
4. Israelachvilli, J., Intermolecular and Surface Forces. 3rd ed.; Academic Press: New York, 2011.
5. Bevan, M. A.; Prieve, D. C., Direct Measurement of Retarded van der Waals Attraction. Langmuir 1999, 15, (23), 7925-7936.
6. Prieve, D. C.; Russel, W. B., Simplified predictions of Hamaker constants from Lifshitz theory. Journal of Colloid and Interface Science 1988, 125, (1), 1-13.
7. Eichmann, S. L.; Meric, G.; Swavola, J. C.; Bevan, M. A., Diffusing Colloidal Probes of Protein-Carbohydrate Interactions. Langmuir 2013.
8. Brenner, H., The Slow Motion of a Sphere Through a Viscous Fluid Towards a Plane Surface. Chem. Eng. Sci. 1961, 16, (3-4), 242-251.
9. Bevan, M. A.; Prieve, D. C., Hindered diffusion of colloidal particles very near to a wall: Revisited. The Journal of Chemical Physics 2000, 113, (3), 1228-1236.
10. Saxton, M. J., Lateral diffusion in an archipelago. Single-particle diffusion. Biophysical Journal 1993, 64, (6), 1766-1780.
11. Kim, I. C.; Torquato, S., Diffusion of finite-sized Brownian particles in porous media. The Journal of Chemical Physics 1992, 96, (2), 1498-1503.
12. Happel, J., Low Reynolds number hydrodynamics. In Brenner, H., Ed. Prentice-Hall: Englewood Cliffs, N.J., 1965.
138
Chapter 5:
Experimental Set-Up and Parameters for Microscopy Studies
5.1 Chemicals and Materials
5.1.1 Chemicals
Acetone and isopropanol were purchased from Fisher Scientific (Pittsburgh, PA,
USA) and used to clean microscope slides. Sulfuric acid and hydrochloric acid were
purchased from Sigma-Aldrich (St. Louis, MO, USA). Sulfuric acid was mixed with
Nochromix powder (Godax Labs, Takoma Park, MD, USA) to create an oxidizing
solution used to remove organic impurities from the surfaces of all microscope slides and
coverslips. Hydrochloric acid was used to treat the slides as well as adjust the pH of the
solutions. All chemicals were used as received and without purification.
Potassium hydroxide and sodium chloride were also purchased from Fisher
Scientific and used without purification. Potassium hydroxide was used to treat
microscope surfaces prior to experiments and adjust the pH of solutions. Sodium chloride
solutions were used to set the ionic strength of a given experiment to the desired
conditions.
5.1.2 Materials
Plain glass microscope slides from Fisher Scientific had a manufacturer reported
density of 2.48 grams/cm3 and a soda lime composition of approximately 72% silicon
dioxide, 14% sodium oxide, 6% calcium oxide, 4% magnesium oxide, 1% aluminum
oxide, 1% potassium oxide, <1% other trace elements. The microscope slides were first
wiped clean with lens paper and then sonicated in a Branson Ultrasonics Corporation
139
1510 ultrasonicator (Danbury, CT, USA) for 30min in acetone and 30min in isopropanol.
The slides were then rinsed thoroughly with deionized (DI) water (18.3MΩ) from a Milli-
Q Academic ultrafiltration system (Milli-Pore, Danvers, MA, USA) using a Millipak 20
Express filter (0.22μm). To remove impurities from the glass surface, the slides were
soaked in Nochromix overnight. In the morning, slides were rinsed thoroughly with DI
water, then soaked in 0.1M KOH for 30min prior to use. Slides were again rinsed with
deionized water and dried with nitrogen (Airgas, Salem, NH, USA) before use.
Glass coverslips (long: 24cm x 60cm; small: 18cm x 18cm) were purchased from
Corning (Corning, NY, USA). The long coverslips were cleaned in the same manner as
the microscope slides for all experiments where rod-wall interactions were being
measured (Chapter 7). For porous media experiments (Chapter 8) these slides were
soaked in acidic (pH = 1) water after soaking in Nochromix overnight. Small coverslips
were wiped with lens paper purchased from Fisher Scientific and place directly into the
Nochromix. Upon removal they were rinsed with DI water and soaked in 0.1M KOH
solution for 30min, rinsed again, and then dried with high purity nitrogen from Airgas
(Salem, NH, USA).
Viton O-rings (5mm ID) were purchased from McMaster Carr (Robbinsville, NJ,
USA) and used to contain colloidal samples in one-wall systems. Vacuum grease
purchased from Dow Corning (Midland, MI, USA) and Loctite professional heavy duty
epoxy from Henkel Consumer Adhesives (Avon, OH, USA) were used to seal sample
cells, to simultaneously contain the colloidal suspension being examined, and to prevent
convection and dust from entering the sample cell. Lens paper was used to wipe away
excess dust from slides and coverslips before cleaning, and also to wick away liquid from
140
the edges of the small coverslip that created the top of a confined cell unit.
Refractive index matching oil (n=1.515) from Cargille (Cedar Grove, NJ, USA)
was used to couple the microscope slide/coverslip cells to a 68º dovetail prism from Red
Optronics (Mountain View, CA, USA). The prism was used to create the evanescent
wave for use in total internal reflection microscopy (TIRM) experiments (Chapter 6).
5.2 Colloids
5.2.1 Silica Microspheres
Colloidal SiO2 (nominal diameter of 2.34 microns) were purchased from
Bangs Laboratories (Fishers, IN, USA) and used without further purification. The non‐
porous amorphous SiO2 colloids are synthesized by a precipitation method using pure
tetraethyl orthosilicate and reagents with minimal trace elements. Colloidal SiO2
dispersions used for TIRM experiments were prepared by diluting 0.7μL of the
manufacturer stock dispersion (10% solids in ethanol) into 1mL of a solution which had
been set to the desired pH and ionic strength. These solutions were made by diluting
concentrated stocks of NaCl (4M), KOH (1M), and HCl (1M). Each day before use, the
stock solutions were measured using an Accument AR20 pH and conductivity probe from
Fisher Scientific to obtain an accurate concentration of each salt. From here, a calculated
volume of each salt, based on the stock concentration, was dispensed and diluted
accordingly to create the solutions needed for experiments. After the final addition of the
silica, this suspension was sonicated for 15min, then diluted 100 with the appropriate
solution and sonicated again before use.
141
For experiments where the silica microspheres were used as spacer particles a
diluted stock was prepared. For experiments where silica was sparsely implemented to
keep confining walls at a set distance (Chapter 7), the dispersion consisted of 0.5μL of
silica stock diluted in 4mL of DI water. For porous media experiments (Chapter 8), a
silica dispersion was created by adding 100μL of the stock to a 1mL total volume of
0.1mM NaCl solution.
5.2.2 Gold Rods
Gold rods were synthesized at Pennsylvania State University (State College, PA,
USA) using an electrochemical deposition process. This process was adapted from
several deposition methods.1, 2 An anodic aluminum oxide (AAO) membrane from
Whatman Inc. (purchased from Sigma Aldrich) was coated on one side with a thin film of
silver using a Kurt Lesker (Jefferson Hills, PA, USA) Lab-18 electron beam evaporator
before deposition to increase conductivity. A two-electrode system was used for
deposition, the membrane serving as the working electrode and platinum as the reference.
A sacrificial layer of silver was first deposited into the pores of the membrane, then gold
was added on top by electrochemically growing the rods to a prescribed length using a
current density of -1.24mA/cm2. The alumia template was first rinsed with DI water and
dried. Then the entire membrane was soaked in 1:1 HNO3 to dissolve the silver and free
the rods, followed by soaking in 0.5M NaOH to dissolve the AAO membrane. The rods
were rinsed with DI water until neutral. This process led to the creation of rods on the
order of 1 x 109 per mL.2 The rods used in these experiments have a diameter of
approximately 300nm as determined by scanning electron microscopy.
142
5.2.2.1 Estimation of Surface Potential
Zeta potential measurements were used as an estimation of the surface
potential (ψ) for gold rods at four different ionic strength conditions. Though the
zeta potential exists further away from the surface, encompassing both the
adsorbed and diffuse layers of ions, it is often used as an approximation when
direct measurements of are not possible. Using a Malvern ZetaSizer Nano-ZS,
three sets of five separate measurements were taken per sample, each
measurement consisting of 10 – 15 scans, to obtain the average and standard
deviation. The Smoluchowski model was used to determine the zeta potential
from electrophoretic mobility measurements. A more in depth explanation of zeta
potential can be found in Section 2.4.3.
5.3 Preparation of Samples
5.3.1 One-Wall Cells
Experiments where only the interaction of the particle with a single planar wall
was of interest were performed using what from this point forward is referred to as a one-
wall cell. These cells are the most commonly used, in all forms of microscopy discussed
above, and rely on particles that are of significant weight such that they will levitate at a
height relatively close to the bottom wall. These cells are created by taking a clean glass
microscope slide and bonding a 5mm (ID) O-ring to the slide with vacuum grease that
envelops the O-ring and covers up to but not over its outer edge. A 120μL aliquot of the
colloidal dispersion of interest was added to the O-ring and allowed to sediment for one
143
minute before a small glass coverslip was used to top the O-ring. The coverslip was then
pressed down into the excess vacuum grease around the O-ring’s edge to seal the small
glass coverslip to the O-ring, preventing unwanted air currents that would cause
convection, or dust particles from falling into the sample during experiments.
5.3.2 Confined Cells
Confined cells, also called two-wall cells, were used to trap particles within a
small gap. This method was used for very small particles (diameters usually on the order
of <1μm) because gravity is not great enough to contain these particles at focal distances
comparable to the objectives being used so that they appear blurry in bright field
microscopy, or because they levitate at distances outside the evanescent wave in TIRM.
The sample used for these cells is a mixture of colloidal rods and “spacer” particles,
which in this case are the same 2.1μm silica particles used above. It must be a more
concentrated suspension since a much smaller volume is used. To create the sample,
aliquots of salt solution, gold rods, and spacer particles were mixed in a 34:15:1 ratio.
The cells are assembled by taking a cleaned long glass coverslip and applying a 10μL
aliquot of the prepared gold rod-silica spacer mixture to the center of the coverslip. A
clean small glass coverslip was then placed on top of the liquid mixture.
Using a piece of lens paper, excess liquid was then wicked away from the edge of
the coverslip by placing the lens paper along the edge of the top coverslip. Using a
fingertip to hold the lens paper in place at one end, the other hand gently pressed down on
the surface and wiped along the edge. This was repeated for all four sides of the small
coverslip. Then the lens paper was placed on top of the sample cell so that it covered the
small coverslip completely, and very gently a fingertip was run across all four sides. This
144
was performed twice, and then the sample cell was checked for diffraction patterns and
small air pockets at the edges of the glass, which indicate that enough liquid had been
wicked away. If too much liquid had been removed, large dry areas would appear
between the two coverslips. Once enough liquid was removed, the epoxy resin and
hardener were mixed and immediately used to seal around all four sides.
5.3.3 Porous Media
To create slides for 2-dimensional (2-D) porous media experiments, a
concentrated silica stock in 0.1mM NaCl was applied to the surfaces of long glass
coverslips using a Laurell Technologies Corporation WS-400BZ-6NPP/LITE spin coater
(North Wales, PA, USA). Placing the coverslip onto the spin coater, a 100μL aliquot of
the silica stock was added to the surface. Closing the lid, the spin coater was then run at
1000rpms for 40s to evenly distribute the silica microspheres. Depending on the desired
density of porous media, this process was performed one to five times, where for more
dense concentrations the same coverslip was left on the spin coater and a second, third,
etc. 100μL aliquot of silica was added in succession. Afterwards, the coverslips were
moved to a hotplate and tented with aluminum foil, then left to dry overnight at 50°C.
The next day, the coverslip was removed from the hotplate and rinsed gently with
DI water from a squirt bottle, then placed back on the hotplate to dry for ten minutes.
This rinsing step was performed to remove any excess salt crystals that may have formed
upon the 0.1mM NaCl solution drying. This procedure was repeated three to five times
depending on the density of porous media on the coverslip. After the last drying step, a
10μL aliquot of the gold rod stock was deposited onto the center of the coverslip. A clean
small glass coverslip was then placed on top of the liquid mixture, and the sample cell
145
was removed of excess liquid and sealed with epoxy in a manner identical to that for
confined cells.
5.4 Microscopy Techniques
5.4.1 Bright Field
Bright field microscopy is the most traditional form of optical microscopy, which
uses a compound microscope to image small objects. These microscopes consist of a light
source, a condenser lens to focus the light onto the sample stage, and oculars to view the
sample.3 Various illumination sources and objectives can be used to enhance the
resolution and performance in bright field microscopy to image objects on the order of
~250nm across. The resolution of the objective being used is defined as the ability to
distinguish small details of an object in an image. Good optical microscopes today use
Köhler illumination, which implements a tungsten lamp as the illumination source and a
series of lenses and condensers to split the light into two different light paths. The
separate illuminating and imaging paths help produce even illumination of the sample,
resulting in high resolution magnified images. The resolution of an image is also a
product of the ocular magnification, the objective magnification, focal length, and
numerical aperture (NA).
The total magnification of the system is the product of the magnification of the
objective and the magnification of the eyepiece. Eyepieces typically have a magnification
of 10, but the magnification of objective lenses can range from 4 to 100 which
correspond to focal lengths equaling 40mm and 2mm respectively. Magnification is
146
related to the focal length (f) by,
oo
dM
f (5.1)
where d is the distance from the lens to the object being examined and the subscript o
stands for objective. The focal length measures the distance at which the rays of light are
brought to a single focal point.
The objective and oculars create the ability to magnify a sample, but the resolving
power of the objective is determined by its NA. The NA is a dimensionless number that
describes the range of angles at which the light will be accepted to pass through the
objective, defined by,
NA sinn (5.2)
where n is the refractive index of the medium in which the objective is working (nair =
1.00) and θ is the half-angle of the maximum accepted cone of light. The NA is changed
by adjusting the band around the objective, allowing more or less light in, which helps
resolve the image. The finest detail that can be resolved by an objective is proportional to
0.61λ/NA, where λ is the wavelength of light being used or emitted, if the NA of the
objective and condenser are the same.
For experiments performed in bright field in the following chapters, a Zeiss
Axioplan 2 upright optical microscope and a Zeiss Axio Observer A1 inverted optical
microscope (Oberkocken, Germany) were used in conjunction with either a 40 objective
(air NA = 0.65) or a 63 objective (air NA = 0.6), and 10 eyepieces. Particle tracking
was captured on video with a Hamamatsu Photonics ORCA-ER 12bit CCD camera
147
(Hamamatsu, Japan) operated in 4-binning mode at ~27.6fps over 30,000 frames. The
exposure time was set between 2 – 5ms for imaging silica particles, and 0.5ms for gold
rods. The software program Streampix 3.2.1, by Norpix (Montreal, Quebec, Canada), was
used to track the lateral diffusion and rotation of particles.
5.4.2 Dark Field
Dark field microscopy is a technique used in optical microscopy to enhance the
contrast of a sample without the use of a stain. A special condenser attachment is used to
block the central beam light path, allowing only light from a thin ring around the edge to
illuminate the sample. The small amount of light is focused and passed through the
sample, but only light that is scattered off the sample at oblique angles is collected by the
objective. The rest of the light is directed away from the objective opening and is not
collected, giving the resulting image a dark background with bright features that is
characteristic of the technique.4 A schematic of the dark field set condenser and its
relation to the light source and objective can be seen in Figure 5.1.5
For experiments performed in dark field in the following chapters, a Zeiss Axio
Observer A1 inverted optical microscope was used in conjunction with a 63 objective
(air NA = 0.6), a Zeiss dry dark field condenser (NA = 0.8/0.95), and 10 eyepieces.
Particle tracking was captured on video with a Hamamatsu Photonics ORCA-ER 12bit
CCD camera (Hamamatsu, Japan) operated in 4-binning mode at 10fps over 30,000
frames. The exposure time was set between 25 – 35ms for imaging gold rods and silica-
based porous media. Streampix 3.2.1 was used to capture the lateral diffusion and
rotation of particles.
148
5.4.3 Total Internal Reflection
Total internal reflection microscopy (TIRM) is a technique developed in the
1990s that uses the non-intrusiveness of light scattering to measure the colloidal
interactions of a single particle with a flat plate using an optical microscope6
Measurements of particles are made possible by tracking the light scattered by the
particle and recording the light intensity as a function of time. This allows for the
separation distance between a spherical colloidal particle and a planar surface to be
determined, while achieving greater sensitivity in measurements of force and energy
Figure 5.1 – Schematic representation of dark field set-up. Adapted from Hu et. al.5
Objective
CCD Camera
149
compared to other surface force techniques (e.g., surface force apparatus, SFA; atomic
force microscopy, AFM). This is possible because instead of using a cantilever to
measure the separation distance, which relies on the limitations of a spring constant to
determine the force, a laser is used. More recently, measurements of ensembles of
particles was made possible by developing a technique that combined TIRM with video
microscopy, which allowed for the scattering intensities of multiple individual particles to
be tracked simultaneously.7
The sample of interest is placed on top of a specially cut dove-tail prism, which is
then situated onto the translating stage of the optical microscope. A laser is focused onto
one side of the prism at an angle so that the laser is completely reflected back at the
interface of the prism and the sample so that it exits on the opposite side. This internal
reflection is predicted by Snell’s law as,
1 2sin sini rn n (5.3)
where θr > θi and the incident laser passes through a material of a higher refractive index
n2
n1
θr
θi
Figure 5.2 – Internal reflection of a laser as predicted by Snell’s Law.
150
(n) than that of the material or medium on the other side of the interface. Figure 5.2
illustrates this relationship where the black arrows depict the path of the internally
reflected beam when θr is sufficient to cause internal reflection, and the red arrow shows
when θr is not large enough.
This internally reflected light generates an evanescent wave that propagates into
the medium above it and decays exponentially with distance from the surface. In our
case, this would be the sample cell sitting atop the prism. As a particle of interest
undergoes Brownian motion within the sample cell it will translate in the x-y plane, but it
will also experience a variety of height excursions in the z-direction. As the particle
samples different heights (h) the intensity of the scattered light will change, where the
particle scatters more light as it gets closer to the surface, and therefore, farther into the
evanescent wave. The intensity of the scattered light also decays exponentially and is
given by,
0( ) exp( )I h I h (5.4)
where I0 is the scattering intensity of a particle in direct contact with the planar surface (h
= 0) and β is the penetration depth of the laser, which can be calculated as,
2 21 2
4sin in n
(5.5)
This exponential decay allows for high resolution measurements in the z-axis (down to
1nm). A schematic representation of the TIRM set-up is illustrated in Figure 5.3.7
The intensity of a given particle at any time can be used to calculate the height of
that particle, and then create a distribution of heights over the duration of the experiment.
151
The height a particle samples the most frequently is considered the most probable height
(hm). This hm corresponds to the lowest potential energy experienced by the particle. The
number of times all heights are sampled can be translated into a potential energy via
Boltzmann’s equation,
( ) ( ) ( )
ln( )
m m
B
u h u h p h
k T p h
(5.6)
where kB is Boltzmann’s constant and T is the temperature.
TIRM experiments were performed using the Zeiss Axioplan 2 upright optical
microscope, to which the dovetail prism was coupled. A 15mW HeNe laser (λ =
632.8nm) from Melles Griot (Carlsbad, CA, USA) was focused onto one end of the
prism, striking it at an incident angle of 68° to create an evanescent wave with a decay
CCD, PC h
I(h)
Figure 5.3 – Schematic representation of TIRM set-up, inset shows exponential decay of evanescent wavewith a spherical particle scattering light. Adapted from Wu and Bevan.7
152
length (β-1) of 113.7nm. Sample cells were indexed matched with oil to the prism.
Streampix 3.2.1 was used to capture the lateral diffusion and variations in scattering
intensity of particles.
5.5 Image and Data Analysis
Image analysis algorithms8 coded in FORTRAN were used to analyze videos
taken in the above-mentioned experiments. Compaq Visual Fortran 6.6 (Houston, TX,
USA) was used to generate specific codes to separately track the scattering intensity,
lateral trajectories, and rotational diffusion of spherical and anisotropic particles in bright
field, dark field, or total internal reflection microscopy. These codes provided the ability
to translate scattering intensities of ensembles of particles into potential energies using
Equations 5.4 – 5.6, calculate the mean squared translational and angular displacements,
calculate lengths of colloidal rods, and determine the heights sampled by particles using
the theories described in Chapter 4. These codes also created tagged image files (*.tif)
that were then utilized as a tool for tracing particle behavior (e.g., irreversibly bound,
diffused out of frame, collided with another particle).
Directly from Streampix, small video clips were extracted to make sizeable files
for presentation material in either audio video interleave (*.avi) or *.tif formats.
