Texas Tech University, Madhusudhan R. Pallaka, December 2019

Texas Tech University, Madhusudhan R. Pallaka, December 2019

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Calorimetric Characterization of Nanoconfined Melts, Glasses and Reactive Monomers

by

Madhusudhan R. Pallaka, B.Tech Chemical Engineering

A Dissertation

In

Chemical Engineering

Submitted to the Graduate Faculty

of Texas Tech University in

Partial Fulfillment of

the Requirements for

the Degree of

DOCTOR OF PHILOSOPHY

Approved

Dr. Sindee L. Simon

Chair of Committee

Dr. Gregory McKenna

Dr. Wei Li

Dr. Jingjing Qiu

Dr. Mark Sheridan

Dean of the Graduate School

December 2019


0

Copyright 2019, Madhusudhan R. Pallaka


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ACKNOWLEDGEMENTS

PhD has been an emotional journey – lots of downs, lots of nothingness, and a

few ups. At the end of the day, all I strive for are those “few ups”. Those “few ups”

would not have been possible without strong, motivational and good people around me.

I would like to first thank my research advisor, Dr. Sindee Simon, for being a

constant source of motivation throughout my doctoral studies, without her support and

guidance I would not have made it this far. I hope the mentee-mentor relationship

continues for years to come. I would also like to thank Dr. Gregory McKenna for his

insightful polymer and viscoelasticity lectures, general research advice, and for allowing

me to use his lab facilities. I would also like to thank Dr. Wei Li, Dr. Jingjing Qiu, and

Dr. Burak Aksak for their time and also for agreeing to be a part of my PhD defense

committee.

I would also like to acknowledge Dr. Daniel Unruh for his insight and assistance

with X-ray diffraction experiments. I would also like to thank Dr. Kristin Hutchins for

allowing me to use the GPC instrument for polymer molecular weight measurements. I

would also like to thank Dr. Heedong Yoon, Qi Li, Amer and Dejie Kong for their

tassistance in AFM measurements. I am also extremely grateful for Dr. Yung Koh’s

invaluable help and advice. I would also like to thank all of Dr. Simon’s group members -

it was a wonderful experience working with you all. I would like to specially thank Naz,

Dr. Zhiyuan Qian, Qian, Rozana, and Alex for their friendship and fruitful research

collaborations.


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To my undergraduate and school friends - Firstly, I would like to thank my dear

friend Rohit Joshi who motivated me to take up the mammoth task of pursing a PhD in

chemical engineering. I would also like to thank Dilip and Prashant for their continued

support and camaraderie. Shanker, Goutham and Abhitej, I thank each one of you for

putting up with me for 18 long years. I hope you guys never get to read this!

To my Lubbock friends – Apoorva, Srinivas, Malini, Chumki, Sriram, Ashwin,

Dinesh, Iyeswaria, Chandu, Bala, Srikant and Sagnik. I have had the best of my times

with you all, a big thank you for your friendship.

I cannot end this acknowledgement without thanking my “bestest” and sweetest

friend, Richa. I can proudly say that you are my best friend, hands down! I am extremely

thankful for your selfless friendship, motivation, care, and best of all, for being an ear to

all my problems. I cannot thank you enough for what you have done for me.

To my family – I would like to thank Malli mama, Ratna akka, Venkat bava garu

Latha akka, Chatterjee uncle and Shibani aunty, for being my family away from home. I

would also like to thank my grandmother, Eswaramma, for always being the first one to

support me in all my endeavors – you never stop to inspire me! Thank you, Anil bava,

Raghu anna, Leela akka, Sailu akka and Pedamma for your love and support.

Lastly, my parents and sister – Thank you, Amma, Nanna, and Chinnu, for being

my source of strength and encouragement through thick and thin. Thank you, Amma and

Nanna, for letting me follow my dreams, for teaching me grit, patience and perseverance.

Thank you, Chinnu, for your love and support, and for being my stress buster. Lastly,

thank you all for making this journey with me.


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TABLE OF CONTENTS

ACKNOWLEDGEMENTS ................................................................................................ ii

ABSTRACT ...................................................................................................................... vii

LIST OF TABLES ............................................................................................................. ix

LIST OF FIGURES ............................................................................................................ x

1. INTRODUCTION .......................................................................................................... 1

References ....................................................................................................................... 5

2. BACKGROUND ............................................................................................................ 7

2.1 Differential and fast scanning calorimetry ................................................................ 7

2.2 Melting and melting behavior under nanoconfinement ............................................ 9

2.3 Glass transition and Glass transition behavior under nanoconfinement ................. 12

2.4 Structural recovery and structural recovery under nanoconfinement ..................... 19

2.5 Step-growth polymerization under nanoconfinement ............................................. 25

References ..................................................................................................................... 28

3. MATERIALS ................................................................................................................ 54

3.1 Nanopore confinement ............................................................................................ 54

3.2 n-alkanes.................................................................................................................. 55

3.3 Polystyrene films on different substrates ................................................................ 55

3.4 Indium and vapor-deposited gold ............................................................................ 56

3.5 AAO supported and stacked polystyrene nanorods ................................................ 57

3.6 Epoxy-amine monomer mixture for linear epoxy polymerization .......................... 59

References ..................................................................................................................... 60

4. MELTING BEHAVIOR OF N-ALKANES IN ANODIC ALUMINUM OXIDE

(AAO) NANOPORES USING FLASH DIFFERENTIAL SCANNING

CALORIMETRY .......................................................................................................... 66

4.1 Introduction ............................................................................................................. 66

4.2 Experimental ........................................................................................................... 67

4.2.2 Methodology .................................................................................................... 67

4.3 Data analysis ........................................................................................................... 69

4.3.1 Symmetry analysis ........................................................................................... 69

4.4 Results ..................................................................................................................... 72

4.4.1 Melting of C16 in the bulk and AAO nanopores ............................................... 72


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4.4.2 Solid-solid transition and melting of C19 in bulk and AAO nanopores ............ 73

4.5 Discussion ............................................................................................................... 75

4.6 Conclusions ............................................................................................................. 78

References ..................................................................................................................... 80

5. ORIGIN OF THE BROAD ENDOTHERMIC PEAK OBSERVED AT LOW

TEMPERATURES FOR POLYSTYRENE AND METALS IN FLASH

DIFFERENTIAL SCANNING CALORIMETRY ....................................................... 93

5.1 Introduction ............................................................................................................. 93

5.2 Experimental ........................................................................................................... 94

5.2.1 Methodology .................................................................................................... 94

5.3 Results ..................................................................................................................... 98

5.3.1 Aging of polystyrene on different substrates ................................................... 98

5.3.2 Cooling rate dependence of polystyrene on different substrates .................... 100

5.3.3 Cooling rate dependence and aging of indium and vapor-deposited gold ..... 102

5.4 Discussion ............................................................................................................. 104

5.5 Conclusions ........................................................................................................... 107

6. THE GLASS TRANSITION BEHAVIOR OF ANODIC ALUMINUM OXIDE

(AAO) SUPPORTED AND STACKED POLYSTYRENE NANORODS USING

FLASH DIFFERENTIAL SCANNING CALORIMETRY ....................................... 122

6.1 Introduction ........................................................................................................... 122

6.2 Experimental ......................................................................................................... 125

6.2.1 Methodology .................................................................................................. 125

6.3 Results ................................................................................................................... 128

6.3.1 Stacked PS nanorods in ionic liquid ............................................................... 128

6.3.2 AAO supported PS nanorods ......................................................................... 131

6.3.3 Low temperature endotherm in stacked and AAO supported PS nanorods ... 132

6.4 Discussion ............................................................................................................. 134

6.5 Conclusions ........................................................................................................... 137

References ................................................................................................................... 139

7. ENTHALPY RECOVERY OF 2D STACKED POLYSTYRENE

NANORODS USING FLASH DIFFERENTIAL SCANNING CALORIMETRY ... 155

7.1 Introduction ........................................................................................................... 155

7.2 Experimental ......................................................................................................... 157

7.2.1 Methodology .................................................................................................. 157


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7.3 Results and discussion ........................................................................................... 161

7.4 Conclusions ........................................................................................................... 169

References ................................................................................................................... 171

8. REACTION KINETICS OF LINEAR EPOXY POLYMERIZATION IN CPG

NANOPORES ............................................................................................................. 182

8.1 Introduction ........................................................................................................... 182

8.2 Experimental ......................................................................................................... 183

8.2.1 Methodology ...................................................................................................... 183

8.3 Results ................................................................................................................... 184

8.4 Discussion ............................................................................................................. 191

8.5 Conclusions ........................................................................................................... 192

References ................................................................................................................... 193

9. CONCLUSIONS......................................................................................................... 205

10. FUTURE WORK ...................................................................................................... 210

10.1 Glass transition behavior and structural recovery of polynorbornene

thin films using Flash differential scanning calorimetry ................................... 210

10.2 Glass transition behavior and enthalpy relaxation of thermoplastic

epoxy reinforced with multi-walled carbon nanotubes using Flash DSC........... 211

10.3 Obtaining three Kovacs’ signatures of structural recovery for 20 nm

stacked PS rods and 20 nm ultrathin PS film, and modeling with

the modified TNM model ................................................................................... 212

10.4 Reaction kinetics of alumina and silica filled epoxy polymerization ................. 213

References ................................................................................................................... 215


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ABSTRACT

Nanoconfined materials exhibit altered and interesting behavior different from the

bulk. Understanding the behavior of nanoconfined materials is of great importance to

both nanoscience and nanotechnology communities. This work aims to elucidate the

effect of nanoconfinement on melting, the glass transition and associated structural

relaxation kinetics, and reactivity using Flash and conventional differential scanning

calorimetry.

The feasibility of anodic aluminum oxide nanopores (AAO) as a form of 2D

nanoconfinement on the Flash DSC is investigated by studying the melting behavior of n-

hexadecane and n-nonadecane. Depressed melting and solid-solid transition temperatures

are observed in the AAO nanopores which validates the use of AAO as a

nanoconfinement matrix. The results suggest an abnormal melting behavior in the AAO

nanopores which is investigated using X-ray diffraction.

The glass transition behavior of 20, 55, and 350 nm AAO supported and stacked

polystyrene (PS) nanorods is studied using Flash DSC. The results indicate that the glass

transition temperatures are depressed for stacked PS nanorods less than 100 nm; on the

other hand, bulk-like behavior is observed for AAO supported PS nanorods irrespective

of rod diameter. The effect of spatial dimensionality on glass transition behavior is also

investigated.

The structural recovery kinetics of 20 and 350 nm stacked PS nanorods is

investigated using Flash differential scanning calorimetry. The results indicate an

enhanced overall structural recovery rate for 20 nm stacked PS rods when compared to


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350 nm stacked PS rods. Importance of comparing structural recovery rates at same

distances from their respective glass transition temperature is highlighted. In addition, the

effect of spatial dimensionality on structural recovery is also investigated using a

relaxation time map.

The reaction kinetics of step-growth linear epoxy polymerization is studied in

CPG nanopores using conventional DSC. The results suggest an enhanced reaction in the

nanopores. The glass transition behavior of cured linear epoxy polymer is also studied.

In addition to the nanoconfinement effects, the current controversies regarding the

mechanisms of structural recovery are also investigated.


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LIST OF TABLES

3.1 Specifications of AAO nanopore templates. ………………………… 64

3.2 Specifications of CPG nanopores. …………………………………… 65

3.3 Polystyrene Molecular weights from GPC. ………………………….. 66

4.1 Liquid state specific heat capacities, Cp = a + bT + cT2 with T in K. 85

5.1 Summary of sample masses, substrate types or conditions. …………. 111

5.2 WLF parameters for PS on top of different substrates for ∆Tf, Hi+Lo in

Figure 5.5.c. ………………………………………………………….. 112

6.1 WLF parameters C1 and C2; fragility and activation Energy of

stacked PS rods in ionic liquid*, AAO supported PS rods*, PS thin

films, and bulk PS. ……………………………………………………

144

7.1 WLF parameters C1 and C2; fragility and activation Energy of 20 and

350 nm stacked PS rods dispersed in ionic liquid, 20 nm ultrathin PS

films, and bulk. ………………………………………………………. 174

8.1 Kinetic parameters from the autocatalytic model for bulk. Kinetic

Parameters from the second order model for 55 and 7.5 nm CPG. ...... 197

8.2 Summary of glass transition temperature, step change in heat

capacities for epoxy polymer synthesized in bulk, 55 and 7.5 nm

CPG……………………………………………………………………

198


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LIST OF FIGURES

2.1 Schematic of a DSC heating scan with glass transition, melting, and

an exothermic reaction. ………………………………………………. 43

2.2 Schematic of a UFS 1 sensor (reproduced from [14] with permission

from Elsevier). The inset image shows the heating area of UFS1 chip

sensor marked with an orange boundary. ……………………………

44

2.3 Enthalpy versus temperature schematic for melting transition. ……… 45

2.4 Schematic of a heat flow scan showing depressed melting point in

overfilled nanopores. ………………………………………………… 46

2.5 Enthalpy versus temperature schematic of glass transition on cooling. 47

2.6 Enthalpy versus temperature schematic for fictive temperature

obtained on heating. ………………………………………………… 48

2.7 Schematic showing DSC traces obtained on heating after cooling

different rates. Fictive temperature calculation using Moynihan’s

method. ……………………………………………………………… 49

2.8 (a) Schematic of enthalpy recovery during isothermal aging at Ta (b)

Enthalpy recovery of polystyrene for intrinsic isotherm experiments.

(adapted from Lopez and Simon [126] with permission from ACS) ... 50

2.9 (a) Schematic of asymmetry of approach experiment, where down

and up jumps are made from equilibrium (b) Enthalpy recovery of

polystyrene for down and up jump experiments showing asymmetry

of approach. (adapted from Lopez and Simon [126] with permission

from ACS) ……………………………………………………………

51

2.10 (a) Schematic of memory effect experiment, where Ta is reached in

two steps: 1) a down jump to T1 from To and partial aging at T1 until

fictive temperature equals Ta, 2) a final jump from partially aged state

to Ta (b) Enthalpy recovery of polystyrene demonstrating memory

effect. (adapted from Lopez and Simon [126] with permission from

ACS) ………………………………………………………………… 52


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2.11 (a) Enthalpy versus temperature and (b) Heat flow versus temperature

schematics showing the broad low-temperature endotherm. ………… 53

3.1 Preparation of AAO supported and stacked PS nanorods using

vacuum melt infiltration technique. ………………………………… 61

3.2 Scanning electron micrographs of PS nanorods after dissolving the

AAO and before and after separation from the film substrate. The

samples were sputtered with a thin layer of iridium (2- 5 nm) before

imaging. ……………………………………………………………… 62

4.1 Flash DSC chip with AAO template in the heating area. …………… 84

4.2 (a) symmetry analysis for a heat flow scan with phase transition of

C16 in AAO. The heat flow scans in red and blue represent the raw

data. The sections highlighted in black on the red and blue curves are

the regions chosen to determine the symmetry line. The orange line

denotes the symmetry line that is to be subtracted from the raw data.

(b) Corrected heat capacity data of Figure 4.2.a after symmetry

analysis. (The y-axis is labelled positive on either side of the zero-

axis since the heat capacity of a material is always positive.) ……… 85

4.3 A schematic of overfilled and underfilled nanopores. Resolved peaks

after deconvolution of overfilled pores are shown in green and red for

confined and bulk melting, respectively. …………………………… 86

4.4 Heat flow data for n-hexadecane in bulk and (a) 55 nm AAO pores

(b) 20 nm AAO pores; the melting in the nanopores is shown as a

function of pore fullness. The bulk melting peak obtained by

deconvolution is indicated by arrows for the bulk and overfilled pores 87

4.5 Heat flow data for bulk n-nonadecane and n-nonadecane in (a) 55 nm

AAO pores and (b) 20 nm AAO pores. The heat flow data for

nanoconfined C19 with varying pore fullness is also presented. …… 88

4.6 The magnitude of the melting point depression for C16 in 55 and 20

nm AAO pores (inverted solid red triangle), Linear fit through the

ΔTms of 55 and 20 nm AAO pores (red dashed line), experimental

data for silica-gel nanopores as function of inverse pore diameter

from reference 11 (upright brown triangles), linear fit through the

ΔTms of 55 nm AAO and silica-gel nanopores (brown dashed line),

experimental data for KIT-6 (solid purple square); SBA-15 (solid

lime green diamond); C-SBA-15 (cyan right angled triangle); native

CPG (solid green circles) from reference 40, experimental data for

silanized CPG as a function of inverse pore diameter from reference

13 (open blue circles). Also shown are the Gibbs-Thomson (G-T)

predictions of ΔTm using Equation 2.1 with the surface energy from 89


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reference 13 (blue dashed line). The properties of aforementioned

nanopore matrices are summarized in the appended table. …………

4.7 ∆Tm vs 1 d⁄ (solid red circles) and ∆Tss vs 1 d⁄ (purple solid squares)

of C19 in AAO nanopores. The red dashed line and purple solid line

are obtained by linear regression of the presented data. …………… 90

4.8 (a) Overlaid Powder X-ray patterns of C16 in bulk (red), in 55 nm

AAO pores (green) and in 18 nm AAO pores (blue) at -18 °C. (b)

Overlaid Powder X-ray patterns of C19 in bulk (red), in 55 nm AAO

pores (green) and in 18 nm AAO pores (blue) at room temperature. 91

5.1 Evolution of DSC scans of polystyrene on a bare chip at Ta = 20.5 °C

as a function of aging time (ta) (b) Excess specific heat of polystyrene

film aged for 8 hours on different substrates at Ta = 20.5 °C

(deconvoluted peaks of polystyrene film on a bare chip are shown as

dashed lines). ………………………………………………………… 113

5.2 (a) Enthalpy of aging (ΔHa) as a function of aging time for

polystyrene on different substrates (b) The change in fictive

temperature (ΔTf = Tf0 – Tf(ta)) as a function of aging time for

polystyrene on different substrates. The solid symbols represent ΔHa

and ΔTf that were obtained inclusive of both low and high

temperature endotherms and the open symbols represent those

obtained only from high temperature endotherms. …………………

114

5.3 Evolution of DSC scans of polystyrene as a function of different

cooling rates on different substrates scanned to (a) 30 °C and (b) -80

°C. …………………………………………………………………… 115

5.4 Limiting fictive temperatures as a function of cooling rate for

polystyrene on different substrates when scanned to (a) 30 °C and (b)

-80 °C. In case of limiting fictive temperatures when scanned to -80

°C, the low temperature endotherm is excluded. Also shown are

results from our earlier studies. ……………………………………… 116

5.5 (a) Excess specific heat scans of polystyrene on top of different

substrates at a cooling rate of 0.1 K/s with 1000 K/s as the reference

curve. (b) Enthalpy values of polystyrene on top of different

substrates as a function of cooling rates (c) The change in fictive

temperature corresponding to the values in Figure 5.5.b as a function

of cooling rates. The solid and open symbols correspond to values

excluding the low temperature endotherm and values including the

low temperature endotherm, respectively. The WLF fits are shown as

solid lines. …………………………………………………………… 117


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5.6 (a) Cooling rate dependent melting scans of Indium. (b) Aging time

dependent melting scans of indium obtained at an aging temperature

of 20.5 °C. (c) Excess specific heat of melting of indium at various

cooling rates with respect to 1000 K/s. (d) Excess specific heat of

melting of indium at various aging times with respect to the unaged

scan. In all cases indium was cooled to -80 °C before obtaining the

heating scan. …………………………………………………………

118

5.7 Cooling rate dependent melting scans of indium when scanned to 30

°C. …………………………………………………………………… 119

5.8 (a) Cooling rate dependent and (b) aging time dependent heat flow

scans of gold at Ta = 20.5 °C. Gold was deposited at two substrate

temperatures, Ts = 23 °C and 125 °C. The inset figures show data at a

substrate temperature of 125 °C. ……………………………………

120

5.9 (a) ΔH vs log q and (b) ΔH vs log ta for indium, and gold at Ts = 23

°C and 125 °C. ……………………………………………………… 121

6.1 (a) Averaged heat flow scans of stacked 20 nm polystyrene rods

dispersed in ionic liquid at a heating rate of 600 K/s after cooling at

rates varying from 0.1 to 1000 K/s. (b) Comparison of averaged

specific heat vs temperature data of different sizes of stacked

polystyrene rods dispersed in ionic liquid at various cooling rates. … 145

6.2 Fictive temperature as a function of cooling rate for 20, 55 and 350

stacked polystyrene rods dispersed in ionic liquid compared with

bulk data from previous work. The solid lines are the WLF fits

obtained from the parameters listed in Table 6.1. …………………… 146

6.3 Comparison of specific heat flow scans of annealed 20 nm stacked

PS rods and 20 nm Stacked PS rods before annealing. ……………… 147

6.4 Heat flow scans of polystyrene nanorods supported in (a) 20 nm

AAO (b) 55 nm AAO (c) 350 nm AAO. …………………………… 148

6.5 Limiting fictive temperatures as function of cooling rate for

polystyrene nanorods supported in 20 nm AAO, 55 nm AAO, 350 nm

AAO; the data is compared to stacked PS nanorods and bulk films

from previous studies. ……………………………………………… 149


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6.6 (a) Low temperature heat flow scans of 20 nm stacked PS rods on

bare chip and dispersed in ionic liquid (b) excess specific heat flows

of 20 nm stacked PS rods on bare chip and ionic liquid at 0.1 K/s

with respect to 1000 K/s, inset shows excess specifc heats as a

function of cooling rate for 20 nm stacked PS rods on bare chip. ……

150

6.7 Change in fictive temperatures for 20 nm stacked PS rods on bare

chip and dispersed in ionic liquid as a function of cooling rate, inset

shows fictive temperatures of the same samples as a function of

cooling rate. ………………………………………………………… 151

6.8 (a) Low temperature heat flow scans of AAO supported rods 20 nm

polystyrene nanorods (b) excess specific heat data of AAO supported

20 nm polystyrene nanorods for various cooling rates with respect to

1000 K/s. …………………………………………………………… 152

6.9 Magnitude of Tg depressions at 0.1 K/s (6 K/min) for different sizes

of stacked PS rods in ionic liquid (filled green circles), single

ultrathin PS films (filled red squares), PS nanowires in aqueous

dispersion (filled lime green left-angled triangles), PS nanospheres in

aqueous dispersion (filled pink diamonds), and PS nanospheres (open

diagonal square). The black dashed lines are Roth and Dutcher’s

upper and lower limits, the solid black line is obtained from modified

Keddie and Jones’ data. ………………………………………………

153

6.10 Magnitude of Tg depressions for different sizes of AAO Supported

PS nanorods from this work (left corner-filled green squares;

Torkelson and co-workers31 (solid black triangles); Zhu and co-

workers37 (lower half-filled triangles); Xue and co-workers36 (ΔTg,hi;

right half-filled violet squares, ΔTg,lo; left half-filled violet squares). 154

7.1 Flash DSC heating scans as a function of aging time for (a) 20 nm

stacked PS nanorods (green) after aging at Ta = 80.5 °C (b) 350 nm

stacked SP nanorods (red) after aging at Ta = 90.5 °C. The aging

temperatures are at the same distance from their respective Tfo

obtained at a cooling rate of 1000 K/s. ……………………………… 175

7.2 Flash DSC heat flow scans for 20 nm stacked PS nanorods on heating

from -80 °C as function of aging time at aging temperatures (a) 80.5

°C and (b) -20.5 °C. The insets show the excess specific heats with

respect to the unaged specific heat (1000 K/s) as a function of aging

temperature and aging time. ………………………………………… 176


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7.3 (a) Tf -Ta vs log ta for different jump sizes from Tfo for (a) 20 nm

stacked PS nanorods dispersed in ionic liquid (solid green left angled

triangles) and 350 nm stacked rods (solid red diamonds) (b) 20 and

350 nm stacked PS rods compared with 20 nm ultrathin (solid blue

squares) and bulk PS films (red diamonds) from previous studies. … 177

7.4 Aging rate comparison at (a) similar aging temperatures and (b)

similar jump sizes for 20 and 350 nm stacked PS nanorods, 20 nm

ultrathin PS film and bulk. …………………………………………… 178

7.5 Relaxation time map including induction times (tind; diamonds),

average relaxation times (squares) and times to reach equilibrium (t∞,

circles) as a function of (a) T and (b) Tfo-T are shown for 20 (solid

green symbols) and 350 nm (solid red symbols) stacked PS rods

along with 20 nm ultrathin PS film (open blue symbols) and bulk

(open orange symbols). The black dashed line is linear fit to all the

induction times. The colored solid lines (red, blue and green) are the

WLF dependence of average relaxation times obtained using the

cooling rate dependence of Tg. The colored short-dashed lines are the

same WLF dependence data shifted by a constant. ………………… 179

7.6 Excess specific heat data versus temperature on heating from -80 °C

as a function of aging time for 20 nm stacked PS nanorods aged at (a)

80.5 °C and (b) -20.5 °C. ……………………………………………

180

7.7 (a) Tf and (b) Tf -Ta vs log ta for three different aging temperatures

when cooled to -80 °C. ……………………………………………… 181

8.1 Representative reaction exotherms of epoxy polymerization in the (a)

bulk and (b) 55 nm CPG nanopores at various heating rates. ……… 199

8.2 Conversion x as a function of temperature for the bulk reaction. The

black lines are the best fits from the second order autocatalytic

model. ……………………………………………………………… 200

8.3 Conversion x as a function of temperature for reaction in 55 nm CPG

nanopores. The black solid line is the best fit from the second order

reaction model. ……………………………………………………… 201

8.4 (a) Comparison of representative reaction exotherms in bulk, 55 and

7. 5 nm CPG nanopores (b) conversion versus temperature of

reactions in bulk, 55 and 7.5 nm CPG nanopores. The black solid line

for the bulk is the best fit to the second order autocatalytic model and

the black solid lines for 55 and 7.5 nm CPG pores are the best fits to

the second order model. ……………………………………………… 202


xvi

8.5 (a) Isoconversional analysis of the bulk data at different heating rates.

(b) Apparent activation energies of the epoxy reaction in bulk, 55 and

7.5 nm CPG as a function of conversion from KAS isoconversion

method. (the error bars for the activation energy at a given

conversion was obtained from the standard error of the linear fit) …...

203

8.6 Glass transition temperatures obtained on heating at 10 K/min after

cooling at the same rater for bulk, 55 nm CPG and 7.5 nm CPG. …… 204


1

CHAPTER 1

INTRODUCTION

Material properties are significantly affected when the material dimensions are

scaled down from a macro scale or bulk to the nanometer scale (<< 100 nm), where the

nano-dimensions begin to overlap with the molecular length scales of polymers and small

molecules, alike. Understanding the impact of nanoconfinement on material properties

has been a topic of research in the fields of nanotechnology and nanoscience since the

seminal work of Jackson and McKenna.1-2 In addition, the use of novel experimental

techniques to probe the nanoconfinement effects has also increased, including the advent

of nanocalorimetry or Flash differential scanning calorimetry which is able to study ultra-

low sample masses with ultra-rapid heating or cooling rates. In recent years, 1D ultrathin

polymer films3-9 and 3D nanospheres10-11 have been studied using Flash differential

scanning calorimetry to understand the nanoconfinement effects. The work reported in

this dissertation primarily involves employing 2D confinement on the Flash DSC to study

the effect of nanoconfinement on melting, glass transition, and structural recovery. The

work in this dissertation also focusses on addressing the existing controversies in the field

of glass transition and structural recovery, including the existence of a double mechanism

of relaxation during structural recovery in the glassy state10, 12-18, in contrast to a widely

reported single mechanism. These controversial studies also report that the presence of a

low-temperature endotherm is a signature for fast-secondary relaxation mechanism, and

part of the work in this dissertation aims at understanding the origins of this low-

temperature endotherm and its relation to the double mechanism of structural recovery


2

using Flash differential scanning calorimetry. In addition to the effects of

nanoconfinement on melting, the glass transition, and structural recovery, reactions are

also affected by nanoconfinement, and work is reported in this dissertation on the

reaction kinetics of a step growth polymerization under nanoconfinement using

conventional differential scanning calorimetry.

This dissertation consists of ten chapters. Chapter 1 is this introduction. Chapter 2

provides some background on differential scanning calorimetry, melting, glass transition,

structural recovery and step-growth polymerization, as well as background and literature

review on the effect of nanoconfinement. Chapter 3 discusses the materials used in this

dissertation. Chapters 4-8 are manuscripts where each chapter is either adapted from

published work or manuscript in preparation. Each chapter consists of introduction,

methodology, results, discussion and conclusions. Chapter 9 summarizes overall

conclusions of the work in this dissertation. In chapter 10, recommendations for future

work are suggested.

A brief description of each of the major chapters, from 4 to 8, follows. Chapter 4,

entitled “Melting behavior of n-alkanes in anodic aluminum oxide (AAO) nanopores

using Flash differential scanning calorimetry” was published in Thermochimica Acta,

volume 663, pages 157-164, in 2018.19 The work details the efficacy of using AAO

nanopores as 2D nanoconfinement on the Flash DSC through the investigation of the

size-dependent melting behavior of n-alkanes. The chapter also discusses interesting

melting behavior of alkanes in AAO nanopores. The X-ray diffraction measurements

reported in this chapter were performed by Dr. Daniel Unruh, and he is a coauthor of the

paper published.


3

Chapter 5, entitled “Origin of the Broad Endothermic Peak Observed at Low

Temperatures for Polystyrene and Metals in Flash Differential Scanning Calorimetry”

will be submitted for publication. This chapter deals with the origins of the broad low-

temperature endotherm and its relationship with the secondary relaxation using glassy

polystyrene and crystalline metals. The results suggest that the low temperature

endotherm is an artifact. Coworker Rozana Bari performed the cooling rate dependent

measurements on polystyrene reported in this chapter, whereas the current author (MRP)

performed the enthalpy recovery measurements on polystyrene, and the cooling rate

dependent and aging measurements on indium and gold. The work has been written

collaboratively.

Chapter 6, entitled “The Glass Transition Behavior of Anodic Aluminum Oxide

(AAO) Supported and Stacked Polystyrene Nanorods Using Flash Differential Scanning

Calorimetry” will be submitted for publication. Chapter 6 deals with the effect of spatial

dimensionality on the glass transition behavior with AAO supported and stacked

polystyrene nanorods using Flash differential scanning calorimetry and comparing the

results to 1D ultrathin polystyrene films. The AAO supported PS nanorods do not exhibit

any depression in glass transition temperature, whereas the stacked PS rods below 100

nm show a size-dependent glass transition depression that is larger than 1D ultrathin PS

film.