Videomach from Gromada, Wright Cell Imaging Facility (WCIF) ImageJ (Toronto, ON,
Canada), and Scion Image from the Scion Corporation (Frederick, MD, USA) were used
to edit these video clips. SigmaPlot from Systat Software Incorporated (San Jose, CA,
USA), MathCad from the Microsoft Corporation (Redmond, WA, USA), and MATLAB
2011 from Mathworks (Natick, MA,USA) were used to process all data files resulting
153
from image analysis including plotting and theoretical fits.
5.6 References
1. Yu, J.-S.; Kim, J. Y.; Lee, S.; Mbindyo, J. K. N.; Martin, B. R.; Mallouk, T. E., Template synthesis of polymer-insulated colloidal gold nanowires with reactive ends. Chemical Communications 2000, (24), 2445-2446.
2. Wang, W.; Castro, L. A.; Hoyos, M.; Mallouk, T. E., Autonomous Motion of Metallic Microrods Propelled by Ultrasound. ACS Nano 2012, 6, (7), 6122-6132.
3. Saferstein, R., Forensic science handbook. Prentice Hall: 2001.
4. Davidson, M. W. Darkfield Illumination. http://micro.magnet.fsu.edu/primer/techniques/darkfield.html (January 24, 2013),
5. Hu, M.; Novo, C.; Funston, A.; Wang, H.; Staleva, H.; Zou, S.; Mulvaney, P.; Xia, Y.; Hartland, G. V., Dark-field microscopy studies of single metal nanoparticles: understanding the factors that influence the linewidth of the localized surface plasmon resonance. Journal of Materials Chemistry 2008, 18, (17), 1949-1960.
6. Prieve, D. C., Measurement of colloidal forces with TIRM. Advances in Colloid and Interface Science 1999, 82, (1-3), 93-125.
7. Wu, H.-J.; Bevan, M. A., Direct Measurement of Single and Ensemble Average Particle-Surface Potential Energy Profiles. Langmuir 2005, 21, (4), 1244-1254.
8. Crocker, J. C.; Grier, D. G., Methods of Digital Video Microscopy for Colloidal Studies. J. Colloid. Interface Sci. 1996, 179, 298-310.
154
Chapter 6:
Anomalous Silica Colloid Stability and Gel Layer Mediated Interactions
Adapted from: J.L. Bitter, G.A. Duncan, D.J. Beltran-Villegas, D.H. Fairbrother, M.A. Bevan, “Anomalous Silica Colloid Stability and Gel Layer Mediated Interactions”.
Langmuir, 29 (28): 8835-8844, 2013. DOI: 10.1021/la401607z
Total internal reflection microscopy (TIRM) is used to measure SiO2 colloid
ensembles over a glass microscope slide to simultaneously obtain interactions and
stability as a function of pH (4-10) and NaCl concentration (0-100mM). Analysis of SiO2
colloid Brownian height excursions yields kT-scale potential energy vs. separation
profiles, U(h), diffusivity vs. separation profiles, D(h), and whether particles are levitated
or irreversibly deposited (i.e., stable). By including an impermeable SiO2 “gel layer”
when fitting van der Waals, electrostatic, and steric potentials to measured net potentials,
gel layers are estimated to be ~10nm thick and display an ionic strength collapse. The
D(h) results indicate consistent surface separation scales for potential energy profiles and
hydrodynamic interactions. Our measurements and model indicate how SiO2 gel layers
influence van der Waals (e.g., dielectric properties), electrostatics (e.g., shear plane), and
steric (e.g., layer thickness) potentials to understand the anomalous high ionic strength
and high pH stability of SiO2 colloids.
6.1 Introduction
Silica is ubiquitous. It makes up 60% of the earth’s crust and silicates make up
90% of all minerals. It is present in amorphous and crystalline forms important for
155
everyday use, optics, and microelectronics. It is present in food, pharmaceuticals, and
organisms. As such, understanding the chemical and physical properties of bulk silica,
silica surfaces, and colloidal silica is crucial to numerous applications. A great deal of
silica chemistry is well understood and catalogued in the comprehensive book by Iler.1
However, the stability of colloidal silica against aggregation at high ionic strengths and
high pHs is often referred to as “anomalous”2 because it is not well described by the
Derjaguin-Landau-Verwey-Overbeck (DLVO) theory.3, 4
Historical reviews of possible stabilizing mechanisms that might account for
anomalous silica colloid stability are contained within representative papers on the
topic.2, 5-8 Direct measurements of force vs. distance curves with the surface forces
apparatus and the atomic force microscope indicate a short-range repulsion.5-8 While this
measured repulsion appears sufficient to account for anomalous colloidal stability, its
physical origin remains an open question. Two mechanisms suggested in the literature
include structural forces due to interfacial water9 or steric interactions between silica gel
layers.10 The water structuring mechanism does not appear that it would be unique to
silica. The presence of silica gel layers is supported by measurements of adhesion,
friction, contact angle,5 and surface density profiles via scattering/spectroscopic
methods.11-13 Despite some evidence in favor of silica gel layers, direct measurements5-8
do not conclusively support either mechanism or a quantitative potential model. It is also
not clear that the role of silica gel layers has been treated self-consistently in terms of
their effects on all interactions including van der Waals, electrostatic, and steric
interactions.
In this work, we simultaneously measure the interactions and stability of silica
156
colloids over a glass microscope slide as a function of pH (4-10) and ionic strength (0-
100mM NaCl). TIRM is used to non-intrusively measure weak kT-scale interactions
between a glass microscope slide and an ensemble of silica colloids14 by analyzing their
Brownian height excursions, which also reveals whether they are irreversibly deposited
or levitated (i.e., stable). This has the advantage that separation dependent interactions are
obtained simultaneously with measurements of stability, so the two can be
unambiguously linked in the same material system. We also simultaneously obtain
potential energy vs. separation, U(h), and diffusivity vs. separation, D(h), profiles by
fitting the Smoluchowski equation coefficients to the measured particle dynamic
trajectories. The D(h) trajectories yield additional information about particle-wall
separation and fluid mechanics important to interpretation of electrostatic and steric
interactions. As such, the present study provides new measurements and models of silica
gel layer mediated interactions that lead to anomalous silica colloid stability.
6.2 Theory
6.2.1 Potential Energy Profiles
By measuring a statistically significant number of height excursions, h, of a
spherical particle above a planar wall surface, a normalized equilibrium height histogram,
p(h), can be related to net separation dependent interaction potential, U(h), via
Boltzmann’s equation as,
expp h U h kT (6.1)
where k is Boltzmann's constant and T is absolute temperature. Equation 6.1 can be
157
inverted to obtain a measurement of U(h) from measured p(h) data as,
lnU h kT p h (6.2)
Theoretical models of U(h) can be computed from superposition of contributing
potentials as,
( ) ( ) ( ) ( ) ( )G E V SU h U h U h U h U h (6.3)
where the subscripts refer to the gravitational (G), electrostatic (E), van der Waal (V), and
steric (S) interactions. The gravitational potential is associated with a body force, whereas
the other potentials are associated with surface forces. Electrostatic and van der Waals
potentials were considered in the original DLVO theory.3, 4
The gravitational potential energy of each particle depends on its height, h, of the
particle above the wall, multiplied by its buoyant weight, G, as given by,
3( ) 4 3 ( )G p fU h Gh mgh a gh (6.4)
where m is buoyant mass, g is acceleration due to gravity, and p and f are particle and
fluid densities.
The interaction between electrostatic double layers on two plates (from
superposition, non-linear Poisson-Boltzmann equation, 1:1 monovalent electrolyte)15 can
be used in conjunction with the Derjaguin approximation to give the particle-wall
potential as,16
expEU h B h (6.5)
158
2
1 264 tanh tanh4 4
kT e eB a
e kT kT
(6.6)
1 22
2( )Ai i
i
e Nz C
kT
(6.7)
where κ is the inverse Debye length, ε is the solvent dielectric constant, e is the elemental
charge, ψ1 and ψ2 are surface potentials, NA is Avogadro's number, Ci is electrolyte
molarity, and zi is ion valence. The inverse Debye length and surface potentials of the
particle and wall is essential to the fit of the electrostatic repulsion portion of the net
potential and directly related to the solution chemistry. See sections 6.8.1 and 6.8.2 in the
Supplemental Information for greater detail on accurately determining these quantities.
van der Waals attraction between two plates as predicted from the Lifshitz
theory17 (that includes retardation and screening effects) can be used in conjunction with
the Derjaguin approximation to give the particle-wall potential as,18
26V
h
U h a A l l dl
(6.8)
where A(l) is the Hamaker function given by,19, 20
13 23 13 230
3( ) ' [1 ] ln[1 ]
2rn
x x
n
A l kT x e e dx
(6.9)
where the Δ terms include the frequency dependent dielectric properties of the particle
(1), wall (2), and medium (3), and the remainder of the terms are defined in previous
papers.18, 19 The prime (') next to the summation indicates that the first term (n = 0) is
multiplied by ½(1+2l)exp(-2l) to account for screening of the zero-frequency
159
contribution.
The interaction between surfaces coated with macromolecular layers depends on
the free energy change of layers under compression.21-23 For a layer with a brush
architecture on a planar surface with an uncompressed thickness, δ0, and free energy per
area, f0, the compressed free energy per area, f(δ), for ½ < δ/δ0 <1 can be captured
accurately by,24
0 0( ) 1 expB Bf f (6.10)
where ΓB and γB are dimensionless constants specific to the brush architecture.24 Using
this expression in the Derjaguin approximation, the potential between two symmetric
macromolecular brush layers as can be obtained as,24
, 0 0 0( ) 16 exp 2S B B BU h af h (6.11)
For different interfacial macromolecular architectures with different decaying density
profiles at their periphery, different values of Γ and γ can be used in Equation 6.10.
Because Equation 6.11 can be used to accurately model adsorbed macromolecular layer
repulsion for a broad range of δ0, f0, Γ and γ, a general repulsive steric potential of the
form,
( ) expSU h h (6.12)
is broadly applicable (by lumping unknown constants together), particularly when the
uncompressed layer properties and architecture are not well characterized (which has also
been shown for asymmetric interactions between layers of different properties24).
160
6.2.2 Diffusivity Profiles
In contrast to measuring the equilibrium probability p(h) to obtain U(h) via
Equation 6.2, measurements of the time-dependent probability, p(h,t), can be used to
obtain both U(h) and the separation dependent diffusivity, D(h), as described by the
Smoluchowski equation,25
, , ,p h t p h t p h t dU h
D ht h h kT dh
(6.13)
which reduces to Boltzmann’s equation in the long-time limit as equilibrium is
approached. In previous work, we have reported non-equilibrium analysis of colloidal
trajectories to obtain U(h) and D(h). Measured D(h) are modeled using,
0( ) ( )D h D f h (6.14)
where D0 is the Stokes-Einstein coefficient of an unbounded spherical particle given by,
0 6
kTD
a (6.15)
where η is the fluid medium viscosity, and f(h) accounts for particle-wall hydrodynamic
interactions from Brenner,26 which is accurately captured by the simple expression,27
Table 6.1 – Constants used in theoretical fits.
Variable (units) Value Equation ρp (g/cm3) 1.96 (6.4)
ρf (g/cm3) 1.00 (6.4)
εw 78 (6.7)
T (K) 295 (6.7)
η (Pa·s) 1.002 x 10-3 (6.15)
161
2
2 2
6 2( )
6 9 2
h ahf h
h ah a
(6.16)
6.3 Materials and Methods
6.3.1 Colloids and Surfaces
Hydrochloric acid, potassium hydroxide, sodium chloride (all from Fisher
Scientific), and colloidal SiO2 (nominal diameter of 2.34 microns, Bangs Laboratories)
were used as purchased and without further purification. The non‐porous amorphous SiO2
colloids are were synthesized by a precipitation method using pure reagents with minimal
trace elements. Glass microscope slides (Fisherbrand Plain Microscope Slides) had a
manufacturer reported density of 2.48 grams/cm3 and a soda lime composition
(approximately 72% silicon dioxide, 14% sodium oxide, 6% calcium oxide, 4%
magnesium oxide, 1% aluminum oxide, 1% potassium oxide, <1% other trace elements).
The microscope slides were sonicated for 30min in acetone, 30min in isopropanol, rinsed
with deionized water, and soaked in Nochromix overnight. Slides were rinsed thoroughly
before soaking in 0.1M KOH for 30min prior to use. Slides were again rinsed with
deionized water and dried with nitrogen before use. Colloidal SiO2 dispersions were
prepared by diluting 0.7μL of the manufacturer stock dispersion into 1mL of the desired
pH and ionic strength solution, which was sonicated for 15min before diluting 100X
before introduction into the measurement cell.
6.3.2 Ensemble Total Internal Reflection Microscopy
All experiments were performed in cells consisting of a 5mm ID Viton O-ring
(McMaster Carr) sealed with vacuum grease (Corning) to cleaned microscope slides.
162
100μL of colloidal SiO2 dispersions were added to the O-ring and covered with a
coverslip. Experiments were performed using a Zeiss Axioplan 2 optical microscope with
a 40x objective. Particle scattering was recorded with a 12bit CCD camera (Hamamatsu
ORCA-ER) operated in 4-binning mode at ~27.6fps for 30,000 frames. The evanescent
wave was generated by a 15mW 632.8nm HeNe laser (Melles Griot) focused onto a
dovetail prism (Red Optronics) at an incident angle of 68° to create a decay length of
113.7nm. Image analysis algorithms28 coded in FORTRAN were used to track the lateral
trajectories and scattering intensity of each particle.
6.3.3 Diffusivity Landscape Analysis
Fitting measured particle dynamics with the Smoluchowski equation (Equation
6.13) to obtain the coefficients (i.e., U(h), D(h)) is described in previous29 and recent30
papers from our group. Our previous analysis of local dynamics at each elevation
provides a more intuitive explanation of how D(h) can be extracted simultaneously with
U(h).29, 31 In this work, we employ a less obvious but numerically more robust scheme
based on a global analysis of excursions between all elevations to find an optimal fit to
the Smoluchowski equation. The development of the global analysis algorithm is
described elsewhere,32 and specific details relevant to colloidal interactions are provided
in our recent paper.30 In brief, a FORTRAN program was used to construct a matrix
enumerating the number of times all particles jumped from each initial height to all other
heights on a given time scale. By using a Monte Carlo sampling scheme, values of U(h)
and D(h) are optimized to fit the measured data. Convergence is determined when U(h)
and D(h) fluctuate about a solution that shows a minimum difference with the measured
dynamics. The magnitude of the fluctuations about the solution provides an estimate of
163
error bars on the solution.
6.4 Results and Discussion
6.4.1 Example Deviation from DLVO Theory
DLVO theory is used to understand the stability of charged colloids in aqueous
media in terms of pair potentials that are the superposition of electrostatic repulsion and
van der Waals attraction. However, to demonstrate how DLVO theory can be an
oversimplification, even in apparently model systems, Figure 6.1 shows a measured
potential for ~2.1μm SiO2 colloids interacting with a glass microscope slide in 20mM
NaCl at pH = 10. As noted in more detail in the materials sections, the colloids are non‐
porous, amorphous, pure SiO2 and the microscope slide has a soda lime glass
composition. We chose this system to be representative of typical commercially available
silica materials with compositions that might also be encountered in environmental
applications. The theoretical prediction using only electrostatic and van der Waals
potentials (Equations 6.5, 6.8) with independently measured parameters displays a deeper
secondary minimum than the experimental data and does not match the potential shape.
The predicted potential also indicates a lower energy barrier and particle stability against
deposition on the wall. This finding is consistent the anomalous SiO2 colloid stability
reported in the past.2-8
By simply adding an additional repulsive potential, it is possible to more
accurately capture the attractive well depth, shape, and range. As already reviewed in the
introduction of this paper, a solvated gel layer, which is also possibly a polyelectrolyte, is
164
thought to provide a stabilization mechanism through a repulsive steric interaction.
However, simply introducing a short range repulsion cannot provide stability in the
presence of a long range van der Waals attraction; the mechanism must be more complex
than this simple picture and it must be physically realistic. In the following, we provide
more measurements and potential fits like the one illustrated in Figure 6.1 to understand
the mechanism of silica colloid stability beyond the standard DLVO theory.
6.4.2 Interaction Potentials vs. Ionic Strength (at fixed pH = 10)
Figure 6.2A shows potential energy profiles between 2.1μm SiO2 colloids
interacting with a glass microscope slide at pH=10 for [NaCl] = 0 – 85mM. The
gravitational potential energy, which corresponds to a body force, has been subtracted
Figure 6.1 – Example of disagreement between ensemble TIRM measured particle-wall potential energy profile (points) and DLVO theory (red solid line) for 2μm SiO2 in [NaCl]=20mM at pH=10. Addition of a steric potential to the DLVO potentials produces a net potential prediction (blue dashed line) in better agreement with the depth of the secondary minimum and produces an energy barrier consistent with the particles’ observed stability.
(h-hm)/nm
-50 0 50 100 150
U(h
)/kT
-4
-2
0
2
4
165
from the measured potential energy profiles to leave only the contributions due to
colloidal/surface forces. The remaining net potentials display the correct qualitative trend
based on expectations that the range of electrostatic repulsion decreases with increasing
ionic strength to reveal a shorter range attractive interaction. However, quantitative curve
fits to the net interaction potentials, which are discussed in detail in the following
sections, are not accurately captured for all conditions by DLVO potentials alone.
To analyze the measured interactions reported in Figure 6.2A, the net potentials
were fit with either DLVO potentials only (Equation 6.3 with UE+UV) shown by solid
lines or DLVO plus a steric contribution (Equation 6.3 with UE+UV+US) shown by
dashed lines. The DLVO potentials were fit to the measured profiles for [NaCl] = 0 –
5mM, and the DLVO plus steric potential was fit to measured profiles for [NaCl] = 10 –
85mM. The solid lines representing purely DLVO interactions were obtained without any
adjustable parameters by using independent measurements of the solution conductivity
and pH to predict from Equation 6.7 and using a literature model summarized in the
Supporting Information (SI).33, 34 Although the SiO2 values in our experiments could
differ from this literature model based on different compositions or cleaning procedures,
we proceed with this model to minimize adjustable parameters and ultimately show it
captures our measured DLVO potentials with no adjustable parameters. The van der
Waals attraction was modeled using literature dielectric properties for water and SiO2
described in our previous work.18, 35 The agreement of the measured potentials at low
ionic strengths with DLVO theory is consistent with previous TIRM measurements of
interactions between different colloidal materials including SiO2 colloids and glass
surfaces.14, 36 We return to a discussion of the non-DLVO potential fits after first
166
Figure 6.2 – Ensemble TIRM measurements of (A) potential energy profiles, U(h), and (B) diffusivity profiles, D(h), for 2.1μm SiO2 at pH = 10 with [NaCl] = 0.1 – 100mM. The color scheme for lines and points indicates [NaCl] given in the legend in (A). In (A), the points are measured data from an equilibrium analysis of particle trajectories using Equation 6.1, solid lines indicate DLVO potentials only (Equation 6.3 with UE+UV), and dashed lines indicate DLVO plus a short range steric contribution (Equation 6.3 with UE+UV+US). In (B), the points are measured data from a non-equilibrium analysis of particle trajectories using Equation 6.13, solid lines are fits to theoretical predictions from Equation 6.14, and error bars are explained in the Methods section.
h/nm
0 100 200 300 400
U(h
)/k
T
-4.0
-1.5
1.0
3.5
6.0
0.1mM2mM5mM10mM15mM20mM40mM60mM80mM
A
h/nm
0 100 200 300 400
D(h
)/(n
m2/m
s)
0
20
40
60
80
B
167
presenting measurements of separation dependent diffusivity profiles, D(h), to provide
additional information on the SiO2 particle-wall interaction.
6.4.3 Hydrodynamic Interactions vs. Ionic Strength (at fixed pH = 10)
As part of verifying both the DLVO and non-DLVO potential fits in Figure 6.2A,
it is useful to have an independent measurement of absolute separation between the
particle and wall. In Figure 6.2B, we report measurements of particle diffusivity profiles,
D(h), obtained from a dynamic analysis based on Equation 6.13 (see the Methods
section). This analysis also yields potential energy profiles, U(h), essentially identical to
those obtained with the standard Boltzmann inversion in Equation 6.2. This confirms the
dynamic analysis successfully recovers the potential energy due to conservative forces,
which provides confidence in the D(h) data obtained simultaneously in this analysis.
Figure 6.2B shows fit theoretical D(h) curves using the literature value for the
viscosity of water and the particle radius obtained from the gravitational potential energy
fit (Equation 6.4, subtracted from data in Figure 2A). By fitting the measured D(h) curves
to the theoretical prediction in Equations 6.14 – 6.16, we obtain an estimate of the
absolute separation scale by setting h = 0 as the location where D(h) = 0. By measuring
and fitting the complete functional form of D(h), we obtain a more accurate estimate of
separation than previous measurements of spatially averaged diffusivities.27 The D(h)
data become scattered at larger separations due to increasing signal noise and lower
statistical sampling (at corresponding higher energies in the U(h) data), but the curve fits
display good agreement with the less noisy data at short separations.