Chapter 7, entitled “Enthalpy Recovery of 2D Stacked Polystyrene Nanorods

Using Flash Differential Scanning Calorimetry” will be submitted for publication.

Chapter 7 deals with the effect of spatial dimensionality on the enthalpy recovery of 2D

stacked polystyrene nanorods in comparison to that of 1D ultrathin polystyrene films.


4

The results suggest that the enthalpy recovery rate is enhanced for smaller sized stacked

PS rods when compared to bulk-like stacked PS rods. However, effect of spatial

dimensionality is insignificant as the 2D stacked rods and 1D films of 20 nm have similar

enthalpy recovery rates.

Chapter 8, entitled “Reaction Kinetics of Linear Epoxy Polymerization in CPG

nanopores” will be submitted for publication. This chapter deals with the reaction

kinetics of epoxy polymerization in CPG nanopores as a function of pore size. The

reaction kinetics are found to accelerated with the magnitude of acceleration increasing

with decreasing pore size. The effects are attributed to the surface silanol groups on the

nanopore surface.


5

References

1. Jackson, C. L.; McKenna, G. B., The Melting Behavior of Organic Materials

Confined in Porous Solids. J. Chem. Phys. 1990, 93 (12), 9002-9011.

2. Jackson, C. L.; McKenna, G. B., The glass-transition of organic liquids confined to

small pores. J. Non-Cryst. Solids 1991, 131, 221-224.

3. Koh, Y. P.; Simon, S. L., Enthalpy recovery of ultrathin polystyrene film using

Flash DSC. Polymer 2018, 143, 40-45.

4. Grassia, L.; Koh, Y. P.; Rosa, M.; Simon, S. L., Complete set of enthalpy recovery

data using Flash DSC: experiment and modeling. Macromolecules 2018, 51 (4),

1549-1558.

5. Koh, Y. P.; Grassia, L.; Simon, S. L., Structural recovery of a single polystyrene

thin film using nanocalorimetry to extend the aging time and temperature range.

Thermochim. Acta 2015, 603, 135-141.

6. Yoon, H.; Koh, Y. P.; Simon, S. L.; McKenna, G. B., An ultrastable polymeric

glass: Amorphous fluoropolymer with extreme fictive temperature reduction by

vacuum pyrolysis. Macromolecules 2017, 50 (11), 4562-4574.

7. Gao, S.; Koh, Y. P.; Simon, S. L., Calorimetric Glass Transition of Single

Polystyrene Ultrathin Films. Macromolecules 2013, 46 (2), 562-570.

8. Shamim, N.; Koh, Y. P.; Simon, S. L.; McKenna, G. B., Glass transition

temperature of thin polycarbonate films measured by flash differential scanning

calorimetry. J. Polym. Sci., Part B: Polym. Phys. 2014, 52 (22), 1462-1468.

9. Koh, Y. P.; Simon, S. L., The glass transition and enthalpy recovery of a single

polystyrene ultrathin film using Flash DSC. The Journal of Chemical Physics 2017,

146 (20), 203329.

10. Perez-De-Eulate, N. G.; Cangialosi, D., Double Mechanism for Structural

Recovery of Polystyrene Nanospheres. Macromolecules 2018, 51 (9), 3299-3307.

11. Perez-de-Eulate, N. G.; Di Lisio, V.; Cangialosi, D., Glass Transition and

Molecular Dynamics in Polystyrene Nanospheres by Fast Scanning Calorimetry.

ACS Macro Letters 2017, 6, 859-863.

12. Monnier, X.; Cangialosi, D., Effect of molecular weight on vitrification kinetics

and molecular mobility of a polymer glass confined at the microscale. Thermochim.

Acta 2019, 677, 60-66.


6

13. Cangialosi, D.; Boucher, V. M.; Alegría, A.; Colmenero, J., Direct evidence of two

equilibration mechanisms in glassy polymers. Phys. Rev. Lett. 2013, 111 (9),

095701.

14. Monnier, X.; Cangialosi, D., Thermodynamic ultrastability of a polymer glass

confined at the micrometer length scale. Phys. Rev. Lett. 2018, 121 (13), 137801.



ACS Macro Letters 2017, 6 (8), 859-863.

16. Boucher, V. M.; Cangialosi, D.; Alegría, A.; Colmenero, J., Reaching the ideal

glass transition by aging polymer films. PCCP 2017, 19 (2), 961-965.

17. Perez-De Eulate, N. G.; Cangialosi, D., The very long-term physical aging of glassy

polymers. PCCP 2018, 20 (18), 12356-12361.

18. Boucher, V. M.; Cangialosi, D.; Alegría, A.; Colmenero, J., Complex

nonequilibrium dynamics of stacked polystyrene films deep in the glassy state. The

Journal of Chemical Physics 2017, 146 (20), 203312.

19. Pallaka, M. R.; Unruh, D. K.; Simon, S. L., Melting behavior of n-alkanes in anodic

aluminum oxide (AAO) nanopores using Flash differential scanning calorimetry.

Thermochim. Acta 2018, 663, 157-164.


7

CHAPTER 2

BACKGROUND

2.1 Differential and fast scanning calorimetry

Calorimetry, which is based on the law of conservation of energy, is a useful

analytical tool in material science for determining the thermal properties by corelating

temperature with specific physical properties of materials. Amongst the many known

types of calorimetry techniques, differential scanning calorimetry1-6 (DSC) is one of the

widely used techniques to follow processes including, but not limited to, phase

transitions, glass transitions and related behavior, and reactions. The DSC technique

measures heat flow, absorbed or dissipated by the material, as a function of temperature

and time; schematic of a typical DSC heating scan with major events including melting,

glass transition, and an exothermic reaction is shown in Figure 2.1.

The DSCs are classified into two types based on how the heat flow of the sample

is obtained1-6: 1) heat flux DSC, and 2) power-compensated DSC. In case of a heat flux

DSC, a sample pan with material, and an empty reference pan are heated simultaneously

on a thermoelectric disk inside a furnace. Based on the heat capacity (Cp) of the material

enclosed in the sample pan or due to an endothermic or exothermic process in the sample

material, a temperature difference occurs between the sample and the reference pan. The

temperature difference is correlated to the heat flow using the thermal equivalence of

Ohm’s law.1-2, 6 In a power compensated DSC, the sample pan and the reference are

heated separately in two different furnaces. The sample and the reference pans are


8

maintained at the same temperature, and the difference in power required to maintain the

temperature is recorded as a function of time and temperature.2, 4 In this dissertation

work, both power-compensated and heat flux DSCs were used.

The conventional DSC that was used for some part of this dissertation work; i.e.,

in chapter 8, was a Mettler Toledo (MT) 823e, which is a heat flux DSC with a ceramic

sensor/heater connected to a gold-gold/palladium thermocouple. The sample and

reference pans are usually sealed in 20 µl standard or hermetic aluminum pans and placed

on two separate measuring platforms for measurement; a purge gas like N2 is

continuously circulated into the cell to prevent oxidation and degradation. A modern

conventional DSC like MT 823e requires sample masses in the range of milligrams

which obviates the study of single polymer ultrathin films with ultra-low sample masses;

and also, a conventional DSC can only achieve scan rates as high as 300 K/min with

proper sample handling, but are not enough to emulate industrial scale polymer

processing conditions7, suppress crystallization and decomposition8-10, and prevent

reorganization phenomenon in metastable phases11.

The aforementioned limitations of conventional DSCs led to the development of

fast scanning calorimetry.7, 11-14 The only commercially available calorimeter adopting

the fast scanning ability is a Mettler Toledo Flash DSC which was also used in the work

described in chapters 4-7. Flash DSC operates using a UFS 1 chip sensor in the power-

compensation mode with a signal time constant less than 1 ms which helps to achieve

rapid heating and cooling rates (40,000 K/s). The scanning rates can also reach as low as

0.1 K/s because of the sensor’s high sensitivity; thus, a range of the scanning rates

overlap with those of the conventional DSC.15 The UFS 1 chip sensor is based on MEMS


9

technology (MEMS: Micro-Electro-Mechanical-Systems) and is embedded in a ceramic

support.15 The sensor has a sample and reference side (twin calorimeters) as in the

conventional heat flux DSC except, there is no need of pans or crucibles.15-16 The

schematic of a UFS 1 sensor is shown in Figure 2.2.15-16 The UFS 1 sensor has two

silicon nitride (SIN) membranes (sample and reference side) with a thickness of 2 µm

and length of 1.6 mm. The heating area or the sample furnace on the SIN membrane is in

the center with an effective heating area17 of 0.09 mm2, as shown in the inset of Figure

2.2; the heating area has been coated with 0.5 µm aluminum for a homogenous

temperature profile, and the heat capacity is 600 nJ/K. The temperature is measured with

eight thermocouples connecting the bottom of the furnace to the thick silicon frame as

shown in Figure 2.2. The bottom of the furnace has been coated with silicon dioxide to

act as a dielectric layer.

2.2 Melting and melting behavior under nanoconfinement

Melting is a first order thermodynamic phase transition from an ordered crystal

phase into a disordered liquid phase. Melting is classified as a first order transition in the

Ehrenfest sense18 because of the discontinuity in the first derivative of Gibbs free energy

with respect to temperature or pressure. The melting transition is described in the

enthalpy versus temperature schematic in Figure 2.3. According to modified

Lindemann’s criterion19-21, upon heating a material from the crystalline phase the thermal

vibrations increase with the increase in temperature and there comes a temperature at

which the root-mean square of amplitude of vibrations and the interatomic distance

reaches a critical value, this is when the first drop of liquid forms, and is called the

melting point (Tm) . The material stays at a constant temperature until all the crystal


10

phase transforms into a liquid phase. The energy associated with the transition is called

the latent heat and can be obtained from the enthalpy difference of the liquid state and the

crystalline state at Tm as shown in the enthalpy versus temperature schematic. Since

energy is absorbed during melting, the process is endothermic, and shows up as an

endothermic peak in the heat flow scan of a DSC measurement, as shown in the

schematic in Figure 2.1. The onset of the endothermic peak is the melting point, and the

area of the endotherm is the enthalpy or latent heat of melting. The schematic in Figure

2.3 holds true for small molecules and pure substances like metals, but it is different for

polymers since the melting point of polymers is dependent on various factors including

molecular weight, degree of crystallinity, tacticity, impurities and degree of branching.

The study of melting behavior under nanoconfinement is relevant in many

physical, biological and chemical applications.22-31 Regardless of the material and

application, size-dependent melting behavior is observed at the nanoscale. In nanopores,

the effect of nanoconfinement on melting manifests as a depression in the melting point

of the confined material when compared to the bulk, and the magnitude of depression

increases with decrease in nanopore diameter. The size-dependent melting behavior can

be described using the Gibbs-Thomson equation:32-35

∆Tm = Tm − Tm(d) =AσslTm

d∆Hfρs

(2.1)

where Tm is the bulk melting temperature, Tm (d) is the melting temperature in the pores

with a constant diameter d, A is the geometry factor, σsl is the surface energy of the solid-

liquid interface, ρs is the crystal density of the bulk material, and ∆Hf is the bulk heat of


11

fusion. The depression in the melting point at the nanoscale is attributed to the reduced

crystal size, enhanced volume to surface ratio, and surface curvature.36-40 The Gibbs-

Thomson equation was first derived for the liquid-gas transition by Defay and Prigogine34

where the liquid droplet is in equilibrium with its own vapor. Defay and Prigogine’s

derivation was later extended to a solid-liquid equilibrium, where the pressure difference

between the solid and liquid layer given by the Laplace equation, the equated chemical

potentials of the solid and liquid phases at equilibrium given by the Gibbs-Duhem

equation, and the heat of fusion at constant temperature and constant external pressure

can be solved to obtain the size-dependent melting form of Gibbs-Thomson equation.40-41

When investigating the melting behavior at the nanoscale, especially in the nanopores,

factors including surface chemistry, pore geometry and tortuosity also influence the size-

dependent melting behavior.22-23, 25-26, 38, 42-48 The effect of surface chemistry has been

incorporated into the Gibbs-Thomson equation and can be formulated as modified Gibbs-

Thomson equation:25, 43-44, 49

∆Tm = Tm − Tm(d) =A(σlw − σsw)Tm

d∆Hfρs

(2.2)

where σlw and σsw are the interfacial energies of liquid-wall and solid-wall respectively.

If σlw > σsw, an elevation in melting temperature of the nanoconfined solid is observed,

and a depression in melting temperature is observed when σlw < σsw.

In addition to the size-dependent melting behavior, nanoconfinement is also

known to influence the crystal structure and lead to polymorphism45, 47-48, 50-59;

nanoconfinement induced polymorphism also influences the melting point in the


12

nanopores in combination with the nanoconfined melting effect and gives rise to

unexpected melting behavior in the nanopores.47, 50-52, 60 In addition, polymorphism in the

nanopores occurs due a combination of factors including, pore geometry and tortuosity.45,

48, 50, 52, 55-59, 61-70

Melting behavior in the nanopores has been predominantly studied using

differential scanning calorimetry since the pioneering work of Jackson and McKenna.37,

71 A schematic of a DSC heat flow scan of melting in the nanopores when filled in excess

is shown in Figure 2.4; ΔTm is the magnitude of melting point depression. In addition,

results for nanoconfined melting of alkanes in 2D AAO nanopores on the Flash DSC is

described in chapter 4 of this thesis.

2.3 Glass transition and Glass transition behavior under nanoconfinement

Upon cooling a glass forming material from its equilibrium liquid state, the

molecular mobility slows down with decreasing temperature; at some point during the

cooling process, the time scale for molecular rearrangements becomes longer than the

time scale of the experiment and the material falls out of equilibrium and transitions into

the glassy state as shown in the schematic of enthalpy versus temperature in Figure 2.5.

The glass transition temperature can be obtained from the intersection of the extrapolated

glass line and the extrapolated equilibrium liquid line as shown schematically in Figure

2.5. Unlike melting, the glass transition is a not an equilibrium process, and depends on

the time scale of the experiment performed, for example on the cooling rate in

temperature scans and on the aging time in isothermal aging experiments. In the case of

cooling rate experiments Kovacs72 demonstrated that Tg decreases with decreasing

cooling rate or increasing time scale of the measurement, and the glass line shifts to lower


13

enthalpy values as shown in Figure 2.5; in general, a 3 K change in Tg is observed for an

order of magnitude change in cooling rate.72

Since the glass transition is defined on cooling, Tg should be measured only on

cooling.73-76 However, in DSC measurements it is generally measured on heating owing

to historical difficulties in calibration, temperature control, and sensitivity during slow

cooling. Upon heating a material from the glassy state, the material first follows the glass

line, overshoots the liquid line, and then regains equilibrium at high temperatures. The

magnitude of the overshoot and the temperature at which the glass reaches equilibrium

depends on the cooling rate at which it was formed; a dense or low enthalpy glass formed

by slow cooling has lower molecular mobility and requires a larger overshoot and higher

temperatures to reach equilibrium when compared to a high temperature glass formed by

faster cooling as shown schematically in Figure 2.6.73, 77 The measure of glass structure

on heating in the case of cooling rate experiments is quantified using the limiting fictive

temperature (Tfˈ).78-79 Tfˈ can be obtained from the intersection of the extrapolated

enthalpy liquid line and the enthalpy glass line, and is approximately equivalent to Tg

(within 1 K) when measured on cooling at the same rate.73, 75-76

The heat flow or specific heat trace from a DSC measurement is essentially the

derivative of the enthalpy versus temperature data and has a step change at the glass

transition with an endothermic overshoot at the end of it; schematic in Figure 2.7 shows

the DSC traces obtained at slow and fast cooling rates, respectively. Limiting fictive

temperatures from the heat flow or specific heat scans are obtained using the Moynihan’s

method79 which is an area matching method as defined in Equation 2.3:

(2.3)


14

∫ (��𝑙 − ��𝑔)𝑑𝑇 = ∫ (�� − ��𝑔)𝑑𝑇 𝑇≫𝑇𝑔

𝑇≪𝑇𝑔

𝑇≫𝑇𝑔

𝑇𝑓ˈ

where �� is the heat flow of the aged scan, ��𝑙 is the liquid state heat flow, and ��𝑔 is the

glassy state heat flow. Since the areas being equated using Equation 2.3 have common

areas, the area matching is simplified to matching the similarly colored portions as shown

in Figure 2.7.

The glass transition appears to be a second order thermodynamic transition in the

Ehrenfest18 sense because of its discontinuity in heat capacity or the second derivative of

Gibbs-free energy (ΔG). However, it is not a true second order transition even though at

the first glance it might look like one, because Cp,glass < Cp,liquid ; on the other hand,

experimental observations clearly show the kinetic aspect of glass transition.72, 74, 78, 80-81

The two leading theories, Gibbs-DiMarzio configurational entropy model82-84 and free

volume model85-86, attempt to explain the glass transition behavior from a thermodynamic

and kinetics aspect, respectively.

The Gibbs-DiMarzio configurational entropy model is developed based on the

Flory-Huggins lattice model87-88. The lattice model, which is based on the polymer chains

and vacant sides in a lattice, predicts that the configurational entropy decreases with

decreasing temperature due the reduction of number of configurational arrangements of

molecules in the glassy state. At longer time scales, the configurational entropy reaches

zero at the second order transition temperature (T2). T2 is also known as the ideal

thermodynamic Tg or the lower limit for Tg, and is often empirically related to the Vogel

temperature89,T∞, from the viscosity models, at which the viscosity reaches infinity

approximately ~50 K below the nominal Tg measured at 10 K/min; it is also related to the


15

Kauzmann temperature90 (TK). The Gibbs-DiMarzio configurational entropy model also

resolves the Kauzmann’s negative configurational entropy paradox83, 91 with a

thermodynamic approach where the configurational entropy stays at zero even below T2;

however, T2 is a theoretically postulated value and cannot be measured experimentally.

Recently, Simon and McKenna demonstrated the non-existence of a thermodynamic

glass transition (T2) using extrapolated entropy and enthalpy 130 K below TK, where the

equilibrium entropy was found to be nonzero even at a finite temperature.92 In addition,

there is no diverging time scale (i.e., WLF is not followed at low temperatures) so the

value T∞ is not “real” and its equivalence to TK is not an evidence of an underlying

thermodynamic transition.93-94 Nevertheless, Adam and Gibbs introduced the concept

called cooperatively rearranging region (CRR) to describe the relaxation behavior of

glassy materials. The CRR has an inverse relationship with temperature and the glass

transition happens when the length scale of CRR is greater than a certain size. In

addition, the reduction in Tg under nanoconfinement has been attributed to the decrease in

CRR95-98, though the Gibbs-DiMarzio model predicts an increase in Tg due to the

decrease in configurational entropy under nanoconfinement.

Free volume models are based on an empirical Doolittle equation86, 99 which

relates temperature dependence of viscosity to free volume:

ln 𝜂 = ln 𝐴 + ln 𝐵 [𝜗 − 𝜗𝑓

𝜗𝑓]

(2.4)

where 𝜂 is the viscosity, A and B are constants, 𝜗 is specific volume, and 𝜗𝑓 is the free

volume. Fox and Flory were the first to relate free volume to Tg;100-101 they suggested that


16

a material undergoes glass transition when the free volume becomes constant. William

Landell and Ferry85, further enhanced the free volume concept assuming a linear

dependence of free volume on temperature: 𝑓 = 𝑓𝑜 + 𝛼𝑓(𝑇 − 𝑇𝑜); where 𝑓 =𝜗

𝜗𝑓 is the

fractional free volume, 𝑇𝑜 is the reference temperature, and 𝛼𝑓 is the volumetric thermal

expansion coefficient of free volume. Further, equation 2.4 can be expressed as:

log 𝑎𝑇 =ln 𝜂 (𝑇)

ln 𝜂 (𝑇𝑜)=

𝐵

2.303[1

𝑓−

1

𝑓𝑜]

(2.5)

Substituting f in equation 2.5 gives:

log 𝑎𝑇 =− (

𝐵2.303𝑓𝑜

) (𝑇 − 𝑇𝑜)

𝑓𝑜 𝛼𝑓⁄ + (𝑇 − 𝑇𝑜)

(2.6)

Comparing equation 2.6 with the exiting form of WLF relationship, once can deduce that

C1= 𝐵

2.303𝑓𝑜 and C2 = 𝑓𝑜 𝛼𝑓⁄ and 𝑇𝑜 = 𝑇𝑔.85 Equation 2.6 can also be expressed in terms of

relaxation time for glass forming materials above Tg (Tg + 10 ≤T < Tg + 100).

The super-Arrhenius temperature dependence of viscosity follows the well-known

Vogel-Fulcher- Tammann (VFT) relationship89, 102-103:

𝜂 = 𝜂𝑜𝑒𝑥𝑝 [𝐵

𝑇 − 𝑇∞]

(2.7)

where 𝜂𝑜 and 𝐵 are material dependent VFT parameters, 𝑇∞ is the temperature at which

viscosity goes to infinity; it is also known as the Vogel temperature which is 50 K

below 𝑇𝑔. Mathematically VFT parameters are related to WLF parameters by 𝐵 =


17

2.303𝐶1𝐶2 and 𝑇∞ = 𝑇𝑔 − 𝐶2. The free volume theory also solves the Kauzmann paradox

by demonstrating a kinetic divergence of viscosity at 𝑇∞. However, the divergence is

disproved by McKenna and co-workers.104-105

The glass transition behavior under nanoconfinement has been a topic of interest

since the pioneering discoveries of Jackson and McKenna,71, 106 and Keddie and Jones107

where Tg depressions at the nanoscale were observed for organic liquids and PS thin

films, respectively.106-107 Over the last 25 years, the challenges in understanding the glass

transition behavior at the nanoscale became much more complex with contrasting glassy

behavior under nanoconfinement.95-97, 108-118 In general, for a glassy polymer under

nanoconfinement the Tg can increase, decrease or remain unchanged when compared to

the bulk. The key factors that contribute to the sign and magnitude of change in Tg under

nanoconfinement include spatial dimensionality or geometry, interfacial effects. In case

of spatial dimensionality, enhanced volume to surface ratio in the order of 1D < 2D < 3D

can contribute to a higher magnitude of Tg depression in 3D confinement. For example,

Priestley and co-workers119-120, and Cangialosi and co-workers121 observed a stronger

confinement effect and a larger Tg depression in 3D PS nanospheres when compared to

1D supported polystyrene (PS) thin films107, 122 at the same length scale.120 Priestley and

co-workers119-120 attributed the larger magnitude of depression to the enhanced volume to

surface ratio; similar findings for 2D stacked PS nanorods are reported in chapter 6 of

this dissertation. Priestley and co-workers also laid emphasis on the enhancement of free

surface with increasing dimensionality as a reason for larger Tg depression; in addition,

the depressed Tgs reverted to the bulk for PS nanospheres capped with a silica shell.120 A

similar effect of free surface has been observed by Sharp and Forrest for supported PS


18

thin films capped with gold;116 however, a weak dependence of Tg depression on free

surface was reported by Forrest and Dalnoki-Veress.115 In addition, Koh and Simon123

reported Tg depressions for PIB-PS-PIB trilayer film with eliminated free surfaces for a

60 nm PS film; and also, for silica-supported and silica-capped PS films. The

freestanding PS films with two free surfaces show a dramatic decrease in Tg,116 but

similar magnitude of Tg depressions were not observed in case of other free standing

polymer thin films like PMMA112-113 and PVAc114.

Contrasting results were also observed for 2D nanorods confined in anodic

aluminum oxide (AAO) nanopores with no free surface, where two Tgs, one depressed

and one elevated, were reported by Xue and co-workers124 for PMMA and PS, depressed

Tgs with a molecular weight effect on the magnitude of Tg were reported by Torkelson

and co-workers125 for PS, and a slight elevation in Tg was reported by Zhu and co-

workers126 for PS. Results for a high molecular weight PS with and without AAO

nanopores are reported in chapter 6. In addition, both PS and PMMA exhibit elevated Tgs

when fabricated as nanotubes inside AAO nanopores,127-128 where elevation of Tg in PS

has been attributed to a curvature effect128, and a strong interfacial effect with the

hydroxyl groups in case of PMMA.127 Increase in Tg under nanoconfinement has been

observed when there is a strong surface interfacial effect with hydrogen bonding

polymers like PMMA. Silica-supported PMMA thin films108, 110, and previously

mentioned PMMA nanotubes and nanorods in AAO demonstrated increase in Tg when

compared to the bulk. On the other hand, when strong interacting surfaces were absent,

Tg depressions were observed for free standing 1D PMMA thin films112 and 3D PMMA


19

nanospheres111, whereas bulk values were observed for PMMA nanotubes127 and

nanorods129 without AAO support.

2.4 Structural recovery and structural recovery under nanoconfinement

A material in the glassy state is not in equilibrium; hence the thermodynamic

quantities like volume and enthalpy continuously evolve towards equilibrium when held

isothermally in the glassy state.130-131 The process of evolution of thermodynamic

quantities towards equilibrium is called structural recovery or structural relaxation.

Depending on the measured thermodynamic quantity, the process can be classified as

volume recovery or enthalpy recovery. The term physical aging is also used to indicate

structural recovery, but generally denotes the change in mechanical properties132-135

during structural recovery; in addition, physical aging is also used to differentiate from

irreversible aging processes such as chemical, thermal, gamma and biological aging.

The process of structural recovery can be followed by using the fictive

temperature which is a measure of glass structure as defined by Tool.78 The fictive

temperature (Tf) is the intersection of extrapolated enthalpy liquid line with the

extrapolated glass line as shown schematically in Figure 2.8. The schematic also shows

the evolution of glass structure with aging; the fictive temperature goes from Tfo to Ta

assuming equilibrium line is reached. The fictive temperature of an aged scan on the DSC

is calculated using the Moynihan’s method (Equation 2.3) and is shown schematically in

Figure 2.7.

The essential kinetic features of structural recovery were demonstrated in the

seminal work of Kovacs72 using departure from equilibrium (δ) as a measure of recovery


20

towards equilibrium. δ is simply a measure of how far a given glass is from the

extrapolated equilibrium liquid line; it is (𝜈 − 𝜈∞) 𝑣∞⁄ in case of volume and 𝐻 − 𝐻∞ in

case of enthalpy.136-137 Kovacs’ three signatures of structural recovery include intrinsic

isotherms, asymmetry of approach, and memory effect.72 Kovacs performed volume

recovery experiments on PVAc to obtain the three signatures.137 Recently, Lopez and

Simon136 obtained the three signatures of Kovacs in the enthalpy space using Flash DSC;

they captured the complete recovery process starting from the initial plateau at zero

departure because of the ability to capture short time aging response. Prior to Lopez and

Simon’s work,136 intrinsic isotherm and asymmetry of approach experiments has been

obtained in the enthalpy space138-143, but the complete memory effect experiment

including the initial departure at zero plateau has not previously been performed. An

intrinsic isotherm experiment is similar to the schematic shown in Figure 2.8.a, and

Figure 2.8.b shows the enthalpy recovery for bulk PS in terms of departure for several

intrinsic isotherms as a function of aging time where the equilibrium was attained for all

aging temperatures.136 The schematic for asymmetry of approach experiment is shown in

Figure 2.9.a. In the asymmetry of approach experiment, aging is performed at the same

aging temperature which is accessed by an up jump and a down jump from equilibrium of

equal size but in opposite directions, as shown schematically in Figure 2.9.a. The

structural recovery is followed by the red and blue arrows as shown in Figure 2.9.a. The

enthalpy recovery responses for the asymmetry of approach experiment is shown in

Figure 2.9.b.136 The recovery responses clearly show the asymmetric approach of up and

down jumps. The recovery would have been symmetric if the structural recovery is only

dependent on the departure temperature, but the responses clearly demonstrate that the


21

structure of the glass also plays an important role alongside temperature; in addition, the

auto-retarded shape of the down jump response is due to the continuous decrease in

mobility, and the auto-acceleration response of the up jump is due to the continuous

increase in mobility. The memory effect experiment involves a two-step temperature

history as shown schematically in Figure 2.10.a. The two steps involve a down jump

from To at equilibrium to T1 where partial isothermal aging is performed at T1 until the

fictive temperature reaches Ta, and then a final jump is made to Ta where the enthalpy

recovery is followed with aging time. Since the partially aged glass is at a fictive

temperature equal to the aging temperature, there is no driving force for structural

recovery; however, as aging time increases, the enthalpy of the glass increases from the

equilibrium value reaches a maximum and recovers back to equilibrium again as seen

from Figure 2.10.b, indicating that the glass has memory of the previous thermal

history.136 In addition, a glass with a single relaxation time would not have shown signs

of aging with zero driving force. Thus, the memory effect indicates that the glass has a

distribution of relaxation times.

The essential kinetic features of structural recovery including non-linearity and

non-exponentiality can be described by Tool-Narayanaswamy-Moynihan (TNM)78, 144-145

and Kovacs-Aklonis-Hutcheson-Ramos (KAHR) models137 of structural recovery. The

TNM model adopts a continuous relaxation time distribution of Kolrasusch-William-

Watts function85, 146 to achieve the non-exponential decay of fictive temperature:

𝑑𝑇𝑓

𝑑𝑇= 1 − exp [− (∫ (

𝑑𝑡

𝜏)

𝑡

0

)

𝛽

]

(2.8)


22

where 𝛽 is the non-exponentiality parameter, varying from 0 to 1. The parameter 𝛽

indicates the width of relaxation times, where 𝛽 = 1 transforms equation 2.8 into a simple

exponential decay with a single relaxation time. The non-linearity of structural recovery

kinetics is achieved in the TNM model by expressing the relaxation time, 𝜏, as a

temperature- and structure-dependent parameter using an Arrhenius type equation, with

the fictive temperature used to describe the instantaneous state of the glass structure.

𝜏 = 𝐴 𝑒𝑥𝑝 [∆ℎ

𝑅𝑇+

(1 − 𝑥)∆ℎ

𝑅(

1

𝑇𝑓−

1

𝑇)]

(2.9)

where 𝐴 is the pre-exponential factor, ∆ℎ is the apparent activation energy of structural

recovery, and x varies from 0 to 1. When x = 1, the relaxation time of structural recovery

is linear, devoid of structural dependence; as x decreases, the relaxation time shifts from

being linear to non-linear due to more contribution from structure. In addition, Bari and

Simon evaluated and recommended the best routes to determine the nonlinearity and

activation energy parameters to use the TNM model to simulate enthalpy relaxation data

of PS obtained at high cooling rates on the Flash DSC.147

In general, the TNM and KAHR models do a good job in capturing the kinetics

associated with structural recovery, but there are limitations148-154 in utilizing a single set

of model parameters to quantitatively describe all types of structural recovery data.148-156

Since, the TNM model utilizes an Arrhenius temperature dependence of relaxation time,

the applicability of the equation is limited to only in the glassy state below Tg and for a

limited range of temperatures. Recently, Grassia and Simon modified the existing TNM

model by using an odd symmetric function of WLF equation to extend the temperature


23

range of relaxation times to incorporate both non-equilibrium glassy states and

equilibrium liquid states.143, 157 The modified TNM model requires the fit of two

parameters along with the two WLF parameters obtained from cooling rate dependent

experiments.143, 157 The modified TNM model can describe the structural recovery for

aging temperature in the vicinity of Tg as well as quantitatively reproducing experimental

results for the three signatures of structural recovery with a single set of parameters.143, 157

Nanoconfinement not only affects the glass transition behavior of materials but

also the kinetics of structural recovery. The rates of structural recovery under

nanoconfinement are reported to be enhanced158-163, reduced164-165 or unchanged126, 166

relative to the bulk. The results reported are dependent on the type of measurement

technique, confinement, and material. Since structural recovery depends on driving force

and mobility, it is important to compare structural recovery rates at same distance from

Tg for nanoconfined polymers with reduced Tgs, because the aging temperature for

nanoconfined case will be closer to Tg when compared at same aging temperatures;

hence, nanoconfined polymers will have a higher recovery rate at a given temperature (or

zero recovery rate above their Tg).

In addition to influencing the rate of structural recovery, nanoconfinement is also

known to influence the mechanism of structural recovery. Cangialosi and co-workers

reported a two-step mechanism for structural recovery in the enthalpy space in case of 1D

stacked PS films163, 167-170 and 3D PS nanospheres171; a two-step mechanism has also been

observed in bulk PS and other polymers, but at much longer time scales.169, 171-172

Cangialosi and co-workers attributed the fast secondary relaxation mechanism to a broad


24

low temperature endotherm present in addition to the primary endotherm related to the

glass transition.

The presence of broad-low temperature endotherms has been observed by

Cangialosi and co-workers for both bulk and nanoconfined polymers;168-171, 173-174

Cangialosi and co-workers attributed the presence of low temperature endotherms to a

fast-secondary relaxation mechanism which could be helpful in obtaining low energy

state glasses. From the results reported, the low temperature endotherms are both cooling

rate dependent173-174 and aging time dependent168-171, and are observed on the heating

scan from an ultra-low temperature (-90 °C). A schematic depicting the presence of a low

temperature endotherm in enthalpy space as a function of temperature is shown in Figure

2.11.a. The blue solid line is the unaged glass or glass obtained at a high cooling rate

(1000 K/s) with a glassy slope of Cpgo, the red dashed line is a heating scan from room

temperature after aging at a temperature Ta for a given time t or after cooling at a rate

slower than that used to obtain the unaged glass (blue solid line), and the green dotted

line is a heating scan from an ultra-low temperature (-90 °C) after aging at a temperature

Ta for a given time t or after cooling to an ultra-low temperature at a rate slower than that

used to obtain the unaged glass (blue solid line). The green dotted line, which is the

heating scan from an ultra-low temperature, shows the increase in slope from Cpg = Cpgo

to Cpg > Cpgo as the glass is heated, and the slope reverts to Cpgo in the vicinity of the glass

transition. The gradual increase in the slope of the glass line of the dotted green curve

manifests into a board low-temperature endotherm in the DSC heat flow scan as shown

schematically in Figure 2.11.b. The low temperature endotherms have been observed in

both conventional and Flash DSCs. Using the conventional DSC, the low temperature


25

endotherms have been observed for 1D stacked PS thin films and bulk polymers

including polysulfone, poly(arylate), and polycarbonate.168-170 The fictive temperature of

a 30 nm stacked PS thin film aged at 243 K (Tg-100) reached the predicted Kauzmann

temperature for PS (270 to 280 K) under less than 2 days of aging due to the presence of

low temperature endotherm. Using the Flash DSC, cooling rate dependent and aging time

dependent low temperature endotherms have been observed for micronscale poly (4-tert-

butyl styrene) films and 3D PS nanospheres, respectively.171, 173-174 In case of micronscale

poly (4-tert-butyl styrene) films, the presence of a low temperature endotherm at a

cooling rate of 0.1 K/s contributed to a fictive temperature decrease of ~ 80 K when

compared to the nominal Tg of the polymer.174 In chapters 5-7, the origins and

implications of the low temperature endotherms are discussed for micronscale polymer

films, metals, and stacked and AAO supported PS nanorods using Flash DSC.

2.5 Step-growth polymerization under nanoconfinement

Step-growth polymerization usually occurs through the reaction of different

functional groups including, but not limited to, -COOH, -OH, -NH2, OCN, NCO, -COC-

.175-176 Polymer formation via step growth mechanism occurs only when the monomers in

the reaction mixture at least have a functionality ≥ 2. The functionality dictates

crosslinking, branching, and linear growth of the polymer. The molecular weight during a

step-growth polymerization reaction increases slowly with time; most step-growth

polymerization reactions proceed by formation of dimers, trimers, oligomers, and

eventually the polymer.175

Epoxies are an important class of polymers that are synthesized via step-growth

polymerization. One of the ways to synthesize epoxy polymers is by the reaction of an


26

epoxide functional group with an amine functional group (NH2). Most epoxy resins are

multifunctional with two or more reactive epoxide groups, and the functionality of the

amine dictates what type of polymer is formed; if the functionality of the amine is > two,

branching or crosslinking occurs and if the functionality is equal to 2, a linear epoxy

polymer is formed. The step-growth polymerization of epoxy proceeds via three most

important reaction pathways, including the uncatalyzed, self-promoted, and alcohol-

catalyzed reaction pathways.177-178 The uncatalyzed pathway only involves the epoxy and

amine species and is least likely to happen because of the other amine and alcohol

impurities present in the system. The alcohol-catalyzed pathway is the most favorable

and the one with the lowest activation energy barrier; the alcohol-catalyzed pathway

plays an important role in accelerating the polymerization in the later stages of the

conversion once the hydroxyl groups are formed from the cleavage of the epoxide group.

The initial stages of the reaction in the absence of a catalyst may proceed via both

uncatalyzed and self-promoted pathways, where the self-promoted pathway has a faster

reaction rate. In addition, each of the three reaction pathways proceed via an acyclic or a

cyclic transition state depending on the favorability or entropy of activation.177 In the

cyclic transition, bond cleavage and bond transfer of epoxy-primary amine or secondary

amine can occur simultaneously, leading directly to the formation of the product, but this

route is prone to steric crowding leading to a higher activation energy; on the other hand,

the acyclic transition state avoids steric crowding and have lower energy barriers at the

expense of multiple intermediate steps.177

In addition to melting, glass transition, and structural recovery, nanoconfinement

is also known to influence reactions. In the case of step-growth polymerization reactions,


27

the reaction rates are enhanced under nanoconfinement. Step-growth polymerization

under nanoconfinement has been studied for phenolic resins179, cyanate esters180-183,

epoxy-amines184, and polyurethanes.185 The step-growth polymerization under

nanoconfinement is usually followed using either Raman or FTIR (Fourier transform

Infrared) spectroscopy or DSC. In chapter 8 of this work, a DSC was used to follow the

reaction kinetics of epoxy polymerization under nanoconfinement.


28

References

1. Höhne, G.; Hemminger, W. F.; Flammersheim, H.-J., Differential scanning

calorimetry. Springer Science & Business Media: 2013.

2. Charsley, E.; Price, D.; Hunter, N.; Gabbott, P.; Kett, V.; Gaisford, S.; Priestley, I.;

Duncan, J.; Royall, P.; Scowen, I., Principles of thermal analysis and calorimetry.

Royal society of chemistry: 2019.

3. Höhne, G.; Schawe, J., Dynamic behaviour of power compensated differential

scanning calorimeters: Part 1. DSC as a linear system. Thermochim. Acta 1993,

229, 27-36.

4. Tanaka, S., Theory of power-compensated DSC. Thermochim. Acta 1992, 210, 67-

76.

5. Weber-Anneler, H.; Arndt, R., Thermal methods of analysis/differential scanning

calorimetry in theory and application. Thermochim. Acta 1985, 85, 271-274.

6. Gill, P.; Moghadam, T. T.; Ranjbar, B., Differential scanning calorimetry

techniques: applications in biology and nanoscience. Journal of biomolecular

techniques: JBT 2010, 21 (4), 167.

7. Zhuravlev, E.; Schick, C., Fast scanning power compensated differential scanning

nano-calorimeter: 2. Heat capacity analysis. Thermochim. Acta 2010, 505 (1), 14-

21.

8. Magoń, A.; Wurm, A.; Schick, C.; Pangloli, P.; Zivanovic, S.; Skotnicki, M.; Pyda,

M., Heat capacity and transition behavior of sucrose by standard, fast scanning and

temperature-modulated calorimetry. Thermochim. Acta 2014, 589, 183-196.

9. Cebe, P.; Hu, X.; Kaplan, D. L.; Zhuravlev, E.; Wurm, A.; Arbeiter, D.; Schick, C.,

Beating the heat-fast scanning melts silk beta sheet crystals. Scientific reports 2013,

3.

10. Cebe, P.; Partlow, B. P.; Kaplan, D. L.; Wurm, A.; Zhuravlev, E.; Schick, C., Using

flash DSC for determining the liquid state heat capacity of silk fibroin.

Thermochim. Acta 2015, 615, 8-14.

11. Schick, C.; Mathot, V., Fast Scanning Calorimetry. Springer: 2016.

12. Poel, G. V.; Istrate, D.; Magon, A.; Mathot, V., Performance and calibration of the

Flash DSC 1, a new, MEMS-based fast scanning calorimeter. J. Therm. Anal.

Calorim. 2012, 110 (3), 1533-1546.

13. Mathot, V.; Pyda, M.; Pijpers, T.; Poel, G. V.; Van de Kerkhof, E.; Van

Herwaarden, S.; Van Herwaarden, F.; Leenaers, A., The Flash DSC 1, a power


29

compensation twin-type, chip-based fast scanning calorimeter (FSC): first findings

on polymers. Thermochim. Acta 2011, 522 (1-2), 36-45.

14. Van Herwaarden, S.; Iervolino, E.; Van Herwaarden, F.; Wijffels, T.; Leenaers, A.;

Mathot, V., Design, performance and analysis of thermal lag of the UFS1 twin-

calorimeter chip for fast scanning calorimetry using the Mettler-Toledo Flash DSC

1. Thermochim. Acta 2011, 522 (1), 46-52.

15. Schawe, J. E.; Pogatscher, S., Material characterization by fast scanning

calorimetry: practice and applications. In Fast Scanning Calorimetry, Springer:

2016; pp 3-80.


nano-calorimeter: 1. The device. Thermochim. Acta 2010, 505 (1), 1-13.

17. Simon, S. L.; Koh, Y. P., The glass transition and structural recovery using flash

DSC. In Fast Scanning Calorimetry, Springer: 2016; pp 433-459.

18. Ehrenfest, P. In Phase changes in the ordinary and extended sense classified

according to the corresponding singularities of the thermodynamic potential, Proc

Acad Sci Amsterdam, 1933; pp 153-157.

19. Gilvarry, J. J., The Lindemann and Grüneisen laws. Phys. Rev. 1956, 102 (2), 308.

20. Lindemann, F., The calculation of molecular vibration frequencies Phys. Z 1910,

11, 609.

21. Chakravarty, C.; Debenedetti, P. G.; Stillinger, F. H., Lindemann measures for the

solid-liquid phase transition. The Journal of chemical physics 2007, 126 (20),

204508.

22. Lee, K.; Yu, G.; Woo, E.; Hwang, S.; Shin, K., Freezing and Melting in Nanopores.

In Adsorption and Phase Behaviour in Nanochannels and Nanotubes, Dunne, L. J.;

Manos, G., Eds. Springer Netherlands: Dordrecht, 2010; pp 257-272.

23. Christenson, H. K., Confinement effects on freezing and melting. J. Phys.:

Condens. Matter 2001, 13 (11), R95.

24. Gelb, L. D.; Gubbins, K.; Radhakrishnan, R.; Sliwinska-Bartkowiak, M., Phase

separation in confined systems. Rep. Prog. Phys. 1999, 62 (12), 1573.

25. Alba-Simionesco, C.; Coasne, B.; Dosseh, G.; Dudziak, G.; Gubbins, K.;

Radhakrishnan, R.; Sliwinska-Bartkowiak, M., Effects of confinement on freezing

and melting. J. Phys.: Condens. Matter 2006, 18 (6), R15.

26. Jiang, Q.; Ward, M. D., Crystallization under nanoscale confinement. Chem. Soc.

Rev. 2014, 43 (7), 2066-2079.


30

27. Padhye, R.; Aquino, A. J.; Tunega, D.; Pantoya, M. L., Fluorination of an Alumina

Surface: Modeling Aluminum–Fluorine Reaction Mechanisms. ACS applied

materials & interfaces 2017, 9 (28), 24290-24297.

28. Padhye, R. Altering surface properties toward enhanced reactivity. 2017.

29. Padhye, R.; Smith, D. K.; Korzeniewski, C.; Pantoya, M. L., Tailoring surface

conditions for enhanced reactivity of aluminum powders with solid oxidizing

agents. Appl. Surf. Sci. 2017, 402, 225-231.

30. Padhye, R.; Aquino, A. J.; Tunega, D.; Pantoya, M. L., Effect of polar environments

on the aluminum oxide shell surrounding aluminum particles: simulations of

surface hydroxyl bonding and charge. ACS applied materials & interfaces 2016, 8

(22), 13926-13933.

31. Padhye, R.; McCollum, J.; Korzeniewski, C.; Pantoya, M. L., Examining

Hydroxyl–Alumina Bonding Toward Aluminum Nanoparticle Reactivity. The

Journal of Physical Chemistry C 2015, 119 (47), 26547-26553.

32. Pawlow, P., On the melting temperature of the corns of salol. Z. Phys. Chem 1910,

74, 562.

33. Jackson, K.; Chalmers, B., Freezing of liquids in porous media with special

reference to frost heave in soils. J. Appl. Phys. 1958, 29 (8), 1178-1181.

34. Defay, R.; Prigogine, I.; Bellemans, A.; Everett, D., Surface tension and adsorption.

1966. Longmans, London.

35. Thomson, W., 4. On the Equilibrium of Vapour at a Curved Surface of Liquid.

Proceedings of the Royal Society of Edinburgh 1872, 7, 63-68.

36. Park, J. Y.; McKenna, G. B., Size and confinement effects on the glass transition

behavior of polystyrene/o-terphenyl polymer solutions. Physical Review B 2000,

61 (10), 6667-6676.



38. Alcoutlabi, M.; McKenna, G. B., Effects of confinement on material behaviour at

the nanometre size scale. J. Phys.: Condens. Matter 2005, 17 (15), R461.

39. McKenna, G. B.; Spe, Size and confinement effects on the glass transition. 2000; p

2004-2008.

40. Sun, J.; Simon, S., The melting behavior of aluminum nanoparticles. Thermochim.

Acta 2007, 463 (1), 32-40.


31

41. Sun, J. Thermodynamics and kinetics at the nanoscale: thermal behavior of

aluminum nanoparticles and development of nanoporous low-k dielectrics. Texas

Tech University, 2004.

42. Tang, X.-P.; Mezick, B. K.; Kulkarni, H.; Wu, Y., Elevation of melting temperature

for confined palmitic acid inside cylindrical nanopores. The Journal of Physical

Chemistry B 2007, 111 (7), 1507-1510.

43. Dosseh, G.; Xia, Y.; Alba-Simionesco, C., Cyclohexane and benzene confined in

MCM-41 and SBA-15: confinement effects on freezing and melting. The Journal

of Physical Chemistry B 2003, 107 (26), 6445-6453.

44. Maheshwari, P.; Dutta, D.; Sharma, S.; Sudarshan, K.; Pujari, P.; Majumder, M.;

Pahari, B.; Bandyopadhyay, B.; Ghoshray, K.; Ghoshray, A., Effect of interfacial

hydrogen bonding on the freezing/melting behavior of nanoconfined liquids. The

Journal of Physical Chemistry C 2010, 114 (11), 4966-4972.

45. Graubner, G.; Rengarajan, G. T.; Anders, N.; Sonnenberger, N.; Enke, D.; Beiner,

M.; Steinhart, M., Morphology of porous hosts directs preferred polymorph

formation and influences kinetics of solid/solid transitions of confined

pharmaceuticals. Crystal Growth & Design 2013, 14 (1), 78-86.

46. Kim, B. S.; Jeong, Y. G.; Shin, K., Influence of surface property on the

crystallization of hentetracontane under nanoscopic cylindrical confinement. The

Journal of Physical Chemistry B 2013, 117 (19), 5978-5988.

47. Huber, P., Soft matter in hard confinement: phase transition thermodynamics,

structure, texture, diffusion and flow in nanoporous media. J. Phys.: Condens.

Matter 2015, 27 (10), 103102.

48. Wang, L. P.; Li, Q. F.; Wang, C.; Lan, X. Z., Size-Dependent Phase Behavior of

the Hexadecane–Octadecane System Confined in Nanoporous Glass. The Journal

of Physical Chemistry C 2014, 118 (31), 18177-18186.

49. Takei, T.; Nakada, M.; Yoshikawa, N.; Hiroe, Y.; Yoshida, H., Effect of organic

functional groups on the phase transition of organic liquids in silica mesopores. J.

Therm. Anal. Calorim. 2016, 123 (3), 1787-1794.

50. Huber, P.; Soprunyuk, V. P.; Knorr, K., Structural transformations of even-

numbered n-alkanes confined in mesopores. Physical Review E 2006, 74 (3),

031610.

51. Henschel, A.; Hofmann, T.; Huber, P.; Knorr, K., Preferred orientations and

stability of medium length n-alkanes solidified in mesoporous silicon. Physical

Review E 2007, 75 (2), 021607.

52. Huber, P.; Wallacher, D.; Albers, J.; Knorr, K., Quenching of lamellar ordering in

an n-alkane embedded in nanopores. EPL (Europhysics Letters) 2004, 65 (3), 351.


32

53. Cheng, S.; McKenna, G. B., Nanoconfinement Effects on the Glass Transition and

Crystallization Behaviors of Nifedipine. Molecular pharmaceutics 2019, 16 (2),

856-866.

54. Burger, A.; Ramberger, R., On the polymorphism of pharmaceuticals and other

molecular crystals. I. Microchimica Acta 1979, 72 (3), 259-271.

55. Rengarajan, G.; Enke, D.; Steinhart, M.; Beiner, M., Stabilization of the amorphous

state of pharmaceuticals in nanopores. J. Mater. Chem. 2008, 18 (22), 2537-2539.

56. Beiner, M.; Rengarajan, G.; Pankaj, S.; Enke, D.; Steinhart, M., Manipulating the

crystalline state of pharmaceuticals by nanoconfinement. Nano Lett. 2007, 7 (5),

1381-1385.

57. Wang, L. P.; Sui, J.; Zhai, M.; Tian, F.; Lan, X. Z., Physical Control of Phase

Behavior of Hexadecane in Nanopores. The Journal of Physical Chemistry C 2015,

119 (32), 18697-18706.

58. Fu, D.; Su, Y.; Gao, X.; Liu, Y.; Wang, D., Confined Crystallization of n-

Hexadecane Located inside Microcapsules or outside Submicrometer Silica

Nanospheres: A Comparison Study. The Journal of Physical Chemistry B 2013,

117 (20), 6323-6329.

59. Su, Y.; Liu, G.; Xie, B.; Fu, D.; Wang, D., Crystallization features of normal

alkanes in confined geometry. Acc. Chem. Res. 2013, 47 (1), 192-201.



Thermochim. Acta 2018, 663, 157-164.

61. Ravikovitch, P. I.; Neimark, A. V., Density functional theory of adsorption in

spherical cavities and pore size characterization of templated nanoporous silicas

with cubic and three-dimensional hexagonal structures. Langmuir 2002, 18 (5),

1550-1560.

62. Mu, R.; Malhotra, V., Effects of surface and physical confinement on the phase

transitions of cyclohexane in porous silica. Physical Review B 1991, 44 (9), 4296.

63. Fette, E. V.; Pham, A.; Adalsteinsson, T., Crystallization and melting transitions of

hexadecane droplets in polystyrene nanocapsules. The Journal of Physical

Chemistry B 2008, 112 (17), 5403-5411.

64. Kutnjak, Z.; Kralj, S.; Lahajnar, G.; Žumer, S., Calorimetric study of

octylcyanobiphenyl liquid crystal confined to a controlled-pore glass. Physical

Review E 2003, 68 (2), 021705.


33

65. Grigoriadis, C.; Duran, H.; Steinhart, M.; Kappl, M.; Butt, H.-J. r.; Floudas, G.,

Suppression of phase transitions in a confined rodlike liquid crystal. ACS nano

2011, 5 (11), 9208-9215.

66. Jiang, K.; Xie, B.; Fu, D.; Luo, F.; Liu, G.; Su, Y.; Wang, D., Solid− Solid Phase

Transition of n-Alkanes in Multiple Nanoscale Confinement. The Journal of

Physical Chemistry B 2009, 114 (3), 1388-1392.

67. Farasat, R.; Vyazovkin, S., Nanoconfined Solid–Solid Transitions: Attempt To

Separate the Size and Surface Effects. The Journal of Physical Chemistry C 2015,

119 (17), 9627-9636.

68. Toriyama, K.; Okazaki, M., Molecular packing of long-chain n-alkanes in the

MCM-41 nanochannel as probed by the free radicals produced by γ-irradiation. The


69. Suzuki, Y.; Duran, H.; Steinhart, M.; Kappl, M.; Butt, H.-J. r.; Floudas, G.,

Homogeneous nucleation of predominantly cubic ice confined in nanoporous

alumina. Nano Lett. 2015, 15 (3), 1987-1992.

70. Kumar, M. V.; Prasad, S. K., Influence of quenched disorder created by nanosilica

network on phase transitions in tetracosane. RSC Advances 2012, 2 (22), 8531-

8538.

71. Jackson, C. L.; McKenna, G. B., Vitrification and crystallization of organic liquids

confined to nanoscale pores. Chem. Mater. 1996, 8 (8), 2128-2137.

72. Kovacs, A., Glass transition in amorphous polymers: a phenomenological study.

Adv. Polym. Sci 1963, 3 (3), 394-507.

73. Badrinarayanan, P.; Zheng, W.; Li, Q.; Simon, S. L., The glass transition

temperature versus the fictive temperature. J. Non-Cryst. Solids 2007, 353 (26),

2603-2612.

74. Plazek, D. J.; Bero, C. A., Precise glass temperatures. J. Phys.: Condens. Matter

2003, 15 (11), S789.

75. Plazek, D.; Frund Jr, Z., Epoxy resins (DGEBA): the curing and physical aging

process. J. Polym. Sci., Part B: Polym. Phys. 1990, 28 (4), 431-448.

76. Plazek, D. J.; Ngai, K. L., The glass temperature. In Physical properties of polymers

handbook, Springer: 2007; pp 187-215.

77. Badrinarayanan, P.; Simon, S. L., Origin of the divergence of the timescales for

volume and enthalpy recovery. Polymer 2007, 48 (6), 1464-1470.

78. Tool, A. Q., Relation between inelastic deformability and thermal expansion of

glass in its annealing range. J. Am. Ceram. Soc. 1946, 29 (9), 240-253.


34

79. Moynihan, C. T.; Easteal, A. J.; De BOLT, M. A.; Tucker, J., Dependence of the

fictive temperature of glass on cooling rate. J. Am. Ceram. Soc. 1976, 59 (1‐2), 12-

16.

80. McKenna, G. B.; Simon, S. L., The glass transition: Its measurement and

underlying physics. Handbook of thermal analysis and calorimetry 2002, 3, 49-

109.

81. McKenna, G., Comprehensive polymer science. Polymer properties 1989, 2, 311-

362.

82. DiMarzio, E.; Gibbs, J., Chain stiffness and the lattice theory of polymer phases.

The Journal of Chemical Physics 1958, 28 (5), 807-813.

83. Gibbs, J. H.; DiMarzio, E. A., Nature of the glass transition and the glassy state.

The Journal of Chemical Physics 1958, 28 (3), 373-383.

84. Gibbs, J. H., Nature of the glass transition in polymers. The Journal of Chemical

Physics 1956, 25 (1), 185-186.

85. Williams, M. L.; Landel, R. F.; Ferry, J. D., The Temperature Dependence of

Relaxation Mechanisms in Amorphous Polymers and Other Glass-forming Liquids.

J. Am. Chem. Soc. 1955, 77 (14), 3701-3707.

86. Doolittle, A. K., Studies in Newtonian flow. II. The dependence of the viscosity of

liquids on free‐space. J. Appl. Phys. 1951, 22 (12), 1471-1475.

87. Huggins, M. L., Some properties of solutions of long-chain compounds. The

Journal of Physical Chemistry 1942, 46 (1), 151-158.

88. Flory, P. J., Principles of polymer chemistry. Cornell University Press: 1953.

89. Vogel, H., The law of the relation between the viscosity of liquids and the

temperature. Phys. Z 1921, 22, 645-646.

90. Kauzmann, W., The nature of the glassy state and the behavior of liquids at low

temperatures. Chem. Rev. 1948, 43 (2), 219-256.

91. Stillinger, F. H., Supercooled liquids, glass transitions, and the Kauzmann paradox.

The Journal of chemical physics 1988, 88 (12), 7818-7825.

92. Simon, S. L.; McKenna, G. B., Experimental evidence against the existence of an

ideal glass transition. J. Non-Cryst. Solids 2009, 355 (10-12), 672-675.

93. Zhao, J.; Simon, S. L.; McKenna, G. B., Using 20-million-year-old amber to test

the super-Arrhenius behaviour of glass-forming systems. Nature Communications

2013, 4.


35

94. Zhao, J.; Ragazzi, E.; McKenna, G. B., Something about amber: Fictive

temperature and glass transition temperature of extremely old glasses from copal to

Triassic amber. Polymer 2013, 54 (26), 7041-7047.

95. Ellison, C. J.; Torkelson, J. M., The distribution of glass-transition temperatures in

nanoscopically confined glass formers. Nature materials 2003, 2 (10), 695.

96. Ellison, C. J.; Ruszkowski, R. L.; Fredin, N. J.; Torkelson, J. M., Dramatic

reduction of the effect of nanoconfinement on the glass transition of polymer films

via addition of small-molecule diluent. Phys. Rev. Lett. 2004, 92 (9), 095702.

97. Ellison, C. J.; Mundra, M. K.; Torkelson, J. M., Impacts of polystyrene molecular

weight and modification to the repeat unit structure on the glass transition−

nanoconfinement effect and the cooperativity length scale. Macromolecules 2005,

38 (5), 1767-1778.

98. Campbell, C. G.; Vogt, B. D., Examination of the influence of cooperative

segmental dynamics on the glass transition and coefficient of thermal expansion in

thin films probed using poly (n-alkyl methacrylate) s. Polymer 2007, 48 (24), 7169-

7175.

99. Doolittle, A. K., Studies in Newtonian flow. I. The dependence of the viscosity of

liquids on temperature. J. Appl. Phys. 1951, 22 (8), 1031-1035.

100. Fox, D., Physics and chemistry of the organic solid state. Interscience Publishers:

1963; Vol. 2.

101. Flory, P.; Fox, T., Treatment of intrinsic viscosities. J. Am. Chem. Soc. 1951, 73

(5), 1904-1908.

102. Tammann, G.; Hesse, W., The dependence of viscosity upon the temperature of

supercooled liquids. Z. Anorg. Allg. Chem 1926, 156, 245-257.

103. Fulcher, G. S., Analysis of recent measurements of the viscosity of glasses. J. Am.

Ceram. Soc. 1925, 8 (6), 339-355.




105. Yoon, H.; McKenna, G. B., Testing the paradigm of an ideal glass transition:

Dynamics of an ultrastable polymeric glass. Science advances 2018, 4 (12),

eaau5423.

106. Jackson, C. L.; McKenna, G. B., The glass-transition of organic liquids confined to

small pores. J. Non-Cryst. Solids 1991, 131, 221-224.


36

107. Keddie, J. L.; Jones, R. A.; Cory, R. A., Size-dependent depression of the glass

transition temperature in polymer films. EPL (Europhysics Letters) 1994, 27 (1),

59.

108. Grohens, Y.; Brogly, M.; Labbe, C.; David, M.-O.; Schultz, J., Glass transition of

stereoregular poly (methyl methacrylate) at interfaces. Langmuir 1998, 14 (11),

2929-2932.

109. Porter, C. E.; Blum, F. D., Thermal characterization of PMMA thin films using

modulated differential scanning calorimetry. Macromolecules 2000, 33 (19), 7016-

7020.

110. Priestley, R. D.; Mundra, M. K.; Barnett, N. J.; Broadbelt, L. J.; Torkelson, J. M.,

Effects of nanoscale confinement and interfaces on the glass transition temperatures

of a series of poly (n-methacrylate) films. Aust. J. Chem. 2007, 60 (10), 765-771.

111. Feng, S.; Chen, Y.; Mai, B.; Wei, W.; Zheng, C.; Wu, Q.; Liang, G.; Gao, H.; Zhu,

F., Glass transition of poly (methyl methacrylate) nanospheres in aqueous

dispersion. PCCP 2014, 16 (30), 15941-15947.

112. Roth, C.; Pound, A.; Kamp, S.; Murray, C.; Dutcher, J., Molecular-weight

dependence of the glass transition temperature of freely-standing poly (methyl

methacrylate) films. The European Physical Journal E 2006, 20 (4), 441-448.

113. Sharp, J.; Forrest, J., Thickness dependence of the dynamics in thin films of

isotactic poly (methylmethacrylate). The European Physical Journal E 2003, 12

(1), 97-101.

114. O'connell, P.; McKenna, G., Rheological measurements of the thermoviscoelastic

response of ultrathin polymer films. Science 2005, 307 (5716), 1760-1763.

115. Forrest, J.; Dalnoki-Veress, K.; Dutcher, J., Interface and chain confinement effects

on the glass transition temperature of thin polymer films. Physical Review E 1997,

56 (5), 5705.