For the [NaCl] = 0 – 5mM data fit with only DLVO potentials (UE+UV) in Figure
6.2A, the particle-wall absolute separation scales from the U(h) and D(h) fits are in good
168
agreement with no adjustable parameters (see Table 6.1 and Figure S6.5). Specifically,
the location of the most probable separation, hm, at the potential energy minimum, and
where the sum of the forces equal zero, is similar in both the DLVO potential fits to the
U(h) data using Equation 6.3 and the hydrodynamic interaction model fits to the D(h)
data using Equation 6.14. As already noted, this finding is consistent with numerous
previous TIRM studies that report excellent agreement with DLVO theory at low ionic
strengths,14, 18, 27, 36, 37 as well as, measurements that have confirmed the accuracy of the
theoretical expression for D(h).27, 38, 39 When fitting the DLVO + steric potentials to the
data for [NaCl] > 10mM in Figure 6.2A, we also use D(h) data to confirm the validity of
the separation scale inferred from the conservative forces and to confirm some
assumptions about the fluid flow in the presence of gel layers. Before discussing the
potential fits that include steric contributions in Figure 6.2A, we first discuss several
conceptual issues related to including a gel layer in a manner that consistently treats
electrostatic and van der Waals potentials.
6.4.4 Role of “Gel” Layer in van der Waals, Electrostatic, and Steric Potentials
The primary conceptual issue to address for computing net potentials in the
presence of silica gel layers is the reference separation for each potential. Four illustrative
cases are depicted in Figure 6.3 showing: (1) no gel layer with UE and UV on a scale, h,
between the H2O/SiO2 interfaces, (2) a gel layer composed of nearly pure SiO2 with UE
and UV on the h scale, and a steric interaction, US, on a separation scale, L, between the
SiO2 gel/bulk interfaces, (3) a gel layer with mostly water properties that is permeable to
fluid flow and has charge on the SiO2 gel/bulk interfaces; this suggests UE, UV, and US
should all be on the L scale, and (4) a gel layer with mostly water properties that is
169
impermeable to fluid flow and has a no-slip surface/potential originating on the H2O/SiO2
gel interfaces; this suggests UV and US should all be on the L scale and UE should be on
the h scale. This list is not exhaustive, but these are the four physically meaningful cases
that bound other cases including gel layer dielectric properties intermediate to pure
H2O/pure SiO2 and/or charge distributed (and a shear plane) between the H2O/SiO2 and
SiO2 gel/bulk interfaces.
These cases can be compared and contrasted to decide on an appropriate model
for the net potentials in Figure 6.2A. Case 1 is the standard model for the DLVO theory.
Case 2 illustrates a gel layer that has no stabilizing effect. In particular, if the gel layer is
composed almost entirely of SiO2, the van der Waals attraction will still be as strong on
the h-scale as in Case 1.40-42 However, since steric repulsion between the gel layers is not
generated until h = 0, the strong van der Waals attraction for h > 0 would cause
irreversible surface adhesion. In fact, Case 1 and Case 2 have the same van der Waals and
electrostatic interactions, but the repulsion at contact is weaker (soft steric repulsion
instead of hard wall repulsion). Clearly a different mechanism is required to produce
stabilization by a silica gel layer.
Cases 3 and 4 illustrate gel layers with a predominantly water composition and
therefore water dielectric properties. This effectively weakens van der Waals on the h-
scale by moving UV to the L-scale in the limit of a purely water layer. The difference
between Cases 3 and 4 is whether the electrostatic potential originates at the SiO2
gel/bulk interfaces (Case 3) or the H2O/SiO2 gel interfaces (Case 4). These cases are
limits of intermediate cases that depend on whether the layer is a polyelectrolyte, how
charge is spatially distributed within the layer, and whether ions are mobile within the
170
Figure 6.3 – Schematics and predicted potentials (for pH = 10, [NaCl] = 80mM in Figure 6.2A) based on various cases for including SiO2 gel layers. In the schematics and predictions, h is the separation between the outer edges of the SiO2 gel layers (i.e. the H2O/SiO2 gel interfaces), and L is the separation between the inner edges of the SiO2 gel layers (i.e. the SiO2 gel/bulk interface). See text for detailed explanation of each case, but in brief: (top-to-bottom) (1) the typical configuration with no gel layers considered in the DLVO theory, (2) gel layers of mostly SiO2 composition, (3) gel layers of mostly H2O composition that are permeable to fluid flow, (4) gel layers of mostly H2O composition that are impermeable to fluid flow. The potentials are color coded as: electrostatics (red), van der Waals (blue), steric (yellow), and net (green).
h
L
silicasilica watergel gel
h/nm-5 0 5 10 15
u(h
)/kT
-20
-10
0
10
20
L/nm
15 20 25 30 35
h
silica silicawater
h/nm0 5 10 15 20
u(h
)/k
T
-20
-10
0
10
20
h
L
water silicasilica gel gel
h/nm0 5 10 15 20
u(h
)/kT
-20
-10
0
10
20
L/nm10 15 20 25 30
h
L
water silicasilica gel gel
h/nm-20 -15 -10 -5 0
u(h
)/kT
-20
-10
0
10
20
L/nm0 5 10 15 20
1
2
3
4
171
layer.10, 43 Both of these cases can produce net potentials that correspond to stable
particles and can be fit to the data in Figure 6.2A. In short, Case 4 has more electrostatic
repulsion and as a result has a smaller steric contribution, whereas Case 3 has less
electrostatic repulsion and therefore requires a greater steric contribution. The key effect
in Cases 3 and 4 compared to Case 2 is that van der Waals attraction is weaker due to the
gel layer.
6.4.5 Fitting DLVO and Steric Interactions in the presence of a “Gel” Layer
Based on the discussion of the different cases in Figure 6.3, the measured profiles
for [NaCl] > 10mM in Figure 6.2A are fit using models based on Cases 3 and 4. As in the
purely DLVO fits for [NaCl] < 5mM, the same ionic strength and pH dependent κ from
Equation 6.12 and the ψ model in the SI27, 28 are used in the DLVO potentials for [NaCl]
> 10mM. For the steric potential in Equation 6.12, a prefactor of Γ = 100kT is assumed,
and the steric inverse decay length, γ, becomes the sole adjustable parameter in the net
potential. While Γ = 100kT is somewhat arbitrary, it is of the correct order of magnitude
based on the few cases where the steric prefactor has been estimated22 and based on what
is necessary to generate the observed stability. We decided to fix Γ = 100kT for several
reasons including (1) a greater sensitivity of the fit to the decay length than the prefactor
when both parameters are varied, (2) some uncertainty in the strong, short-range
repulsion due to noise, which affects estimates of the intercept, and (3) the prefactor in
steric interactions cannot generally be predicted a priori based on independent
parameters.22 On the basis on this prefactor, the gel layer thickness, Δ, can be estimated
as 2Δ = L – h = 5γ-1, which corresponds to a decay from 100kT to ~0.5kT based on the
properties of the exponential function. As a result, the difference between Cases 3 and 4
172
is simply whether all potentials are on the same separation scale (Case 3) or whether the
electrostatic potential is shifted outward by 5γ-1 (Case 4). We return to a discussion of the
validity of the assumed prefactor after reporting and discussing the fit steric decay
lengths.
Figure 6.4 reports the inferred decay lengths, γ-1, and gel thicknesses, Δ= 0.5(L –
h) = 2.5γ-1 as a function of ionic strength from the fits to the pH=10 profiles in Figure 6.2.
Data corresponding to fits based on Case 3 indicate decay lengths of γ-1 ≈ 4 – 7nm and
thicknesses of Δ ≈ 10 – 17nm, whereas fits based on Case 4 give γ-1 ≈ 2 – 4nm and Δ≈ 5
– 10nm. It should be noted that these fit parameters are obtained by generating a
repulsion that results in the correct attractive well depth, which then determines the
potential energy minimum location at the most probable separation, hm. This approach is
necessary since the actual repulsive decay corresponds to a strong force approaching the
Figure 6.4 – Steric decay length, γ-1, (left) and gel layer thickness, Δ, (right) vs. [NaCl]/mM at pH=10 from fits in Figure 6.2A based on models for Cases 3 (red triangles) and 4 (blue circles) in Figure 6.3.
[NaCl]/mM
0 25 50 75 100
n
m
1.5
3.0
4.5
6.0
7.5
/n
m
4
8
12
16
173
noise limit of the TIRM method,44, 45 which limits the accuracy of the measured repulsive
decay length. In short, noise softens strong forces (i.e., large energy changes over small
distances) at short separations and high ionic strengths, so that matching the potential
energy minimum well depth and location is a better measure of the net repulsion than the
decay length.
When considering the absolute values of the layer dimensions inferred in Figure
6.4, it is important to recall that Cases 3 and 4 bound some limiting physical models. For
example, distributing charge anywhere in between the SiO2 gel/bulk interfaces (Case 3)
or the H2O/SiO2 gel interfaces (Case 4) would produce gel layer estimates in between the
two curves shown in Figure 6.4. If the layers contain a higher concentration of SiO2 than
the nearly pure H2O layers in Cases 3 and 4, then the two cases in Figure 6.4 represent
lower bounds where the layer thickness would diverge to infinity as the layers approach
pure SiO2 (as in case 2 where the gel layer is not capable of generating a stabilizing
repulsion beyond the range of van der Waals attraction). One way to overcome this
problem, is to also include surface roughness in addition to the gel layer, which will
weaken van der Waals18 and still allow gel layers without pure water properties.46, 47
6.4.6 Do Inferred Gel Layer Properties Make Sense?
The inferred gel layers in Figure 6.4 from the measured potentials in Figure 6.2
display the expected trend by showing a decreasing thickness vs. increasing ionic
strength. This behavior is consistent with the gel behaving as a polyelectrolyte where
screening of electrostatic repulsion within the layers allows for a dimensional collapse.48,
49 It is also expected that this collapse will not occur until high ionic strengths when the
Debye length is on the order of the separation of charges within the gel layer. This
174
dimensional collapse will expel water from the gel layer and enrich it in pure SiO2
properties, which is reminiscent of solvent quality mediated collapse of adsorbed polymer
layers.42, 46, 50, 51 Such a collapse will reduce stability both by decreasing steric repulsion
and increasing the van der Waals attraction due to changing layer dielectric properties.42
The observed stability behavior also has the character of a solvent quality
mediated collapse of a repulsive steric interaction. Specifically, an attractive energy
minimum evolves beyond the range of an infinitely repulsive steric barrier, which
progressively increases bond lifetimes with an exponential dependence on well-depth.24,
43 When the attractive well is deep enough to produce most probable bond lifetimes
longer than the observation time, then the particle appears to be irreversibly deposited.
This type of destabilization mechanism contrasts the typical mechanism for only DLVO
interactions, where the height of an energy barrier determines the probability of forming
an irreversible bound state involving strong van der Waals attraction at contact. Our
results appear to display stability behavior consistent with a decreasing range of steric
repulsion due to collapsing impenetrable gel layers
The values of the inferred thicknesses are larger than the ~2nm estimates from
mechanical force measurements (e.g. SFA,5 AFM6) but are comparable to gel thicknesses
obtained from surface spectroscopic/scattering methods (e.g. nuclear resonance
profiling,11 neutron, x-ray reflectivity12, 13). One way to reconcile the differences between
layer thicknesses inferred from SFA and AFM force profiles and the TIRM potential
energy profiles in Figure 6.2A is the much higher sensitivity to small energies (and
forces) with TIRM.37 In particular, very weak steric interactions between silica gel layers
could go undetected with mechanical methods until they generate ≥10pN of repulsion. In
175
contrast, TIRM is capable of detecting the very onset of silica gel layer compression on
the kT energy scale and fN force scale (e.g., 1kT/100nm ≈ 10fN). This sensitivity can be
expected to produce thicker layer estimates, and because TIRM is not mechanically
limited, it might produce estimates closer to non-intrusive spectroscopic/scattering
methods. In short, the 5 – 17nm SiO2 gel layers are reasonable based on literature neutron
and x-ray measurements.12, 13
It is also useful to consider the D(h) data and fits in Figure 6.2B. The D(h) fits
serve the purpose of confirming that steric potentials occur on separation scales
consistent with hydrodynamically measured surface separation. In particular, estimates of
hm from non-DLVO fits to U(h) data in Figure 6.2A for both Cases 3 and 4 agree with hm
estimates from the D(h) fits in Figure 6.2B within the uncertainty of the measurements
(see Figure S6.1). The pH = 10, [NaCl] = 80mM potentials in Figure 6.3 can be used to
illustrate this point; the net potential in Figure 6.3C for Case 3 has Lm = 13nm, whereas
the net potential in Figure 6.3D for Case 4 has hm = 8nm, which are both within the
uncertainty of hm = 7nm from the D(h) fit in Figure 6.2B (it should be noted the Lm and
hm are used in this example since L is the hydrodynamic separation scale in Case 3 and h
is the hydrodynamic separation scale in Case 4). As a result, steric potentials with Γ =
100kT and layer thicknesses of Δ= 2.5γ-1 produce net U(h) profiles on the same
separation scale as the D(h) data and fits. However, the D(h) fits do not resolve difference
between Cases 3 and 4.
Of Cases 3 and 4 presented in Figure 6.3, Case 4 is more likely for several
reasons. Because the electrostatic repulsion is longer range in Case 4, the silica gel layer
thicknesses in Case 4 are thinner and closer to the estimates from spectroscopic/scattering
176
methods. Based on previous measurements of adsorbed polymers,46 it is more likely the
gel layers are impermeable to flow (Case 4). The electrostatic potential appears more
likely to originate from a surface potential at the outer edge of the silica gel layer (Case
4).
6.4.7 Potentials and Stability vs. Ionic Strength and pH
To understand how the silica gel layer influences stability as a function of both
pH and ionic strength, Figure 6.5 reports results that summarize both stability and
potential energy profile measurements. In addition to the pH = 10 results already
discussed in Figures 6.2 – 6.4, ionic strength dependent results are shown for pHs of 7,
5.5, and 4. The points show several states indicating whether: (1) all particles were
Figure 6.5 – Summary of whether DLVO theory fit measured potentials and the degree of particle stability vs. solution pH and [NaCl]. Points indicate: (1) robust levitation, accurately modeled by DLVO theory (green circles), (2) robust levitation, modeled by DLVO + steric repulsion (green triangles), (3) slow deposition of particles, levitated particles are modeled by DLVO + steric repulsion (yellow inverted triangles), and (4) irreversible deposition (red squares).
[NaCl]/mM
0.01 0.1 1 10 100
pH
4.0
5.5
7.0
8.5
10.0
177
robustly levitated throughout the entire observation time and had potentials captured by
DLVO theory (green circles), (2) all particles were robustly levitated and had potentials
that required DVLO theory + a steric repulsion (green triangles), (3) some particles
became irreversibly deposited during the observation time and the particles that remained
levitated had potentials that required DVLO theory + a steric repulsion (yellow inverted
triangles), or (4) all particles were irreversibly deposited during the observation time (red
squares). The measured ionic strength dependent potentials for each pH are included in
the SI in Figures S6.4 – S6.6 with fit parameters reported in Table 1. The agreement
between measured potentials and theoretical fits for other pHs in Figures S6.4 – S6.6 are
similar to the agreement observed for the pH = 10 data in Figure 6.2A.
At each pH, there is a clear progression with increasing ionic strength through
states 1 – 4 described in the previous paragraph. The ionic strength dependence is
different at each pH showing a more compressed transition through states 1 – 4 at lower
pHs. For example, at pH = 10 the transition from stable particles described by DLVO
theory to irreversibly deposited particles occurs between [NaCl] = 5 – 100mM whereas
the same transition occurs at pH=4 between [NaCl] = 0.1 – 10mM. At each pH, the
potentials and stability are well described by DLVO theory at low ionic strengths, but an
additional repulsion, presumably due to steric gel layer interactions, is required to fit the
measured potentials and capture the stability at high ionic strengths.
The agreement between measured low ionic strength potentials with DLVO
theory is easy to understand at all pHs; the long range electrostatic repulsion does not
allow particle-wall separations to become small enough to observe a steric repulsion
between silica gel layers in contact. However, as the ionic strength is increased at each
178
pH, a steric repulsion is required to capture the observed repulsion, lack of attraction, and
stability at higher ionic strengths. The fits to measured potentials at all pHs and ionic
strengths (Figures 6.2A, S6.4 – S6.6) have no adjustable parameters in the electrostatic
and van der Waals contributions by using κ from Equation 6.7 and the ψ model in the
SI.27, 28
The different trends at each pH in Figure 6.5 are accounted for by the ionic
strength and pH dependence of the van der Waals and electrostatic potentials, which
suggests the silica gel layer repulsion that is relatively insensitive to pH. This is perhaps
most readily illustrated by noting the steric decay length vs. solution ionic strength is
essentially the same for each pH within the limits of uncertainty of the fit points (see γ-1
data in Table 6.2). Because intramolecular electrostatic repulsion within a polyelectrolyte
brush determines its degree of swelling,48 decreasing such interactions either by screening
at elevated ionic strengths or reducing the total charge via pH dependent weak acid
groups could produce a dimensional collapse of the layers and an associated decreasing
steric repulsion. The steric interaction indeed appears to weaken as the Debye length
changes from ~5nm down to <1nm, which is consistent with the screening length
becoming comparable to spatial dimensions of intramolecular charge separation within
the gel layer to cause its dimensional collapse.48 By analogy, it might be expected that
decreasing charge density with decreasing pH might also influence the average charge
separation and intramolecular electrostatic repulsion within the gel layers to also cause a
dimensional collapse. Although it is non-trivial to demonstrate quantitatively, we
speculate that the average charge separation (i.e., inverse of charge density) is smaller
than the characteristic range of intramolecular electrostatic repulsion for pH > 4 so that
179
γ-1 does not change in this pH range (but might be expected to decrease as pH is
lowered further). Ultimately, the results in Fig. 6.5 in addition to the results in Figures 6.2
pH 2a
(μm) NaCl (mM)
κ-1 (nm)
pH -ψ
(mV)
-1
(#3) (nm)
hm-U (nm)
-1 (#4) (nm)
hm-U (nm)
hm-D (nm)
10
2.17 0.11 30.0 10.02 120 - 320.5 - 320.5 300 2.15 2.1 6.6 10.01 100 - 76.4 - 76.4 80 2.15 5.2 4.2 10.00 83 - 48.1 - 48.1 50 2.16 9.9 3.0 9.93 61 7.2 39.2 4.2 33.4 45 2.13 16.1 2.5 10.01 44 6.3 35.1 3.4 25.9 30 2.17 21.1 2.1 9.91 36 5.9 29.7 3.5 21.5 25 2.13 40.6 1.5 9.88 26 4.7 17.6 2.33 11.6 15 2.15 60.8 1.2 9.92 25 4.3 14.1 2.1 9.1 7 2.15 84.2 1.1 9.77 24 4.1 13.4 2.0 7.5 7
x 111 0.96 9.94 24 x x x x x
7
2.13 0.05 44.2 7.01 94 - 443.6 - 443.6 2.22 2.2 6.8 7.10 85 - 76.7 - 76.7 2.20 5.0 4.3 6.99 70 7.0 47.6 3.1 47.8 2.15 11.3 3.0 7.05 49 6.7 37.7 2.6 30.6 2.13 17.2 2.5 7.00 36 6.4 35.4 3.4 23.8 2.08 22.8 2.1 7.01 30 5.5 25.1 2.7 18.4
x 34.1 1.8 7.08 25 x x x x
5.5
2.22 0.04 51.2 5.52 70 - 480.0 - 480.0 2.10 2.1 6.8 5.48 64 - 73.6 - 73.6 2.08 5.1 4.3 5.50 54 8.2 53.0 2.7 47 2.07 10.3 3.0 5.51 40 8.5 47.8 7.0 30.3 2.02 16.3 2.5 5.55 30 6.8 34.8 4.8 21.6 2.08 20.9 2.1 5.44 24 7.6 43.3 6.0 20.3
x 31.8 1.8 5.46 19 x x x x
4
2.18 0.13 29.9 3.98 30 - 245.7 - 245.7 2.13 2.0 6.6 4.00 29 10.0 67.7 3.0 62.6 2.03 4.5 4.2 3.97 25 9.3 57.6 4.0 39.7
x 11.1 3.0 3.98 15 x x x x
Table 6.2 – Experimental parameters for each pH and ionic strength condition examined. The column labeled as “-1 (#3)” is the steric decay length from a net potential fit based on Case 3 in Fig. 3, and “-1 (#4)” is the steric decay length from a net potential fit based on Case 4. The columns labeled as hm-U are most probable particle-wall separations obtained from potential energy profile fits, and hm-D is the most probable height from diffusivity profile fits. Dashes indicate cases without a steric contribution, and “x”s indicate irreversibly deposited particles where potential energy and diffusivity profiles could not be measured.
180
– 6.4show potentials and stability that are well described by a silica gel layer that reduces
van der Waals attraction, preserves electrostatic repulsion, and contributes an additional
steric repulsion.