116. Sharp, J.; Forrest, J. A., Free surfaces cause reductions in the glass transition

temperature of thin polystyrene films. Phys. Rev. Lett. 2003, 91 (23), 235701.

117. Reiter, G., Mobility of polymers in films thinner than their unperturbed size. EPL

(Europhysics Letters) 1993, 23 (8), 579.

118. Arndt, M.; Stannarius, R.; Gorbatschow, W.; Kremer, F., Dielectric investigations

of the dynamic glass transition in nanopores. Physical Review E 1996, 54 (5), 5377.

119. Zhang, C.; Boucher, V. M.; Cangialosi, D.; Priestley, R. D., Mobility and glass

transition temperature of polymer nanospheres. Polymer 2013, 54 (1), 230-235.


37

120. Zhang, C.; Guo, Y.; Priestley, R. D., Glass transition temperature of polymer

nanoparticles under soft and hard confinement. Macromolecules 2011, 44 (10),

4001-4006.




122. Keddie, J.; Jones, R., Glass Transition Behavior in Ultra‐Thin Polystyrene Films.

Isr. J. Chem. 1995, 35 (1), 21-26.

123. Koh, Y. P.; McKenna, G. B.; Simon, S. L., Calorimetric glass transition

temperature and absolute heat capacity of polystyrene ultrathin films. Journal of

Polymer Science Part B-Polymer Physics 2006, 44 (24), 3518-3527.

124. Teng, C.; Li, L.; Wang, Y.; Wang, R.; Chen, W.; Wang, X.; Xue, G., How thermal

stress alters the confinement of polymers vitrificated in nanopores. The Journal of

Chemical Physics 2017, 146 (20), 203319.

125. Askar, S.; Wei, T.; Tan, A. W.; Torkelson, J. M., Molecular weight dependence of

the intrinsic size effect on T g in AAO template-supported polymer nanorods: A

DSC study. The Journal of Chemical Physics 2017, 146 (20), 203323.

126. Wei, W.; Feng, S.; Zhou, Q.; Liang, H.; Long, Y.; Wu, Q.; Gao, H.; Liang, G.; Zhu,

F., Study on glass transition and physical aging of polystyrene nanowires by

differential scanning calorimetry. Journal of Polymer Research 2017, 24 (3), 38.

127. Tan, A. W.; Torkelson, J. M., Poly (methyl methacrylate) nanotubes in AAO

templates: Designing nanotube thickness and characterizing the T g-confinement

effect by DSC. Polymer 2016, 82, 327-336.

128. Chen, J.; Li, L.; Zhou, D.; Wang, X.; Xue, G., Effect of geometric curvature on

vitrification behavior for polymer nanotubes confined in anodic aluminum oxide

templates. Physical Review E 2015, 92 (3), 032306.

129. Li, L.; Zhou, D.; Huang, D.; Xue, G., Double glass transition temperatures of poly

(methyl methacrylate) confined in alumina nanotube templates. Macromolecules

2013, 47 (1), 297-303.

130. Hodge, I. M., Enthalpy relaxation and recovery in amorphous materials. J. Non-

Cryst. Solids 1994, 169 (3), 211-266.

131. Hodge, I. M., Physical aging in polymer glasses. Science 1995, 267 (5206), 1945.

132. Qian, Z. Viscoelastic and nanomechanical behaviors of polymeric materials. 2018.


38

133. Qian, Z.; McKenna, G. B., Mechanical spectral hole burning of an entangled

polymer solution in the stress-controlled domain. Physical Review E 2018, 98 (1),

012501.

134. Qian, Z.; McKenna, G. B., Expanding the application of the van Gurp-Palmen plot:

New insights into polymer melt rheology. Polymer 2018, 155, 208-217.

135. Qian, Z.; Risan, J.; Stadnick, B.; McKenna, G. B., Apparent depth‐dependent

modulus and hardness of polymers by nanoindentation: Investigation of surface

detection error and pressure effects. J. Polym. Sci., Part B: Polym. Phys. 2018, 56

(5), 414-428.

136. Lopez, E.; Simon, S. L., Signatures of structural recovery in polystyrene by

nanocalorimetry. Macromolecules 2016, 49 (6), 2365-2374.

137. Kovacs, A. J.; Aklonis, J. J.; Hutchinson, J. M.; Ramos, A. R., Isobaric volume and

enthalpy recovery of glasses. II. A transparent multiparameter theory. Journal of

Polymer Science: Polymer Physics Edition 1979, 17 (7), 1097-1162.

138. Fujimori, H.; Oguni, M., Non-exponentiality of the enthalpy relaxation under

constant-temperature conditions in the time domain in supercooled liquids and

glasses. J. Non-Cryst. Solids 1994, 172, 601-607.

139. Fujimori, H.; Fujita, H.; Oguni, M., Nonlinearity of the enthalpic response function

to a temperature jump and its interpretation based on fragility in liquid glasses. Bull.

Chem. Soc. Jpn. 1995, 68 (2), 447-455.

140. Boucher, V. M.; Cangialosi, D.; Alegria, A.; Colmenero, J., Enthalpy recovery of

PMMA/silica nanocomposites. Macromolecules 2010, 43 (18), 7594-7603.

141. Hofer, K.; Perez, J.; Johari, G., Detecting enthalpy ‘cross-over’in vitrified solids by

differential scanning calorimetry. Philos. Mag. Lett. 1991, 64 (1), 37-43.

142. Adachi, K.; Kotaka, T., Volume and enthalpy relaxation in polystyrene. Polym. J.

1982, 14 (12), 959.



Thermochim. Acta 2015, 603, 135-141.

144. Narayanaswamy, O., A model of structural relaxation in glass. J. Am. Ceram. Soc.

1971, 54 (10), 491-498.

145. Moynihan, C.; Macedo, P.; Montrose, C.; Montrose, C.; Gupta, P.; DeBolt, M.;

Dill, J.; Dom, B.; Drake, P.; Easteal, A., Structural relaxation in vitreous materials.

Ann. N.Y. Acad. Sci. 1976, 279 (1), 15-35.


39

146. Kohlrausch, R., Theorie des elektrischen Rückstandes in der Leidener Flasche.

Annalen der Physik 1854, 167 (2), 179-214.

147. Bari, R.; Simon, S. L., Determination of the nonlinearity and activation energy

parameters in the TNM model of structural recovery. J. Therm. Anal. Calorim.

2018, 131 (1), 317-324.

148. Grassia, L.; Simon, S. L., Modeling volume relaxation of amorphous polymers:

modification of the equation for the relaxation time in the KAHR model. Polymer

2012, 53 (16), 3613-3620.

149. Scherer, G. W., Volume relaxation far from equilibrium. J. Am. Ceram. Soc. 1986,

69 (5), 374-381.

150. Moynihan, C.; Crichton, S.; Opalka, S., Linear and non-linear structural relaxation.

J. Non-Cryst. Solids 1991, 131, 420-434.

151. Vyazovkin, S.; Sbirrazzuoli, N.; Dranca, I., Variation of the effective activation

energy throughout the glass transition. Macromol. Rapid Commun. 2004, 25 (19),

1708-1713.

152. Hodge, I., Effects of annealing and prior history on enthalpy relaxation in glassy

polymers. 6. Adam-Gibbs formulation of nonlinearity. Macromolecules 1987, 20

(11), 2897-2908.

153. Hodge, I., Adam-Gibbs formulation of nonlinearity in glassy-state relaxations.

Macromolecules 1986, 19 (3), 936-938.

154. Hodge, I. M.; Huvard, G. S., Effects of annealing and prior history on enthalpy

relaxation in glassy polymers. 3. Experimental and modeling studies of

polystyrene. Macromolecules 1983, 16 (3), 371-375.

155. McKenna, G. B.; Simon, S. L., Structural recovery and physical aging of polymeric

glasses. In Polymer Glasses, CRC Press: 2016; pp 39-70.

156. McKenna, G. B.; Simon, S. L., 50th Anniversary Perspective: Challenges in the

dynamics and kinetics of glass-forming polymers. Macromolecules 2017, 50 (17),

6333-6361.



1549-1558.

158. Boucher, V. M.; Cangialosi, D.; Alegría, A.; Colmenero, J.; González-Irun, J.; Liz-

Marzan, L. M., Accelerated physical aging in PMMA/silica nanocomposites. Soft

Matter 2010, 6 (14), 3306-3317.


40

159. Bian, Y.; Pejanović, S.; Kenny, J.; Mijović, J., Dynamics of multifunctional

polyhedral oligomeric silsesquioxane/poly (propylene oxide) nanocomposites as

studied by dielectric relaxation spectroscopy and dynamic mechanical

spectroscopy. Macromolecules 2007, 40 (17), 6239-6248.





146 (20), 203329.

162. Guo, Y.; Zhang, C.; Lai, C.; Priestley, R. D.; D’Acunzi, M.; Fytas, G., Structural

relaxation of polymer nanospheres under soft and hard confinement: isobaric versus

isochoric conditions. ACS nano 2011, 5 (7), 5365-5373.

163. Boucher, V. M.; Cangialosi, D.; Alegría, A.; Colmenero, J., Enthalpy recovery in

nanometer to micrometer thick polystyrene films. Macromolecules 2012, 45 (12),

5296-5306.

164. Pye, J. E.; Rohald, K. A.; Baker, E. A.; Roth, C. B., Physical aging in ultrathin

polystyrene films: Evidence of a gradient in dynamics at the free surface and its

connection to the glass transition temperature reductions. Macromolecules 2010,

43 (19), 8296-8303.

165. Green, P. F.; Glynos, E.; Frieberg, B., Polymer films of nanoscale thickness: linear

chain and star-shaped macromolecular architectures. Mrs Communications 2015, 5

(3), 423-434.

166. Koh, Y. P.; Simon, S. L., Structural Relaxation of Stacked Ultrathin Polystyrene

Films. Journal of Polymer Science Part B-Polymer Physics 2008, 46 (24), 2741-

2753.



095701.




polymers. PCCP 2018, 20 (18), 12356-12361.





41



172. Cangialosi, D.; Boucher, V. M.; Alegria, A.; Colmenero, J., Direct Evidence of

Two Equilibration Mechanisms in Glassy Polymers. Phys. Rev. Lett. 2013, 111 (9),

5.



Acta 2019, 677, 60-66.



175. Odian, G., Principles of polymerization. John Wiley & Sons: 2004.

176. Gupta, S. K.; Kumar, A., Reaction engineering of step growth polymerization.

Springer Science & Business Media: 2012.

177. Ehlers, J.-E.; Rondan, N. G.; Huynh, L. K.; Pham, H.; Marks, M.; Truong, T. N.,

Theoretical study on mechanisms of the epoxy− amine curing reaction.

Macromolecules 2007, 40 (12), 4370-4377.

178. Jang, J.; Kim, S. C.; Lee, Y., Reaction pathway of liquid crystalline epoxy

resin/aromatic diamine curing system. Macromol. Rapid Commun. 2000, 21 (14),

960-963.

179. Amanuel, S.; Malhotra, V. M., Effects of physical confinement (< 125 nm) on the

curing behavior of phenolic resin. J. Appl. Polym. Sci. 2006, 99 (6), 3183-3186.

180. Li, Q.; Simon, S. L., Surface Chemistry Effects on the Reactivity and Properties of

Nanoconfined Bisphenol M Dicyanate Ester in Controlled Pore Glass.

Macromolecules 2009, 42 (10), 3573-3579.

181. Koh, Y. P.; Li, Q.; Simon, S. L., T g and reactivity at the nanoscale. Thermochim.

Acta 2009, 492 (1), 45-50.

182. Lopez, E.; Simon, S. L., Trimerization Reaction Kinetics and T g Depression of

Polycyanurate under Nanoconfinement. Macromolecules 2015, 48 (13), 4692-

4701.

183. Li, Q.; Simon, S. L., Curing of bisphenol M dicyanate ester under nanoscale

constraint. Macromolecules 2008, 41 (4), 1310-1317.

184. Tarnacka, M.; Dulski, M.; Starzonek, S.; Adrjanowicz, K.; Mapesa, E. U.;

Kaminski, K.; Paluch, M., Following kinetics and dynamics of DGEBA-aniline

polymerization in nanoporous native alumina oxide membranes–FTIR and

dielectric studies. Polymer 2015, 68, 253-261.


42

185. Sanz, B.; Ballard, N.; Marcos-Fernández, Á.; Asua, J. M.; Mijangos, C.,

Confinement effects in the step-growth polymerization within AAO templates and

modeling. Polymer 2018, 140, 131-139.


43

Figure 2.1 Schematic of a DSC heating scan with glass transition, melting, and an

exothermic reaction.


44

Figure 1.2 Schematic of a UFS 1 sensor (reproduced from [14] with permission from

Elsevier). The inset image shows the heating area of UFS1 chip sensor marked with a

red boundary.


45

Figure 2.3 Enthalpy versus temperature schematic for melting transition.


46

Figure 2.4 Schematic of a heat flow scan showing depressed melting point in overfilled

nanopores.


47

Figure 2.5 Enthalpy versus temperature schematic of glass transition on cooling.


48

Figure 2.6 Enthalpy versus temperature schematic for fictive temperature obtained

on heating.


49

Figure 2.7 Schematic showing DSC traces obtained on heating after cooling

different rates. Fictive temperature calculation using Moynihan’s method.


50

Figure 2.8 (a) Schematic of enthalpy recovery during isothermal aging at Ta (b)

Enthalpy recovery of polystyrene for intrinsic isotherm experiments (adapted from

Lopez and Simon [136] with permission from ACS)


51

Figure 2.9 (a) Schematic of asymmetry of approach experiment, where down and up

jumps are made from equilibrium (b) Enthalpy recovery of polystyrene for down

and up jump experiments showing asymmetry of approach (adapted from Lopez

and Simon [136] with permission from ACS)


52

Figure 2.10 (a) Schematic of memory effect experiment, where Ta is reached in two

steps: 1) a down jump to T1 from To and partial aging at T1 until fictive temperature

equals Ta, 2) a final jump from partially aged state to Ta (b) Enthalpy recovery of

polystyrene demonstrating memory effect (adapted from Lopez and Simon [136]

with permission from ACS).


53

Figure 2.11 (a) Enthalpy versus temperature and (b) Heat flow versus temperature

schematics showing the broad low-temperature endotherm.


54

CHAPTER 3

MATERIALS

3.1 Nanopore confinement

Two types of nanopores matrices, Anodic Aluminum Oxide nanopores (AAO)

and borosilicate controlled pore glass (CPG), were used in this study. AAO nanopores

were used for experiments in chapters 4-7, whereas CPG nanopores were used for

experiments in chapter 8. The specifications of AAO nanopores and CPG nanopores are

listed in Tables 3.1 and 3.2, respectively. In chapter 4, the AAO nanopores with a

thickness of 5 µm and pore diameters of 20 and 55 nm were used to study the effect of

nanoconfinement on melting, whereas AAO templates with 50 µm thickness and pore

diameters of 18 and 55 nm were used for X-ray diffraction measurements to improve the

signal to noise ratio. In chapter 5, the AAO nanopores with a thickness of 5 µm and pore

diameters of 55 and 350 nm were used as substrates for micronscale polystyrene films. In

chapter 6, the AAO nanopores with a thickness of 5 µm and pore diameters of 20, 55 and

350 nm were used to prepare AAO supported PS nanorods of chosen diameter. The AAO

nanopores were also used as molds to prepare 2D stacked nanorods to study glass

transition behavior; 20 and 350 nm stacked PS rods were also used in chapter 7 for

enthalpy recovery studies. The thickness of the AAO template was limited to 5 μm for

Flash DSC in order to minimize the thermal lag effects on the Flash DSC.1-3 The AAO

templates were cleaned to remove the surface impurities by immersing in

dichloromethane for 3-5 minutes and subsequently washing them several times with

methyl alcohol before drying them in the vacuum oven for two hours at 150 °C. The


55

vacuum dried templates were then stored under a desiccant to prevent absorption of

adventitious moisture. In chapter 8, CPG nanopores with pore diameters 7.5 and 55 nm

were used as a nanoconfinement matrix to study the effect of nanoconfinement on epoxy-

amine step-growth polymerization kinetics. Prior to use, CPG was cleaned with boiling

nitric acid at 110 °C for 10 hours and subsequently washed with deionized water several

times before vacuum drying at 285 °C for 24 hours. Cleaned and dried CPG was stored

under desiccant to prevent absorption of adventitious water.

3.2 n-alkanes

The n-alkanes used in chapter 4 of this dissertation were n-hexadecane (Sigma-

Aldrich, 99 % purity) and n-nonadecane (Arcos Organics, 99 % purity), both were used

without further purification.

3.3 Polystyrene films on different substrates

This section lists the materials and sample making procedures that were used for

experiments in chapter 5.

A high molecular weight, atactic polystyrene (PS) (Scientific Polymer Products

Inc., USA) with a weight-average molecular weight of 2287 kg/mol and a PDI of 1.04 was

used to prepare films placed on the bare chip, Krytox oil and 55 nm AAO template. Another

atactic polystyrene (PS) with a number-average molecular weight of 2415 kg/mol and a

PDI of 1.15 was used to prepare the film placed on top of 350 nm AAO template.

Polystyrene films were prepared by spin-coating 10 wt % solution of polystyrene

in toluene (99.999% purity, HPLC grade, Sigma-Aldrich) on hydrophilic silicon and mica

substrates. The thicknesses of the films made using both the molecular weights were


56

measured using an atomic force microscope (Agilent technologies) in tapping mode by

making a scratch on the film on top of silicon wafer; the thicknesses were measured to be

as 1.3 ± 0.1 µm and 1.3 ± 0.3 µm for Mn = 2,199,000 and 2,100,000 g/mol, respectively.

Polystyrene films were placed on the Flash DSC sensors on top of four different

substrates. In case of PS films on Krytox oil and bare chip, two PS films were cut directly

from the silicon substrate where one PS film was placed on top of Krytox oil (DuPontTM)

already present on the heating area of the chip sensor, and the other film was transferred

directly on to the surface of the heating area using a wire loop with a blob of water to

prevent folding of the film. The PS film that was transferred directly onto the chip with the

help of water was dried for a week at room temperature under a desiccant to eliminate

water. The PS films that were placed on AAO substrates were floated on water from the

mica substrate and picked up on a wire mesh, which was followed by a day of ambient

drying and 2 days of vacuum drying at 50 °C. The dried films were placed on top of two

AAO substrates of pore diameters 55 and 350 nm (see Table 3.1 for specifications),

respectively; additionally, the films were allowed to adhere to the template for 30 minutes

at 120 °C in a vacuum oven.

3.4 Indium and vapor-deposited gold

In addition to polystyrene, gold (Kurt J. Lesker Company, Purity: 99.99 %) and

indium (Mettler Toledo, Purity: 99.995 %) were also used for experiments in chapter 5. 50

± 2 nm thick gold was vapor-deposited on the heating area of the Flash DSC chip under

vacuum at two different substrate temperatures (Ts), 23 and 125 °C. In case of indium, a

small pellet was flattened out to approximately ~1 µm thickness and placed on the heating

area of the Flash DSC chip.


57

3.5 AAO supported and stacked Polystyrene nanorods

This section lists the materials and sample making procedures for samples used

for experiments in chapters 6 and 7.

The high-molecular-weight atactic polystyrene (PS) (Mw = 2415 kg/mol, PDI =

1.15) used in this study was purchased from Polymer Source Inc; a high molecular

weight PS was specifically used to prevent the stacked rods from melting together and

form a bulk polymer. The weight average molecular weight (Mw) and the number average

molecular weight (Mn) of as received PS was obtained by performing gel permeation

chromatography (Tosoh EcoSEC) with an RI detector. The GPC samples were prepared

by dissolving PS in HPLC-grade THF for 24 hours at room temperature. The dissolved

solutions were filtered through a 0.45 µm PTFE syringe filter before loading into the

auto-sampler. Manufacture reported and recharacterized molecular weights of PS are

shown in Table 3.3

The AAO supported and stacked polystyrene nanorods were synthesized by

vacuum melt infiltration of a precursor polystyrene film into an AAO template4-5. In case

of supported polystyrene nanorods, the thickness of a precursor film was chosen to

exactly fill the pores of the AAO template. After various trials based on the available

volume in the pores, films with thicknesses of 0.45 μm, 0.70 μm, and 1.3 μm were chosen

to be vacuum infiltrated into 20, 55 and 350 nm AAO templates (specifications in Table

3.1), respectively. The vacuum infiltration into the aforementioned templates was done at

190 °C for 4 hours to yield AAO supported PS nanorods of chosen diameter. The

precursor films were produced by spin-coating concentrated (~10 wt. %)

polystyrene/toluene solutions (using HPLC-grade, 99.99 % pure toluene) onto cleaved


58

mica; subsequently, the films were floated on water, picked up by a tweezer and dried for

48 hours under vacuum at 50 °C before they were placed atop the AAO template for

infiltration. The schematic of the infiltration process for AAO supported PS nanorods is

shown in the upper section of Figure 3.1. In case of stacked PS nanorods, a thicker

polystyrene film (~ 50 μm), prepared by compression molding under vacuum in a hot

press at 170 °C, was chosen to infiltrate into AAO templates for all the pore diameters

mentioned. The infiltration conditions were similar to that of AAO supported PS

nanorods. After infiltration, the AAO template was removed by dissolving it in 1 M

sodium hydroxide solution; the supernatant and the excess PS film holding PS nanorods

was vacuum filtered with copious amounts of deionized (DI) water. The excess PS film

with the nanorods was collected and dried in vacuo at 50 °C for 24 hours. The PS

nanorods were separated from the excess PS film by delicately cutting them with a

scalpel. The schematic describing the infiltration process for stacked PS nanorods is

shown in the lower section of Figure 3.1. The stacked PS rods that were characterized for

glass transition behavior in chapter 6, are also used in chapter 7 to perform enthalpy

recovery studies. SEM images of stacked PS nanorods are shown in Figure 3.2. Images

were captured using a Hitachi S-4300 high resolution SEM after removal of the AAO

template and before and after the separation of nanorods from the excess PS film

substrate. The molecular weights of polystyrene nanorods was obtained from the same

GPC using the excess polystyrene film which was under similar processing conditions as

the nanorods; molecular weights of polystyrene nanorods are shown in Table 3.3. The

weight average molecular weight of the polymer significantly reduced to 1000 kg/mol


59

and the PDI increased to 1.48; as observed from previous studies6-7, the resulting change

in Tg due to change in molecular weight is approximately 0.05 K.

3.6 Epoxy-amine monomer mixture for linear epoxy polymerization

The liquid epoxy resin, Bisphenol A diglycidyl ether (DGEBA, Sigma Aldrich,

Purity: > 99 %) was used in this study; its epoxy equivalent weight is 176 g/eq. An

aromatic amine, aniline (Alfa Aesar, Purity: 99.99 %), was used as the curing agent; its

amine hydrogen equivalent weight is 46.6 g/eq. A 1:1 stoichiometric cure mixture was

prepared by mixing 26.5 parts by weight of aniline and 100 parts by weight of DGEBA;

applying the rule of mixtures the density of the monomer mixture is 1.16 g/cm3. Several

batches of the cure mixture were prepared and stored under a desiccant in a freezer below

-10 °C to avoid curing during storage. The monomer mixture was used in chapter 8 to

study the nanoconfinement effect on linear epoxy polymerization.


60

References

1. Toda, A.; Konishi, M., An evaluation of thermal lags of fast-scan microchip DSC

with polymer film samples. Thermochim. Acta 2014, 589, 262-269.

2. Schawe, J. E., Measurement of the thermal glass transition of polystyrene in a

cooling rate range of more than six decades. Thermochim. Acta 2015, 603, 128-

134.



21.

4. Martín, J.; Maiz, J.; Sacristan, J.; Mijangos, C., Tailored polymer-based nanorods

and nanotubes by" template synthesis": From preparation to applications. Polymer

2012, 53 (6), 1149-1166.

5. Zhang, M.; Dobriyal, P.; Chen, J.-T.; Russell, T. P.; Olmo, J.; Merry, A., Wetting

transition in cylindrical alumina nanopores with polymer melts. Nano Lett. 2006, 6

(5), 1075-1079.

6. Plazek, D. J.; O'Rourke, V. M., Viscoelastic behavior of low molecular weight

polystyrene. Journal of Polymer Science Part A‐2: Polymer Physics 1971, 9 (2),

209-243.

7. Simon, S. L.; Sobieski, J.; Plazek, D., Volume and enthalpy recovery of

polystyrene. Polymer 2001, 42 (6), 2555-2567.


61

Table 3.1 Specifications of AAO nanopore templates

Pore Diameter (nm) Template Thickness (µm) Manufacturer

18 ± 1.8 a 50 Synkera Technologies, USA

55 ± 2.0 a 5 and 50 Synkera Technologies, USA

20 ± 1.5 a 5 Universidad de Oviedo, Spain

350 ± 45.0a 5 Universidad de Oviedo, Spain a Standard deviations were provided by the manufacturers


62

Table 3.2 Specifications of CPG nanopores

Avg. Pore

Diametera (nm)

Specific Pore Volumea

(cm3

/g)

Surface Areac

(m2

/g)

CPG

8.0 ± 0.7b 0.49 197

54.8 ± 5.5b 1.18 49.5

a Determined by mercury intrusion method b Standard deviations were measured by ultrasonic sieving method

c Measured by nitrogen adsorption method


63

Table 3.3 Polystyrene Molecular weights from GPC

Sample Mn (kg/mol) Mw (kg/mol) PDI

As received PSb 2100 2415 1.15

As received PSa 1700 ± 150 2000 ± 110

1.17

PS Nanorods 675 ± 80 1000 ± 180 1.48

a manufacturer reported b recharacterized using GPC


64

Figure 3.1 Preparation of AAO supported and stacked PS nanorods using vacuum

melt infiltration technique


65

Figure 3.2 Scanning electron micrographs of PS nanorods after dissolving the AAO

and before and after separation from the film substrate. The samples were sputtered

with a thin layer of iridium (2- 5 nm) before imaging.


66

CHAPTER 4

MELTING BEHAVIOR OF N-ALKANES IN ANODIC ALUMINUM

OXIDE (AAO) NANOPORES USING FLASH DIFFERENTIAL

SCANNING CALORIMETRY

4.1 Introduction

A widely used experimental technique to probe nanoscale confinement effects is

differential scanning calorimetry (DSC). Advancements in the field of calorimetry have

led to the advent of fast scanning calorimetry, allowing heating and cooling rates as high

as 105 K/s.1-3 Such rapid scanning rates are able to mirror conditions during industrial

scale polymer processing,1 as wells as facilitating measurements of the melting point of

sucrose4 and silk fibroin protein5 and the glass transition of rapidly crystallizing

materials6. In addition, the rapid scanning rates offer advantages in terms of measuring

small samples, with sample masses typically ranging from 10 ng to 1 μg. This advantage

enables the study of the properties of single ultra-thin polymeric films,7-9 which otherwise

is tedious in a conventional DSC due to the need for milligrams of material. Although

thin films have been used to probe the nanoconfinement effects with the Flash DSC, the

2D nanopore confinement geometry has never been used with rapid scanning DSC to the

best of our knowledge, and that is the aim of this work.

In this study, an anodic aluminum oxide (AAO) nanoporous membrane is used as

a nanoconfinement matrix for investigation of the phase transitions of n-hexadecane

(C16H34) and n-nonadecane (C19H40) with rapid scanning Flash DSC. The results are

compared to previous studies.10-13 Although our primary objective is to demonstrate the

ability to study nanopore-confined samples with Flash DSC, nanoconfinement of


67

paraffins (n-alkanes) also finds application in the field of thermal energy storage as phase

change materials (PCMs) especially for thermal energy demands below 120 °C due to the

high latent heat and negligible supercooling.14 Furthermore, microencapsulation and

nanoencapsulation of n-alkanes has contributed to increasing the efficiency of thermal

energy storage in PCMs by enhancing the heat transfer area and broadening the range of

melting temperatures utilizing the size-dependent melting behavior.15-17 Nanoconfined n-

alkanes have also been used as model systems to understand the morphology and melting

behavior of polyolefins at the nanoscale18.

4.2 Experimental

4.2.2 Methodology

Flash differential scanning calorimetry

The experiments were performed on a Mettler Toledo Flash DSC 1 equipped with

a Freon intercooler maintained at -105 °C and a nitrogen gas purge of 20 ml/min. UFS 1

calorimetric chips, both bare and gold coated (a layer of 38.0 ± 0.6 nm is deposited in-

house using physical vapor deposition), were conditioned and corrected according to the

manufacturer’s procedure prior to use. The gold-coated chips were used to verify that

chip surface energy did not influence Tm of n-alkanes. In addition to the manufacturer’s

correction, an additional temperature correction was made for each individual chip based

on the melting of bulk n-hexadecane (C16) and n-nonadecane (C19), as discussed later.

All of the measurements for bulk and nanoconfinement studies for a particular

material followed a similar temperature program with a fixed heating and cooling rate of

±600 K/s. C16 was scanned between -55 and 50 °C, whereas C19 was scanned between 0

and 70 °C. Six cooling and heating cycles were used in both cases, and data were


68

analyzed on heating. The upper temperature for cooling/heating cycles was chosen such

that negligible sample loss due to vaporization occurred during the six cycles performed;

this was confirmed as the scans superposed exactly within the noise of the measurements

(0.015 ± 0.001 mW).

The Flash DSC measurement procedure involved the following steps: 1) An

empty sensor was first scanned following the cooling and heating cycle described above.

2) A piece of an AAO template (≤ 0.09 mm2) was cut from the parent template under a

microscope and transferred onto the calorimetric sensor, shown in Figure 4.1; and a heat

flow measurement similar to the empty sensor was performed on the blank AAO

template. 3) The AAO template was moved to the side and n-alkane was transferred onto

the heating area and the thermal behavior of the bulk n-alkane was measured. 4) The

piece of AAO template was then placed on the bulk n-alkane and imbibement occurred

spontaneously. The measurements commenced immediately on the generally overfilled

sample (i.e., filled template + bulk excess sample); in some cases, additional alkane was

added after step 4 to obtain an overfilled sample. For studies of the effect of pore fullness,

repeated evaporation was performed at 100 °C for C16 and 160 °C for C19 followed by a

heating scan, and this cycle was repeated until evaporation was complete.

X-ray diffraction

The powder X-ray diffraction patterns were obtained using a Rigaku Ultima Ⅲ

powder diffractometer using CuKα (1.5418 Å) radiation. The incident X-ray beam was

modified using the Rigaku Cross Beam Optics system to create parallel beam geometry.