6.5 Conclusions
TIRM was used to measure SiO2 colloid ensembles on a glass microscope slide to
simultaneously obtain particle-wall potential energy profiles, diffusivity profiles, and
stability as a function of ionic strength and pH. To interpret the measured potentials and
explain anomalous high ionic strength stability, a model was developed based on
electrostatic and van der Waals potentials from the DLVO theory plus a steric repulsion
attributed to silica gel layers on the particle and wall. For such a model to successfully
quantify the measured potentials, the van der Waals attraction must be weakened by a
layer that has some solvent composition rather than pure silica properties, although
surface roughness could account for some weakening. By including an impermeable gel
layer when fitting van der Waals, electrostatic, and steric potentials to measured net
potentials, gel layer thicknesses of 5 – 10nm were obtained from the model, consistent
with literature scattering measurements. Such gel layers also indicate consistent surface
separation scales for both potential energy profiles and diffusivity profiles based on
theoretical models. The net potential model reported here accurately captures measured
potentials and stability for [NaCl] = 0 – 100mM and pH = 4 – 10 by including a gel layer
that collapses at high ionic strengths but is relatively insensitive to pH. Our findings
indicate a model of silica gel layers that captures measured van der Waals, electrostatic,
steric, and hydrodynamic interactions and their role in the anomalous high ionic strength
stability of silica colloids.
181
6.6 Appendix
Here we describe a curve fit to A(l) computed by the Lifshitz theory (Equation
6.9). The form of the expression provides an accurate representation of both retardation
and screening effects captured by the Lifshitz theory. This expression is convenient for
computing the van der Waals potential via the Derjaguin Approximation (Equation 6.8)
while avoiding the complexity and computational expense of re-computing A(l) from
Equation 6.9 each time. The form we choose is,
0 11 2 [1 2 ]exp[ 2 ]A l l l A A l (6.17)
where A0 is obtained from Equation 6.9 for n = 0 (without the prefactor of ½(1+2l)exp(-
2l) indicated by the prime symbol), and A1∞(l) is obtained from Equation 6.9 for n = 1 –
∞. This form accounts for the fact that the zero frequency term (n = 0) is screened but not
retarded and all higher frequency terms (n > 0) are not screened but are retarded. The
function of A1∞(l) is accurately fit by,
21 1f f f fA l a b l c l d l (6.18)
where the constants A0, af, bf, cf, and df are reported in Table 6.1. Figure 6.6 shows the
expression in Equation 6.17 accurately captures of A(l) curves computed using the
Lifshitz theory (Equation 6.9).
182
6.7 Acknowledgements
We acknowledge financial support by the National Science Foundation (CHE-
1112335, CBET-1066254).
Table 6.3 – Constants used in to fit the Hamaker function from Lifshitz theory.
Variable (units) Value Equation A0 (kT) 1.501 (6.17) af (kT) 1.962 (6.18)
bf (kT·nm-1) 0.0281 (6.18)
cf (nm-1) 0.0593 (6.18)
df (nm-2) 0.0033 (6.18)
Figure 6.6 – Hamaker functions for two silica half spaces vs. separation and medium ionic strength. Points were computed from the Lifshitz theory in Eq. 6.9 for salt concentrations of 0.01 mM (blue), 0.1 mM (pink), 1 mM (green), 10 mM (red), 100 mM (black), as well as an infinite salt case computed by neglecting the n=0 term in Eq. 6.9 (black triangles). The infinite salt case was fit by Eq. 6.18 (solid black line), which was used in Eq. 6.17 to capture all other salt concentrations (dashed lines).
l/nm
0.1 1 10 100 1000
A(l
)/kT
0.00
0.75
1.50
2.25
3.00
183
6.8 Supplemental Information
6.8.1 Solution Chemistry
Understanding how the surface forces of the particle or surface are affected by the
medium is directly related to the solution chemistry of a sample. To accurately determine
the inverse Debye length, , and surface potentials, , used in the calculation of the
electrostatic potential it is necessary to know the solution ionic strength and pH. For the
aqueous media consisting of CO2 saturated H2O, with added NaCl, KOH, and HCl, it is
necessary to determine the following concentrations: [H+], [OH-], [K+], [Na+], [Cl-],
[CO2], [H2CO3], [HCO3-], and [CO3
-2]. By measuring pH, the concentration of [H+] is
determined using the definition of pH as,
pHH 10 (S6.1)
which can be used to determine [OH-] based on the dissociation equilibrium for H2O as,
OH HWk (S6.2)
(where kw and all other constants in this section are reported in Table S1). The
equilibrium value of [CO2] can be determined from Henry’s law as,
2 22 CO COCO P kh (S6.3)
where PCO2 is the partial pressure of CO2 in the atmosphere and khCO2 is Henry’s constant
at 25°C. The values of [H+] and [CO2] can then be used to determine the equilibrium
concentrations of dissolved CO2 species as,
22 3 2H CO CO COKh (S6.4)
184
2 3
3 1
H COHCO
HaK
(S6.5)
32
3 2
HCOCO
HaK
(S6.6)
where KhCO2 is the hydration equilibrium constant for carbonic acid at 25°C, Ka1 and Ka2
are the dissociation constants for the diprotic carbonic acid species. While [K+], [Na+],
and [Cl-] are known from careful solution preparation and dilutions, these values can be
confirmed by measuring the solution conductivity, KM, which can be compared with the
predicted conductivity based on the concentrations of all charged species using,
M
0 0 0 1 2
0
( , ) ( )
i ii
i i i i
c c a ai i i i i
K C
C A B C
z z
(S6.7)
where Λi0 is the molar ionic conductivity at infinite dilution for a given salt, z is the
valence charge of the ion, λ is the molar ionic conductivity for a specific ion, Λi(C, Λi0) is
Variable (units) Value Equation kW (M2) 1 x 10-14 (S6.2)
PCO2 (Pa) 40.53 (S6.3) khCO2 (Pa·L/mol) 3.015 x 106 (S6.3)
KhCO2 1.7 x 10-3 (S6.4) Ka1 (mol/L) 4.266 x 10-7 (S6.5) Ka2 (mol/L) 4.677 x 10-11 (S6.6)
A [(S·cm2/mol)·(L/mol)1/2] 60.2 (S6.7) B (L/mol)1/2) 0.232 (S6.7)
Table S6.1 – Constants used in theoretical fits.
185
the concentration dependent molar ionic conductivity of a particular species, A and B are
constants determined by the ratio of cations to anions. From the total concentration of
dissolved ions in solution we can accurately determine the Debye screening length (κ-1)
for all experiments.
6.8.2 pH and Ionic Strength Dependent Surface Potentials
To model pH and ionic strength dependent SiO2 surface potentials, we found
literature measurements on quartz33 and an associated amphoteric site binding model34
that accurately capture values inferred from our U(h) data. We fit these results with a
convenient expression as,
Figure S6.1 – Empirical fit to literature data33 and model34 for quartz surface potential vs. pH and ionic strengths of 1mM (green squares), 10mM (red triangles), and 100mM (black circles). The lines are fits to the data given by Eq. (S6.8).
pH
3.0 4.5 6.0 7.5 9.0
/m
V
-100
-75
-50
-25
0
186
( , ) ( ) ( ) exp[ ( ) ]
136 111 1 exp 105
( ) 209 2.06 0.0129
( ) 0.313 0.358 1 exp 54.9
C pH a C b C b C pH
a C C
b C C
c C C
(S6.8)
where the units on all constants are either mV, pH, or M where appropriate. Figure S6.1
shows the expression in Equation S6.8 accurately captures literature data33 and model34
for quartz.
6.8.3 Potential Energy Profiles at Various Solution Conditions
As seen in section 6.4.7, experiments were conducted at a variety of pH and ionic
strength conditions to determine if there was a dependence of the gel layer on the solution
conditions. Figures S6.2 – S6.4 show the experimental data for pH values 7, 5.5, and 4,
and the net potential curves derived from fitting the only adjustable parameter, the steric
inverse decay length, .
Figures S6.2 – Ensemble TIRM measurements of potential energy profiles, U(h), at pH 7 with same format as pH = 10 data and fits in Fig. 6.2A. The ionic strengths range from [NaCl] = 0.1 – 20mM with exact values reported in Table 6.2.
h/nm
0 200 400 600 800
U(h
)/kT
-1.5
0.0
1.5
3.0
4.5
187
h/nm
0 200 400 600 800
U(h
)/kT
-1.5
0.0
1.5
3.0
4.5
Figures S6.3 – Ensemble TIRM measurements of potential energy profiles, U(h), at pH 5.5 with same format as pH = 10 data and fits in Fig. 6.2A. The ionic strengths range from [NaCl] = 0.1 – 20mM with exact values reported in Table 6.2
h/nm
0 125 250 375 500
U(h
)/kT
-1.5
0.0
1.5
3.0
4.5
Figures S6.4 – Ensemble TIRM measurements of potential energy profiles, U(h), at pH 4 with same format as pH = 10 data and fits in Fig. 6.2A. The ionic strengths range from [NaCl] = 0.1 – 5mM with exact values reported in Table 6.2.
188
6.8.4 Comparison of hm Derived from Different Gel Layer Scenarios
The most probable height, hm, can be estimated in one of two ways: through
fitting the net potential curve to experimental data or by fitting diffusivity data. Both
approaches were undertaken in this study in an effort to provide the most rigorous
estimate under all conditions examined. Using Equation 6.3 we were able to fit data from
experiments performed at pH 10 with different gel layer scenarios (see Section 6.4.5). By
testing the extreme cases of where the charge on the silica surface would lie, analysis
produced two different estimations of gel layer thicknesses and surface to surface
separations, where thinner layers were produced when the charge laid at the edge of the
gel layer (hm – Case 4), and thicker gel layers when the charge was at the interface
Figure S6.5 – The most probable separation at the potential energy minimum, and where the sum of the forces equal zero, for the potential energy profiles at pH = 10 in Fig. 6.2A. The x-axis shows estimates of hm from DLVO (closed symbols) and non-DLVO (open symbols) fits of Eq. 6.3 to the U(h) data in Fig. 6.2A for both Cases 3 (red triangles) and 4 (blue circles), and the y-axis shows estimates of hm from fits of Eq. 6.14 to the D(h) data in Fig. 6.2B. The x-axis is labeled as Lm and hm since L is the hydrodynamic separation scale in Case 3 and h is the hydrodynamic separation scale in Case 4. A 1:1 line shows when the two measurements are equivalent.
Lm - U(L)/nm , hm - U(h)/nm
10 100
hm
- D
(h)/
nm
10
100
189
between the gel layer and bulk silica (Lm – Case 3). The results were then compared to
heights determined by fitting diffusivity profiles with Equation 6.13 and are plotted in
Figure S6.5. A linear correlation indicated good agreement between the two methods of
finding the surface to surface separation, which supported not only the method of analysis
but also the degree of accuracy of our results.
6.9 References
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3. Derjaguin, B. V.; Landau, L., Theory of the stability of strongly charged lyophobic sols and of the adhesion of strongly charged particles in solutions of electrolytes. Acta Physicochim. URSS 1941, 14, 633-662.
4. Verwey, E. J. W.; Overbeek, J. T. G., Theory of the stability of lyophobic colloids. Elsevier: Amsterdam, 1948.
5. Vigil, G.; Xu, Z. H.; Steinberg, S.; Israelachvili, J., Interactions of Silica Surfaces. Journal of Colloid and Interface Science 1994, 165, (2), 367-385.
6. Adler, J. J.; Rabinovich, Y. I.; Moudgil, B. M., Origins of the Non-DLVO Force between Glass Surfaces in Aqueous Solution. Journal of Colloid and Interface Science 2001, 237, (2), 249-258.
7. Valle-Delgado, J. J.; Molina-Bolivar, J. A.; Galisteo-Gonzalez, F.; Galvez-Ruiz, M. J.; Feiler, A.; Rutland, M. W., Hydration forces between silica surfaces: Experimental data and predictions from different theories. The Journal of Chemical Physics 2005, 123, (3), 034708-12.
8. Grabbe, A.; Horn, R. G., Double-Layer and Hydration Forces Measured between Silica Sheets Subjected to Various Surface Treatments. Journal of Colloid and Interface Science 1993, 157, (2), 375-383.
9. Derjaguin, B. V.; Churaev, N. V., Structural component of disjoining pressure. Journal of Colloid and Interface Science 1974, 49, (2), 249-255.
10. Tadros, T. F.; Lyklema, J., Adsorption of potential-determining ions at the silica-
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11. Lanford, W. A.; Davis, K.; Lamarche, P.; Laursen, T.; Groleau, R.; Doremus, R. H., Hydration of soda-lime glass. Journal of Non-Crystalline Solids 1979, 33, (2), 249-266.
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13. Brennan, T.; Dalgliesh, R. M.; Lovell, M. R.; Richardson, R. M.; Barnes, A. C.; Sergeant, S. A., An X-ray and Neutron Reflection Study of Water Penetration into Fluorocarbon Doped Silica Gel Films†Langmuir 2003, 19, (19), 7761-7767.
14. Wu, H. J.; Bevan, M. A., Direct Measurement of Single and Ensemble Average Particle-Surface Potential Energy Profiles. Langmuir 2005, 21, (4), 1244-1254.
15. Russel, W. B.; Saville, D. A.; Schowalter, W. R., Colloidal Dispersions. Cambridge University Press: New York, 1989.
16. Bike, S. G.; Prieve, D. C., Measurements of Double-Layer Repulsion for Slightly Overlapping Counterion Clouds. Int. J. Multiphase Flow 1990, 16, (4), 727-740.
17. Dzyaloshinskii, I. E.; Lifshitz, E. M.; Pitaevskii, L. P., The general theory of van der Waals forces. Adv. Phys. 1961, 10, 165-209.
18. Bevan, M. A.; Prieve, D. C., Direct measurement of retarded van der Waals attraction. Langmuir 1999, 15, (23), 7925-7936.
19. Prieve, D. C.; Russel, W. B., Simplified Predictions of Hamaker Constants from Lifshitz Theory. J. Colloid Interface Sci. 1988, 125, 1.
20. Parsegian, V. A., Van der Waals Forces. Cambridge University Press: Cambridge, 2005.
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22. Milner, S. T., Polymer Brushes. Science 1991, 251, (4996), 905-914.
23. Milner, T.; Witten, T. A.; Cates, M. E., Theory of the grafted polymer brush. Macromolecules 1988, 21, (8), 2610-2619.
24. Eichmann, S. L.; Meric, G.; Swavola, J. C.; Bevan, M. A., Diffusing Colloidal Probes of Protein-Carbohydrate Interactions. Langmuir 2013.
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25. Murphy, T. J.; Aguirre, J. L., Brownian Motion of N Interacting Particles.1. Extension of Einstein Diffusion Relation to N-Particle Case. J. Chem. Phys. 1972, 57, (5), 2098.
26. Brenner, H., The Slow Motion of a Sphere Through a Viscous Fluid Towards a Plane Surface. Chem. Eng. Sci. 1961, 16, (3-4), 242-251.
27. Bevan, M. A.; Prieve, D. C., Hindered Diffusion of Colloidal Particles Very Near to A Wall: Revisited. J. Chem. Phys. 2000, 113, (3), 1228-1236.
28. Crocker, J. C.; Grier, D. G., Methods of Digital Video Microscopy for Colloidal Studies. J. Colloid. Interface Sci. 1996, 179, 298-310.
29. Beltran-Villegas, D. J.; Sehgal, R. M.; Maroudas, D.; Ford, D. M.; Bevan, M. A., Fokker–Planck Analysis of Separation Dependent Potentials and Diffusion Coefficients in Simulated Microscopy Experiments. J. Chem. Phys. 2010, 132, 044707.
30. Beltran-Villegas, D. J.; Edwards, T. D.; Bevan, M. A., Self-Consistent Colloidal Energy and Diffusivity Landscapes in Macromolecular Solutions. submitted 2013.
31. Kopelevich, D. I.; Panagiotopoulos, A. Z.; Kevrekidis, I. G., Coarse-grained kinetic computations for rare events: Application to micelle formation. J. Chem. Phys. 2005, 122, 044908.
32. Hummer, G., Position-dependent diffusion coefficients and free energies from Bayesian analysis of equilibrium and replica molecular dynamics simulations. New J. Phys. 2005, 7, 34.
33. Li, H. C.; De Bruyn, P. L., Electrokinetic and adsorption studies on quartz. Surface Science 1966, 5, (2), 203-220.
34. James, R. O., Characterization of Colloids in Aqueous Systems. Advances in Ceramics 1987, 21, 349-410.
35. Parsegian, V. A.; Weiss, G. H., Spectroscopic Parameters for Computation of van der Waals Forces. J. Colloid Interface Sci. 1981, 81, 285-289.
36. Wu, H.-J.; Pangburn, T. O.; Beckham, R. E.; Bevan, M. A., Measurement and Interpretation of Particle−Particle and Particle−Wall Interactions in Levitated Colloidal Ensembles. Langmuir 2005, 21, (22), 9879-9888.
37. Prieve, D. C., Measurement of Colloidal Forces with TIRM. Adv. Colloid Interface Sci. 1999, 82, (1-3), 93-125.
38. Oetama, R. J.; Walz, J. Y., Simultaneous investigation of sedimentation and diffusion of a single colloidal particle near an interface. J. Chem. Phys. 2006, 124, (16), 164713.
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39. Pagac, E. S.; Tilton, R. D.; Prieve, D. C., Hindered Mobility Of A Rigid Sphere Near A Wall. Chem. Eng. Comm. 1996, 148, 105.
40. Vold, M. J., The Effect of Adsoprtion on the van der Waals Interaction of Spherical Colloidal Particles. Journal of Colloid Science 1961, 16, 1-12.
41. Parsegian, V. A., Model for van der Waals Attraction between Sphereical Particles with Nonuniform Adsorbed Polymer. J. Colloid Interface Sci. 1975, 51, (3), 543-546.
42. Bevan, M. A.; Petris, S. N.; Chan, D. Y. C., Solvent quality dependent continuum van der Waals attraction and phase behavior for colloids bearing nonuniform adsorbed polymer layers. Langmuir 2002, 18, (21), 7845-7852.
43. Napper, D. H., Polymeric Stabilization of Colloidal Dispersions. Academic Press: New York, 1983.
44. Odiachi, P. C.; Prieve, D. C., Total internal reflection microscopy: Distortion caused by additive noise. Industrial & Engineering Chemistry Research 2002, 41, (3), 478-485.
45. Odiachi, P. C.; Prieve, D. C., Removing the effects of additive noise from TIRM measurements. Journal of Colloid and Interface Science 2004, 270, (1), 113-122.
46. Bevan, M. A.; Prieve, D. C., Forces and hydrodynamic interactions between polystyrene surfaces with adsorbed PEO-PPO-PEO. Langmuir 2000, 16, (24), 9274-9281.
47. Dagastine, R. R.; Bevan, M. A.; White, L. R.; Prieve, D. C., Calculation of van der Waals forces with diffuse coatings: Applications to roughness and adsorbed polymers. J. Adhesion 2004, 80, (5), 365-394.
48. Zhulina, E. B.; Klein Wolterink, J.; Borisov, O. V., Screening Effects in a Polyelectrolyte Brush: Self-Consistent-Field Theory. Macromolecules 2000, 33, (13), 4945-4953.
49. Fleer, G. J.; Stuart, M. A. C.; Scheutjens, J. M. H. M.; Cosgrove, T.; Vincent, B., Polymers at Interfaces. Chapman & Hall: New York, 1993.
50. Israelachvili, J. N., Intermolecular and Surface Forces. 2nd ed.; Academic Press: New York, 1992; p 450.
51. Zhulina, E. B.; Borisov, O. V.; Pryamitsyn, V. A.; Birshtein, T. M., Coil-Globule Type Transitions in Polymers. 1. Collapse of Layers of Grafted Polymer Chains. Macromolecules 1991, 24, 140.
193
Chapter 7:
Diffusion of Micron-Sized Gold Rods across Silicate Surfaces and through Slit Pores
Optical microscopy was used to track the translational and rotational diffusion of
micron sized gold rods over silicate surfaces in both two wall (confined) and one wall
(open) systems. Experiments were performed as a function of NaCl concentration (0-
5mM) to determine the effects on the absolute separation and rate of diffusion between
particles and walls. Brownian excursions were analyzed using novel tracking and analysis
algorithms developed in our lab. Calculations were performed using a string of beads
model to acquire equations for bulk and interfacial diffusion coefficients of cylindrically
shaped particles as a function of aspect ratio and absolute separation above a surface. The
equations derived from these simulations were used to fit experimental diffusion
coefficients from rods of various lengths by using a squared error function to fit the
height parameter of the translational diffusion data. The equations developed from our
simulation model were found to accurately capture the concentration dependent
separation of gold rods over silicate surfaces, for a one-wall system. This research has
allowed us to establish a simpler format to explain the translational and rotational
diffusion of cylindrical particles as a function of their length and height.