The patterns were obtained for C16 and C19, in bulk, in 55 nm AAO and in 18nm AAO. In

case of C16, the patterns were collected at -18 °C (maintained using a cold metal block


69

immersed in liquid nitrogen) in the 2θ range of 3 – 45°; in case of C19, the patterns were

obtained at room temperature in 2θ range of 3 – 40°. In both cases, the data collection

rates were set at 5°/min with a step width of 0.02°.

4.3 Data analysis

4.3.1 Symmetry analysis

When a sample is heated and cooled at the same rate, the heat flow curves on

heating and cooling are expected to be asymmetric about the x-axis due to the heat losses

and due to the heat capacity of the UFS 1 sensor (~ 1.7 x 10-8 J/g).2, 19 Heat flows are,

thus, corrected using a symmetry analysis19 in order obtain the absolute heat capacity. To

perform the symmetry analysis, regions away from transitions are chosen as shown in

Figure 4.2.a, i.e., below and above the region of phase transitions. The chosen regions are

linearly fitted, and then a symmetry line with two sections is constructed by taking the

arithmetic average of the fitted lines for cooling and heating scans. The entire symmetry

line is constructed by interpolating in the region of transition(s). Finally, the sample heat

flows are corrected by subtracting the symmetry line and the symmetry corrected empty

sensor heat flows. In the case of material confined in the nanopores, an additional

contribution of heat flow from the AAO templates also exists. So, for the symmetry

analysis of nanoconfined samples, the symmetry corrected heating and cooling heat flows

of blank AAO templates are subtracted from the nanoconfined heat flows. A typical

result is shown for corrected heat capacity data in Figure 4.2.b for C16 in AAO.

3.2.2 Estimation of Sample Mass and Pore Fullness

Flash DSC requires ultra-low sample masses for the experiments. Since sample

masses cannot be determined by weighing, they are determined from the data obtained


70

from the experiment. The first method used to calculate sample mass is based on the

corrected heat capacity coupled with data from the literature:20-22

m =Cp,meas

Cp,lit

(4.1)

where m is sample mass, Cp,meas is the corrected heat capacity from the measurements in

JK−1, and Cp,lit is the specific heat capacity in Jg−1K−1 from the literature; the latter are

obtained from the parameters in Table 4.120 for two liquids of interest.

A second technique used in the calculation of mass is to use the enthalpic change

relative to that in the literature for a first order transition:

m =∆Hmeas

∆Hf

(4.2)

where m is the sample mass, ∆Hmeas is the heat released during melting in J, and ∆Hf is

the bulk heat of fusion of the material in Jg−1. The values of sample masses calculated

from Equation 4.1 (1.86 ng) and Equation 4.2 (1.94 ng) for the symmetry-corrected data

in Figure 4.2.a agree quite well. For the described experiments, the sample masses ranged

from 4 to 100 ng with a typical error of ~ 5 %.

Pore fullness in the overfilled pores is determined by first deconvolution of

overlapped peaks associated with bulk and nanoconfined melting as shown in Figure 4.3.

The pore fullness is determined from the relative amount of heat release:


71

Pore fullness =(

∆Hmeas,bulk

∆Hf) + (

∆Hmeas,conf

∆Hf(d))

(∆Hmeas,conf

∆Hf(d))

(4.3)

where ∆Hmeas,bulk and ∆Hmeas,conf are the measured heats in J associated with the

melting peaks for the bulk and nanoconfined n-alkane, respectively (i.e., the areas under

red and green peaks in Figure 4.3), ∆Hf is the bulk heat of fusion of the material in Jg−1,

and ∆Hf(d) is the heat of fusion of the material in nanopores of pore diameter (d) in Jg−1.

For C16, ∆Hf(d) is available13, but in case of C19, due to a lack of data in the literature, it

is assumed that ∆Hf(d) ≈ ∆Hf. This latter assumption is expected to give a reasonable

estimate for pore fullness; for example, for C16, the error in assuming ∆Hf(d) ≈ ∆Hf is

negligible in 55 nm AAO pores and less than 3 % in 20 nm AAO pores. Similarly, if a

polymorph with a different heat of fusion is present in the pores, similar magnitudes of

error are expected in the degree of filling since the change in ∆Hf for various polymorphs

of organic crystals are typically in the range of 10-20 %.23-24 As we show later, the

melting point depression is independent of the degree of fullness; hence, reasonable

estimates of pore fullness are sufficient for this work.

For underfilled pores, which are obtained by partially evaporating the n-alkane

from overfilled samples, the pore fullness is:

Pore fullness =∆Hmeas,underfilled

∆Hmeas,conf

(4.4)

where ∆Hmeas,underfilled is the measured heat released during the melting of n-alkane in

partially filled nanopores (area under the black peak for underfilled pores) and


72

∆Hmeas,conf is again the measured heat released during the melting of n-alkane in

completely full nanopores; the latter is the area under the red peak in Figure 4.3, obtained

from the previous scans of the same sample with overfilled pores, i.e., prior to partial

vaporization.

4.4 Results

4.4.1 Melting of C16 in the bulk and AAO nanopores

Representative scans of symmetry-corrected melting endotherms of bulk and

nanoconfined C16 are shown in Figure 4.4.a and Figure 4.4.b for 55 and 20 nm pores,

respectively. The melting point is taken as the onset point. For the bulk samples shown in

the uppermost scans, Tm= 19.88 °C (Figure 4.4.a) and Tm= 18.47 °C (Figure 4.4.b), are

higher than the NIST literature value (Tm= 18 °C).25 Melting temperatures for the bulk

ranged from 15.30 to 20.60 °C with an average of 17.84 °C ± 1.96 °C when measured on

ten different flash DSC sensors. For six sensors coated with gold the Tms ranged from

16.00 to 19.50 °C with an average of 18.17 ± 1.38 °C. The deviations of Tm from

literature values on both bare and gold-coated chips are typical of the errors for Flash

sensors8 and indicate that additional calibration of a given sensor is needed for more

accurate data. In fact, n-hexadecane can be used as a temperature calibrant for the Flash

DSC; and, it is indeed used in this study as an internal standard to determine the melting

point depression in the nanopores (Tm(d)), as discussed below.

The melting of C16 in 55 and 20 nm overfilled AAO nanopores results in two

overlapping peaks as shown in Figure 4.3 and Figures 4.4.a and 4.4.b for the scans with

pore fullness greater than 100 %. The lower temperature peak is related to the melting of


73

C16 in the nanopores, whereas the peak at the higher temperature is related to the bulk,

which provides an internal reference to quantify the magnitude of depression (ΔTm =

Tm − Tm(d)) in the nanopores. The melting points are obtained from the onsets of the

resolved peaks after deconvolution (with the resolved bulk melting peaks shown in green

and the corresponding onsets indicated by arrows in Figures 4.4.a and 4.4.b).

The average melting point depression (∆Tm) for 55 nm overfilled samples is 4.20

± 0.60 °C based on the average of four overfilled samples on three chips. Similarly, the

∆Tm for 20 nm overfilled samples is 6.01 ± 0.24 °C based on the average of ten overfilled

samples on one chip. By systematically evaporating the material from the overfilled

pores, we obtain underfilled pores with pore fullness less than 100 %; also shown in

Figures 4.4.a and 4.4.b. The melting point of AAO nanoconfined C16 is found to be

independent of pore fullness with an average melting point of 13.77 ± 0.18 °C in 55 nm

AAO pores and 11.99 ± 0.21 °C in 20 nm AAO pores, respectively. These melting point

values were calculated based on overfilled and underfilled samples on various chips and

with the temperature corrected based on the bulk Tm of C16 on the respective chip.

4.4.2 Solid-solid transition and melting of C19 in bulk and AAO nanopores

Symmetry-corrected heat flows for the melting of bulk and nanopore-confined C19

are shown in Figures 4.5.a and 4.5.b. The representative heating scans for the bulk C19,

uppermost scans, reveal a solid-solid transition along with the melting transition.

Polymorphic transitions like solid-solid transitions occur in odd numbered n-alkanes

starting from n-nonane (n-C9H20) and have been suggested to arise from transition

between a stable crystalline phase to a rotator phase with conformational disorder prior to

melting.20, 26-27 In the case of C19, specifically, the transition is from an orthorhombic


74

crystal phase to a hexagonal rotator phase.12 The bulk solid-solid transition temperature

(Tss) and the bulk melting point (Tm) for the representative sample in Figure 4.5.a are

22.50 °C and 31.90 °C, whereas they are 22.95 °C and 32.45 °C for the sample shown in

Figure 4.5.b. The average transition temperatures for samples measured on six different

chips are Tss = 24.18 ± 1.86 °C and Tm = 33.67 ± 1.84 °C, respectively. Although the

transition temperatures are typically 2 to 3 °C higher than the literature values28 (Tss =

22.81 °C, Tm = 31.96 °C), the average difference in the two transition temperatures (∆T =

9.43 ± 0.30 °C) is constant and consistent with the literature (∆T = 9.15 °C). Hence, we

use the bulk Tm of C19 to perform an additional temperature correction for the chips and

as an internal reference for the nanoconfined samples, similar to the analyses for our C16

data.

Representative scans of C19 in 55 and 20 nm overfilled pores are shown in Figures

4.5.a and 4.5.b, for pore fullnesses greater than 100 %, and overlapping peaks are

observed for bulk and nanoconfined transitions for both melting and solid-solid

transitions. The overlapping peaks were deconvoluted and resolved into bulk and

nanoconfined peaks for each respective transition. The onsets of bulk transitions are

indicated by arrows and the deconvoluted bulk melting peaks and bulk solid-solid

transitions peaks are shown in green and violet in Figures 4.5.a; only the deconvoluted

bulk melting peaks are shown in Figure 4.5.b. The average melting point depression

(ΔTm) and solid-solid transition depression (ΔTss = Tss − Tss(d)) for two overfilled

samples in 55 nm pores are ΔTm = 2.46 ± 0.40 °C and ΔTss = 1.94 ± 0.15 °C; and, for five

overfilled samples in 20 nm pores the ΔTm and ΔTss are 4.2 ± 0.51 °C and 3.01 ± 0.29 °C,

respectively. Also shown in Figure 4.5.a and Figure 4.5.b are representative scans for 55


75

and 20 nm underfilled pores with pore fullness less than 100 %, obtained after

systematically evaporating the material from the overfilled pores; due to the low sample

mass, the solid-solid transition in underfilled nanopores cannot be discerned. Similar to

the case of C16 in AAO, pore fullness does not influence nanoconfined Tm. The average

melting point of C19 in the overfilled and underfilled nanopores was determined after the

corrections based on the bulk Tm; it was found to be independent of pore fullness at 29.50

± 0.40 °C for 55 nm pores and 27.76 ± 0.17 °C for 20 nm pores.

4.5 Discussion Melting of C16 in the 55 and 20 nm AAO pores resulted in melting point

depressions (ΔTms) of 4.20 ± 0.60 °C and 6.01 ± 0.24 °C, respectively. The results are

compared to the size-dependent melting behavior of C16 in various nanopore systems for

a range of pore sizes and pore matrices10-11, 13 in Figure 4.6. The melting behavior of C16

in different nanopore systems studied in the literature can be broadly categorized into two

trends, barring the lone point for 8 nm native CPG. The lower trend is the fit (blue dashed

line) obtained from the Gibbs-Thomson relationship (Equation 2.1) with σsl = 0.014 J m-

2,13 which is in good agreement with the ΔTms of silanized CPG, KIT-6, SBA-15, C-

SBA-15, and 300 nm native CPG nanopores.10, 13 The upper trend is a linear fit (brown

dashed line) through the ΔTms of silica-gel nanopores,11 which is also consistent with our

ΔTm in 55 nm AAO nanopores, although our ΔTm in 20 nm AAO pores is somewhat

lower and a linear fit for just our data is shown as the red dashed line. The magnitude of

ΔTm is known to depend on the surface chemistry and pore geometry, and these factors

along with tortuosity are tabulated in Figure 4.6 for the various nanoconfinement systems

plotted.


76

The surface chemistry of the nanopore matrices mentioned above are either

hydrophilic or hydrophobic as seen in Figure 4.6. The hydrophilic surfaces are defined by

the surface hydroxyl moieties (Al-OH29, Si-OH30), and the hydrophobic surfaces have

either trimethyl silyl groups (-Si(CH3)330) or carbon10. The confined material, C16, is a

non-polar, long-chain, n-alkane molecule with no specific interactions with either

hydrophilic or hydrophobic pore surfaces. A recent study by Takei et al. on the melting

behavior of short-chain n-hexane in nanopores confirmed that melting points were

“almost the same” in hydrophilic and hydrophobic pores (with the difference being less

than 2 °C for 6.4 nm pores).31 The data in Figure 4.6 are consistent with this finding that

the behaviors observed cannot be explained by pore chemistry as the lower trend is

comprised of both hydrophilic and hydrophobic nanopore systems.

Pore geometry defines the spatial dimensionality of the pore matrix. Several

studies reveal that a stronger confinement effect is expected in higher dimensional

pores;32-34 the Gibbs-Thomson model suggests otherwise, however, since the geometry

factor (A) is reduced for higher dimensional pores.13, 35-36 The upper trend in Figure 4.6

demonstrates a larger melting point depression, and hence a stronger confinement effect,

but the nanopore geometries that show this behavior include both 3D silica-gel and 2D 55

nm AAO nanopores. Most importantly, the lower trend, which demonstrated a weaker

confinement effect includes nanopore systems with spatial dimensionality ranging from

1D to 3D. Hence, spatial dimensionality cannot explain the different trends observed.

Tortuosity, which is defined as “the ratio of the mean effective path length and the

shortest possible distance in the absence of obstacles”37, also cannot account for different


77

trends given that nanopore matrices with low (1) and high (˃ 1.5) tortuosity exhibit each

behavior.

An alternative explanation to explain different size-dependent melting behavior is

the possible presence of a polymorph of C16 in the AAO nanopores and possibly the

silica-gel system comprising the upper trend. The non-zero intercepts of the trend lines

for both nanopore systems in Figure 4.6 indicate that the melting point of the crystal at

infinite size (i.e., 1/d = 0) differs from the nominal bulk value, indicating a different

crystal structure24. A similar behavior is observed in case of C19 in AAO nanopores, as

shown in Figure 4.7, for both melting and solid-solid transitions. The confinement of a

crystal in the nanopores can influence the crystal orientation due to preferential

packing,10, 24, 34, 37-42 and the orientation of the crystal is expected to be strongly

dependent on surface chemistry, pore geometry and tortuosity.34, 37 For example, phase

behavior of long chain n-alkanes in straight nanopores of MCM-41 and AAO nanopores

revealed a side by side stacking of molecules, parallel to the pore axis;38, 40, 43 on the other

hand, n-alkane molecules in Vycor glass nanopores assumed a 2D close-packed

arrangement as opposed to 3D arrangement in the bulk.10, 12, 44 The preferential

orientation of crystals in the nanopores can lead to polymorphism and different melting

behavior.12, 34, 41

The powder X-ray diffraction patterns in Figures 4.8.a and 4.8.b corroborate the

preferential orientation of n-alkanes in the AAO nanopores. The diffraction patterns of

bulk C16 and C19 shown in Figures 4.8.a and 4.8.b (upper most XRD patterns in red)

validate the expected triclinic and orthorhombic crystal structures for the bulk;34, 45

however, the diffraction patterns of C16 and C19 in the AAO nanopores (green XRD


78

pattern (55 nm) and blue XRD pattern (18 nm)) show preferential reflections at 2θ =

21.6° and 2θ = 35.4°, with the latter only strongly observed for C16 in the 18 nm AAO

pores. In other work on C19 in Vycor glass, Huber et al. observed that the Bragg

reflections from low diffraction angles (2θ < 15) were absent for material in Vycor glass

pores, indicating that the characteristic lamellar ordering of the bulk has been sacrificed

in the nanopores12. In addition, they found peak broadening at temperatures comparable

to ours,indicating some disorder, which may arise from the tortuous nature of the Vycor

pores. Here we similarly find an absence of low angle diffraction peaks for C16 and C19 in

both 55 and 18 nm AAO pores (shown in Figures 4.8.a and 4.8.b); however, we only see

slight peak broadening, presumably due to our straight pores. The suppression of the

lamellar ordering in the nanopores transforms the ordered bulk crystal structure into a

nematocrystalline structure with chains parallel to the pore axis.12, 34 This change in

crystal structure from the bulk has an additional influence in lowering the melting point

in the nanopores along with the size-dependent melting effect.

4.6 Conclusions

Anodic aluminum oxide (AAO) templates were successfully used as

nanoconfinement matrices on the Flash DSC. The influence of nanoconfinement on the

phase transitions of n-hexadecane and n-nonadecane was studied as a function of pore

diameter and pore fullness. Melting of n-hexadecane in the AAO pores revealed a

melting point depression (ΔTm) of 4.20 ± 0.60 °C in 55 nm AAO pores and 6.01 ± 0.24

°C in 20 nm AAO pores compared to the bulk, and was found to be independent of pore

fullness. Melting of n-nonadecane in AAO pores resulted in ΔTms of 2.46 ± 0.40 °C and

of 4.2 ± 0.51 °C and solid-solid transition depressions (ΔTsss) of 1.94 ± 0.15 °C and 3.01


79

± 0.29 °C in 55 and 20 nm AAO pores, respectively; the depressions were again

independent of pore fullness. A comparison of ∆Tm vs 1/d of C16 in AAO nanopores with

various nanopore matrices studied in the literature revealed at least two distinct trends for

nanoconfined melting behavior. Possible explanations to elucidate the different melting

behaviors based on surface chemistry, pore geometry, and tortuosity were ruled out.

Rather, the presence of a nematocrystalline structure in AAO confined C16 is the

presumed origin of the observed distinct melting behavior, as corroborated by the

presence of the Bragg peaks at only 2θ = 21.6° and 2θ = 35.4° and the absence of low

angle Bragg peaks (2θ < 15) for the confined material. The ∆Tm vs 1/d behavior for

melting and solid-solid transition for C19 similarly do not extrapolate to bulk values at

infinite crystal size (1/d = 0). C19 also only shows one Bragg peak at 2θ = 21.6°: These

results indicate that a nematocrystalline structure is formed in the AAO nanopores.


80

References

1. Poel, G. V.; Istrate, D.; Magon, A.; Mathot, V., Performance and calibration of the

Flash DSC 1, a new, MEMS-based fast scanning calorimeter. J. Therm. Anal.

Calorim. 2012, 110 (3), 1533-1546.



21.


nano-calorimeter: 1. The device. Thermochim. Acta 2010, 505 (1), 1-13.






3.

6. Shamim, N.; Koh, Y. P.; Simon, S. L.; McKenna, G. B., The glass transition of

trinitrotoluene (TNT) by flash DSC. Thermochim. Acta 2015, 620, 36-39.





Thermochimica Acta 2015, 603, 135-141.




10. Wang, L. P.; Sui, J.; Zhai, M.; Tian, F.; Lan, X. Z., Physical Control of Phase

Behavior of Hexadecane in Nanopores. The Journal of Physical Chemistry C 2015,

119 (32), 18697-18706.

11. Illeková, E.; Miklošovičová, M.; Šauša, O.; Berek, D., Solidification and melting

of cetane confined in the nanopores of silica gel. J. Therm. Anal. Calorim. 2011,

108 (2), 497-503.

12. Huber, P.; Wallacher, D.; Albers, J.; Knorr, K., Quenching of lamellar ordering in

an n-alkane embedded in nanopores. EPL (Europhysics Letters) 2004, 65 (3), 351.


81

13. Qin, Q.; McKenna, G. B., Melting of solvents nanoconfined by polymers and

networks. J. Polym. Sci., Part B: Polym. Phys. 2006, 44 (24), 3475-3486.

14. Rao, Z.; Wang, S.; Peng, F., Self diffusion and heat capacity of n-alkanes based

phase change materials: A molecular dynamics study. Int. J. Heat Mass Transfer

2013, 64, 581-589.

15. Konuklu, Y.; Paksoy, H. O.; Unal, M., Nanoencapsulation of n-alkanes with poly

(styrene-co-ethylacrylate) shells for thermal energy storage. Applied Energy 2015,

150, 335-340.

16. Zhang, J.; Feng, Y.; Yuan, H.; Feng, D.; Zhang, X.; Wang, G., Thermal properties

of C 17 H 36/MCM-41 composite phase change materials. Computational

Materials Science 2015, 109, 300-307.

17. Zhang, D.; Tian, S.; Xiao, D., Experimental study on the phase change behavior of

phase change material confined in pores. Solar Energy 2007, 81 (5), 653-660.

18. Su, Y.; Liu, G.; Xie, B.; Fu, D.; Wang, D., Crystallization features of normal

alkanes in confined geometry. Acc. Chem. Res. 2013, 47 (1), 192-201.




20. Huang, D.; Simon, S. L.; McKenna, G. B., Chain length dependence of the

thermodynamic properties of linear and cyclic alkanes and polymers. The Journal

of chemical physics 2005, 122 (8), 084907.

21. Ditmars, D.; Ishihara, S.; Chang, S.; Bernstein, G.; West, E., Enthalpy and heat-

capacity standard reference material: synthetic sapphire (a-Al2O3) from 10 to 2250

K. J. Res. Natl. Bur. Stand 1982, 87 (2), 159-163.

22. Vélez, C.; Khayet, M.; de Zárate, J. O., Temperature-dependent thermal properties

of solid/liquid phase change even-numbered n-alkanes: n-Hexadecane, n-

octadecane and n-eicosane. Applied Energy 2015, 143, 383-394.

23. Burger, A.; Ramberger, R., On the polymorphism of pharmaceuticals and other

molecular crystals. I. Microchimica Acta 1979, 72 (3), 259-271.

24. Beiner, M.; Rengarajan, G.; Pankaj, S.; Enke, D.; Steinhart, M., Manipulating the

crystalline state of pharmaceuticals by nanoconfinement. Nano Lett. 2007, 7 (5),

1381-1385.

25. Wolf, E. M.; Simon, S. L.; Plazek, D. J.; Soc Plast, E., Volume and enthalpy

recovery of polystyrene. 1998; Vol. 44, p 3411-3414.


82

26. Jiang, K.; Xie, B.; Fu, D.; Luo, F.; Liu, G.; Su, Y.; Wang, D., Solid− Solid Phase

Transition of n-Alkanes in Multiple Nanoscale Confinement. The Journal of


27. Maroncelli, M.; Qi, S. P.; Strauss, H. L.; Snyder, R. G., Nonplanar conformers and

the phase behavior of solid n-alkanes. J. Am. Chem. Soc. 1982, 104 (23), 6237-

6247.

28. http://webbook.nist.gov/chemistry/.

29. Buijnsters, J. G.; Zhong, R.; Tsyntsaru, N.; Celis, J.-P., Surface wettability of

macroporous anodized aluminum oxide. ACS applied materials & interfaces 2013,

5 (8), 3224-3233.



31. Takei, T.; Nakada, M.; Yoshikawa, N.; Hiroe, Y.; Yoshida, H., Effect of organic

functional groups on the phase transition of organic liquids in silica mesopores. J.

Therm. Anal. Calorim. 2016, 123 (3), 1787-1794.

32. Alba-Simionesco, C.; Coasne, B.; Dosseh, G.; Dudziak, G.; Gubbins, K.;

Radhakrishnan, R.; Sliwinska-Bartkowiak, M., Effects of confinement on freezing

and melting. J. Phys.: Condens. Matter 2006, 18 (6), R15.

33. Richert, R., Dynamics of nanoconfined supercooled liquids. Annu. Rev. Phys.

Chem. 2011, 62, 65-84.

34. Huber, P., Soft matter in hard confinement: phase transition thermodynamics,

structure, texture, diffusion and flow in nanoporous media. J. Phys.: Condens.

Matter 2015, 27 (10), 103102.

35. Sun, J.; Simon, S., The melting behavior of aluminum nanoparticles. Thermochim.

Acta 2007, 463 (1), 32-40.

36. Defay, R.; Prigogine, I.; Bellemans, A.; Everett, D., Surface tension and adsorption.

1966. Longmans, London.

37. Graubner, G.; Rengarajan, G. T.; Anders, N.; Sonnenberger, N.; Enke, D.; Beiner,

M.; Steinhart, M., Morphology of porous hosts directs preferred polymorph

formation and influences kinetics of solid/solid transitions of confined

pharmaceuticals. Crystal Growth & Design 2013, 14 (1), 78-86.

38. Okazaki, M.; Toriyama, K.; Anandan, S., Dynamics and packing mode of long-

chained n-alkane molecules in the nano-channel of MCM-41. Chem. Phys. Lett.

2005, 401 (4), 363-367.


83

39. Kumar, M. V.; Prasad, S. K., Influence of quenched disorder created by nanosilica

network on phase transitions in tetracosane. RSC Advances 2012, 2 (22), 8531-

8538.

40. Toriyama, K.; Okazaki, M., Molecular packing of long-chain n-alkanes in the

MCM-41 nanochannel as probed by the free radicals produced by γ-irradiation. The


41. Henschel, A.; Hofmann, T.; Huber, P.; Knorr, K., Preferred orientations and

stability of medium length n-alkanes solidified in mesoporous silicon. Physical

Review E 2007, 75 (2), 021607.

42. Wang, L. P.; Li, Q. F.; Wang, C.; Lan, X. Z., Size-Dependent Phase Behavior of

the Hexadecane–Octadecane System Confined in Nanoporous Glass. The Journal

of Physical Chemistry C 2014, 118 (31), 18177-18186.

43. Kim, B. S.; Jeong, Y. G.; Shin, K., Influence of surface property on the

crystallization of hentetracontane under nanoscopic cylindrical confinement. The


44. Huber, P.; Soprunyuk, V. P.; Knorr, K., Structural transformations of even-

numbered n-alkanes confined in mesopores. Physical Review E 2006, 74 (3),

031610.

45. Craig, S. R.; Hastie, G. P.; Roberts, K. J.; Sherwood, J. N., Investigation into the

structures of some normal alkanes within the homologous series C13H28 to

C60H122 using high-resolution synchrotron X-ray powder diffraction. J. Mater.

Chem. 1994, 4 (6), 977-981.


84

Table 4.1 Liquid state specific heat capacities, 𝐂𝐩 = 𝐚 + 𝐛𝐓 + 𝐜𝐓𝟐 with T in K, from

Ref. 20

Material a

(𝐉𝐠−𝟏𝐊−𝟏)

103×b

(𝐉𝐠−𝟏𝐊−𝟐)

105×c

(𝐉𝐠−𝟏𝐊−𝟑)

Temperature range

(°C)

n-hexadecane

(C16) 2.779 -6.5421 1.5543 22 to 55

n-nonadecane

(C19) 0.7256 6.3427 -0.4694 33 to 56


85

Figure 4.1 Flash DSC chip with AAO template in the heating area.


86

Figure 4.2 (a) symmetry analysis for a heat flow scan with phase transition of C16 in

AAO. The heat flow scans in red and blue represent the raw data. The sections

highlighted in black on the red and blue curves are the regions chosen to determine

the symmetry line. The orange line denotes the symmetry line that is to be subtracted

from the raw data. (b) Corrected heat capacity data of Figure 4.2.a after symmetry

analysis. (The y-axis is labelled positive on either side of the zero-axis since the heat

capacity of a material is always positive.)


87

Figure 4.3 A schematic of overfilled and underfilled nanopores. Resolved peaks

after deconvolution of overfilled pores are shown in green and red for confined and

bulk melting, respectively.


88

Figure 4.4 Heat flow data for n-hexadecane in bulk and (a) 55 nm AAO pores (b) 20

nm AAO pores; the melting in the nanopores is shown as a function of pore fullness.

The bulk melting peak obtained by deconvolution is indicated by arrows for the bulk

and overfilled pores.


89

Figure 4.5 Heat flow data for bulk n-nonadecane and n-nonadecane in (a) 55 nm AAO

pores and (b) 20 nm AAO pores. The heat flow data for nanoconfined C19 with

varying pore fullness is also presented.


90

Figure 4.6 The magnitude of the melting point depression for C16 in 55 and 20 nm

AAO pores (inverted solid red triangle), Linear fit through the 𝚫𝐓𝐦s of 55 and 20 nm

AAO pores (red dashed line), experimental data for silica-gel nanopores as function

of inverse pore diameter from reference 11 (upright brown triangles), linear fit

through the 𝚫𝐓𝐦s of 55 nm AAO and silica-gel nanopores (brown dashed line),

experimental data for KIT-6 (solid purple square); SBA-15 (solid lime green

diamond); C-SBA-15 (cyan right angled triangle); native CPG (solid green circles)

from reference 40, experimental data for silanized CPG as a function of inverse pore

diameter from reference 13 (open blue circles). Also shown are the Gibbs-Thomson

(G-T) predictions of 𝚫𝐓𝐦 using Equation 2.1 with the surface energy from reference

13 (blue dashed line). The properties of aforementioned nanopore matrices are

summarized in the appended table.


91

Figure 4.7 ∆𝐓𝐦 vs 𝟏 𝐝⁄ (solid red circles) and ∆𝐓𝐬𝐬 vs 𝟏 𝐝⁄ (purple solid squares) of

C19 in AAO nanopores. The red dashed line and purple solid line are obtained by

linear regression of the presented data.


92

Figure 4.8 (a) Overlaid Powder X-ray patterns of C16 in bulk (red), in 55 nm AAO

pores (green) and in 18 nm AAO pores (blue) at -18 °C. (b) Overlaid Powder X-ray

patterns of C19 in bulk (red), in 55 nm AAO pores (green) and in 18 nm AAO pores

(blue) at room temperature.


93

CHAPTER 5

ORIGIN OF THE BROAD ENDOTHERMIC PEAK OBSERVED AT

LOW TEMPERATURES FOR POLYSTYRENE AND METALS IN

FLASH DIFFERENTIAL SCANNING CALORIMETRY

5.1 Introduction

Broad low-temperature endothermic overshoots have been observed for polymers

in the glassy state (T<<Tg), both nano and micron scale alike, when studied using Flash

differential scanning calorimetry.1-3 The low temperature endotherms of micrometer thick

poly(4-tert butylstyrene) films demonstrated a cooling rate dependence, where the area of

the endotherm increased with decrease in cooling rate1-2. In addition, broad low-

temperature endotherms were also observed for polystyrene nanospheres3 whilst

performing structural recovery studies, where the low temperature endotherms increased

with increase in aging time and decrease in aging temperature; intermediate plateaus were

also observed during the relaxation process at as small as 100 s for 230 nm polystyrene

nanospheres.3 The presence of low temperature endotherm has been interpreted by

Cangialosi and co-workers1, 3-6 to mean that the glassy dynamics is faster at temperatures

T<<Tg where the glassy material exhibits highly viscous conditions, and slower dynamics

at vicinity of the Tg where a glassy material exhibit low viscosity, which is in contrast

with the fact that glassy dynamics slow down with increase in viscosity. In addition to the

studies using Flash differential scanning calorimetry, low temperature structural recovery

studies (Ta<<Tg) of various glassy polymers on conventional DSC also exhibited low

temperature broad endothermic peaks. Room temperature aging of three polymers,

poly(acrylate), poly(bisphenol-A-carbonate), and polysulfone showed aging plateau


94

between aging times of 60 days to 30 years due to the presence of a low temperature

endotherm.5 1D Stacked polystyrene thin films with thicknesses in the range of 30 nm

and 95 nm also exhibited broad low temperature endotherms contributing to the two-step

structural recovery process.4, 6 The existence of an endotherm at low temperature for

glassy polymers is certainly controversial due to the lack of systematic and scientific

studies. We hypothesize that the residual stresses have contributed to the low temperature

endotherm.

In this study, we investigate the existence and consistency of the low temperature

endothermic overshoots by performing cooling rate dependent and room temperature

aging experiments using Flash differential scanning calorimetry on 1.3-micron thick

polystyrene films atop different substrates including Krytox oil, 350 nm AAO template,

55 nm AAO template, and directly on the bare chip. The different substrates allow a

systematic change of residual stress with the direct contact one being the one with the

highest stress. In addition to the studies on glassy polystyrene, we also studied the

influence of cooling rate dependence and aging on crystalline metals, indium and vapor-

deposited gold at two different substrate temperatures, to probe the possible origins of the

broad low-temperature endotherms.

5.2 Experimental

5.2.1 Methodology

Flash differential scanning calorimetry

A Mettler Toledo Flash DSC 1 with a Freon intercooler maintained at -100 °C

was used to perform measurements; a 20 ml/min nitrogen gas purge was used for inert


95

atmosphere. The chip sensors were conditioned and corrected according to the

manufacturer’s recommendation. To explore the low temperature endothermic peak two

different measurements were performed: 1) cooling rate dependent measurements, and 2)

aging or structural recovery measurements. In cooling rate dependent measurements a

heating scan was obtained at 1000 K/s after cooling at various rates in the range of 0.1 to

1000 K/s for two different scanning ranges, -80 to 190 °C and 30 to 190 °C, for

polystyrene samples on four different substrates and 1 µm thick indium sample (Tm =

156.9 °C); in case of 50 nm vapor deposited gold samples, the high end temperature was

380 °C instead of 190 °C. Structural recovery or aging experiments involved obtaining

the aged scan at a heating rate of 1000 K/s from -80 °C after isothermally aging at 20 °C

for a prespecified time ranging from 0.01s to 8 hours; all the aged scans were followed by

unaged scans and the high end temperatures are similar to the cooling rate dependent

measurements.

The sample masses for polystyrene films on the bare chip and Krytox oil, and 50

nm vapor deposited gold samples were obtained by dividing the symmetry corrected heat

flow 7-8 with the absolute heat capacity of polystyrene9 or gold10 at a defined temperature.

The sample masses of polystyrene films on 55 nm and 350 nm AAO could not obtained

using symmetry analysis because the heat flow of empty AAO templates could not be

measured separately; hence, the sample masses were obtained from the step change in

heat flow measured at Tg and the change in heat capacity (∆𝐶𝑝) for a bulk polystyrene

film defined in equation 5.1:11-13


96

∆𝐶𝑝 = 0.433 − 0.00148𝑇𝑓 ˈ (℃)

(5.1)

where 𝑇𝑓 ˈ is the limiting fictive temperature of a polystyrene sample for a cooling rate of

1000 K/s. The sample mass of indium was obtained by dividing the measured heat flow

of melting with the enthalpy of melting14 (28.41 J/g). The sample masses of all the

samples are listed in Table 5.1.

Calculation of Enthalpy difference and Fictive Temperature

The enthalpy difference as a function of aging time (ta) and different cooling rates

(q) relative to a reference state is obtained from Equation 5.2:

𝛥𝐻 =1

𝑚𝛽∫ (𝛥��)𝑑𝑇

𝑇ℎ𝑖𝑔ℎ

𝑇𝑙𝑜𝑤

(5.2)

where 𝛥�� is difference in heat flows of an aged scan at a given ta and an unaged scan

(��𝐴𝑔𝑒𝑑(𝑡𝑎) − ��𝑈𝑛𝑎𝑔𝑒𝑑) for aging experiments, and difference in heat flows of heating

scans after cooling at a rate q and 1000 K/s (��𝑞 − ��1000) for cooling rate dependent

experiments, 𝑚 is the sample mass, and 𝛽 is the heating rate of 1000 K/s. The integration

limits, 𝑇ℎ𝑖𝑔ℎ and 𝑇𝑙𝑜𝑤, for all polystyrene measurements was varied to obtain the high

temperature area (related to the glass transition), and the total area (high temperature area

+ low temperature area) to study the evolution of the low temperature endothermic peak.

In case of gold and indium, integration limits spanned the entire breadth of their

respective measurements.


97

The limiting fictive temperature (Tfˈ) was determined from the superposed Flash

DSC heating scans after cooling at various rates between 0.1 to 1000 K/s by Moynihan’s

method15 for cooling rates > 10 K/s and by a simplified form, Richardson’s method16, for

cooling rates < 10 K/s where Tfˈ is lower than the onset of devitrification. The

Moynihan’s method and Richardson’s method are defined here in terms of heat flow:

∫ (��𝑙 − ��𝑔)𝑇≫𝑇𝑔

𝑇𝑓

𝑑𝑇 = ∫ (�� − ��𝑔)𝑇≫𝑇𝑔

𝑇≪𝑇𝑔

𝑑𝑇 (5.3)

∫ (��𝑙 − ��)𝑇≫𝑇𝑔

𝑇𝑓

𝑑𝑇 = 0 (5.4)

where ��, ��𝑙, and ��𝑔 are the sample heat flow, liquid heat flow, and glass heat flow,

respectively. The fictive temperature, Tf, is related to the enthalpy difference obtained in

Equation 5.2 by:

𝛥𝐻 = − ∫ ∆𝐶𝑝

𝑇𝑓

𝑇𝑓0

𝑑𝑇 (5.5)

where Tf0 is the initial fictive temperature or the fictive temperature of the unaged glass

in case aging experiments and the limiting fictive temperature, Tfˈ, for a cooling rate of

1000 K/s in case of cooling rate dependent experiments, and ∆𝐶𝑝 is the temperature

dependent step change in heat capacity from Equation 5.1.

The cooling rate dependence on fictive temperature Tfˈ can be described by the

Williams-Landel-Ferry (WLF)17 equation:


98

𝑙𝑜𝑔 (𝑞𝑟𝑒𝑓

𝑞) =

−𝐶1(𝑇𝑔 − 𝑇𝑔,𝑟𝑒𝑓)

𝐶2 + (𝑇𝑔 − 𝑇𝑔,𝑟𝑒𝑓)

(5.6)

where Tg,ref is the reference glass transition temperature obtained at a reference cooling

rate of qref = 0.1 K/s, Tg is the glass transition temperature at a particular cooling rate, and

C1 and C2 are WLF constants.

The fictive temperatures were corrected for static and dynamic temperature

gradients according to the method suggested by Schawe.18 The correction factor is the

obtained from average of the difference between Tg obtained on cooling at 1000 K/s and

Tf obtained on heating at 1000 K/s. The correction factor was subtracted from fictive

temperatures obtained for other cooling rates and the values are 2.2, 0.4, 3.8, and 6.1 °C

for PS on bare, Krytox, 350 nm AAO, and 55 nm AAO, respectively. In addition, an

isothermal temperature correction factor of 0.5 K was also applied for aging temperatures

as reported in previous studies.19-20

5.3 Results

5.3.1 Aging of polystyrene on different substrates

Specific heat scans of bulk polystyrene film on bare chip obtained on heating after

aging at 20.5 °C as a function of aging time are shown Figure 5.1.a. The evolution of heat

flow as a function of aging time is more prominent for the broad low-temperature

endothermic peak spanning from -80 °C to 100 °C when compared to the high

temperature endothermic peak related to the glass transition; the area of broad-low

temperature endotherm increases with increase in aging time. The low temperature


99

endotherm was also followed for polystyrene films on different substrates including

Krytox oil, 350 nm AAO and 55 nm AAO. The excess specific heat scans with respect to

the unaged specific heat scans of polystyrene films on different substrates after aging for

8 hours at 20.5 °C are shown in Figure 5.1.b. Upon qualitative comparison, the high

temperature endothermic peaks for all the samples have similar devitrification

temperatures and peak areas irrespective of the substrate, but the low temperature

endotherms have peak areas dependent on the substrate with the polystyrene film on the

bare chip having the largest area. The enthalpies of aging, which were obtained using

Equation 5.3 for the deconvoluted high temperature (open symbols) and low temperature

(solid symbols) peaks, are shown for all aging times in Figure 5.2.a; the corresponding

change in fictive temperatures, estimated from Equation 5.5, are shown in Figure 5.2.b.

The enthalpies of aging of the high temperature peaks (ΔHa,Hi = 1.9 ± 0.1 J/g) are

reproducible for different substrates at a given aging time; and also, the corresponding

average change in fictive temperature for a 1.3 µm thick polystyrene that has been aged

for 8 hours at 20.5 °C on different substrates is ΔTf,Hi = 7.1 ± 0.3 °C, which is somewhat

similar to that observed in a recent study21, but the ΔHa,, Hi+Lo is 22.5 J/g and the

corresponding ΔTf,, Hi+Lo is approximately ~ 90 °C for polystyrene film on bare chip

which is quite close to being Tf = Ta. In addition, the variation in ΔTf,,Hi+Los across

substrates is significant; ΔTf,, Hi+Lo of polystyrene film on bare chip is 300 % larger than

the ΔTf,, Hi+Lo for polystyrene film on 55 nm AAO.


100

5.3.2 Cooling rate dependence of polystyrene on different substrates

Specific heat scans on heating for bulk polystyrene film on the bare chip as a

function of different cooling rates from 0.1 to 1000 K/s are shown in Figure 5.3, with the

left panel (Figure 5.3.a) showing the results when scanned to 30 °C and the right panel

(Figure 5.3.b) showing the results when scanned to -80 °C. In both the cases, the enthalpy

overshoots shift to higher temperatures and larger areas as cooling rate decreases. The

experimental data obtained for the two cases have similar devitrification points with well

superposed liquid lines, whereas glass lines are well superposed only in the case of

cooling to 30 °C. The glass lines when scanned to -80 °C are not well superposed and an

evolution of a broad low-temperature endothermic overshoot similar to what was

observed in case of aforementioned aging experiments is observed with decreasing

cooling rates.

Tfˈs as a function of cooling rates for different substrates and scanning to different

temperatures is shown in Figure 5.4; Tfˈs are estimated using Moynihan’s or

Richardson’s method for only high temperature endothermic peaks. The resulting Tfˈs for

scans performed to 30 (open symbols) and -80 °C (solid symbols) on different substrates

are comparable within the error as shown in Figure 5.4. The Tfˈs as a function of cooling

rates are well described by the WLF equation and are plotted as solid lines, and the

parameters are C1 = 18.9, C2 = 55.3, and Tg,ref = 374.7 K (at a reference cooling rates of

0.1 K/s) which are comparable to the values reported by Simon and co-workers.9, 13, 19-20,

22-23 The Tfˈs from this work are also compared with those obtained using conventional

DSC and Flash DSC from previous studies,11-13, 20 and they show good agreement.


101

The contribution of the low temperature endotherm to change in fictive

temperature cannot be quantified using Moynihan’s or Richardson’s method; hence, they

are estimated using the same method that was used in case of aging experiments. The

excess specific heat data for 0.1 K/s with respect to 1000 K/s for polystyrene on top of

four different substrates are shown in Figure 5.5.a, where the largest low temperature

endotherm is observed in the case of polystyrene film on bare chip for scans performed to

-80 °C which is in agreement with the aging behavior observed for the same sample aged

at 20.5 °C for 8 hours. The enthalpy values which are obtained from Equation 5.3 using

the excess heat flow scans are shown in Figure 5.5.b as a function of cooling rate for all

four substrates. Similar enthalpy values are observed for H- H1000, Hi (near Tg) plotted as

open symbol, and at 0.1 K/s; the average value for all four samples is 3.4 ± 0.2 J/g.

However, H- H1000, Hi+lo, (plotted as solid symbol) values are irreproducible when the low

temperature endotherm is included. Polystyrene on the bare chip has the highest enthalpy

(H- H1000, Hi+lo), presumably due to residual stress developed between the Flash DSC

sensor and the polystyrene film on cooling to -80 °C. The enthalpy values for different

cooling rates are further used to obtain the change in fictive temperatures by using ∆Cp

from Equation 5.1. The change in fictive temperatures, ∆Tf, Hi+Lo and ∆Tf,Hi, are shown in

Figure 5.5.c as a function of cooling rate, as solid and open symbols, respectively. The

average ∆Tf,Hi is 13.1 ± 0.8 °C for 0.1 K/s cooling rate.

The H- H1000, Hi+lo = 14.8 ± 0.7 J/g for polystyrene film on bare chip (∆Tf, Hi+Lo

=56.9 ± 2.8 °C) bare chip is approximately five times higher when compared to the value

obtained including the high temperature overshoot near Tg. In addition, the inconsistent

cooling rate dependent ∆Tf, Hi+Los which decrease in the order of bare chip > Krytox oil >


102

350 nm AAO > 55 nm AAO, indicate a strong substrate effect. Also, the WLF fit to the

∆Tf, His shown in Figure 5.5.c is well described by the same WLF parameters that used to

fit the data in Figure 5.4.

The fit of the WLF equation for ∆Tf, Hi+Lo are also plotted (except the data for PS

film on 55 nm AAO) using the parameters reported in Table 5.2, and the values of C1 and

C2 are not comparable to the universal values17, C1 = 17.44 and C2 = 51.6, or the values

reported by Koh et al.20. The ∆Tf, Hi+Lo data for PS film on 55 nm AAO could not be fitted

with a WLF equation as the endotherm at low temperature did not follow any trend as a

function of different cooling rates.

5.3.3 Cooling rate dependence and aging of indium and vapor-deposited gold

In the previous sections, we have seen that the low temperature endotherm of

micronscale PS films is inconsistent across substrates, which suggests that the low

temperature endotherm is possibly an artifact and not a signature of secondary relaxation.

To further eliminate the idea of attributing the low temperature endotherm to a secondary

relaxation, similar aging and cooling rate dependent experiments are performed on

crystalline metals, indium and vapor-deposited gold, which are in solid state equilibrium

with no known relaxations in the temperature range of interest (-80 to 110 °C).

Melting scans of 1 µm thick indium at a heating rate of 1000 K/s from -80 °C

after cooling at various rates in the range of 0.1 to 1000 K/s are shown in Figure 5.6.a,

and after aging at 20.5 °C for various times in the range of 0.01 s to 8 hours are shown in

Figure 5.6.b. In both the figures melting transitions of indium are observed, and the

onsets and enthalpies of melting are found to be independent of cooling rates and aging


103

times. In additon to the melting transition, broad low-temperature endotherms,

reminiscent to those observed in case of PS films are observed.

The broad low temperature endotherms also exhibit cooling rate dependent

behavior where the low temperature endotherm area increases with decreasing cooling

rate as shown in Figure 5.6.a; the low temperature exotherms also evolve with increasing

aging time as shown in Figure 5.6.b. The evolution of the low temperature endotherms as

a function cooling rates and aging times are better captured in the excess specific heat

scans shown in Figures 5.6.c and 5.6.d, respectively. On the other hand, the low

temperature endotherms are not observed when indium is cooled to 30 °C instead of -80

°C, as shown in Figure 5.7.

Cooling rate and aging time dependent excess specific heats of 50 nm vapor-

deposited gold are shown in Figures 5.8.a and 5.8.b; the main figures show the excess

specific heats at a substrate temperature of 23 °C, while the insets show the data at a

substrate temperature of 125 °C. The excess specific heats exhibit similar broad

endotherms as seen in polystyrene films and indium. The endotherms commenced at low

temperatures and ended at ~ 300 °C for all the excess specific heat scans irrespective of the

type of experiment (cooling rate dependent and aging) and substrate temperatures. In case

of polystyrene films and indium the low temperature endotherms ended before the onset of

their respective transitions, but in case of gold the melting temperature is distant from the

ending temperature of low temperature endotherm.

The enthalpies of the low temperature endotherms from cooling rate dependent and

aging time dependent excess specific heats of indium and 50 nm vapor-deposited gold are

shown in Figures 5.9.a and 5.9.b. As mentioned before the enthalpies increase with


104

decreasing cooling rate and increase with increaing aging time for all gold and indium

samples. The enthalpies are found to be slightly higher in case of 50 nm vapor deposited

gold at Ts = 125 °C for cooling rate dependent and aging experiments, respectively. In

cases of the slowest cooling rate (0.1 K/s) and highest aging time (8 hours), the enthalpies

are in the range of 40-45 J/g for both gold samples and 6-10 J/g for indium. The enthalpies

when quantified to the change in fictive temperatures (∆Tfs) using the ΔCp of polystyrene,

the ∆Tfs are about ~ 130-150 °C for vapor deposited gold samples and ~ 20-30 °C for

indium at the slowest cooling rate (0.1 K/s) and highest aging time (8 hours).

5.4 Discussion

The effect of different cooling rates on limiting fictive temperature for PS bulk film

was reported previously by Simon and co-workers where PS was scanned to 30 °C.12-13, 22,

24 Here, we studied and compared the heat flow curves and resulting Tfˈs by scanning to

two different end temperatures, -80 and 30 °C, for micronscale PS films on four different

substrates. The Tfˈs obtained by Moynihan’s or Richardson’s method for two different end

temperatures gave comparable results for polystyrene samples on top of four different

substrates and are in agreement with our previous work as shown in Figure 5.4.11-13, 20

Similarly, enthalpy values obtained by integrating the high temperature area (glass

transition region) from 110 to 160 °C for polystyrene on top of four different substrates are

also comparable with an average value of 3.44 ± 0.18 J/g at a cooling rate of 0.1 K/s, which

is slightly lower than the average value (4.18 ± 0.43 J/g) from previous studies9, 12-13, 23. In

case of aging experiments at 20.5 °C, the enthalpy of aging of the glass transition area (110

to 160 °C) also demonstrated good agreement with an average value of 1.62 ± 0.14 J/g for

an aging time of 8 hours across different substrates. On the other hand, the enthalpy values


105

obtained including the low temperature endotherm for both cooling rate and aging time

dependent experiments were different for all the substrates studied; in case of cooling rate

experiments, the enthalpy difference for polystyrene on bare chip is ~200 % larger than

that obtained for polystyrene film on 55 nm AAO at 0.1 K/s; in case of aging experiments,

the enthalpy is ~300 % larger at an aging time of 8 hours. In both types of experiments the

largest area was observed for polystyrene on the bare chip, and smallest area was observed

for polystyrene film on 55 nm AAO pores; the enthalpy difference between substrates is

presumably due to the stresses developed between the sensor membrane and the sample

when cooled to ultra-low temperature. In addition, the lack of reproducibility of the

enthalpy values for polystyrene on top of different substrates by considering the low

temperature endotherm suggests that this low temperature endotherm is an artifact rather a

secondary relaxation.

The idea of correlating the low-temperature endotherms observed on Flash DSC

with a fast secondary relaxation mechanism was first suggested by Cangialosi and co-

workers3, where polystyrene nanospheres aged at low temperatures for longer times

exhibited a low-temperature endotherm, and supposedly contributed to a two-step

structural recovery process. In addition, Cangialosi and co-workers3 reported that the low-

temperature endotherm was not observed for bulk nanospheres, contrary to what was

observed in this work on 1.3 µm polystyrene films (bulk). Cangialosi and co-workers also

reported the appearance of low temperature endotherms1 for different micron sized poly(4-

tert-butylstyrene) films as a function of cooling rates and thicknesses of micronscale films;

thinner micronscale films showed larger low-temperature endothermic overshoots and

hence an 80 °C change in Tf for 2.5 µm thick film.1 The large change in Tf was attributed


106

to the fast-secondary relaxation contributed by the low-temperature endotherm; however,

bulk-like mobilities were reported for all micronscale poly(4-tert-butylstyrene) films

irrespective of the large changes in Tf.1 In this work for a 1.3 µm polystyrene film on bare

chip, ΔTf,Hi+Lo was as large as ~ 56 °C at 0.1 K/s and as large as ~ 90 °C for an 8 hour aged

sample at 20.5 °C; the ΔTf,Hi+Los decreased in the order of: bare chip > Krytox Oil > 350

nm AAO > 55 nm AAO due to the reduction in the area of the low-temperature endotherm.

The effect of the substrate on ΔTf,Hi was not observed and therefore have values from

cooling rate dependent and aging time dependent studeis in good agreement with previous

studies in our lab9, 13, 21, 23. The largest reduction in fictive temperatures observed from this

work, and Cangialosi and co-workers1 are higher than the fictive temperature depressions

observed in nanoconfined polymers9, 13, 22, 25-30, 20 million year aged amber31-32, and

ultrastable molecular and polymer glasses33-35

The low temperature endotherms, both cooling rate dependent and aging time

dependent, were also observed in the case of metals such as indium and gold. Broader and

larger low temperature endotherm appears at the slowest cooling rate (0.1 K/s) and longest

aging time (8 hours) for both indium and gold. In the case of vapor-deposited gold, the low

temperature endotherm is slightly larger for the deposition temperature of 125 °C when

compared to 23 °C, presumably due to more residual stress developed due to larger

temperature difference from the deposition temperature to -80 °C. Indium and gold are

crystalline metals in solid state equilibrium with no known relaxations, further proving that

the low-temperature endotherms are not related to a material property, but presumably

occur from the interaction between the membrane of the Flash DSC sensor and the sample.


107

5.5 Conclusions

Flash differential scanning calorimetry was used to study the origin of low

temperature endotherms with 1.3 µm polystyrene films on top of four different substrates,

indium, and vapor-deposited gold. The low temperature endotherms were observed for 1.3

µm polystyrene film on different substrates, indium, and vapor-deposited gold for both

aging and cooling rate experiments when scanned to an ultra-low temperature of -80 °C.

The low temperature endotherms were non-existent in case of cooling rate dependent

experiments for all polystyrene samples and indium when the low-end temperature was

limited to 30 °C. In addition, the area of the low temperature endotherm for both cooling

rate and aging time dependent experiments was found to be dependent on the substrate

type, whereas the high temperature endotherm in the vicinity of Tg was found to be

independent of the substrate type at a given cooling rate or aging time. The inconsistency

in the magnitude of areas pertinent to the low temperature endotherm suggest that the low

temperature endotherm is an artifact and not a material property. In addition, the occurrence

of low temperature endotherms in crystalline materials like indium and vapor-deposited

gold further strengthens the fact that the low temperature endotherm lacks the physics of

being a secondary relaxation mechanism.


108

References


confined at the micrometer length scale. Physical review letters 2018, 121 (13),

137801.



Acta 2019, 677, 60-66.






polymers. PCCP 2018, 20 (18), 12356-12361.






Thermochim. Acta 2018, 663, 157-164.







10. Takahashi, Y.; Akiyama, H., Heat capacity of gold from 80 to 1000 k. Thermochim.

Acta 1986, 109 (1), 105-109.

11. Koh, Y. P.; Simon, S. L., Structural relaxation of stacked ultrathin polystyrene

films. Journal of Polymer Science Part B: Polymer Physics 2008, 46 (24), 2741-

2753.






109

14. http://webbook.nist.gov/chemistry/.

15. Moynihan, C. T.; Macedo, P. B.; Montrose, C. J.; Gupta, P. K.; DeBolt, M. A.; Dill,

J. F.; Dom, B. E.; Drake, P. W.; Easteal, A. J.; Elterman, P. B., Structural relaxation

in vitreous materials*. Annals of the New York Academy of Sciences 1976, 279 (1),

15-35.

16. Richardson, M.-J.; Savill, N., Derivation of accurate glass transition temperatures

by differential scanning calorimetry. Polymer 1975, 16 (10), 753-757.

17. Williams, M. L.; Landel, R. F.; Ferry, J. D., The Temperature Dependence of

Relaxation Mechanisms in Amorphous Polymers and Other Glass-forming Liquids.

J. Am. Chem. Soc. 1955, 77 (14), 3701-3707.



134.

19. Koh, Y. P.; Gao, S.; Simon, S. L., Structural recovery of a single polystyrene thin

film using Flash DSC at low aging temperatures. Polymer 2016, 96, 182-187.



Thermochimica Acta 2015, 603, 135-141.



1549-1558.



146 (20), 203329.

23. Gao, S.; Simon, S. L., Measurement of the limiting fictive temperature over five

decades of cooling and heating rates. Thermochim. Acta 2015, 603, 123-127.

24. Koh, Y. P.; Gao, S.; Simon, S. L., Structural Recovery for a Single Polystyrene

Ultrathin Film Using Flash DSC. Bulletin of the American Physical Society 2015,

60.

25. Roth, C.; Pound, A.; Kamp, S.; Murray, C.; Dutcher, J., Molecular-weight

dependence of the glass transition temperature of freely-standing poly (methyl

methacrylate) films. The European Physical Journal E 2006, 20 (4), 441-448.

26. Sharp, J.; Forrest, J., Thickness dependence of the dynamics in thin films of

isotactic poly (methylmethacrylate). The European Physical Journal E 2003, 12

(1), 97-101.


110



56 (5), 5705.

28. Sharp, J.; Forrest, J. A., Free surfaces cause reductions in the glass transition

temperature of thin polystyrene films. Phys. Rev. Lett. 2003, 91 (23), 235701.

29. Reiter, G., Mobility of polymers in films thinner than their unperturbed size. EPL

(Europhysics Letters) 1993, 23 (8), 579.



2753.


the super-Arrhenius behaviour of glass-forming systems. Nature communications

2013, 4, 1783.




33. Swallen, S. F.; Kearns, K. L.; Mapes, M. K.; Kim, Y. S.; McMahon, R. J.; Ediger,

M. D.; Wu, T.; Yu, L.; Satija, S., Organic glasses with exceptional thermodynamic

and kinetic stability. Science 2007, 315 (5810), 353-356.




35. Yoon, H.; McKenna, G. B., Testing the paradigm of an ideal glass transition:

Dynamics of an ultrastable polymeric glass. Science advances 2018, 4 (12),

eaau5423.


111

Table 5.1 Summary of sample masses, substrate types or conditions

Material Substrate Type or Condition Sample Mass

(ng)

1.3 µm Polystyrene

Film

Bare Chip 137a, 166b

Krytox 96a, 102b

350 nm AAO 190b

55 nm AAO 83b

50 nm Gold

Vapor Deposited at Ts = 23 °C on

Bare Chip 120a

Vapor Deposited at Ts = 125 °C on

Bare Chip 90a

Indium Bare chip 176c

a Sample mass obtained from symmetry analysis b Sample mass obtained from ΔCp c Sample mass obtained from ΔHf


112

Table 5.2 WLF parameters for PS on top of different substrates for for ∆Tf, Hi+Lo in

Figure 5.5.c

PS on Top of: C1 C2 C2/C1

Bare chip 94.7 1435.5 15.2

Krytox 10.4 55.2 5.3

350 AAO 15.6 78.3 5


113

Figure 5.1 (a) Evolution of DSC scans of polystyrene on a bare chip at Ta = 20.5 °C as

a function of aging time (ta) (b) Excess specific heat of polystyrene film aged for 8

hours on different substrates at Ta = 20.5 °C (deconvoluted peaks of polystyrene film

on a bare chip are shown as dashed lines).


114

Figure 5.2 (a) Enthalpy of aging (ΔHa) as a function of aging time for polystyrene on

different substrates (b) The change in fictive temperature (ΔTf = Tf0 – Tf(ta)) as a

function of aging time for polystyrene on different substrates. The solid symbols

represent ΔHa and ΔTf that were obtained inclusive of both low and high temperature

endotherms and the open symbols represent those obtained only from high

temperature endotherms.


115

Figure 5.3. Evolution of DSC scans of polystyrene as a function of different cooling

rates on different substrates scanned to (a) 30 °C and (b) -80 °C.


116

Figure 5.4 Limiting fictive temperatures as a function of cooling rate for polystyrene

on different substrates when scanned to (a) 30 °C and (b) -80 °C. In case of limiting

fictive temperatures when scanned to -80 °C, the low temperature endotherm is

excluded. Also shown are results from our earlier studies. 11-13, 20


117

Figure 5.5 (a) Excess specific heat scans of polystyrene on top of different substrates

at a cooling rate of 0.1 K/s with 1000 K/s as the reference curve. (b) Enthalpy values

of polystyrene on top of different substrates as a function of cooling rates (c) The

change in fictive temperature corresponding to the values in Figure 5.5.b as a function

of cooling rates. The solid and open symbols correspond to values excluding the low

temperature endotherm and values including the low temperature endotherm,

respectively. The WLF fits are shown as solid lines.

-80 -40 0 40 80 120 160

C

p (

0.1

-1000)

(Jg

-1K

-1)

T (°C)

0.0

5 J

g-1

K-1

Ex

o

Krytox oil

350 nm AAO

55 nm AAO

Bare Chip

(a)

0

5

10

15

-2 -1 0 1 2 3

H-H

1000 (

Jg

-1)

log (q/K/s)

PS film on: H-H1000,Hi H-H1000,Lo+HiBare Chip

Krytox oil

350 nm AAO

55 nm AAO

(b)

-10

0

10

20

30

40

50

60

-2 -1 0 1 2 3

PS+K with endoK (w/o endo)350AAO endo350AAO w/o endo55AAO endo55AAO w/o endoWT endoWT w/o endoKrytox(withendo)350AAO (with endo)55AAO (With endo)WT(With endo)Krytox(W/O endo)

log (q/K/s)

T

f (°

C)

(c)


118

Figure 5.6 (a) Cooling rate dependent melting scans of Indium. (b) Aging time

dependent melting scans of indium obtained at an aging temperature of 20.5 °C. (c)

Excess specific heat of melting of indium at various cooling rates with respect to 1000

K/s. (d) Excess specific heat of melting of indium at various aging times with respect

to the unaged scan. In all cases indium was cooled to -80 °C before obtaining the

heating scan.