7.1 Introduction
Micro and nanomaterials of widely varying sizes, shapes, and compositions are
employed in a variety of industries including food and pharmaceuticals, optics,
194
electronics, manufacturing, and energy. With such widespread usage in everyday
consumer products one has to consider the environmental implications of such
technology. The fate of these engineered materials could be in our lakes and oceans if
released from point sources, or our bodies if used for medicinal or agricultural purposes.
Rod/cylinder-shaped, or anisotropic, particles are among those of interest for use in
various technologies. One especially important consideration is that these materials,
regardless or the environment they find themselves in will be interacting with any
number of surfaces. However, tracking the motion of rod-shaped micro and
nanomaterials as they interact with cellular or mineral surfaces can be difficult, and
obtaining ways of accurately measuring the diffusion and interaction energies of these
particles in a simple model that is easy to implement is an even more difficult task.
Many groups in the last century have used theoretical applications to determine
various coefficients and equations related to the diffusion of anisotropic particles. In
1915, G. B. Jeffery attempted to solve for the motion of a viscous fluid caused by the
rotation of axisymmetric particles (ellipsoid, circular disk, 2 non-concentric spheres, and
a sphere with a plate).1 Though thorough in his calculations, his approach attacked the
problem from the standpoint of the liquid motion and not the motion of the particle, but it
did take into consideration the extra resistance that would be imparted when a particle
was close to a surface. By the 1950s two different approaches were being undertaken:
determining the diffusion rates of a cylinder-shaped particle in the bulk medium2 and
between or next to a wall.3Both methods were now approaching the problem by
examining the drag on the cylinder to calculate the translational and rotational motion of
the particle. However, these equations were very long and complex, often involving any
195
assortment of derivatives, integrals, and matrices, and they also were different for each
particle shape and shear flow through the medium. Howard Brenner attempted to unify
the variety of equations by creating a general theory to explain the rheological properties
of rigid axisymmetric Brownian particles (spheroids, long slender bodies, dumbbells, and
circular disks).4
Using an experimental approach, Broersma5, 6 attempted to correct discrepancies
found in earlier experimental findings of lengths for tobacco mosaic viruses (TMV) that
were determined by solving for their rotational diffusion coefficients. The author
concluded that the discrepancy arose from a geometric problem that was not being
accounted for. By creating end corrections that would assume a cylinder with a flattened
top and bottom, and adding these to an updated version of existing theories, Broersma
was able to extract rotational and translational diffusion coefficients. In doing so, the
author was able to produce a table of values that came much closer to lengths for TMV
found using electron microscopy.
Broersma’s work was used as the standard calculations for rod-like particles until
Tirado and de la Torre7published their equations in 1979. They modeled rigid cylindrical
particles with concentric beads, and use their symmetry aspects to simplify the
calculation of a translational friction tensor. A cylindrical coordinate system was
employed to reduce the number of individual friction elements one must take into
account, using sets of symmetry elements instead, thereby allowing for a greater number
of total elements in their model and wider ranges of aspect ratios (p = L/d) to be
examined. Their results were similar to Broersma’s as p approached infinity, but as p
decreased their results diverged so much that Tirado stated that Broersma’s work “should
196
be disregarded as representative of the frictional behavior of finite cylinders.” Broersma
soon corrected his original work,8 and these two groups are frequently cited when
examining the diffusion behavior of cylindrically shaped particles in the bulk.
Computational simulations of cylindrical particles using various models9-11
greatly increased the knowledge of these hydrodynamic interactions. Aragon and
Flamik11 created tables of equations that only required the input of the correct
dimensional qualities of the desired component that were much easier to implement than
many previous papers. A study by Mukhija and Solomon12 combined experiment and
simulation, using confocal microscopy to study fluorescent poly(methyl methacrylate)
rods. By altering the viscosity of the medium, it allowed them to explore the 3-
dimensional degrees of freedom by computing the azimuthal and polar coordinates and
angles of the suspended rods. Good agreement was found between their experiments and
previously published literature on diffusion of rods in a bulk medium.
Work on cylinders next to or confined by walls was a question being explored
simultaneously. Experimental13, 14 and theoretical15, 16strides were made in determining
the influence of a wall on the drag and torque acting on a single rod-shaped particle
(using a string of beads model). Padding and Briels17 used molecular dynamics
simulations to examine the friction on a rod-shaped particle of p = 10 as a function of
distance and angle with a planar surface. Their results suggested that friction does not
become significant until the distance is on the same order as the rod. Their results were
used to capture experiments of carbon nanofibers tethered to the surface at one end to test
very small separation distances.18 Once tethered, all diffusion was purely rotational, and
197
the authors suggest that either diffusion is caused by the tethering action itself or a stick-
slip adherence to the surface.
All of the previously mentioned studies have in some way helped contribute to
our current understanding of the hydrodynamics for cylinder-shaped particles. This is
important for many biological and industrial purposes. In biology, studying the diffusion
behavior of model systems, such as the tobacco mosaic virus (TMV),19-22fd virus,23, 24 or
various bacteria25, 26 can bring insight on the hydrodynamic interactions of these particles
in a bulk fluid or near a surface. It has been suggested that cylindrical particles show
enhanced circulation through blood vessels,27 that coupled with model systems research
can open doors to explore how biological moieties such as DNA fragments,28kinesin
molecules,29 or actin filaments30 translate through the body. For industrial purposes,
understanding how polymer and micelles,31 cellulose whiskers,32 and carbon nanotubes33-
35 diffuse is important for building better composite materials and electronic devices. It is
also important to understand their diffusion in thin films and interfaces36-38 for the
advancement of devices such as semiconductors, antireflective coatings, and thin film
batteries.
This study examined the diffusion behavior of varying length micron-sized gold
rod particles as they interact with silicate surfaces under various solution conditions. New
tracking algorithms were developed to analyze videos of particles taken with an optical
microscope. Lengths, as well as translational and rotational diffusion coefficients were
experimentally determined for each individual rod in an ensemble. These coefficients
were plotted as a function of aspect ratio and fit using equations generated from
simulations with a string of bead model to determine the hydrodynamic interactions at the
198
bulk and interfacial separation distances. The distances determined for the particle height
above a surface was compared to theoretical potential energies to gather information
regarding surface potential heterogeneities on the gold particles.
7.2 Theory
7.2.1 Potential Energy Profiles
Theoretical models of the potential energy for a rod-plate interaction, U(z),
can be calculated by the addition of contributing potentials as,
( ) ( ) ( )G EU z U z U z (7.1)
where the subscripts refer to the gravitational (G) and electrostatic (E) interactions, z is
the center particle to surface distance seen in Figure 1 (z = h + a) where h is the particle
surface to planar surface separation distance and a is the radius of the rod. The
gravitational potential is associated with a body force, whereas the electrostatic potential
is associated with surface forces, but both are dependent on the length of the rod.
The gravitational potential energy of each rod depends on its length, L, and its separation
from the wall, z, multiplied by its buoyant weight, G, as given by,
2( ) ( ) ( ) ( )G p fU z Gz mg h a a L g h a
(7.2)
where m is buoyant mass, g is acceleration due to gravity, and rp and rf are particle and
fluid densities respectively.
The interaction between the electrostatic double layers on a rod and plate depend
on how thick they are. For thin double layers (κa>>1), the interaction can be described
199
from the superposition, non-linear Poisson-Boltzmann equation for a 1:1 monovalent
electrolyte,39 and can be used in conjunction with the Derjaguin approximation to give
the rod-wall potential as,40
exp ( )
2E
aU z LB h a
(7.3)
2
64 tanh tanh4 4
p we ekT
Be kT kT
(7.4)
1 222( )A
i ii
e Nz C
kT
(7.5)
where κ is the Debye screening length, ε is the solvent dielectric constant which is the
product of permittivity in a vacuum (ε0) and the relative permittivity of water (εw), e is the
elemental charge, ψp and ψw are the surface potentials of the particle and the wall
respectively, NA is Avogadro's number, Ci is electrolyte molarity, and zi is ion valence.
For thick double layers (κa~1) the above expression will generally over-estimate
the electrostatic interaction since the Derjaguin approximation no longer holds. We
instead model the rod as a rigid chain of touching spheres, and approximate the potential
energy for a rod levitated above wall by summing up for the potential energy of the
spheres composing the rod. This means that the net potential uses the geometry of a series
of spheres to determine the gravitational contribution,
3,
1
4(z) ( )
3
p
G sphere s f ii
U a gz
(7.6)
and the electrostatic repulsion contribution given as,
200
,
1
(z) exp( ( ))p
E sphere ii
U B z a
(7.7)
where zi is the mass center for ith particle composing the rod, and B is the prefactor for the
electrostatic repulsive interactions based on the linear superposition approximation
(LSA), which can be used for thick double layers, given as,
2 22
42 4
kT a eB
e h a kT
(7.8)
The electrostatic repulsion for a series of spheres from Equation 7.7 can be related to the
UE(z) for a rod through the aspect ratio, p,
, ,( ) ( )E rod E sphereU z pU z (7.9)
UE,sphere(z) is the result of an integration over all spheres in the rigid chain. More detail
regarding this calculation can be found in the Supplemental Information.
The most probably height (hm) of a rod-shaped particle above a planar surface can
be determined by taking the derivative of the net potential and solving for h. The value of
hm calculated from either approximation using a form similar to,
1 lnm
ABLh
G
(7.10)
where L is the length, G is the prefactor from the equation for the gravitational potential,
B is the prefactor from electrostatic repulsion, and A is a constant that contains geometric
corrections. However, it is likely that as a rod undergoes Brownian motion it will sample
many heights. We can determine this height average (havg) by integrating over a range of
heights that may be sampled as,
201
0
0
( )
( )
n
avg n
hp h dh
h
p h dh
(7.11)
where p(h) is the probability distribution of heights sampled obtained from the net
potential energy given by,
( )( ) exp NETu h
p hkT
(7.12)
7.2.2 Bulk Diffusion Modes
Theoretical equations for the parallel and perpendicular translational motion of a
rod-shaped particle freely diffusing in the bulk, DB(p), were derived for rods of varying
aspect ratios (p) using Brownian dynamics (BD) simulations. These equations consist of
Stokes-Einstein type diffusion coefficient, D0, multiplied by a factor dependent on the
aspect ratio of the particle, f(p), where the bulk parallel diffusion coefficient is given by,
|| 0|| ||( ) ( )BD p D f p (7.13)
0|| 2
kTD
pd
(7.14)
2
|| 2
0.4536 1.772 41.5( ) ln( )
34.38 18.96
p pf p p
p p
(7.15)
and the perpendicular bulk diffusion coefficient is given by,
0( ) ( )BD p D f p (7.16)
202
0 4
kTD
pd (7.17)
2
2
0.3604 28.36 72.63( ) ln( )
36.29 34.9
p pf p p
p p
(7.18)
where h is the fluid medium viscosity, and p is the particle aspect ratio where L is the
length and d the diameter.
7.2.2.1 Bulk Translational Diffusion Coefficients
A 2-dimensional translational diffusion coefficient for the motion of a rod
in bulk medium can be established by combining the parallel and perpendicular
modes to achieve,
|| ( ) ( )( )
2B B
T
D p D pD p
(7.19)
7.2.2.2 Bulk Rotational Diffusion Coefficients
The same set of theoretical equations can be derived for the rotational
motion of a rod-shaped particle freely diffusing in the bulk, DB(p), as given by,
0( ) ( )BR R RD p D f p (7.20)
0 3
3
( )R
kTD
pd
(7.21)
3 2
3 2
1.373 19.39 148.1 265.2( ) ln( )
56.43 54.35 268.4R
p p pf p p
p p p
(7.22)
203
7.2.3 Interfacial Diffusion Modes
A translational diffusion coefficient can be obtained for the parallel motion for a
rod of aspect ratio, p, as a function of its particle surface-wall separation, h, above a
planar surface by multiplying the bulk diffusion coefficient, DB(p), by a correction factor
dependent on h and another correction factor dependent on p in the forms,
|| || || ||( , ) ( ) ( )BD p h D f h g p (7.23)
3 2
|| 3 2
0.9909 0.3907 0.1832 0.001815( )
2.03 0.3874 0.07533
z a z a z af h
z a z a z a
(7.24)
|| ( ) 1.1669 0.0091g p p (7.25)
and the translational perpendicular diffusion coefficient is,
( , ) ( ) ( )BD p h D f h g p (7.26)
3 2
3 2
0.9888 0.788 0.207 0.004766( )
3.195 0.09612 0.1523
z a z a z af h
z a z a z a
(7.27)
|| ( ) 1.2239 0.0120g p p (7.28)
For a rod of aspect ratio, p, a second set of translational diffusion coefficients can
be obtained for a scenario where a rod is diffusing between two parallel plates of
separation, Δ, in the forms,
11 1
|| || || || ||( , ) ( ) ( ) (( ) 2 ) 1BD p h D f h g p f a z a (7.29)
204
11 1( , ) ( ) ( ) (( ) 2 ) 1BD p h D f h g p f a z a
(7.30)
7.2.3.1 Interfacial Translational Diffusion Coefficients
A 2-dimensional translational diffusion coefficient for the motion of a rod near a
flat surface can be established by combining the parallel and perpendicular modes
to achieve,
|| ( , ) ( , )( , )
2T
D p h D p hD p h
(7.31)
7.3.2.2 Interfacial Rotational Diffusion Coefficients
The rotational diffusion coefficient for a given rod-shaped particle as
function of its aspect ratio and height above the planar surface is given by,
( , ) ( ) ( )R BR R RD p h D f h g p (7.32)
3 2
3 2
0.998 131.1 21.25 0.01275( )
128.7 121.1 2.897R
z a z a z af h
z a z a z a
(7.33)
( ) 1.154 0.0096Rg p p (7.34)
and for a rod of diffusing between two parallel plates of separation, Δ,
11 1( , ) ( ) ( ) (( ) 2 ) 1R BR R R RD p h D f h g p f a z a
(7.35)
205
7.3 Materials and Methods
7.3.1 Colloids & Surfaces
Potassium hydroxide, sodium chloride (both from Fisher Scientific) and colloidal
SiO2 (nominal diameter of 2.34 microns, Bangs Laboratories) were used as received and
without further purification. Gold rods were synthesized by electrochemically growing
them to a prescribed length in the pores of an anodic aluminum oxide membrane. The
alumina template was then dissolved in base, and the rods were freed from a thin film of
gold using nitric acid.41 Zeta potential (ζ) was used as an estimation of the surface
potential for gold rods (ψp), and was measured at four ionic strength conditions using a
Malvern ZetaSizer Nano-ZS. Three sets of five separate measurements were taken per
sample, each measurement consisting of 10 – 15 scans, to create an average and standard
deviation. The Smoluchowski model is used to determine the zeta potential from
electrophoretic mobility measurements.
Table 7.1 – Constants used in theoretical fits.
Variable (units) Value Equation a (μm) 0.3 (7.2), (7.3), (7.6), (7.7), (7.8), (7.10)
ρp (g/cm3) 19.3 (7.2), (7.6)
ρf (g/cm3) 1.00 (7.2), (7.6)
ε0 (farad/m) 8.852 x 10-12 (7.4), (7.5), (7.8)
εw 78 (7.4), (7.5), (7.8)
T (K) 294 (7.4), (7.5), (7.8), (7.12), (7.14), (7.17), (7.21)
e (C) 1.602 x 10-19 (7.4), (7.5), (7.8)
η (Pa·s) 1.002 x 10-3 (7.14), (7.17), (7.21)
Δ (μm) 2.1 (7.29), (7.30), (7.35)
206
Long glass microscope coverslips (Corning, 24 x 60 mm) were wiped clean with
lens paper, then sonicated for 30min in acetone and30min in isopropanol before being
soaked in Nochromix overnight. Small glass coverslips (Corning, 18 x 18 mm) were
wiped with lens paper and placed directly into Nochromix. Coverslips were rinsed with
deionized (DI, 18.3MΩ) water and soaked in 0.1M KOH for 30min, then rinsed with DI
water again and dried with nitrogen before use.
Particle solutions were prepared by making sodium chloride solutions of desired
concentrations and measuring the pH and conductivity. A colloidal silica spacer solution
was created by diluting 0.5μL of the stock silica suspension in 4mL of DI water.
Colloidal gold rod dispersions were prepared by diluting 60μL of the electrochemically
prepared stock dispersion into 136μL of the desired pH and ionic strength solution, and
adding 4μL of silica spacer solution. This vial was then sonicated for 15min before use.
Confined sample cells were created by dropping 10μL of the gold/silica spacer
particle mixture onto the center of a clean and dried long coverslip. A small coverslip was
placed on top of the droplet to sandwich the particle solution between the two walls. Lens
paper was then used to wick away extraneous solution from between the walls until
enough solution has been removed to cause interference patterns to appear. Once this
occurred, the two coverslips were sealed together using Loctite Epoxy.
O-ring sample cells were constructed by using vacuum grease (Corning) to adhere
a 5mm ID Viton O-ring (McMaster Carr) to a cleaned long coverslip. An aliquot of the
sample used in the confined experiments was diluted using the appropriate NaCl stocks,
and then sonicated for 15min. 120μL of the newly prepared gold rod dispersion was
207
pipetted into the O-ring, and a clean small coverslip was placed on top and pressed into
the vacuum grease around the O-ring to seal the sample cell.
7.3.2 Ensemble Video Microscopy
Two wall (confined) experiments were performed using a Zeiss Axioplan 2
upright optical microscope with a 63x objective. One wall (O-ring) experiments were
performed on a Zeiss Axio Observer A1 inverted microscope with a 63x objective.
Particle diffusion was recorded with a 12bit CCD camera (Hamamatsu ORCA-ER)
operated in 4-binning mode at ~27.6fps for 30,000 frames. Image analysis algorithms
coded in FORTRAN were used to track the lateral and rotational trajectories of each
particle.
7.3.3 Image Analysis
A new image analysis algorithm was coded in FORTRAN to determine the
translational and rotational diffusion of rod-shaped particles from video microscopy
(VM) experiments. The rods block the incident light and appear as dark regions on the
otherwise gray image as shown in Figure 7.1A. The grayscale of each image is first
inverted to make the rods appear as white regions on a black background as shown in
Figure 7.1B. The image can then be thresholded, as shown in Figure 7.1C, to identify the
coordinates of each point on the backbone of the rods. To discriminate between multiple
rods in the image, the coordinates found from thresholding are grouped using a search
algorithm to identify neighboring coordinates. To find points neighboring a coordinate i,
a 25 square pixel box is centered on coordinate i. All coordinates within this box are
labeled as neighbors of coordinate i and therefore a part of the same rod. The search box
si
al
tr
id
ca
ize used wa
lgorithm wa
To de
racked over
dentified, th
alculated as,
Figure 7.1 – inverted versioon the invertepoints (D). Afunction of tim
as found em
s able to effi
etermine the
time. With
he coordinat
,
Cropped (120 on of the sameed version of tlso included a
me to illustrate
mpirically as
ficiently proc
translationa
h the coordi
tes of the c
pixel x 120 pe image (B), ththe image (C)are plots of thehow the tracki
208
individual
cess large set
al diffusivity
inates of ea
center of m
ixel) and scalehe result after t, and the orige center of maing algorithm w
rods were i
ts of images
y of each rod
ach point on
mass of each
ed 2x: the origthe thresholdin
ginal image noass position (Eworks.
identified ac
s.
d, the center
n individual
h rod, xcm
ginal experimeng algorithm how with markeE) and angular
ccurately an
r of each rod
l rods, xi an
and ycm, ca
ntal image (A)has been perfored centers and r rotation (F)
nd the
d was
nd yi,
an be
), an rmed
end as a
209
n
ii
cm
xx
n
(7.36)
n
ii
cm
yy
n
(7.37)
To determine the rotational diffusivity of each rod, the position of the end points
of the rod were tracked over time in polar coordinates. The root mean squared distance of
each point on the rod from the center of mass, ri, can be calculated as,
2 2( ) ( )i cm i cm ir x x y y
(7.38)
The center of mass of each rod is indicated in Fig 7.1D with a red cross. The angular
position of each point on the rod with respect to the center of mass, i, is calculated as
arctan( )cm i
icm i
y y
x x
(7.39)
To obtain unique polar angles for each point on the rod ranging from 0 to 2π, the
arctan2 function in FORTRAN is used to account for the quadrant each coordinate is
located and 2π is added when i < 0. The end points of the rod are then determined based
on the polar coordinates of each point on the backbone of the rod. The coordinate i in
quadrant 1 or 4, where 0 < i < π/2 or 3π/2 < i < 2π, with the largest ri is labeled as one
endpoint and the coordinate j in quadrant 2 or 3, where π/2 ≤ j ≤ 3π/2, with the largest rj
is labeled as the second endpoint. Including both a distance and orientation criteria in the
endpoint determination ensures that two unique endpoints are found on opposite ends of
210
the rod and are shown in Fig 7.1D as green crosses. Sample changes in radii and θ that
are tracked with this analysis method are plotted in Figures 7.1E and 7.1F.