119

Figure 5.7 Cooling rate dependent melting scans of indium when scanned to 30 °C.


120

Figure 5.8 (a) Cooling rate dependent and (b) aging time dependent heat flow scans

of gold at Ta = 20.5 °C. Gold was vapor deposited at two substrate temperatures, Ts

= 23 °C and 125 °C. The inset figures show data at a substrate temperature of 125

°C.


121

Figure 5.9 (a) ΔH vs log q and (b) ΔH vs log ta for indium, and gold at Ts = 23 °C

and 125 °C


122

CHAPTER 6

THE GLASS TRANSITION BEHAVIOR OF ANODIC ALUMINUM

OXIDE (AAO) SUPPORTED AND STACKED POLYSTYRENE

NANORODS USING FLASH DIFFERENTIAL SCANNING

CALORIMETRY

6.1 Introduction

Properties of polymers under nanoconfinement have been of significant interest

due to their role in many practical applications including coatings, composites, and

membrane technology. Among the key properties, the glass transition temperature (Tg)

has been well studied and is found to be significantly affected at the nanoscale when

compared to the bulk. At the nanoscale, Tg can increase, decrease or remain unchanged

based on different factors1-6: 1) nanoconfinement geometry, 2) interaction between the

confined material and substrate, 3) glass former molecular structure and architecture.

Recently, the influence of nanoconfinement geometry on Tg for a variety of polymers has

attracted attention due to their potential applications in the semiconductor industry where

size and dimensionality play a key role. Nanoconfinement geometry is categorized based

on spatial dimensionality which includes, 1-D thin films, 2-D nanowires/nanorods and 3-

D nanospheres. In the case of polystyrene (PS), size-dependent Tg of 1-D thin films has

been extensively studied using various experimental techniques for supported, free-

standing, sandwiched, and stacked films.3, 7-26 In general, for polystyrene, Tg is depressed

in ultrathin films on neutral or weakly interacting substrates,3, 7-26 and a non-linear

dependence on film thickness (h), independent of molecular weight is observed:13-14


123

𝑇𝑔(ℎ) = 𝑇𝑔𝑏𝑢𝑙𝑘 [1 − (

𝛼

ℎ)

𝛿

]

(6.1)

where 𝑇𝑔(ℎ) is the glass transition temperature at film thickness h, 𝑇𝑔𝑏𝑢𝑙𝑘 is the bulk glass

transition temperature (373.8 ± 0.7 K for polystyrene), and 𝛼 and 𝛿 are the fitting

parameters whose values have been reported to be 1.3 nm and 1.28, respectively.11-14 The

existence of Tg depression for 1D thin films has been generally attributed to an interplay

of two factors: 1) enhanced mobility at the free surface and 2) intrinsic size effect.3, 7-35

The work on the size-dependent Tg of 2-D polystyrene nanorods is relatively new

and has been mainly studied using anodic aluminum oxide (AAO) nanopores29, 31, 36-37 as

a support and in aqueous dispersion. Zhu and co-workers reported a 3 K increase in Tg

for polystyrene (Mw = 280 kg/mol) inside AAO nanopores irrespective of pore diameter;

they also reported a depression of 24 K for aqueous dispersed 100 nm-diameter PS wires

prepared via electrospinning 37. On the other hand, Torkelson and co-workers31 reported a

Tg depression for polystyrene nanorods when 𝑑 ≤ 2𝑅𝑔 where 𝑑 is the diameter of

nanorods and 𝑅𝑔 is the radius of gyration – a maximum depression of 8 K was reported

for 24 nm polystyrene rods with a molecular weight (Mw) of 1420 kg/mol.31 In a study by

Xue and co-workers36 where low molecular weights (6 – 60 Kg/mol) were used, two Tgs

were reported at intermediate cooling rates (10 K/min), whereas bulk values were

observed at the highest rates (120 K/s).36 In our study the first objective is to probe the

existence of two Tg’s in case of high molecular weight polystyrene (2100 kg/mol)

nanorods supported inside different sizes of AAO at rapid heating and cooling rates using


124

Flash differential scanning calorimetry; also, the results will be compared to similarly-

sized stacked polystyrene nanorods where the nanorods are devoid of AAO support and

other relevant work on polystyrene nanorods confined in AAO31, 37-38. The feasibility of

the use of AAO nanopores as a form of nanoconfinement on the Flash DSC has been

previously demonstrated in our group where size-dependent melting behavior of n-

alkanes was successfully studied.39

In case of 3D polystyrene nanospheres, the size-dependent glass transition

behavior has been studied using different environments and experimental techniques.

Priestley and co-workers27, 33 reported Tg depressions for aqueous dispersed27 and air

exposed33 nanospheres when diameter was less than 400 nm – a maximum depression of

56 K was observed for aqueous dispersed nanospheres with d = 90 nm. When the

nanospheres were capped with silica27, no Tg depressions were observed. Cangialosi and

co-workers40 also reported Tg depressions when 3D PS nanospheres dispersed in

poly(dimethylsiloxane) were studied on the Flash DSC. In addition to the first objective,

we also intend to compare our results from AAO supported and stacked 2D polystyrene

nanorods to 1D ultra-thin polystyrene films and 3D polystyrene nanospheres from the

literature to study the effect of spatial dimensionality on Tg.

In the results reported in chapter 5 on bulk polystyrene films on Flash DSC, we

observed a broad low-temperature endotherm on heating after cooling to an ultra-low

temperature of -80 °C, i.e., 180 K below the nominal Tg. The low temperature endotherm

was found to be cooling rate dependent, similar to the endothermic overshoot associated

with the glass transition, but unlike the magnitude of the overshoot at Tg which does not

depend on the substrate for a given cooling rate, the magnitude of the low temperature


125

endotherm was found to be substrate dependent with the largest overshoot observed at a

cooling rate of 0.1 K/s for bulk polystyrene film on bare chip. Additionally, in chapter 5,

we also found cooling rate dependent broad low-temperature endotherms in case of

crystalline metals, indium and vapor deposited gold, when scanned to -80 °C. The

presence of cooling rate dependent broad low-temperature endotherms has been

attributed to a secondary relaxation by Cangialosi and co-workers for micronscale

poly(4-tert butyl styrene) films studied on Flash DSC,41-42 but based on results in chapter

6 on bulk polystyrene films on multiple substrates, and crystalline metals it was

concluded that the low temperature endotherm is not a signature of secondary relaxation

and attributed it to residual stresses, presumably between the sample and chip membrane

when scanned to ultra-low temperatures. In this work, we extend the studies on bulk

polystyrene films from our previous work and perform similar low temperature

experiments on stacked and AAO supported polystyrene rods to probe the low

temperature endotherms using Flash DSC.

6.2 Experimental

6.2.1 Methodology

Flash Differential Scanning Calorimetry

The glass transition behavior of AAO supported and stacked PS nanorods was

studied using a Mettler Toledo Flash DSC 1 with a Freon intercooler and 20 ml/min

nitrogen gas purge. Prior to the measurements, UFS 1 calorimetric chips were

conditioned and corrected at a sensor temperature of -100 °C following the

manufacturer’s procedure. In addition to the aforementioned correction, an additional

temperature calibration was performed using phenanthrene (Tm= 98.7 °C) on the


126

reference side of the chip. The Tfˈs were also corrected for dynamic heat transfer effects

following the preocedure recommended by Schawe et al.43, where a correction factor,

equal to the average of the differnece between glass transition temperatures measured on

cooling and subsequent heating at ±600 K/s, is subtracted from all Tfs (since all are

obtained on heating at 600 K/s). Correction factors were in the range of 3-4 K for stacked

PS nanorods, and 6-9 K in case of AAO supported PS nanorods.

In case of AAO supported PS nanorods, a small piece (< 0.09 mm2) was cut from

the parent template and transferred onto the chip with the help of a hair; on the other

hand, stacked PS nanorods were first separated from the PS film with the help of a micro-

scalpel and then a sufficient amount was transferred similarly with a hair, and later

[C7C1im] [NTf2] ionic liquid was added for better thermal contact; no plasticization was

observed, but a slight increase (~2 K) in Tg was observed when compared to bare

nanorods.

The measurement protocol comprised of two steps - a dummy step and a main

step. The dummy step was the first step that was performed after the sample was placed

onto the sensor and was done only once on each of the samples. The dummy step

comprised of five to six simultaneous heating and cooling steps from 25 to 180 °C at

±600 K/s; it was crucial in establishing good thermal contact between the sample and the

chip sensor. In the main step, the sample was heated from 25 °C to 180 °C at 600 K/s and

was isothermally held for 0.5 s to erase the thermal history. The sample devoid of

thermal history was then cooled from 180 °C to two either, -80 or 30 °C, at different rates

in the range of 0.1 – 1000 K/s. The cooling scan was followed by a heating scan to 180

°C at 600 K/s. The main step was repeated 10 times where each of them had three


127

reference scans of ±600 K/s at various stages of the measurement to verify

reproducibility, and all the heating scans for respective cooling rates were averaged to

improve the signal to noise ratio. The measurements with end temperature as 30 °C were

used to calculate the limiting fictive temperatures (Tf) and those to -80 °C were used to

study the low temperature endotherms.

The limiting fictive temperatures were calculated using Moynihan’s method

(Equation 6.2) for cooling rates greater than 10 K/s, whereas Richardson’s method

(Equation 6.3) was used for slower cooling rates with large overshoots; although the two

methods are equivalanet at slow cooling rates, the Richardson’s method does not involve

fitting the glass line and, hence, its use is less subjective in the range it can be applied,

i.e., when the onset of devitrification is greater than Tfˈ:

∫ (𝑄𝑙 − 𝑄��)𝑑𝑇 = ∫ (�� − 𝑄��)𝑑𝑇

𝑇≫𝑇𝑔

𝑇≪𝑇𝑔

𝑇≫𝑇𝑔

𝑇𝑓

(6.2)

∫ (𝑄𝑙 − ��)𝑑𝑇 = 0

𝑇≫𝑇𝑔

𝑇𝑓

(6.3)

where 𝑄𝑙 and 𝑄�� are the heat flows in the liquid and glassy states, respectively, and �� is

the appararent heat flow of the sample. To obtain 𝑄𝑙 and 𝑄��, the averaged heating scans

for each cooling rate were superposed in the liquid and glass regimes by applying a

vertical shift and reducing the sum of squared errors (SSE), and then the averaged scans

were linearly fitted in the respective regimes.


128

The sample mass of the stacked PS nanorods was obtained by symmetry

analysis39, 44, which involves correcting the measured heat flow of stacked PS nanorods

for heat losses and the addenda heat capacity of the empty chip, and dividing the

symmetry-corrected heat flow with glassy absolute heat capacity of polystyrene11 at a

defined temperature. The sample masses of 20, 55, and 350 nm stacked PS nanorods are

145, 86 and 350 ng, respectively. On the other hand, the sample mass of PS in AAO

supported PS rods was obtained by dividing the step change in heat flow at Tg and the

step change in heat capacity for a bulk polystyrene11-12, 45; the sample masses are 74, 96,

and 111 ng for PS supported in 20, 55 and 350 nm AAO templates.

6.3 Results

6.3.1 Stacked PS nanorods in ionic liquid

Flash DSC heating scans for stacked 20 nm PS nanorods dispersed in ionic liquid

are shown as a function of cooling rate (q) in Figures 6.1.a. The area of enthalpy

overshoot increases in magnitude and shifts to higher temperatures as the cooling rate

decreases from 1000 K/s to 0.1 K/s; this phenomenon is well understood and is related to

the kinetics associated with the glass transition. The data for stacked 20 nm PS rods is

transformed to heat capacity and compared to the data for 55 and 350 nm stacked rods in

Figure 6.1.b. The enthalpy overshoots for both 20 and 55 nm stacked PS nanorods shift to

lower temperatures with respect to 350 nm stacked PS rods; the shifts also resulted in

reduced limiting fictive temperatures for 20 and 55 nm stacked PS rods as indicated by

arrows in Figure 6.1.b. A similar but smaller shift in overshoot at Tg was also observed in

case of stacked thin films11, but in case of 20 nm ultrathin films46 only a slight

broadening was observed at the low temperature side. Tg reductions are observed for all


129

the cooling rates in case of 20 and 55 nm stacked PS rods, except at q =1000 K/s for 55

nm stacked PS rods where the reduction was insignificant as shown in Figure 6.1.b. The

results are summarized Figure 6.2 where the glass transition temperature is plotted as a

function of cooling rates for stacked 20, 55 and 350 nm PS rods and is compared to bulk

data of PS from previous studies.11, 45, 47-48 The 350 nm PS rods show bulk-like behavior

with the Tgs comparable to bulk polystyrene within the error of the measurements. On the

other hand, Tg depressions were observed for both 20 and 55 nm stacked PS rods with a

maximum depression of 20.1 ± 2.2 and 8.8 ± 0.7 K at 0.1 K/s, respectively.

The magnitude of Tg depression (ΔTg) decreases with increasing cooling rates for

both 20 and 55 nm PS rods; the ΔTg is < 2 K for 55 nm PS rods at 1000 K/s which is

similar to previous studies.12, 46 However in case of 20 nm PS rods a 9.4 ± 1.6 K Tg

depression is observed even at 1000 K/s which is in contrast to our previous studies on

ultrathin polystyrene films on the Flash DSC.12, 46 Tg depressions at higher cooling rates

(q > 300 K/s) were also reported in case of ultrathin polycarbonate films28 and

polystyrene nanospheres49 which is similar to what is observed in case of 20 nm stacked

PS rods.

The cooling rate dependent Tg values were fitted by William-Landell-Ferry

(WLF) equation:50

𝑙𝑜𝑔(𝑞 𝑞0⁄ ) = 𝐶1 (𝑇𝑔 − 𝑇𝑔0)

𝐶2 + (𝑇𝑔 − 𝑇𝑔0)

(6.4)


130

where 𝑞 is the cooling rate, 𝑞0 is the reference cooling rate where 𝑇𝑔 = 𝑇𝑔0, which is

chosen to be 0.1 K/s in this case, and 𝐶1 and 𝐶2 are the WLF parameters. The fitting

parameters along with the apparent activation energy (𝐸𝑎 𝑅 = 2.3 𝐶1𝑇𝑔2 𝐶2 ⁄⁄ ) for glass

formation and dynamic fragility (𝑚 = −𝑑𝑙𝑜𝑔 𝑞

𝑑(𝑇𝑔0

𝑇𝑔)

= 𝐶1𝑇𝑔 𝐶2 ⁄ ) are shown in Table 6.1. The

activation energy of glass formation decreases with decreasing PS rod diameter; it

decreases from 113 kK to 71 kK to 62 kK for 350, 55 and 20 nm rods, respectively.

While the activation energy for 350 nm rods is comparable to bulk (105 kK) and 71 nm

PS films (102 kK), the values for 55 nm and 20 nm rods are lower than 47 nm (95 kK)

ultrathin PS film, but comparable to 20 nm ultrathin film.12, 34, 46 The dynamic fragilities

(m) of stacked PS nanorods also decrease with decreasing PS rod diameter; it decreases

from 131 to 85 to 76 for 350, 55 and 20 nm rods, respectively. The 20 and 55 nm stacked

PS rods have a reduced dynamic fragility (m) when compared to the bulk, 71 and 47 nm

PS films. The fragility of 20 nm stacked PS rods is only slightly lower than the fragility

film of 84.5 ± 3.6. In spite of the similarities of activation energy and dynamic fragility,

Tg depressions vary significantly between the 20 nm stacked PS rods and 20 nm ultrathin

PS film.

The depressed glass transition temperature of 20 nm stacked PS rods is not

affected even after multiple scans and isothermal holds at 180 °C for 6 s; it is attributed to

long time scales for chain interpenetration for a high molecular weight PS, which is

approximately 30 min based on bulk interlayer diffusion for PS of Mw = 1000 kg/mol.55

On the other hand, the time taken for the molecules to diffuse one radius of gyration (Rg

= 28 nm56) based on self-diffusion coefficient (0.8 × 10-15 cm2/s) at 170 °C for PS of


131

aforementioned molecular weight is approximately 2 hours.11, 55 Interestingly, thermal

annealing of the 20 nm stacked PS nanorods at 160 °C for up to 24 hours did not result in

recovery of Tg towards the bulk, which is in contrast to the behavior demonstrated by

ultrathin films,12 but is similar to what was observed in case of stacked PS thin films

where it was deemed that the time required for polymer diffusion across layers in a

stacked system is longer than that expected in case of a single ultrathin film.11 As

suggested in case of stacked PS thin films11, the recovery of depressed Tgs for 20 nm

stacked PS rods to bulk values also occurred only after a combination of compression

(10,000 psi) and thermal annealing in vacuum at 170 °C for 5 hours in a platen press. The

specific heat data before and after annealing of 20 nm stacked PS rods are shown in

Figure 6.3; the reduced Tgs seen at 0.1 and 1000 K/s clearly reverted to bulk values as

indicated by the shift in overshoots to higher temperatures after annealing in the platen

press.

6.3.2 AAO supported PS nanorods

Representative heat flow scans of PS nanorods supported in 20, 55 and 350 nm

AAO pores for various cooling rates are shown in Figures 6.4.a, 6.4.b, and 6.4.c,

respectively. Identical to the stacked PS nanorods, the AAO supported PS nanorods also

demonstrate cooling rate dependence where the enthalpy overshoots increase in area and

shift to higher temperatures with decrease in cooling rate, as expected. The main

differences that stand out when the heat flow scans of stacked PS nanorods for a given

size are compared with that of AAO supported PS nanorods are the shifts in overshoots’

peak temperatures to higher temperatures, relatively broader breadths of glass transitions,

and the shoulders or peaks that occur at either lower or higher temperature side of the


132

overshoots at slower cooling rates (q ≤ 10 K/s). The shifts of overshoots’ peak

temperatures and the broader breadth of the glass transition occur because of static and

dynamic temperature gradients43 in the AAO supported PS rods. The Tgs of 20, 55 and

350 nm AAO supported PS rods that were obtained on heating for various cooling rates

were corrected for static and dynamic temperature gradients; the Tg values as a function

of cooling rate are shown in Figure 6.5 and are compared to bulk polystyrene films.

The Tgs of 20, 55 and 350 nm AAO supported PS rods demonstrate bulk-like

behavior with the values in good agreement with the bulk polystyrene films, as shown in

Figure 6.5. When the Tgs of AAO supported PS rods are compared with their respective

stacked PS rods, a 21,10 and 3 K increase in Tg is observed for 20, 55 and 350 nm AAO

supported PS rods at 0.1 K/s cooling rate; on the other hand, a 10 K Tg increase is

observed in case of 20 nm AAO supported PS rods and insignificant changes in case of

55 and 350 nm AAO supported rods at 1000 K/s. Fragilities and activation energies of

20, 55 and 350 nm AAO supported PS rods are shown in Table 6.1; their respective

values are comparable to those of PS bulk films11-12, 45 and 350 nm stacked PS rods.

6.3.3 Low temperature endotherm in stacked and AAO supported PS nanorods

The effect of scanning to -80 °C is studied on 20 nm stacked PS rods directly on

bare chip and subsequently, with the addition of ionic liquid; heat flow scans for various

cooling rates in the range of 0.1 to 1000 K/s are shown in Figure 6.6.a. In addition to the

characteristic endotherms at the glass transition shown in Figure 6.3 and 6.6.a, a broad

low-temperature endothermic peak is observed between -50 and 100 °C. The low-

temperature endotherm increases in area as the cooling rate decreases, but unlike the


133

endotherm at Tg, it is dependent on the sample with a 34 % larger area observed for the

case of PS on a bare chip compared to PS dispersed in ionic liquid for a cooling rate of

0.1 K/s, as shown in Figures 6.6.a and 6.6.b. The sample dependent broad low-

temperature endothermic peaks were also observed in case of micronscale PS films on

different substrates where the largest area was observed for PS film on bare chip; on the

other hand, the endotherm related to Tg was constant across substrates. Cangialosi and

co-workers41-42 interpreted the presence of cooling rate dependent low temperature

endotherms as a signature of a fast-secondary relaxation in addition to the primary

relaxation at Tg; an 80 K change in fictive temperature at the 0.1 K/s was reported for 2.5

µm PtBS film where the large change in fictive temperature was attributed to the low

temperature endotherm42

The enthalpy difference associated with the low and high temperature endotherm is related

to the fictive temperature using Equation 6.5:

𝛥𝐻 = − ∫ ∆𝐶𝑝

𝑇𝑓

𝑇𝑓ˈ

𝑑𝑇 (6.5)

∆𝐶𝑝 = 0.407 − 0.0016 𝑇𝑓ˈ (6.6)

where Tfˈ is limiting fictive temperature in °C at a cooling rate of 1000 K/s and ∆𝐶𝑝 is the

temperature dependent step change in heat capacity (Equation 6.6) obtained from the

symmetry corrected 20 nm stacked PS rods data. The change in fictive temperatures for

both the samples at all cooling rates are shown in Figure 6.7 and the inset shows Tf as a

function of cooling rate. ΔTf at 0.1 K/s with the inclusion of the low temperature

endotherm is as large as ~ 85 K for 20 nm stacked PS nanorods on bare chip and as large


134

as ~65 K with the addition of ionic liquid. The ΔTfs in case of stacked PS rods are

comparatively higher than those obtained from micronscale polystyrene films on bare

chip and Krytox oil, but the dependency of ΔTfs on the substrate is similar and suggests

that the low temperature endotherms in 20 nm stacked PS nanorods are also artifacts

arising due to the residual stress between the sample and the chip membrane. In addition,

the cooling rate dependent broad-low temperature endotherms observed in case of

crystalline metals, gold and indium from studies in chapter 5 additionally proves that the

low temperature endotherm is not associated with a secondary relaxation.

On the other hand, 20 nm polystyrene nanorods supported in AAO nanopores did

not show any sign of a low temperature endotherm as seen from the heat flow scans

shown in Figure 6.8.a and the excess specific heat data shown in Figure 6.8.b. This

behavior is consistent with the fact that magnitude the low temperature endotherm

decreased when microscale polystyrene films were placed on 55 nm and 350 nm AAO

where the smallest area was observed in case of PS film on 55 nm AAO.

6.4 Discussion

The magnitude of the Tg depressions (ΔTg = Tg(h*) - Tg,bulk) for stacked PS

nanorods dispersed in ionic liquid as a function of characteristic length (h*) at 0.1 K/s are

shown in Figure 6.9. The characteristic length, h*, is equal to the volume to surface ratio

of the confinement dimensionality/geometry; it is equal to film thickness, h, for 1D

ultrathin films, d/4 for 2D nanorods/nanowires with diameter d, and d/6 for 3D

nanospheres with diameter d. The ΔTgs of 2D stacked PS nanorods are compared to 1D

ultrathin PS films12, 46, 2D PS nanowires37, and 3D PS nanospheres27, 40 along with the

modified result of Keddie and Jones for supported polystyrene films14 from Equation 6.1


135

(solid black lines), and Roth and Dutcher’s upper and lower limits3 (dashed lines) of the

data compiled from the literature in Figure 6.9. The ΔTgs for stacked PS nanorods at 0.1

K/s fall between Roth and Dutcher’s upper limit, and Keddie and Jones’ Equation 6.1 for

supported polystyrene films14, and are in good agreement with the ΔTgs of 1D ultrathin

PS films12, 46 at comparable characteristic lengths (h*). For example, the ΔTg for 55 nm

stacked PS nanorods (h* = d/4 = ~14 nm) is within ~ 3 K when compared to the ΔTg of

20 nm ultrathin polystyrene film (h* = h = ~20 nm), similar agreement is also observed

for 350 nm stacked PS rods (h*= 88 nm) and 71 nm ultrathin PS film (h*= 71 nm). The

ΔTgs of 2D PS nanowires in aqueous dispersion from Zhu and co-workers37 follow

similar non-linear size dependence as that of supported PS thin films and stacked PS

nanorods, but sit at the lower limit of Roth and Dutcher’s compiled data set from the

literature; larger ΔTgs are observed in case of 2D PS nanowires at higher h*. The

differences between characteristic length (h*) dependent ΔTgs of 2D PS nanowires and

2D stacked PS nanorods may be attributable to the difference in sample environment and

method of sample preparation; 2D PS nanowires are aqueous dispersed and are prepared

by electrospinning, whereas 2D stacked PS nanorods from our work are dispersed in

ionic liquid and are prepared by vacuum melt infiltration into AAO nanopores. The effect

of sample environment on ΔTg versus h* is also be observed in case of 3D PS nanospheres

in aqueous dispersion27 versus 3D PS nanospheres in PDMS40 where larger ΔTgs are

observed for PS nanospheres in aqueous dispersion at similar h*s; in addition, good

agreement is observed in case of aqueous dispersed 2D PS nanowires37 and 3D PS

nanospheres40 at low h*s. The characteristic length dependent ΔTgs of 1D ultrathin PS

films46-47 and 2D stacked PS nanorods are also compared to non-aqueous dispersed 3D


136

PS nanospheres40 in Figure 6.9. Even though the data pertinent to this comparison were

all obtained using Flash DSC at a cooling rate of 0.1 K/s with PS molecular weight

greater than 1000 kg/mol, the ΔTg versus h* of 3D PS nanospheres does not fit into the

trend of 1D ultrathin films and 2D stacked PS nanorods. The disagreements of ΔTgs

between different spatial dimensions, especially with 3D PS nanospheres suggest that a

simple volume/surface ratio scaling factor cannot explain the spatial dimension

dependent nanoconfinement effect on ΔTg.

In contrast to the Tg depression observed in stacked PS nanorods, AAO supported

PS rods demonstrate size-independent bulk-like behavior as shown in Figure 6.10. The

bulk-like behavior after capping nanoparticles is also observed in case of silica-capped

PS nanospheres27, where PS nanospheres, when uncapped (aqueous dispersed), exhibited

size-dependent Tg depression, and bulk-like behavior after being capped with silica; the

behavior has been attributed to the eliminated free surface post capping.27 ΔTg versus h*

behavior of AAO supported PS rods at 0.1 K/s is compared with those reported by Zhu

and co-workers37, Torkelson and co-workers31, and Xue and co-workers36 in Figure 6.10.

ΔTgs as a function of h* from this work are in good agreement with those reported by Zhu

and co-workers37 at a cooling rate of 10 K/min (0.17 K/s) and Mw = 280 kg/mol; in both

cases, the ΔTgs are ~2-3 K higher than the bulk. In case of ΔTgs reported by Torkelson

and co-workers31 at a cooling rate of 40 K/min (0.67 K/s) and Mw = 1260 kg/mol, good

agreement with our work is observed for ΔTgs at h* ≥ 15.8 nm (d ≥ 63 nm) at a

comparable cooling rate of 1 K/s, but for lower d or h*, deviations are observed. A ~ 6 K

Tg depression was reported by Torkelson and co-workers31 at h* = 6 nm (d = 24 nm);

however, Tg depressions less than 3 K were observed when the heat flow scans published


137

by Torkelson and co-workers31 were analyzed using the procedure employed in this

work. Xue and co-workers36 reported two Tgs, one depressed and one elevated, for AAO

supported PS nanorods; ΔTg versus h* shown in Figure 6.10 are for PS at Mw = 6 kg/mol.

The results contrast with those reported in this work, Zhu and co-workers37, and

Torkelson and co-workers31 which is presumably due to the low molecular weight PS (6

and 60 kg/mol) used in Xue and co-workers’ study.36

6.5 Conclusions

The glass transition behavior of AAO supported and stacked 2D polystyrene

nanorods was studied using the Flash DSC at cooling rates spanning four decades. The

glass transition temperatures of 20 and 55 nm stacked PS nanorods were found to depressed

by 20.1 ± 2.2 and 8.8 ± 0.7 K when compared to the bulk, respectively. In addition, a Tg

depression of 10 K was also observed at 1000 K/s, in contrast to 20 nm ultrathin films

where no Tg depression was observed at high rates8. The effect of spatial dimensionality

on the Tg depression was observed, with the magnitude of Tg depression for 20 nm stacked

PS rods being ~ 8 K higher than that of the 20 nm ultrathin PS film. Importantly, when the

ΔTgs of 2D stacked PS nanorods were compared with 1D PS thin films and 3D PS

nanospheres as a function of volume to surface ratio, 1D PS thin films and 2D stacked PS

nanorods demonstrated good agreement, and fell within the literature data compiled by

Roth and Dutcher3. The disagreement with 3D PS nanospheres suggests that the effect of

spatial dimensionality is more complex than a simple volume to surface scaling. In case of

AAO supported PS nanorods, bulk-like behavior was observed independent of size, which

contrasts with stacked PS nanorods without AAO support. The behavior is comparable to

silica-capped 3D PS nanospheres versus aqueous dispersed PS nanospheres27 and PS


138

nanowires in AAO versus aqueous dispersed nanowires37, where similar bulk-like behavior

was observed after capping. Also, bulk-like behavior was observed in AAO supported PS

rods was also observed in other studies30-31, 37 at comparable molecular weights. Also, it is

recommended to exercise caution while performing measurements at ultra-low

temperatures due to the occurrence of broad low-temperature endotherms similar to those

observed in this study and previous studies41-42. The low temperature endotherms are

artifacts and not a signature of secondary relaxation because of their irreproducible

behavior and presence in crystalline metals.


139

References

1. Alcoutlabi, M.; McKenna, G. B., Effects of confinement on material behaviour at

the nanometre size scale. J. Phys.: Condens. Matter 2005, 17 (15), R461.

2. McKenna, G. B.; Simon, S. L., 50th Anniversary Perspective: Challenges in the

dynamics and kinetics of glass-forming polymers. Macromolecules 2017, 50 (17),

6333-6361.

3. Roth, C. B.; Dutcher, J. R., Glass transition and chain mobility in thin polymer

films. J. Electroanal. Chem. 2005, 584 (1), 13-22.

4. Napolitano, S.; Glynos, E.; Tito, N. B., Glass transition of polymers in bulk,

confined geometries, and near interfaces. Rep. Prog. Phys. 2017, 80 (3), 036602.

5. Ediger, M.; Forrest, J., Dynamics near free surfaces and the glass transition in thin

polymer films: a view to the future. Macromolecules 2013, 47 (2), 471-478.

6. Richert, R., Dynamics of nanoconfined supercooled liquids. Annu. Rev. Phys.

Chem. 2011, 62, 65-84.