7.3.4 Measuring System Noise
Inherent in any system is noise from fluctuations in light intensity or camera
speed and vibrations due to thermal changes. To measure any influence of noise on the
experimental data, stuck particles were imaged at binning 4 and binning 1 for a set
duration of time and analyzed using the above-mentioned tracking codes. Figure S7.1
shows the length distributions and angles of θ observed for colloidal rods that were
irreversibly bound to the bottom surface of the sample cell. The error measured in this
manner was accounted for by including error bars on the diffusivity measurements
equaling one pixel length in binning 4 (385nm) to the aspect ratio.
7.3.5 Calculations of Position-Dependent Diffusivities
The height-dependent diffusivities obtained in Equations 7.23 – 7.35 were
calculated using a rigid chain of spheres to model the rod-shaped particle. The various
resistance forces acting on each individual sphere in the chain were calculated for a rod
sitting parallel to a flat surface. First, translational and rotational diffusivities at an
infinite distance from the surface were calculated for chains of varying length (i.e., aspect
ratios, p). These diffusivities were then used as normalization factors for finite values of h
for rods of different p. Two correction factors were introduced for the chain of spheres
diffusing near a surface: f, which is a height-dependent factor that approaches 1 as h
approaches infinity and 0 at contact; and g, which corrects for the rod length for surface
to surface separations less than ten radii. Figure 7.2 illustrates the important variables
n
ca
ecessary for
alculations c
Figure 7.2 –pertinent scale
r these calc
can be found
– Comparison es and variable
culations in
d in the Supp
of the schems
211
the two sc
plemental Inf
matics used for
chematics. M
formation.
r experiments
More detail
and calculati
regarding
ions, including
these
g all
212
7.4 Results and Discussion
7.4.1 Measuring the Mean Squared Displacement for Translational and Rotational
Diffusion
The tracking algorithms we created produce output data files with the
translational displacement information in the x and y directions for the center of mass of
each rod in frame, as well as the rotational displacement for each end of the rod in the x-y
plane (θ). This data can be plotted as a function of time and fit with a linear regression to
obtain the translational and rotational diffusion coefficients for a rod of given length.
Histograms of the lengths sampled by each rod while remaining in the experimental
window were used to obtain the weighted average length, which was then used to
determine the aspect ratio, p. Translational and rotational displacements for systems
where the rods interact with a single wall (top) and in an arrangement where the rods are
confined between two parallel walls (bottom) in a solution of 0.1mM NaCl are plotted as
a function of time in Figure 7.3. The trend exhibited by both datasets shows shorter rods
translating and rotating more quickly than their longer counterparts. It can be noted that
this trend is followed more strictly by the rotational diffusion than the translational
diffusion. This arguably makes sense considering the energy penalty for rotating a body
at its center would increase dramatically as the aspect ratio increased, whereas only the
perpendicular translational motion would be greatly affected by a longer body.
Comparing the two experimental geometries, we can see that the colloidal rods in
the more open experimental system with only one wall exhibit faster diffusion rates in
their translational motion than their confined counterparts. The addition of a second wall
above the rods to form a closed system confines the rods to a window of space about 2μm
213
high. This confined arrangement introduces a second surface for the rods to interact with
and be electrostatically repelled from. The presence of electric double layers on both
walls and the surfaces of the rods in close proximity can help to explain the slower
diffusion rates observed for the two-wall geometries. However, it is noticed that this
MS
D,
m2
0.00
0.04
0.08
0.12
0.162.03um4.02um4.05um4.36um4.59um4.92um5.11um5.47um5.58um5.61um
A
Time, ms0 100 200 300 400
MS
D,
m2
0.00
0.02
0.04
0.06
0.08
0.10 3.49um3.90um4.65um4.84um4.96um5.53um6.26um
C
Time, ms0 100 200 300 400
MS rad
2
0.00
0.02
0.04
0.06
0.08
0.103.49um3.90um4.65um4.84um4.96um5.53um6.26um
D
MS , rad
2
0.00
0.02
0.04
0.06
0.084.02um4.05um4.36um4.59um4.92um5.11um5.47um5.58um5.61um
B
Figure 7.3 – Mean squared displacement data plotted as a function of time for the translational (A and C) and rotational (B and D) trajectories of varying length colloidal rods in an open system (top) and confined system (bottom). Closed and open symbols represent actual experimental data acquired from the tracking algorithms and solid lines represent the best fit linear regression to the first five data points in each set.
214
effect is much less pronounced for the rotational diffusion, where the two plots actually
show very similar rates of diffusion for both systems.
Occasionally, deviations were observed from the general trend where shorter rods
diffuse faster. These deviations could be caused by irregularities in the cylindrical shape
of the rods, where a slight curvature in the rod could influence the rotational diffusion.
When a perfectly straight cylinder rolls along the long axis we are unable to distinguish
that movement with our technique. However, if the rod is slightly bent or curved, the end
would look to our tracking codes as if it were rotating more quickly when the rod rolls
and the end being tracked jumps over a measurable distance. This rolling can and has
been observed in rods that showed a curved structure. Deviations could also arise from
heterogeneities in the surface potentials of the silicate surfaces or on the gold rods. A
more negative surface charge on one rod would initiate more electrostatic repulsion
between it and the walls, thereby allowing the rod to achieve a greater surface to surface
separation and potentially a faster translation than one may expect for a rod of that length.
Lastly, deviations may result from the tracking algorithms which assign the center and
end points of each rod (see Figure 7.1). Experiments were performed at binning 4 to
achieve resolution without sacrificing recording speed and creating immense file sizes.
Pixel resolution at binning 4 is 385nm/pixel, meaning that as a rod rotates and translates,
a single pixel may be added or removed from the ends of a rod in each frame depending
on its orientation. This could cause errors in the estimation of rod length, as well as the
position of each end point which are used to calculate the rotational diffusion. This is
why the length of each rod is calculated from a weighted average.
215
7.4.2 Effects of Ionic Strength on Diffusion Coefficients
Experiments in confined and open geometries were performed at multiple ionic
strength conditions to determine if there exists a dependence of ionic strength on either
the translational or rotational diffusion. The resulting diffusion coefficients from the
linear fits to mean square displacement data for translational and rotational data were
plotted as a function of p for both experimental configurations at all ionic strengths
examined. Diffusion coefficients were then fit with the theoretical lines generated by
Equations 17 – 29 for interfacial diffusion coefficients, where the only adjustable
parameter was the height of the gold rod above a surface (h). The highest (hmax, dash),
lowest (hmin, dot-dot-dash), and best fit (hm, solid) lines are plotted in Figure 7.4 with the
corresponding experimental data points for different ionic strength conditions. Best fit
lines were achieved by using a least squares error function to find the particle-surface
separation that would result in the lowest error. The measured surface to surface
separation values can be found in Tables 2 and 3 for one-wall and two-wall geometries,
respectively.
We could see from Figure 3 that the one-wall experiments very clearly show
faster translational diffusion coefficients at short aspect ratios. However, comparing the
resulting diffusion coefficients from the two experimental geometries over the same
range of p (Figure 4) one can see that the one-wall system does exhibit greater diffusivity
than that seen in the confined geometries. As was seen in the mean squared displacement
data for rotational motion in Figure 3, very similar rotational diffusion coefficients were
observed for both systems over the same range of p, though much faster rotation was
216
observed for smaller rods. The experimental parameters for each system configuration
can be found in Tables 2 and 3.
The general trend for both systems shows that with increasing ionic strength
(decreasing inverse Debye screening length, κ-1) rods of similar aspect ratios show a
DR , rad
2/ms
0.0
5.0e-5
1.0e-4
1.5e-4
2.0e-4
2.5e-4DI water0.1mM NaCl1mM NaCl5mM NaCl
B
Aspect Ratio10 12 14 16 18 20 22
DR , rad
2/ms
0.0
5.0e-5
1.0e-4
1.5e-4
2.0e-4
2.5e-4DI water0.1mM NaCl1mM NaCl5mM NaCl
D
DT, m
2/m
s
0.0
5.0e-5
1.0e-4
1.5e-4
2.0e-4
2.5e-4DI water0.1mM NaCl1mM NaCl5mM NaCl
A
Aspect Ratio10 12 14 16 18 20 22
DT, m
2/m
s
0.0
5.0e-5
1.0e-4
1.5e-4
2.0e-4
2.5e-4DI water0.1mM NaCl1mM NaCl5mM NaCl
C
Figure 7.4 – Translational (A and C) and rotational (B and D) diffusion coefficients determined from the fits to mean squared displacement data for each ionic strength condition examined is plotted as a function of rod aspect ratio for colloidal rods in an open system (top) and confined system (bottom). The highest (hmax, dash), lowest (hmin, dot-dot-dash), and best fit (hm, solid) lines are plotted for each data set.
217
decrease in their translational diffusion coefficients. Fits to position dependent
diffusivities show that the rods exhibit smaller and smaller surface to surface separations
as the electrostatic repulsion decreases with increasing ionic strength. This is represented
by the value of h necessary to fit the theoretical line to the experimentally derived
diffusion coefficients. The decrease in separation is directly related to the increase in
ionic strength, which systematically depresses κ-1 through screening effects, and
simultaneously reduces the surface potential on both silicate and gold surfaces. Both of
these effects allow for the two surfaces to approach closer to one another before repulsion
is initiated.
Once again, the differences displayed by the rotational diffusion coefficients at
various ionic strengths are minimal. This assertion applies to both experimental
geometries examined. These results indicate that the drag imposed by a second wall, as
well as the height at which the rod sits above a surface, has a discernable effect on the
[NaCl] (mM) κ-1 (nm) hmin,t (nm) hmax,t (nm) hmin,r (nm) hmax,r (nm) hm (nm)0.03 (DI) 54.5 180 375 285 750 307
0.13 26.7 172.5 262.5 150 345 207 1.06 9.3 127.5 187.5 202.5 345 145.5 5.14 4.3 31.5 82.5 112.5 232.5 45
Table 7.2 – Measured values used in the fitting of one-wall experimental data.
Table 7.3 – Measured values used in the fitting of two-wall experimental data.
[NaCl] (mM) κ-1 (nm) hmin,t (nm) hmax,t (nm) hmin,r (nm) hmax,r (nm) hm (nm)0.03 (DI) 54.5 127.5 184.5 150 244.5 153
0.13 26.7 112.5 154.5 135 168 123 1.06 9.3 93 129 142.5 187.5 111 5.14 4.3 28.5 49.5 60 75 43.5
218
parallel and perpendicular translational motion of anisotropic particles. However, these
same parameters show very little effect on the rotational motion of the rods in the x-y
plane. These two observations have been seen with Stokesian dynamics simulations of
particle clusters,42 which is similar to the string of beads model used for our own
calculations. The collective diffusive modes simulating translation of the cluster slowed
with decreasing particle-wall separation, whereas the relative diffusive mode simulating
rotation showed a relatively uniform diffusion over a range of heights with very small
fluctuations.
7.4.3 Comparing Diffusion Coefficients from Experiment and Theory
To determine how close our theoretical calculations were to the measured values,
translational diffusion coefficients were calculated using the values of hm derived from
various wall surface potentials from both the Derjaguin and linear superposition
approximations. Figure 7.5 illustrates the measured data for the one-wall geometries
(points) and the calculated diffusion coefficients (lines) at three wall surface potentials
(ψw = -10mV, -50mV, -100mV). The resulting diffusion coefficients from each ionic
strength condition were ratioed to the bulk diffusion values. As the ionic strength
increases, the ratio should drop as the surface to surface separation becomes farther from
infinity. For lower ionic strength conditions the values obtained from LSA were used;
and at higher ionic strengths where κ-1 is less than 10nm, the Derjaguin approximation
was employed. We see that the theoretically calculated values show relatively good
agreement with our measured diffusion coefficients. Though the values of hm calculated
at each surface potential increased as the surface potential became more negative, the
values for -50mV and -100mV showed only small differences, especially as the ionic
219
strength increased. This indicates that the surface potentials become relatively insensitive
at higher ionic strengths and values greater than -50mV. The calculated values of hm and
havg (the integral average height from Equation 7.11 can be found in Table 7.4.
Aspect Ratio (p)0 5 10 15 20 25
Dif
fusi
on
Co
effc
ien
t R
atio
, DT(m
easu
red
)/D
T(b
ulk
)
0.0
0.2
0.4
0.6
0.8
1.0
DI water0.1mM NaCl1mM NaCl5mM NaCl
Figure 7.5 – Measured diffusion coefficients from one-wall experiments ratioed to the calculated diffusion coefficients from values of hm obtained from Derjaguin and linear superposition approximations at various ionic strength conditions.
[NaCl] (mM)
κ-1 (nm)
ζ (ψp) (mV)
hm (nm) ψw = -10mV
hm (nm)ψw = -50mV
hm (nm) ψw = -
100mV
havg (nm) ψw = -10mV
havg (nm) ψw = -50mV
havg (nm) ψw = -
100mV 0.03 (DI)
54.5 -24 412 / 385
496 / 360
523 / 390 453 / 320 538 / 402 564 / 429
0.13 26.7 -24 231 / 165
272 / 195
285 / 210 278 / 200 319 / 240 332 / 250
1.06 9.3 -20 93.2 / 75 107 / 75 112 / 90 153 / 102 168 / 114 168 / 140 5.14 4.3 -15 46.1 / 45 52.6 / 45 54.7 / 45 99.3 / 87 106 / 90 109 / 97
Table 7.4 – Calculated values of the most probable and average heights from the Derjaguin and linear superposition approximations (Derjaguin/LSA) used to find diffusion coefficients.
220
7.5 Conclusions
Video microscopy was used to track the translational and rotational diffusion of
colloidal gold rods as a function of ionic strength. Two systems were investigated: an
“open” geometry where the rods interacted with a single planar surface, and a “confined”
geometry where rods diffused between two parallel surfaces in a slit pore. Newly
developed video tracking algorithms allowed us to monitor rod diffusion and determine
the length of individual rods in the frame. However, pixel resolution was responsible for
a variety of lengths being calculated for each rod, as well as small defects such as
curvature affected the calculation of the rotational diffusion coefficients. Using a string-
of-beads model enabled the calculation of translational and rotational diffusion
coefficients of rod-shaped particles as a function of aspect ratio and surface to surface
separation in the bulk and near a planar surface. Fits to these curves showed that the
average surface to surface separation decreased with increasing ionic strength for both
system configurations, where the confined geometry slows the translational diffusion but
not rotational. In fact, it was found that fits to the translational diffusion were a much
more sensitive metric of the surface to surface separation than fits to the rotational
diffusion, providing evidence for similar results seen with Stokesian dynamics
simulations of particle clusters. Electrostatic potentials modeled by the Derjaguin
approximation (high ionic strength conditions) and LSA (low ionic strength conditions)
for a rod-planar surface interaction were used to calculate surface to surface separations
for one-wall geometries. Using zeta potential as an estimation of the particle surface
potential, diffusion coefficients calculated from hm were satisfactorily close to our
experimental results, thereby confirming the legitimacy of our theory.
221
7.6 Acknowledgements
We acknowledge financial support by the National Science Foundation (CHE-
1112335, CBET-1066254). We would also like to thank Wei Wang and Tom Mallouk
from Pennsylvania State University for giving us samples of the gold rods to use in these
studies.
7.7 Supplemental Information
7.7.1 Numerical Calculation of the Electrostatic Repulsion between a Rod in a Parallel
Configuration and a Wall
A rod can be modeled as a rigid linear chain of touching spheres, and the electrostatic
interaction between rod and wall can be approximated by summing up all of the sphere-
wall interactions based on the linear superposition approximation (LSA) for thick double
layers as,
,( ) ( )E E sU h pU h (S7.1)
where p is the aspect ratio. UE,s is the electrostatic repulsion potential between a single
sphere and a wall, which is obtained via integration of the force along the elevation as,
, ( )
h
E sU h Fdh
(S7.2)
where F is the electrostatic force between the sphere and the wall, which only has a z
component due to symmetry. F is given by the stress tensor, σ, integrating through a
222
surface Ω enclosing the sphere and the unit normal vector of the surface pointing outward
(n) as,
ds
F σ n (S7.3)
1Tr( )
2p σ EE I EE I
(S7.4)
and σ contains the electrostatic Maxwell stress and the osmotic pressure, p. I is the unit
tensor, Tr is the trace operation, and ε is the dielectric constant of the solution. The
integration surface, Ω, is chosen as the mid-plane between a sphere and the wall, where
the linear superposition will hold with the minimum amount of error. The electric field,
E, is given by E = −ψ (i.e. the negative gradient of the electrostatic potential field). The
electrostatic potential ψ at Ω is approximated by the sum of the electrostatic potential
generated separately by each sphere and the wall. Mathematically,
w p (S7.5)
,0 exp( )w w h (S7.6)
,0 exp( ( ))pp r a
r
(S7.7)
where ψw,0 and ψp,0 are the surface stern potential of the wall and sphere, h is the distance
to the wall, r is the distance to the mass center of the sphere.
The osmotic pressure from the concentration of NaCl in solution is obtained from the
ideal gas law and the Boltzmann distribution given by,
223
0(exp( ) exp( ))
B B
e ep kT
k T k T
(S7.8)
where ρ0 is the bulk concentration of the salt.
7.7.2 Stokesian Dynamics Simulations
To obtain the height dependent diffusivities of an individual rod above a planar, no-slip
wall, we modeled the rod as a rigid linear chain of spheres. We first employ the grand
resistance tensor (R) for the sphere-chain system above a wall, as given by43
( )
-1PW 2B W 2B, W,R = (M ) + R R R R
(S7.9)
This tensor includes the many-bodied, far-field resistance tensor above a no-slip plane
((M∞PW)-1), as well as the pair-wise lubrication interactions. The pair-wise lubrication
interaction is obtained by first adding the two-body particle-particle exact resistance
tensor R2B and the two-body particle-wall exact resistance tensor RW. The far-field two-
body resistance tensor (R2B∞ + RW∞) is subtracted subsequently the to avoid double
counting the far-field particle-particle and particle-wall interaction in ((M∞PW)-1 and R2B
+ RW. The elements in these tensors can be found in the literature.43-45
After obtaining R, we can calculate the translational and rotational diffusivities
for a rod oriented parallel and with a surface to surface separation distance h from the
wall by the method introduced by Carrasco.46 The diffusivities in the bulk (i.e. setting
h→∞) were first calculated as a function of aspect ratio p, given the diameter of rod, and
then used as a normalization factor for diffusivities with finite values of h.
224
The diffusivities of rods with aspect ratios ranging from 10 to 25 at various
elevations were calculated and normalized by the bulk value. The diffusivity of a rod
with aspect ratio p and at elevation h can be represented as
|| || ||( , ) ( )pBD p h D f h
(S7.10)
where f is the height dependent coefficient function, whose form generally depends on
the value of p. f will approach 1 as h approaches infinity, and approach 0 contact. Other
diffusive modes will take a similar form as Equation S7.10.
7.7.2.1 Approximate diffusivities for cylindrical rod above wall
Here we showed that the height dependent coefficients from the chain-
sphere rod model can be used to approximate the diffusivities of cylinder rod. In
the far-field limit, the flow field generated by the translating object, irrespective
of its shape, can be approximated by the Stokelet, or Oseen, tensor. This
represents the leading term of the multipole expansion of the flow field generated
by a force distribution. In the far-field limit, the hydrodynamic interaction
between a cylindrical object and a wall can therefore be approximated by the
interaction between sphere-chain rod and wall.47 The leading error in the
approximation is expected not to exceed O((a/(h+a))3). Therefore, at h/a >> 1, the
height dependent coefficients of the sphere-chain rod model are the approximate
and upper-bound of the height-dependent coefficients of the cylindrical rod.
At separations of h/a << 1, the height-dependent coefficient can be
approximated using the analytical results for infinite cylinders adjacent to a plane.
The analytical result is the upper-bound for the diffusivities of a finite long
225
cylinder due to the hydrodynamic screening effect (a cylinder surface of length 2L
will experience less drag than 2x that of a cylindrical surface of length L). When h
is about the radius of the sphere, it is no longer appropriate to approximate the
cylindrical particle by either method. The coefficient within this range is found by
fitting a curve that matches the near-field lubrication result and the far-field
Instead, a simpler function accounting for the variation of both p and h will be
needed in practical purpose such as,
|| || || ||( , ) ( ) ( )BD p h D f h g p (S7.11)
where g is the correcting factor for different length of rod, for h < 10a. For
situations where h > 10a, the height dependent coefficient function has a very
weak dependence on the length of rod in the form,
|| || ||( , ) ( )BD p h D f h (S7.12)
7.7.3 Evaluating Stuck Particle Behavior
As discussed in Section 7.3.4, particles that are stuck to the silicate surface can
give information on the noise that is inherent to the system. Figure S7.1 shows example
histograms of a stuck particle resulting from the image analysis algorithms.
226
7.8 References
1. Jeffery, G. B., On the Steady Rotation of a Solid of Revolution in a Viscous Fluid. Proceedings of the London Mathematical Society 1915, s2_14, (1), 327-338.
2. Prager, S., Interaction of Rotational and Translational Diffusion. The Journal of Chemical Physics 1955, 23, (12), 2404-2407.
3. Takaisi, Y., Note on the Drag on a Circular Cylinder moving with Low speeds in a Viscous Liquid between Two Parallel Walls. Journal of the Physical Society of Japan 1956, 11, (9), 1009-1013.
4. Brenner, H., Rheology of a dilute suspension of axisymmetric Brownian particles. International Journal of Multiphase Flow 1974, 1, (2), 195-341.
5. Broersma, S., Rotational Diffusion Constant of a Cylindrical Particle. The Journal of Chemical Physics 1960, 32, (6), 1626-1631.
6. Broersma, S., Viscous Force Constant for a Closed Cylinder. The Journal of Chemical Physics 1960, 32, (6), 1632-1635.
7. Tirado, M. M.; de la Torre, J. G., Translational friction coefficients of rigid, symmetric top macromolecules. Application to circular cylinders. The Journal of Chemical Physics 1979, 71, (6), 2581-2587.
8. Broersma, S., Viscous force and torque constants for a cylinder. The Journal of Chemical Physics 1981, 74, (12), 6989-6990.
Rod 2
Total Length (nm)
4400 4500 4600 4700 4800 4900 5000 5100
Co
un
t
0
1000
2000
3000
4000
5000
6000
Rod 2
Theta 1 (degrees)
162 164 166 168 170 172 174 176
Co
un
t
0
500
1000
1500
2000
2500
3000Rod 2
Theta 2 (degrees)
162 164 166 168 170 172 174 176
Co
un
t
0
500
1000
1500
2000
2500
3000
Figure S7.1 – Histograms of the various length (A) and theta (B and C) values tracked for a rod that was irreversibly bound to the surface. These measurements help to inform on the extent of noise originating from the system as well as the tracking algorithms used.
A B C
227
9. Ortega, A.; de la Torre, J. G., Hydrodynamic properties of rodlike and disklike particles in dilute solution. The Journal of Chemical Physics 2003, 119, (18), 9914-9919.
10. de la Torre, J. G.; del Rio Echenique, G.; Ortega, A., Improved Calculation of Rotational Diffusion and Intrinsic Viscosity of Bead Models for Macromolecules and Nanoparticles. The Journal of Physical Chemistry B 2007, 111, (5), 955-961.
11. Aragon, S. R.; Flamik, D., High Precision Transport Properties of Cylinders by the Boundary Element Method. Macromolecules 2009, 42, (16), 6290-6299.
12. Mukhija, D.; Solomon, M. J., Translational and rotational dynamics of colloidal rods by direct visualization with confocal microscopy. Journal of Colloid and Interface Science 2007, 314, (1), 98-106.
13. Stalnaker, J. F.; Hussey, R. G., Wall effects on cylinder drag at low Reynolds number. Physics of Fluids 1979, 22, (4), 603-613.
14. Marshall, B.; Davis, V.; Lee, D.; Korgel, B., Rotational and translational diffusivities of germanium nanowires. Rheologica Acta 2009, 48, (5), 589-596.
15. Jeffrey, D.; Onishi, Y., The slow motion of a cylinder next to a plane wall. The Quarterly Journal of Mechanics and Applied Mathematics 1981, 34, (2), 129-137.
16. Ristow, G. H., Wall correction factor for sinking cylinders in fluids. Physical Review E 1997, 55, (3), 2808-2813.
17. Padding, J. T.; Briels, W. J., Translational and rotational friction on a colloidal rod near a wall. The Journal of Chemical Physics 2010, 132, (5), 054511-8.
18. Neild, A.; Padding, J. T.; Yu, L.; Bhaduri, B.; Briels, W. J.; Ng, T. W., Translational and rotational coupling in Brownian rods near a solid surface. Physical Review E 2010, 82, (4), 041126.
19. Wilcoxon, J.; Schurr, J. M., Dynamic light scattering from thin rigid rods: Anisotropy of translational diffusion of tobacco mosaic virus. Biopolymers 1983, 22, (3), 849-867.
20. Schumacher, G. A.; van de Ven, T. G. M., Brownian motion of rod-shaped colloidal particles surrounded by electrical double layers. Journal of the Chemical Society, Faraday Transactions 1991, 87, (7), 971-976.
21. Cush, R. C.; Russo, P. S., Self-Diffusion of a Rodlike Virus in the Isotropic Phase Macromolecules 2002, 35, (23), 8659-8662.
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22. Cush, R.; Dorman, D.; Russo, P. S., Rotational and Translational Diffusion of Tobacco Mosaic Virus in Extended and Globular Polymer Solutions. Macromolecules 2004, 37, (25), 9577-9584.
23. Newman, J.; Swinney, H. L.; Day, L. A., Hydrodynamic properties and structure of fd virus. Journal of Molecular Biology 1977, 116, (3), 593-603.
24. Lettinga, M. P.; Barry, E.; Dogic, Z., Self-diffusion of rod-like viruses in the nematic phase. EPL (Europhysics Letters) 2005, 71, (4), 692.
25. Klein, J. D.; Clapp, A. R.; Dickinson, R. B., Direct measurement of interaction forces between a single bacterium and a flat plate. Journal of Colloid and Interface Science 2003, 261, (2), 379-385.
26. Tavaddod, S.; Charsooghi, M. A.; Abdi, F.; Khalesifard, H. R.; Golestanian, R., Probing passive diffusion of flagellated and deflagellated Escherichia coli. The European Physical Journal E C7 - 16 2011, 34, (2), 1-7.
27. Daum, N.; Tscheka, C.; Neumeyer, A.; Schneider, M., Novel approaches for drug delivery systems in nanomedicine: effects of particle design and shape. Wiley Interdisciplinary Reviews: Nanomedicine and Nanobiotechnology 2012, 4, (1), 52-65.
28. Tirado, M. M.; Martinez, C. L.; de la Torre, J. G., Comparison of theories for the translational and rotational diffusion coefficients of rod-like macromolecules. Application to short DNA fragments. The Journal of Chemical Physics 1984, 81, (4), 2047-2052.
29. Hunt, A. J.; Gittes, F.; Howard, J., The force exerted by a single kinesin molecule against a viscous load. Biophysical journal 1994, 67, (2), 766-781.
30. Li, G. L.; Tang, J. X., Diffusion of actin filaments within a thin layer between two walls. Physical Review E 2004, 69, (6).
31. Lehner, D.; Lindner, H.; Glatter, O., Determination of the Translational and Rotational Diffusion Coefficients of Rodlike Particles Using Depolarized Dynamic Light Scattering. Langmuir 2000, 16, (4), 1689-1695.
32. De Souza Lima, M. M.; Wong, J. T.; Paillet, M.; Borsali, R.; Pecora, R., Translational and Rotational Dynamics of Rodlike Cellulose Whiskers. Langmuir 2002, 19, (1), 24-29.
33. Tsyboulski, D. A.; Bachilo, S. M.; Kolomeisky, A. B.; Weisman, R. B., Translational and Rotational Dynamics of Individual Single-Walled Carbon Nanotubes in Aqueous Suspension. ACS Nano 2008, 2, (9), 1770-1776.
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34. Streit, J. K.; Bachilo, S. M.; Naumov, A. V.; Khripin, C.; Zheng, M.; Weisman, R. B., Measuring Single-Walled Carbon Nanotube Length Distributions from Diffusional Trajectories. ACS Nano 2012, 6, (9), 8424-8431.
35. Wu, L.; Gao, B.; Tian, Y.; Muñoz-Carpena, R.; Zigler, K. J., DLVO Interactions of Carbon Nanotubes with Isotropic Planar Surfaces. Langmuir 2013, 29, (12), 3976-3988.
36. Levine, A. J.; Liverpool, T. B.; MacKintosh, F. C., Mobility of extended bodies in viscous films and membranes. Physical Review E 2004, 69, (2), 021503.
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38. Rovner, J. B.; Lapointe, C. P.; Reich, D. H.; Leheny, R. L., Anisotropic Stokes Drag and Dynamic Lift on Cylindrical Colloids in a Nematic Liquid Crystal. Physical Review Letters 2010, 105, (22), 228301.
39. Russel, W. B.; Saville, D. A.; Schowalter, W. R., Colloidal Dispersions. Cambridge University Press: New York, 1989.
40. Israelachvilli, J., Intermolecular and Surface Forces. 3rd ed.; Academic Press: New York, 2011.
41. Yu, J.-S.; Kim, J. Y.; Lee, S.; Mbindyo, J. K. N.; Martin, B. R.; Mallouk, T. E., Template synthesis of polymer-insulated colloidal gold nanowires with reactive ends. Chemical Communications 2000, (24), 2445-2446.
42. Lele, P. P.; Swan, J. W.; Brady, J. F.; Wagner, N. J.; Furst, E. M., Colloidal diffusion and hydrodynamic screening near boundaries. Soft Matter 2011, 7, (15), 6844-6852.
43. Swan, J. W.; Brady, J. F., Simulation of hydrodynamically interacting particles near a no-slip boundary. Physics of Fluids 2007, 19, (11), 113306.
44. Jeffrey, D. J.; Onishi, Y., Calculation of the resistance and mobility functions for two unequal rigid spheres in low-Reynolds-number flow. J Fluid Mech 1984, 139, 261-290.
45. Bossis, G.; Meunier, A.; Sherwood, J. D., Stokesian dynamics simulations of particle trajectories near a plane. Physics of Fluids A: Fluid Dynamics 1991, 3, (8), 1853.
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47. Cox, R. G.; Brenner, H., Effect of finite boundaries on the Stokes resistance of an arbitrary particle Part 3. Translation and rotation. J Fluid Mech 1967, 28, (02), 391-411.
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Chapter 8:
Colloidal Rod Diffusion through Model 2-Dimensional Porous Media
Porous media is not only an essential component in the natural filtration of
groundwater in aquifers, but it also an important instrument of study to understand the
diffusion of molecules and particles in the fields of chemistry, engineering, and medicine.
By creating a model 2-dimensional porous media out of 2.1μm silica microspheres, this
study employs the use of dark field microscopy to track individual colloidal gold rods as
they undergo Brownian diffusion. Preliminary results showed that the length of the
particle and the area fraction of silica spheres were key parameters in determining the
mechanism of diffusion for each rod. Increasing area fraction showed the rods diffusing
more quickly to areas with less obstruction. It was also found that for similarly sized rods
there was an increase in their rate of diffusion with increasing area fraction up to a point
where diffusion was limited by the packing arrangement of silica microspheres. To our
knowledge, this is one of the first reports of real-time tracking of individual rods through
porous media.
8.1 Introduction
Porous media is an important component in a range of different fields including
biology, industry, and the environment. A skeletal component makes up the framework
of the porous media, while the voids within the frame compose the pore space. There
exist two important and distinct frameworks when discussing porous media: i) a network
232
of capillaries which can describe blood flow, acoustics through caves, or the empty space
associated with air pockets in Styrofoam and molded plastics; and ii) an array of close-
packed solid particles which includes packed sand, capillary columns, or even bacterial
colonies. Understanding the diffusion and transport of particles through these types of
media to either retain or screen a particle of molecule of given weight, size, shape, or
chemistry is an important component in science and engineering technology. Especially
with the increasing use of 1D and 2D nanomaterials, knowing how their size and shape
affect their transport and interactions with the surrounding porous media framework is of
great interest.
In biology and medicine where the porous media framework is composed of cells
with varying shapes and surface chemistries, it is being realized that the shape of a drug
delivery particle is a significant variable in determining if the cargo will reach its
destination. Geng et. al. examined the importance of shape on the circulatory lifetime and
delivery capabilities of spheres versus filaments. They found that the anisotropic particles
were able to effectively deliver their cargo and persisted ten times longer in the
circulatory system of mice than spheres because of their ability to streamline through
blood vessels.1 Membranes for filtration or capillary columns in HPLC and GC used for
the separation of particles and molecules are important examples of porous media for
industrial purposes in biology and chemistry. Separation of DNA and proteins using
microfabricated nanochannels2 and lattices3 or ultrafiltration membranes4 occurs when
molecules diffuse through these pore spaces differently due to their size, shape, or surface
charge. Tuning the chemical identity of the porous media framework or creating
gradients of pore sizes is an effective way to capture the ideal molecules for a specific
233
purpose. Studies involving the pore structure of capillary columns5, 6 and microfluidic
devices7 helps industry better understand how separation is dependent on variables such
as flow, pore size, polarity, and particle size, and allows them to create more effective
separation mechanisms.
Transport of liquids and particles through porous media is one of the most widely
studied mechanisms by environmental engineers in efforts to understand how these
materials move through the groundwater system. The sand and clay beneath our feet act
as a natural filter for the water cycle, and by using columns packed with quartz sand8-11
and silica beads11-14 the effects of straining, particle shape, organic matter, and aquatic
solution conditions can be studied. Using engineered materials (latex colloids) to study
the effect of shape, researchers have shown that an increase in the aspect ratio increased
the retention,12 but if they were small enough along their minor-axis than they could flow
similarly to their spherical counterparts.9 Transport of bacteria through columns showed
similar findings, where longer and wider cells were often strained out by the porous
media, and those cells that passed through had aspect ratios greater than 0.5.8 It has also
been found that solution chemistry and the surface chemistry of the media and particles
plays a large role in whether anisotropic bacteria10 or particles are retained in the media.14
However, these types of batch study experiments do not allow us to track a single particle
through the media. To give us more insight into the mechanism of retention, simulations
of these pore structures allows for a more quantifiable examination of the convection-
dispersion theories that determine the flow of particles.15, 16
An important step towards understanding the diffusion of particles through a
porous media structure is examining how colloidal particles diffuse in concentrated
234
dispersions. Medina-Noyola17 postulated that short and long-time self-diffusion worked
by different mechanisms, where short-time diffusion (DS) was a purely hydrodynamic
interaction and long-time diffusion (DL) involved many body collisions. DL is therefore
smaller due to the applied friction from these collisions, and related to DS by the radial
distribution factor (g(r)). Brady18 expanded on this idea, stating that there exists a
temporal transition from short to long-time diffusion behavior that is controlled by the
thermodynamic equilibrium of the overall colloidal structure, which changes as particles
diffuse away from the center. This equilibrium is dependent on the volume fraction of
particles in the suspension, where diffusion ceases as the maximum volume fraction for
packing is reached. A concentrated colloidal dispersion can therefore be likened to a
porous media, where the volume fraction is going to play a significant role in the
diffusion of tracer particles. However, the rate of transition between short and long-time
diffusion will not be related to radial distribution of the particles making up the media
because they will be set in their equilibrium positions for the entirety of a given
experiment.
Within the last decade, direct imaging of spheres diffusing around obstacles has
been observed using different microscopy techniques. Kuznar and Elimelech19 used
fluorescence microscopy to directly image 1μm fluorescently tagged latex spheres as they
flowed through. They examined how solution conditions affected the transition from
secondary minimum deposition, to primary minimum deposition. Eral et. al.20 used
confocal microscopy to examine how the volume fraction of particles in solution affected
their settling and translational diffusion over smooth and rough surfaces. They found that
diffusion was slowed by the presence of sintered particles on the surface, and at certain
235
volume fractions the particles become trapped in layers on top of the sintered particles,
but was not so much as to form a glass. Differential dynamic microscopy was used by He
et. al.21 to track the diffusion of nanoparticles through microfabricated silica posts spaced
1.2 – 10μm apart. Results showed the translational diffusion slowed 25% between the
largest and smallest post spacing, where nanoparticles exhibited similar diffusion rates as
those seen without any posts present when diffusing through post spacing greater than
8μm. Simulation and modeling studies performed by Kim and Torquato22 and Saxton23
corroborate the experimental evidence from Eral and He. Their models suggest that
diffusion not only decreases due to exclusion-volume effects22 with increasing volume
fraction (ϕ) of diffusing particles or obstacles approaching the percolation threshold, but
trapping of a particle becomes more and more likely.23 These studies are useful
comparisons to this study regarding anisotropic particle diffusion because they discuss
sedimentation and Brownian diffusion as opposed to particle motion under flow
conditions24 or external fields.25
Experimentally measuring the diffusion of anisotropic particles in space26, 27 and
near flat surfaces28, 29 has become a subject of great interest in the last decade, building on
the work of Broersma30 and Tirado.31 Brownian dynamics simulations have greatly aided
in the understanding of anisotropic diffusion to help predict the various translational and
rotational diffusion modes. These results have shown that the addition of walls enhances
drag on a particle when the particle-wall separation distance is on the same order as the
particle diameter.29 Results from our previous study examining the influence of system
geometry and solution conditions indicated that the translational diffusion was more
sensitive to these parameters than the rotational diffusion. This has been seen before with
236
simulations performed on clusters of colloidal crystals.32 Our observed slowed diffusion
rates for confined geometries and increased ionic strength conditions correlated to a
measurable decrease in the particle to surface separation. We were able to establish those
heights using equations for the diffusion coefficients that included particle aspect ratio
and separation dependent factors.
Studies that combine the tracking of a single anisotropic particle while it
undergoes Brownian diffusion through a porous medium are few and far between. That is
why in this study we examine the diffusion behavior of anisotropic colloidal particles as
they navigate increasing area fractions of 2-dimensional porous media structures.
Previously developed and new tracking algorithms were used to analyze experiments
performed with dark field microscopy by taking advantage of the scattering efficiency of
two different materials (gold and silica). Lengths, as well as translational and rotational
diffusion coefficients were experimentally determined for individual rods, and were
compared relative to the area fraction of the porous media to determine the effective role
media concentration played in their diffusion behavior. In this chapter, preliminary
results are reported and briefly discussed.
8.2 Theory
To our knowledge, there is not currently a theory that accurately describes the
motion of individual rods through porous media. However, one can make some
qualitative guesses based on previously existing literature, such as the Brownian diffusion
of spherical particles and the diffusion of rods near surfaces.
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8.2.1 Diffusion of Spheres through Obstacles
Calculation of the diffusion of spheres over a flat surface hindered by spherical
obstacles takes advantage of the widely used translational diffusion equations for spheres
(i.e., mean squared displacement (MSD)). However, to accurately describe the diffusion
of a sphere through 2-D porous media there must be factors that account for the size and
number of obstacles in the field that the diffusing sphere may come into contact with.
Saxton23 suggested that the MSD for the lateral diffusion of a sphere through obstacles in
two dimensions follows the form,
2 2
0
4 2 ( , )x t Dt xdxC x t x
(4.51)
for a given point in time, t, where D is a function of the concentration of obstacles at a
particular position and time, C(x,t). These two variables are related by,
21( , ) exp
4 4
xC x t
Dt Dt
(4.52)
His simulation results suggest that at moderate concentrations of random
obstacles the diffusion would decrease, but the probability of a diffusing sphere sampling
many points on the grid would not change. It would not be until the percolation threshold
is reached that a particle would no longer be able to experience long-range paths, but
instead may get trapped in a small area.
Kim and Torquato22 took a similar approach to Saxton by using an “exclusion”
probability function, Eυ(r), and a “void” nearest-neighbor probability density, Hυ(r).
These two variables are defined as the fraction of space available for exploration in a
field of spherical obstacles of density, ρ, by a particle, and the probability that an
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arbitrary point in the system lies near a spherical obstacle between r and r + dr,
respectively, where r is the radius of a spherical empty space in the grid. Eυ(r) and Hυ(r)
are used in the calculation of the volume fraction, ϕ, and specific surface, s, respectively.
From here they suggest a calculation for the effective diffusion coefficient, De, for a
Brownian particle of radius b in a system with spherical obstacles of radius a as
De[ϕ(ρ,a);b]. They relate the De in fluid saturated porous media to the MSD by,
2
26 ( )e
XD
X
(4.53)
where X2 is the MSD and τ(X2) is the average time for a Brownian particle to hit a surface
for the first time.
8.2.2 Diffusion of Rod-Shaped Particles
As discussed at length in Section 7.2.3, we have shown that the theory we
calculated for the motion of rod-shaped particles near a flat surface agrees well with
experimental measurements. The equations generated by our rigid chain of sphere model
can be implemented into the equations for the diffusion of spheres through obstacles.
8.2.3 Diffusion of Rods through Obstacles
Similar variables will be necessary to describe the field in which the rod particles
are diffusing. These include a volume or area fraction of spherical obstacles, ϕ, which can
be used as a dimensionalized variable in place of a concentration in Saxton’s equation,
and a factor that would replace the spherical geometry of diffusing particles with a
cylindrical shape. The next step would be to know the center of mass and rod end point
coordinates at a given point in time to allow for the calculation of the MSD or MSθ,
239
which can then be directly related to an effective diffusion coefficient. This De can also
be compared to the diffusion coefficient calculated for rod-shaped particles under the
same conditions without the presence of physical obstacles that may induce
hydrodynamic hindrances. With these pieces, one could produce a reliable estimation of
the diffusion of rods through obstacles of varying concentration densities.
However, like Saxton discusses, the volume or area fraction of the obstacles is
important for explaining the MSD. Above a given ϕ, called the percolation threshold, a
particle can become trapped in a small space between clusters of obstacles. In this
instance the diffusion of the particle may appear faster than a particle that is diffusing
more freely; this can be the result of the trapped particle’s diffusion appearing more one
dimensional (1-D) in nature as opposed to 2-D. In that case, analyzing the particle’s
trajectory as 2-D motion would falsely give the particle a faster displacement. In these
cases, one must consider that as the area fraction of obstacles increases, there is the
likelihood that a particle’s motion is not strictly 1-D or 2-D, but a fractal dimension
between these two. Thus, a parameter indicating the dimension describing the particle
motion may also be employed to accurately capture the diffusion of rods through spheres.
8.3 Materials and Methods
8.3.1 Colloids and Surfaces
Hydrochloric acid, potassium hydroxide, sodium chloride (purchased from Fisher
Scientific) and colloidal SiO2 (nominal diameter of 2.34 microns, Bangs Laboratories)
were used as received and without further purification. Gold rods were synthesized at
240
Pennsylvania State University (State College, PA, USA) using an electrochemical
deposition process, and suspended in deionized water. Details regarding their synthesis
can be found in Section 7.3.1. Silica microspheres were made into a stock solution where
100μL of silica was removed from the bottle and diluted to 1mL in 0.1mM NaCl
solution.
Long glass microscope coverslips (Corning, 24 x 60 mm) were wiped clean with
lens paper, then sonicated for 30min in acetone and 30min in isopropanol before being
soaked in Nochromix overnight. Coverslips were rinsed with deionized (DI, 18.3MΩ)
water and soaked in 0.1M HCl for 30min, then rinsed with DI water again and dried with
nitrogen. Once dry, the long coverslips were placed on a WS-400BZ-6NPP/LITE spin
coater (Laurell Technologies Corporation, North Wales, PA), the silica stock was added
to the slide in 100μL aliquots, and then spun for 40sec at 1000rpms. These coverslips
were made with aliquots of silica ranging from one to five to increase the density of silica
present on the slide. After spin coating, the coverslip was placed on a hotplate and dried
overnight at 50°C. The next day silica coated coverslips were gently rinsed with DI water
from a squirt bottle and placed back on the hotplate to dry for 10min. Rinsing was
repeated three to five times to remove any crystalized salt from the silica stock before
use.
Small glass coverslips (Corning, 18 x 18 mm) were wiped with lens paper and
placed directly into Nochromix where they soaked overnight. The following day
coverslips were rinsed with DI water and soaked in 0.1M KOH for 30min. These
coverslips were rinsed and then dried with nitrogen before use.
241
Sample cells were created by dropping 12μL of the gold rod stock onto the center
of long coverslip coated with silica microspheres. A small coverslip was then placed on
top of the droplet to sandwich the particle solution between the two walls. Lens paper
was then used to wick away extraneous solution from between the walls until enough
solution has been removed to cause interference patterns to appear. Once this occurred,
the two coverslips were sealed together using Loctite Epoxy.
8.3.2 Dark Field Microscopy
Porous media experiments were performed using a Zeiss Axio Observer A1
inverted microscope with a Zeiss dry dark field condenser attachment (NA = 0.8/0.95).
All experiments were imaged using a 63x objective and particle diffusion was recorded
with a 12bit CCD camera (Hamamatsu ORCA-ER) operated in 4-binning mode at ~10fps
for approximately 30,000 frames.
8.3.3 Image Analysis
Image analysis algorithms coded in FORTRAN that were previously developed in
our lab were employed to determine the translational and rotational diffusion of rod-
shaped particles as the navigated the 2-D porous media. Additionally, a new algorithm
written in MATLAB allowed for the determination of the silica microspheres location
that make up the porous media. An image is exported from the video sequence where the
rods and the silica are not in contact with one another. This image is used by the program
to detect the silica using an 8-point connectivity thresholding process similar to that from
Chapter 7. Once an adequate threshold level has been reached that sufficiently captures
the silica microspheres, a solidity factor is entered. This factor corresponds to the percent
of a thresholded object that is filled (white pixels). Due to the different scattering
242
intensities in dark field, the silica scatters far less than the gold and appears dimmer. The
spheres appear as white halos around dark centers. This solidity factor uses those halos to
A B
C D
E F
Figure 8.1 – Different concentrations of porous media resulting in increasing area fractions of (A) 0.048, (B) 0.085, (C) 0.114, (D) 0.156, (E) 0.210, and (F) 0.245.
243
differentiate between a gold rod and a silica microsphere. From here, boundaries are
drawn around objects that meet the required solid percentage. Boundaries are not drawn
around objects above this limit (i.e., the gold rods). Once the boundaries are determined,
the area fraction (ϕ) of the image contained within those boundaries is calculated and
overlaid onto the video. This enables us to investigate the rods as a function of area
fraction of silica to determine the effects the increasing porous media concentration has
on the diffusion of rods. Figure 8.1 illustrates different area fractions determined by the
thresholded boundary conditions. Sometimes lower values of ϕ may produce more
interesting pores for the rods to navigate because the silica forms smaller clusters as in
Figure 8.1C and 8.1E, whereas the a higher ϕ shows larger, more spaced our crystals of
silica spheres (Figure 8.1D and 8.1F).
8.4 Results and Discussion
8.4.1 Tracking Rod-Shaped Particles through Porous Media
The same tracking algorithm from Chapter 7 was used to monitor the diffusion of
gold rods diffusing through silica spheres. Figure 8.2 shows the trajectories of three
different length particles through a moderately dispersed array of silica spheres. As can
be seen by the trajectories, the rods tend to move more quickly through areas with a
lower concentration of porous media, and often may remain in an open area or pocket
between clusters. All three rods exhibit some part of their trajectory where they remain in
space before diffusing elsewhere, the smallest rod being most evident (blue). The two
longer rods showed similar paths where they moved quickly through the open areas and
were able to weave between the clusters. However, we notice that when the rods do come
244
in close enough contact with the silica, they tend to remain near a cluster for a period of
time before moving on. This could be because the rod and sphere are now close enough
to feel attraction between the two surfaces. The hovering near the silica could be the
result of attractive and repulsive forces balancing each other as the rod samples different
areas of the silica cluster surface. The longest rod, shown in pink, exhibits this type of
sampling where it diffuses, hovers for a while, and then diffuses away.
8.4.2 Deciphering Calculated Mean Squared Displacements
Mean squared displacements (MSD) can give insight into what the trajectory of
the particle reflects about the porous media. Figure 8.3 shows the MSD for the three rods
at three different time intervals. Figure 8.3A examines the very short-time diffusion of
the rods. We would think that the fastest diffusing rod would be the shortest length rod at
this short window of time, but all three profiles show similar slopes. The shortest and
longest rods exhibit the same slope, and examining their position at time zero they are
Figure 8.2 – Plotted trajectories of three differently sized gold rods maneuvering through porous media with an area fraction 0.085. Green = 3.9μm, Blue = 3.4μm, and Pink = 4.5μm.
245
both further away from the silica than the rod that is 3.9μm. The increased slope could be
the result of electrostatic repulsion between the silica and the gold. At longer time
intervals (Figures 8.3B and 8.3C) we see the displacements start to deviate from one
another. At 60sec the slopes of all three rods are still similar, but we see the 3.9μm rod
slow down as it hovers in the open space between clusters. As time continues to progress,
the shortest rod takes advantage of its smaller size and the open pockets of space between
clusters to cover more space in the same time frame. The longest rod followed a similar
progression, but covered a longer lateral distance even if it was not the greatest overall
distance.
8.4.3 Comparing the Effect of Silica Area Fraction
By increasing the concentration of obstacles in the porous media, we hope to see
disruptions in the hydrodynamic interactions of the gold rods. Figure 8.4 shows how the
MSD of rods of similar length (4.5 – 4.9μm) is affected by changes in ϕ. At short
Time, ms
0 100 200 300 400 500 600
MS
D,
m2 /m
s
0.00
0.04
0.08
0.12
0.16
0.20
A
Time, sec0 10 20 30 40 50 60
MS
D, m
2/m
s
0
5
10
15
20
B
Time, sec0 100 200 300 400 500 600
MS
D,
m2/m
s
0
200
400
600
800
C
Figure 8.3 – Mean squared displacement calculations at (A) 600ms, (B) 60sec, and (C) 600sec for the three gold rods maneuvering through porous media with an area fraction 0.085. Green = 3.9μm, Blue = 3.4μm, and Pink = 4.5μm.
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diffusion times the profiles exhibit very similar slopes, which we would expect for rods
of similar sizes. It does not take long to see changes in the diffusion profiles, and a wide
variety of slopes after 10min. There does not appear to be any real trend that the MSD
follows as a function of ϕ, but this could be in part to several factors. Since these are not
standard oriented media, the chance that a rod will sample the same area or same
trajectory as another rod is slim. Increasing the area fraction also does not necessarily
mean that the distribution of silica is uniform. The rods that appear to be translating faster
even under conditions of higher silica concentrations could be the result of the rod
finding a larger open pocket of plain silica surface to diffuse over, or in the opposite case
may be propelled by electrostatic repulsion between itself and the surrounding silica
spheres.
Time, ms0 100 200 300 400 500 600
MS
D,
m2 /m
s
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
A
Time, sec
0 10 20 30 40 50 60
MS
D, m
2/m
s
0
5
10
15
20
B
Time, sec
0 100 200 300 400 500 600
MS
D,
m2/m
s
0
50
100
150
200
250
300
C
Figure 8.4 – Mean squared displacement calculations at (A) 600ms, (B) 60sec, and (C) 600sec for the gold rods of similar sizes (4.5 – 4.9μm) maneuvering through porous media with area fractions 0.0 (black filled circles), 0.048 (red open squares), 0.085 (yellow filled triangles), 0.114 (green open upside down triangles), and 0.156 (blue filled diamonds).
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8.5 Conclusions
Preliminary results of investigating the effect of area fraction of silica spheres on
the diffusion of gold rods of varying size show some positives and negatives.
Examination of the MSD plots at different time intervals allows us to decipher a bit about
how the porous media structure plays a role in diffusion. We saw faster translation when
rods had wide paths between clusters, but also that large open spaces essentially
“trapped” particles causing them to hover in the space for an extended time. Attractive
interactions between the gold and silica can be observed from the MSD, which shows the
rods hovering near the edges of silica clusters. Experiments examining area fraction
density are still inconclusive, as there are too many independent variables that need to be
isolated and tested. More in depth examination is needed to better understand how
exactly the porous media influences the hydrodynamic interactions of rod-shaped
particles diffusing through it.
8.6 Acknowledgements
We acknowledge financial support by the National Science Foundation (CHE-
1112335, CBET-1066254). We would also like to thank Wei Wang and Tom Mallouk
from Pennsylvania State University for giving us samples of the gold rods to use in these
studies.
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JULIE L. BITTER Department of Chemistry, Johns Hopkins University
3400 N. Charles St. NCB 228 Baltimore, MD 21218 [email protected]
609-433-7583 EDUCATION: The Johns Hopkins University, Baltimore, MD, USA Ph.D. Chemistry (Mar 2014)
M.A. Chemistry (Jan 2011) University of Central Florida, Orlando, FL, USA B.S. Forensic Science (May 2008)
Minors: Chemistry & Criminal Justice LABORATORY SKILLS: Chromatography: GC-MS, LC-MS, Thin Layer (TLC) Microscopy: Atomic Force (AFM), Comparison, Confocal, Dark Field, Optical, Polarized
Light (PLM), Scanning Electron (SEM), Total Internal Reflection (TIRM) Spectroscopy: FTIR/ATR, Ion Mobility (IMS), Mass Spectrometry (ion trap, quadrupole),
UV-Visible, X-ray Photoelectron (XPS) Analytical Techniques: Conductivity, Contact Angle, pH, Pipetting, Refractometry,
Sedimentation, Surface Charge Titration, Total Organic Carbon, Wet Chemical Extraction
Light Scattering: Dynamic Light Scattering (DLS), Zeta Potential Computer: AugerScan; CASA XPS; ChemDraw; ImageJ; Mathcad; Microsoft Excel,
PowerPoint, Word; SigmaPlot; StreamPix; VideoMach RESEARCH EXPERIENCE: The Johns Hopkins University, Baltimore, MD, USA Graduate Research Assistant (Sep 2010 to Present) Supervisor: Dr. Michael Bevan Study potential energy interactions of silica microspheres with environmental
surfaces under various aquatic conditions in confined experiments to determine contributions of attractive repulsive forces using TIRM, as well as determine the importance of the role that surface chemistry plays in these interactions
Elucidate new information on the hydrodynamic interactions of rod-shaped particles with silica surfaces and with other particles to garner quantitative measurements of force, potential, and diffusivity.
Track colloidal rods as they navigate 2D porous media to gain understanding of the forces that regulate the transport of nanomaterials in the environment
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Perform literature research, edit documents for coworkers and the principal investigator (manager), develop and edit written and visual proposal/grant content including figures, tables, and plots using Microsoft Office applications and SigmaPlot for my own research or for annual reports to funding agencies
Graduate Research Assistant (Sep 2008 to Present) Supervisor: Dr. Howard Fairbrother Characterize and analyze carbon nanotube structure, colloidal, and transport
properties using UV-Vis, AFM, DLS, XPS, and chemical derivatization techniques
Examine how the physical and chemical nature of CNTs exposed to UV light is altered, as well as examine the products formed by CNTs degraded by the UV light
Create samples for use in the laboratory as well as for others within and outside the university, maintain detailed records of all experimental procedures and results including tables and plots, standardize instruments and keep them in good working order
Perform literature research, edit documents for coworkers and the principal investigator (manager), develop and edit written and visual proposal/grant content including figures, tables, and plots using Microsoft Office applications and SigmaPlot for my own research or for annual reports to funding agencies
Provide XPS analytical services to seven independent research groups both affiliated and not affiliated with The Johns Hopkins University leading to two peer reviewed publications
Provide FTIR analytical services to undergraduate classes and independent research groups both affiliated and not affiliated with The Johns Hopkins University
Train graduate and undergraduate research students in applying knowledge to create and perform useful experiments, and teach them good laboratory and safety protocols
University of Central Florida/National Center for Forensic Science, Orlando, FL, USA Undergraduate Research Assistant (Jan 2006 to May 2008) Supervisor: Dr. Michael Sigman Examined the retention times of explosives (e.g., TNT, RDX, and PETN) on
different solid matrices by analyzing residues with GC-MS and IMS to determine detection limits
Examined pre and post blast material of TATP to compare signature features for trace detection using GC-MS, LC-MS, and IMS
Created methods for sample handling and preservation of explosive residues on evidence to be used in field tests and real life scenarios
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New Jersey State Police Office of Forensic Sciences, Central Regional Lab, Hamilton, NJ, USA Summer Intern (Jun 2007 to Aug 2007) Supervisor: Edward Gainsborg, FSIII Prepared and mounted samples of canine hair requested from purebred breeders
all over the country for a microscopy collection Created tests for hair/fiber examiners using the canine hair samples to discern
differences among similar colors, lengths, and within breeds Shadowed examiners from physical evidence section to assist with casework by
applying knowledge of presumptive and confirmatory tests for blood, semen, saliva, and urine, and other spectroscopic and microscopic techniques for the analysis of trace evidence
TEACHING EXPERIENCE: Independent Tutor General Chemistry I and II to three undergraduate students A.P. Chemistry to one high school student
The Johns Hopkins University Graduate Teaching Assistant (Sep 2008 to June 2010) Teaching assistant for undergraduate physical chemistry lab for three semesters Teaching assistant for undergraduate introduction to chemistry lecture for one
semester Duties included teaching laboratory experiments, grading lab reports, running
recitation sessions, grading exams, and grading oral presentations University of Central Florida Undergraduate Teaching Assistant (Aug 2007 to Dec 2007) Teaching assistant for undergraduate microscopy course for one semester Duties include teaching laboratory experiments, running laboratory
demonstrations, grading quizzes PRESENTATIONS: Platform
1. Bitter, J.L.; Duncan, G.A.; Bevan, M.A.; Fairbrother D.H.; “Quantitative Analysis of Particle-Surface Interactions in Aqueous Environments using Total Internal Reflection Microscopy.” 245th American Chemical Society National Meeting, New Orleans, LA, USA. April 7-11, 2013.
2. Bitter, J.L.; Duncan, G.A.; Fairbrother D.H.; Bevan, M.A. “Using Total Internal Reflection Microscopy to Quantitatively Interrogate Particle Interactions at Silica-Water Interfaces.” 245th American Chemical Society National Meeting, New Orleans, LA, USA. April 7-11, 2013.
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3. Bitter, J.; Duncan, G.; Fairbrother H.; Bevan, M. “Direct Measurements of Non-DLVO Forces between Silica Colloids and Surfaces.” 86th Colloids and Surfaces Symposium, Baltimore, MD, USA. June 10-13, 2012.
4. Bitter, J.; Duncan, G.; Eichmann, S.; Smith, B.; Bevan, M.; Fairbrother, H. “Using Real Time Imaging to Quantify Nanoparticle Dynamics and Surface Interactions in Aquatic Media.” 241st American Chemical Society National Meeting, Anaheim, CA, USA. March 27-31, 2011.
Poster
1. Bitter, J.; Yang, J.; Beigzadehmilani, S.; Jafvert, C.; Fairbrother, H. “Photochemical Transformations of Carbon Nanotubes.” 2nd Gordon Research Conference on Environmental Nanotechnology, Stowe, VT, USA. June 2-7, 2013.
2. Bitter, J.L.; Smith, B.A.; Wepasnick, K.A.; Fairbrother, H. “Influence of Oxygen Containing Functional Groups on the Transport Properties of Carbon Nanotubes in Saturated Porous Media.” 48th Eastern Analytical Symposium, Somerset, NJ, USA. November 16-19, 2009.
3. Bitter, J.; George, K.; Clark, D.; Sigman, M. “Explosive Recovery Off of Solid Matrices Over Time.” 33rd Federation of Analytical Chemistry and Spectroscopy Societies Meeting, Lake Buena Vista, FL, USA. September 24-28, 2006.
JOURNAL PUBLICATIONS:
1. J.L. Bitter, Y. Yang, G.A. Duncan, D.H. Fairbrother, M.A. Bevan, “Capturing the Diffusion of Micron-Sized Gold Rods Across Silicate Surfaces and through Slit Pores.” In Prep.
2. J.L. Bitter, J. Yang, S. Beigzadehmilani, C. Jafvert, D.H. Fairbrother, “Photochemical Transformations of Oxidized Multiwalled Carbon Nanotubes as a Result of Exposure to UVC Irradiation”. In Prep.
3. J. Yang, J. Bitter, B. Smith, H. Fairbrother, W. Ball, “Transport of Oxidized Multi-Walled Carbon Nanotubes through Silica Based Porous Media: Influences of Aquatic Chemistry, Surface Chemistry and Natural Organic Matter”. Environmental Science & Technology, 47: p. 14034-14043, 2013.
4. L. Tang, P. Yi, W. Gu, J. Bitter, H. Fairbrother, K.L. Chen, “Bacterial Anti-Adhesive Properties of Polysulfone Membranes Modified with Poly(allylamine hydrochloride) and Poly(acrylic acid) Multilayers”. Journal of Membrane Science, 446: p. 201-211, 2013.
5. J.L. Bitter, G.A. Duncan, D.J. Beltran-Villegas, D.H. Fairbrother, M.A. Bevan, “Anomalous Silica Colloid Stability and Gel Layer Mediated Interactions”. Langmuir, 29: p. 8835-8844, 2013.
6. B. Smith, J. Yang, J. Bitter, W.P. Ball, and D.H. Fairbrother, “Influence of Surface Oxygen on the Interactions of Carbon Nanotubes with Natural Organic Matter”. Environmental Science and Technology, 46: p. 12839−12847, 2012.
7. W. Boncher, E. Gorlich, K. Tomala, J. Bitter, S. Stoll, “Valence and Magnetic Investigations of Alkali-metal Doped Europium Sulfide”. Chemistry of Materials, 24: p. 4390–4396, 2012.
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8. K. Wepasnick, B. Smith, J. Bitter, D.H. Fairbrother, “Chemical and structural characterization of carbon nanotube surfaces”. Analytical and Bioanalytical Chemistry, 396: p. 1003-1014, 2010.
9. M. Sigman, C.D. Clark, K. Painter, C. Milton, E. Simatos, J. Frisch, M. McCormick, J. Bitter, “Analysis of oligomeric peroxides in synthetic triacetone triperoxide samples by tandem mass spectrometry.” Rapid Communications in Mass Spectrometry, 23: p. 349-356, 2009.
AWARDS: Top 3 Posters – 2013 Gordon Conference on Environmental Nanotechnology University Honors: 2008 Student-Mentor Academic Research Team (SMART) Grant: 2006 Dean’s List – College of Sciences: 2004 to 2008 PROFESSIONAL AFFILIATIONS: American Chemical Society: 2009 to present American Academy of Forensic Sciences: 2006 to 2008
March 2014