7. Roth, C. B.; McNerny, K. L.; Jager, W. F.; Torkelson, J. M., Eliminating the

enhanced mobility at the free surface of polystyrene: fluorescence studies of the

glass transition temperature in thin bilayer films of immiscible polymers.

Macromolecules 2007, 40 (7), 2568-2574.



56 (5), 5705.

9. Forrest, J. A.; Dalnoki-Veress, K., The glass transition in thin polymer films. Adv.

Colloid Interface Sci. 2001, 94 (1-3), 167-195.

10. Forrest, J.; Dalnoki-Veress, K.; Stevens, J.; Dutcher, J., Effect of free surfaces on

the glass transition temperature of thin polymer films. Phys. Rev. Lett. 1996, 77

(10), 2002.




12. Gao, S.Y.; Koh, Y. P.; Simon, S. L., Calorimetric Glass Transition of Single


13. Keddie, J. L.; Jones, R. A.; Cory, R. A., Size-dependent depression of the glass

transition temperature in polymer films. EPL (Europhysics Letters) 1994, 27 (1),

59.


140

14. Keddie, J.; Jones, R., Glass Transition Behavior in Ultra‐Thin Polystyrene Films.

Isr. J. Chem. 1995, 35 (1), 21-26.

15. Pye, J. E.; Roth, C. B., Above, below, and in‐between the two glass transitions of

ultrathin free‐standing polystyrene films: Thermal expansion coefficient and

physical aging. J. Polym. Sci., Part B: Polym. Phys. 2015, 53 (1), 64-75.

16. Pye, J. E.; Roth, C. B., Two simultaneous mechanisms causing glass transition

temperature reductions in high molecular weight freestanding polymer films as

measured by transmission ellipsometry. Phys. Rev. Lett. 2011, 107 (23), 235701.

17. Yin, H.; Cangialosi, D.; Schönhals, A., Glass transition and segmental dynamics in

thin supported polystyrene films: the role of molecular weight and annealing.

Thermochim. Acta 2013, 566, 186-192.

18. Boucher, V. M.; Cangialosi, D.; Yin, H.; Schönhals, A.; Alegría, A.; Colmenero,

J., T g depression and invariant segmental dynamics in polystyrene thin films. Soft

Matter 2012, 8 (19), 5119-5122.

19. Tress, M.; Erber, M.; Mapesa, E. U.; Huth, H.; Muller, J.; Serghei, A.; Schick, C.;

Eichhorn, K.-J.; Voit, B.; Kremer, F., Glassy dynamics and glass transition in

nanometric thin layers of polystyrene. Macromolecules 2010, 43 (23), 9937-9944.

20. O'Connell, P. A.; Hutcheson, S. A.; McKenna, G. B., Creep behavior of ultra‐thin

polymer films. J. Polym. Sci., Part B: Polym. Phys. 2008, 46 (18), 1952-1965.

21. Yoon, H.; McKenna, G. B., Substrate effects on glass transition and free surface

viscoelasticity of ultrathin polystyrene films. Macromolecules 2014, 47 (24), 8808-

8818.

22. Wang, J.; McKenna, G. B., Viscoelastic and glass transition properties of ultrathin

polystyrene films by dewetting from liquid glycerol. Macromolecules 2013, 46 (6),

2485-2495.

23. Yang, Z.; Fujii, Y.; Lee, F. K.; Lam, C.-H.; Tsui, O. K., Glass transition dynamics

and surface layer mobility in unentangled polystyrene films. Science 2010, 328

(5986), 1676-1679.

24. DeMaggio, G.; Frieze, W.; Gidley, D.; Zhu, M.; Hristov, H.; Yee, A., Interface and

surface effects on the glass transition in thin polystyrene films. Phys. Rev. Lett.

1997, 78 (8), 1524.

25. Fukao, K.; Miyamoto, Y., Glass transitions and dynamics in thin polymer films:

dielectric relaxation of thin films of polystyrene. Physical Review E 2000, 61 (2),

1743.


141

26. Kim, G.; Libera, M., Morphological development in solvent-cast polystyrene−

polybutadiene− polystyrene (SBS) triblock copolymer thin films. Macromolecules

1998, 31 (8), 2569-2577.

27. Zhang, C.; Guo, Y.; Priestley, R. D., Glass transition temperature of polymer

nanoparticles under soft and hard confinement. Macromolecules 2011, 44 (10),

4001-4006.




29. Alexandris, S.; Papadopoulos, P.; Sakellariou, G.; Steinhart, M.; Butt, H.-J. r.;

Floudas, G., Interfacial Energy and Glass Temperature of Polymers Confined to

Nanoporous Alumina. Macromolecules 2016, 49 (19), 7400-7414.

30. Tan, A. W.; Torkelson, J. M., Poly (methyl methacrylate) nanotubes in AAO

templates: Designing nanotube thickness and characterizing the T g-confinement

effect by DSC. Polymer 2016, 82, 327-336.

31. Askar, S.; Wei, T.; Tan, A. W.; Torkelson, J. M., Molecular weight dependence of

the intrinsic size effect on T g in AAO template-supported polymer nanorods: A

DSC study. The Journal of Chemical Physics 2017, 146 (20), 203323.

32. Lyulin, A. V.; Balabaev, N. K.; Baljon, A. R.; Mendoza, G.; Frank, C. W.; Yoon,

D. Y., Interfacial and topological effects on the glass transition in free-standing

polystyrene films. The Journal of Chemical Physics 2017, 146 (20), 203314.

33. Zhang, C.; Boucher, V. M.; Cangialosi, D.; Priestley, R. D., Mobility and glass

transition temperature of polymer nanospheres. Polymer 2013, 54 (1), 230-235.



2753.

35. Ediger, M. D.; Yu, L., Polymer glasses: From gas to nanoglobular glass. Nature

materials 2012, 11 (4), 267-268.

36. Teng, C.; Li, L.; Wang, Y.; Wang, R.; Chen, W.; Wang, X.; Xue, G., How thermal

stress alters the confinement of polymers vitrificated in nanopores. The Journal of

Chemical Physics 2017, 146 (20), 203319.




38. Xue, G.; Teng, C.; Xu, J.; Li, L. In Dramatic alteration of Tg of polystyrene

confined in cylindrical nanopores, APS Meeting Abstracts, 2014; p 19006.


142



Thermochim. Acta 2018, 663, 157-164.



ACS Macro Letters 2017, 6, 859-863.



Acta 2019, 677, 60-66.





134.








146 (20), 203329.

47. Koh, Y. P.; Simon, S. L., Enthalpy recovery of polystyrene: does a long-term aging

plateau exist? Macromolecules 2013, 46 (14), 5815-5821.

48. Gao, S.; Simon, S. L., Measurement of the limiting fictive temperature over five

decades of cooling and heating rates. Thermochim. Acta 2015, 603, 123-127.




50. Williams, M. L.; Landel, R. F.; Ferry, J. D., The temperature dependence of

relaxation mechanisms in amorphous polymers and other glass-forming liquids. J.

Am. Chem. Soc. 1955, 77 (14), 3701-3707.




143





1549-1558.



Thermochim. Acta 2015, 603, 135-141.

55. Whitlow, S. J.; Wool, R. P., Diffusion of polymers at interfaces: a secondary ion

mass spectroscopy study. Macromolecules 1991, 24 (22), 5926-5938.

56. Rubinstein, M.; Colby, R. H., Polymer physics. Oxford university press New York:

2003; Vol. 23.


144

Table 6.1 WLF parameters C1 and C2; fragility and activation Energy of stacked PS rods in ionic

liquid*, AAO supported PS rods*, PS thin films, and bulk PS 46, 51-54

Sample Diameter

(nm) Tgo

a (K) C1 C2 (K) Ea/R (kK) m

Stacked

rods in

Ionic

liquid

350 373.2 ± 1.6 12.1 ± 0.6 34.4 ± 2.4 112.9 ± 9.4 131.3 ± 11.4

55 365.6 ± 1.2 22.0 ± 3.4 110.7 ± 17.2 61.6 ± 8.1 73.1 ± 7.3

20 354.5 ± 2.0 13.6 ± 2.1 63.5 ± 5.0 62.0 ± 4.4 76.0 ± 13.2

AAO

supported

rods

350 374.9 ± 1.5 13.80 ± 0.9 40.2 ± 3.3 111.5 ± 7.5 129.3 ± 8.8

55 375.3 ± 1.5 17.8 ± 4.6 50.5 ± 8.7 115.4 ± 9.1 133.64 ±14.4

20 375.2 ± 1.3 16.8 ± 3.2 50.1 ± 6.9 109.1 ± 8.6 126.3 ± 11.2

Thickness

(nm)

Thin films

bulk 374.5 ± 0.2 19.7 ± 3.6 61 ± 13 104.9 ± 3.3 121.7 ± 3.9

71 369.0 ± 0.3 10.4 ± 1.2 32 ± 6 102.2 ± 7.2 120.2 ± 8.6

47 365.2 ± 0.5 9.0 ± 1.2 29 ± 7 95.3 ± 9.8 113.4 ± 11.8

20 362.3 ± 0.3 10.6 ± 0.8 45 ± 5 70.5 ± 3.0 84.5 ± 3.6

a glass transition value at a reference cooling of 0.1 K/s

* current work


145

Figure 6.1 (a) Averaged heat flow scans of stacked 20 nm polystyrene rods dispersed

in ionic liquid at a heating rate of 600 K/s after cooling at rates varying from 0.1 to

1000 K/s. (b) Comparison of averaged specific heat vs temperature data of different

sizes of stacked polystyrene rods dispersed in ionic liquid at various cooling rates.


146

Figure 6.2 Fictive temperature as a function of cooling rate for 20, 55 and 350 stacked

polystyrene rods dispersed in ionic liquid compared with bulk data from previous

work12, 34. The solid lines are the WLF fits obtained from the parameters listed in

Table 6.1


147

Figure 6.3 Comparison of specific heat flow scans of annealed 20 nm stacked PS

rods and 20 nm Stacked PS rods before annealing.


148

Figure 6.4 Heat flow scans of polystyrene nanorods supported in (a) 20 nm AAO (b)

55 nm AAO (c) 350 nm AAO


149

Figure 6.5 Limiting fictive temperatures as function of cooling rate for polystyrene

nanorods supported in 20 nm AAO, 55 nm AAO, 350 nm AAO; the data is compared

to stacked PS nanorods and bulk films from previous studies.11-12, 45


150

Figure 6.6 (a) Low temperature heat flow scans of 20 nm stacked PS rods on bare

chip and dispersed in ionic liquid (b) excess specific heat flows of 20 nm stacked PS

rods on bare chip and ionic liquid at 0.1 K/s with respect to 1000 K/s, inset shows

excess specifc heats as a function of cooling rate for 20 nm stacked PS rods on bare

chip.

q=0.1 K/s


151

Figure 6.7 Change in fictive temperatures for 20 nm stacked PS rods on bare chip

and dispersed in ionic liquid as a function of cooling rate, inset shows fictive

temperatures of the same samples as a function of cooling rate


152

Figure 6.8 (a) Low temperature heat flow scans of AAO supported rods 20 nm

polystyrene nanorods (b) excess specific heat data of AAO supported 20 nm

polystyrene nanorods for various cooling rates with respect to 1000 K/s.


153

Figure 6.9 Magnitude of Tg depressions at 0.1 K/s (6 K/min) for different sizes of

stacked PS rods in ionic liquid (filled green circles), single ultrathin PS films12, 46 (filled

red squares), PS nanowires in aqueous dispersion37 (filled lime green left-angled

triangles), PS nanospheres in aqueous dispersion40 (filled pink diamonds), and PS

nanospheres27 (open diagonal square). The black dashed lines are Roth and Dutcher’s

upper and lower limits3, 14, the solid black line is obtained from modified Keddie and

Jones’ data14.


154

Figure 6.10 Magnitude of Tg depressions for different sizes of AAO Supported PS

nanorods from this work (left corner-filled green squares; Torkelson and co-

workers31 (solid black triangles); Zhu and co-workers37 (lower half-filled triangles);

Xue and co-workers36 (ΔTg,hi; right half-filled violet squares, ΔTg,lo; left half-filled

violet squares)


155

CHAPTER 7

ENTHALPY RECOVERY OF 2D STACKED POLYSTYRENE

NANORODS USING FLASH DIFFERENTIAL SCANNING

CALORIMETRY

7.1 Introduction

Polymeric glasses are nonequilibrium materials whose thermodynamic properties

spontaneously evolve towards equilibrium as a function of time via a process termed as

structural recovery. Structural recovery can either be volume recovery or enthalpy

recovery depending on the thermodynamic quantity that is being measured. Structural

recovery of polystyrene (PS) under nanoconfinement has been a topic of significant

interest for the past 25 years. In our group, extensive studies were performed on the

enthalpy recovery of 1D stacked1 and ultrathin PS films2-6 using conventional and Flash

differential scanning calorimetry, respectively. In the case of 1D stacked PS films, the

overall rate of enthalpy recovery was reported to be similar to that of the bulk when

compared at aging temperatures which are at similar distances from their respective glass

transition temperatures (Tg), but accelerated enthalpy recovery was observed when

compared at same aging temperatures.1 In case of ultrathin PS films, enthalpy recovery of

single 20 nm ultrathin film was studied on the Flash DSC2, 4 which has advantages

including handling nanogram samples, sensitivity to aging times as short as 0.01 s, and

ability to access higher aging temperatures of Tg + 15 °C for the high fictive-temperature

glass created by cooling at very high rates (1000 K/s); more importantly, the overall rate

of enthalpy recovery in the glassy state for a single 20 nm thick ultra-thin polystyrene

film was found to be faster when compared to 1.1 µm thick film (bulk).2, 4, 6 Boucher and

co-workers also reported enhanced enthalpy recovery in case of stacked PS films when


156

compared to the bulk, but these comparisons were made at same aging temperatures

rather than at same jump size from Tg.7 On the other hand, reduced structural recovery

rates were reported by Pye and Roth for volume recovery studies on 30 nm ultrathin PS

film8, and by Frieberg, Glynos, and Green for experiments performed as a function of

aging temperature on linear and star-shaped PS thin films9.

Recently, there has been a growing interest in the influence of spatial

dimensionality/geometry of nanoconfinement on the structural recovery of polystyrene.

Zhu and co-workers studied enthalpy recovery of aqueous-dispersed and AAO-supported

2D PS nanowires10, where the rate of enthalpy recovery below Tg was found to be reduced

in both systems when compared to the bulk.10 Priestley and co-workers investigated the

enthalpy relaxation of aqueous dispersed and silica-capped 3D PS nanospheres, where they

found accelerated enthalpy recovery rates in case of aqueous dispersed PS nanospheres,

and reduced rates in case of silica-capped PS nanospheres;11Cangialosi and co-workers

also reported enhanced enthalpy recovery rates in case of 3D PS nanospheres dispersed in

poly(dimethyl siloxane)12. In this study, one of our objectives is to investigate the enthalpy

recovery of 20 and 350 nm stacked PS nanorods dispersed in ionic liquid using Flash

differential scanning calorimetry as a function of aging temperature and aging time. For

this same system, we previously studied the glass transition behavior, finding a Tg

depression of ~ 20 K for 20 nm stacked PS nanorods and bulk-like behavior for 350 nm

stacked PS nanorods, both dispersed in ionic liquid. The enthalpy recovery results from

stacked PS nanorods will be compared with our group’s previous studies on 1D 20 nm

ultrathin PS film, as well as with literature results for other nanoconfinement geometries.


157

In the majority of the studies on structural recovery of polystyrene, the recovery

towards equilibrium has been reported to be monotonic in both bulk and nanoscale.1-7, 11,

13 However, Cangialosi and co-workers reported a two-step structural recovery towards

equilibrium, in case of 1D stacked PS thin films14-16 and 3D PS nanospheres12. The two

steps have been related to a fast equilibration mechanism with a weak Arrhenius-like

temperature dependence, and the usual slow equilibration mechanism with a super

Arrhenius behavior.12, 14-17 The faster mechanism is related to the presence of a broad low

temperature endotherm at lower than usual aging temperatures for nanoconfined PS.12, 14-

15 These broad low-temperature endotherms ranging from -80 to 100 °C were also

observed in our recent studies for micronscale PS films on various substrates, and for

stacked PS nanorods, as well as for metallic samples with no relaxation mechanisms in

the temperature range of the endotherm. We attribute the low temperature endotherm as

an artifact due its inconsistent area (6 to 28 J/g, aging at 20.5 °C for 8 hours) for bulk PS

films on different substrates, and due to its presence for crystalline metals, gold and

indium. Thus, in addition to examining the kinetics of structural recovery of 2D stacked

PS nanorods, we also examine the implication of our findings on the existence of double

mechanism of structural recovery and its relationship with the low temperature

endotherms with 20 nm stacked PS nanorods on the Flash DSC.

7.2 Experimental

7.2.1 Methodology

Flash Differential Scanning Calorimetry

The enthalpy recovery studies on separated PS nanorods were performed using a

Mettler Toledo Flash DSC 1 equipped with a Freon intercooler and a 20 ml/min nitrogen


158

gas purge. The steady state cooler temperature was set to -100 °C, and the Flash DSC

chips were conditioned and corrected according to the manufacturer’s recommendation.

The temperature of the chip was calibrated using the onset melting temperature of

phenanthrene (Tm = 98.4 °C), and an isothermal correction factor of 0.5 K was used, as

reported in previous studies2, 4-5. The fictive temperatures on heating were also corrected

for static and dynamic temperature gradients following a method suggested by Schawe et

al.18

The separated PS nanorods were transferred onto the heating area of the chip with

the help of a hair. To ensure good contact with the heating area and to get a consistent

signal, the stacked nanorods were heated and cooled between 30 °C and 190 °C at 600

K/s for a total of 10 cycles. A symmetry correction19-20 was performed for 600 K/s

cooling and heating scans to account for heat losses and the addenda heat capacity of the

empty chip. The sample mass of the nanorods was obtained by dividing the symmetry

corrected measured heat flow of the nanorods with the glassy specific heat capacity of

polystyrene. The sample masses for 20 and 350 nm stacked PS nanorods are 145 and 350

ng, respectively. After preliminary measurements on bare stacked PS nanorods, [C7C1im]

[NTf2] ionic liquid was added for better thermal contact; no plasticization was observed,

but a slight increase (~2 K) in Tg was observed when compared to the bare nanorods.

Enthalpy recovery experiments were performed on stacked PS nanorods dispersed

in ionic liquid with two different end temperatures, 30 and -80 °C, respectively. The

enthalpy recovery experiments scanning to 30 °C are similar to those on thin films

previously studied in our group and were performed at various aging temperatures

between 50.5 and 110.5 °C for aging times (ta) ranging from 0.01 to 86400 s (24 hours) at


159

each temperature. Each isothermal aging step was followed by cooling to 30 °C and then

a heating scan of the aged material to 190 °C, followed by cooling to 30 °C and an

immediate heating scan of unaged material; in all the scans an isothermal hold of 6s at

190 °C was performed prior to the cooling step to erase the thermal history. The unaged

reference scan serves as an internal standard and remains unchanged during the course of

the enthalpy recovery experiments indicating that no mass loss or degradation occurs.

Enthalpy recovery experiments scanning to -80 °C follow a temperature protocol that is

similar to those scanned to 30 °C; aging temperatures for these experiments are -20.5,

20.5, and 80.5 °C for aging times from 0.01 s to 28800 s (8 hours) and were performed

only on 20 nm stacked PS nanorods. The cooling and heating rates for all the enthalpy

recovery experiments are set to 1000 K/s to ensure negligible relaxation during the

cooling process and to obtain a high fictive temperature glass.

The enthalpy evolution during structural recovery was followed by determining

the fictive temperature (Tf), which is a measure of glass structure.21 The fictive

temperature after aging for a given time is calculated from the heating scan using the

Moynihan’s method22 (Equation 7.1) or Richardson’s method23 (Equation 7.2):

∫ (��𝑙 − ��𝑔)𝑑𝑇 = ∫ (�� − ��𝑔)𝑑𝑇 𝑇≫𝑇𝑔

𝑇≪𝑇𝑔

𝑇≫𝑇𝑔

𝑇𝑓

(7.1)

∫ (��𝑙 − ��)𝑑𝑇 = 0𝑇≫𝑇𝑔

𝑇𝑓

(7.2)


160

where �� is the heat flow of the aged scan, ��𝑙 is the liquid state heat flow, and ��𝑔 is the

glassy state heat flow. The simplified Richardson’s method23 is applicable to and was

used only for aging scans whose onsets of devitrification are greater than Tf. Although for

these long-time aging scans, Equations 1 and 2 are equivalent, we use Equation 7.2

because it does not require extrapolating the glass lines and hence it provides a more

accurate and robust determination of Tf. The glass and liquid state heat flows in Equation

7.1 and the liquid heat flows in Equation 7.22 are obtained from linear fits in these

regimes after superposing all heat flow scans in order to ensure consistency in the

determination of Tf.

The fictive temperatures of the heat flow scans when scanned to -80 °C were

calculated by relating the enthalpy of aging to change in fictive temperature:

𝛥𝐻𝑎 = − ∫ ∆𝐶𝑝

𝑇𝑓

𝑇𝑓𝑜

𝑑𝑇 (7.3)

∆𝐶𝑝 = 0.407 − 0.0016 𝑇𝑓0 (7.4)

where 𝛥𝐻𝑎 is the enthalpy of aging obtained from the area of the excess specific heat

data (𝐶𝑝,𝑎𝑔𝑒𝑑 − 𝐶𝑝,𝑢𝑛𝑎𝑔𝑒𝑑) at a given aging time, 𝑇𝑓𝑜 is the initial fictive temperature

and ∆𝐶𝑝is the temperature dependent step-change in heat capacity for 20 nm stacked PS

nanorods (Equation 7.4).


161

7.3 Results and discussion

Representative flash DSC heating scans of 20 and 350 nm stacked PS nanorods

are shown in Figures 7.1.a and 7.2.b as a function of aging time at aging temperatures,

80.5 and 90.5, respectively; the heat flow scans are obtained on heating from 30 °C. For

the sake of comparison, the aging temperatures are chosen such that they are at the same

distance from the initial fictive temperatures (Tfo), which are 107.5 ± 1.4 and 116.8 ± 2.0

°C for 20 and 350 nm stacked PS nanorods, respectively, based on the unaged scans. The

overshoots for both 20 and 350 nm stacked PS nanorods increase in magnitude and shift

to higher temperatures as the aging time increases because higher temperatures are

needed to reach the equilibrium liquid line as the mobility decreases during isothermal

aging. The enthalpy recovery process is quantified by the fictive temperature of the aged

scans calculated using Moynihan’s (Equation 7.1) and Richardson’s methods (Equation

7.2).

Flash DSC heat flow scans on heating from -80 °C for 20 nm stacked rods after

aging at temperatures 80.5 and -20.5 °C are shown in Figures 7.2.a and 7.2.b. The aged

scans obtained on heating from -80 °C exhibit braod low-temperature endotherms

spanning from -40 to 110 °C in addition to the primary high temperature endotherm

observed in the vicinity of glass transition. In the case of aging at 80.5 °C, both high and

low temperature endotherms evolve with aging time, whereas in the case of aging at -20.5

°C only the low temperature endotherm evolves with aging time because of the large

jump size from Tfo. The fictive temperatures for the aged scans heated from -80 °C are

obtained using Equations 7.3 and 7.4 for only the primary high temperature endotherm


162

for aging temperatures -20.5, 20.5 and 80.5 °C. The implications of the low temperature

endotherm on enthalpy recovery of stacked PS nanorods will be discussed later.

The fictive temperature data is plotted as departure from equilibrium, Tf -Ta

versus logarithm aging time in Figure 7.3.a, where solid green left-angled triangles and

solid red diamonds represent the enthalpy recovery of 20 and 350 nm stacked PS

nanorods respectively. The enthalpy recovery process of stacked PS nanorods is also

compared with bulk and 20 nm ultrathin PS films from previous studies to understand the

effect of nanoconfinement geometry. Since Tfo of 20 nm stacked PS nanorods is different

from that of 350 nm stacked PS nanorods and PS films, the enthalpy recovery

comparison is made at similar jump sizes (Tfo - Ta) rather than similar aging

temperatures; hence, the initial values are similar for all the samples. The responses for

all the samples evolve from Tfo-Ta to zero for all jump sizes. The time at which Tf -Ta

starts to evolve towards zero has been termed the induction time (tind); interestingly, the

induction times of 20 nm stacked PS nanorods for respective jump sizes are similar to the

350 nm stacked PS nanorods. In addition, the temperature dependence of induction time

is approximately ~20 K/decade which is also similar to that of bulk and 20 nm PS thin

films as shown in Figure 7.3.b; hence, demonstrating insignificant dependence of spatial

dimensionality on tind. PS film. After the induction period, Tf -Ta for 20 and 350 nm

stacked PS rods decreases linearly with logarithm of aging time; the recovery is

monotonic which is in contrast to intermediate plateaus reported by Cangialosi and co-

workers for 3D PS nanospheres at timescales as small as 100 s for 230 nm nanospheres

aged at 353 K (Tfo -Ta = 31 K).12 Post induction time, there are two possibilities in the

enthalpy recovery that are observed based on the magnitude of jump size: 1) Equilibrium


163

is not attained for larger jump sizes in the range of 27 – 67 K even at long aging times. 2)

Equilibrium is attained for smaller jump sizes, 7 and 17 K, where Tf-Ta reaches zero (2.0

± 1.5 K). In addition, no induction times are observed for jump sizes 127 and -4 K,

because in the former case the aging has not commenced yet, whereas in the latter case

the polymer is already in the equilibrium liquid state. Upon qualitative comparison of the

enthalpy recovery of 20 and 350 nm stacked rods, it is evident that the recovery rate for

20 nm stacked PS rods is higher than that of 350 nm stacked PS rods, especially at larger

jump sizes (27 – 67 K); at smaller jump sizes the rates are comparable. On the other

hand, the enthalpy recovery rates of 20 and 350 nm stacked rods are similar to those of 20

nm ultrathin and bulk PS films from previous studies2-6, respectively. At a jump size of

87 K, the recovery rate of 20 nm stacked PS rods is comparable to the that of a bulk PS

film.3

The apparent aging rate (R) is calculated from the slope of linear region of Tf-Ta

versus logarithm aging time:

𝑅 = −𝑑(𝑇𝑓 − 𝑇𝑎)

𝑑𝑙𝑜𝑔𝑡𝑎

(

(7.5)

where R is the aging rate in K/decade and the minus sign is added to make the quantity

positive. The aging rates of 20 and 350 nm stacked PS rods are compared with 20 nm

ultrathin film and the bulk as a function of aging temperatures and jump sizes in Figures

7.4.a and 7.4.b, respectively. The aging rates of 20 nm stacked PS rods are slightly higher


164

than 20 nm ultrathin films for aging temperatures 50.5 and 60.5 °C, but when compared

at similar jump sizes the overall aging rates of the 20nm stacked PS nanorods are very

similar to 20 nm ultrathin film. In both comparisons though, the overall aging rate of 20

nm stacked rods is higher than 350 nm stacked and bulk at lower aging temperatures or

larger jump sizes. As the jump sizes get smaller, the aging rate decreases and both

stacked rods and thin films for all sizes have similar aging rates within error, but when

compared as a function of aging temperature, for example, at Ta = 100 °C the 20 nm

stacked PS rods has a lower aging rate than 350 nm stacked PS rods and thin films

because the material is closer to equilibrium due to the depressed Tg, hence the driving

force to recovery is lower.

The enthalpy recovery behavior of 20 and 350 nm stacked PS rods are compared

using a relaxation map alongside 20 nm ultrathin PS film and the bulk in Figures 7.5.a

and 7.5.b. The relaxation map comprises of time scales including the induction times

(tind), average relaxation times (τavg), and times to reach equilibrium (t∞). The three

relaxation times are plotted as a function of T and Tfo – T in Figures 7.5.a and 7.5.b,

respectively. In case of induction times and times to reach equilibrium, T is equal to the

aging temperature (Ta) and in case of average relaxation times obtained from the cooling

rate dependence of Tg, T is equal to Tg at a given cooling rate. The activation energy

obtained from the William-Landell- Ferry27 (WLF) parameters can be used to obtain the

average relaxation time (τ) at Tg. The WLF parameters, the reference glass transition

temperatures Tg,ref, and the calculated activation energies for 20 and 350 nm stacked rods

along with 20 nm ultrathin and bulk PS films are shown in Table 7.1. The relationship

between apparent activation energy and τ has been established by Hodge28 using the


165

Deborah number (DN) which can be expressed in terms of rate of change of effective

time scale during cooling (dτ dt⁄ ). The relationship simplifies to τ = RTg

2

Eaq and the

average relaxation times for 20 and 350 nm stacked rods are shown in Figures 7.5.a and

7.5.b along as a function T and Tfo-T; also shown are the relaxation times for bulk and 20

nm ultrathin film from previous studies.2, 4-6 The average relaxation times follow the

WLF temperature dependence similar to that of Tfˈ vs log q:

𝑙𝑜𝑔𝜏 = 𝐶1 (𝑇𝑔 − 𝑇𝑔,𝑟𝑒𝑓)

𝐶2 + (𝑇𝑔 − 𝑇𝑔,𝑟𝑒𝑓)+ 𝑙𝑜𝑔𝜏0

(

(7.6)

where C1 and C2 are the WLF parameters listed in Table 7.1, Tg,ref is the reference Tg at a

cooling rate of 0.1 K/s, and τ0 is reference average relaxation time obtained using the

Hodge’s equation 𝜏0 = 𝑅𝑇𝑔0

2

𝐸𝑎𝑞0. The values of logτ0 in Equation 7.6 are 1.36 and 1.10 for 20

and 350 nm stacked PS nanorods, respectively. Since the WLF parameters of 20 and 350

nm stacked PS nanorods are different, they also have different temperature dependence of

average relaxation times when comapred as a function of T and Tfo-T. Interestingly, the

average relaxation times of 20 nm stacked PS rods and 20 nm ultrathin PS film, and 350

nm stacked PS rods and bulk PS have similar temperature dependence when compared as

a function Tfo-T. The similarity in the temperature dependence of the average relaxation

times of 20 nm stacked rods and 20 nm ultrathin film may also be the reason for similar

enthalpy recovery behavior irrespective of the difference in magnitude of Tg depression

and spatial dimensionality.


166

The induction times for 20 and 350 nm stacked PS nanorods are determined from

the intersection of the average intial Tf-Ta with the linear fit obtained from the data up to

3 decades after the initial drop in Tf-Ta. The induction times of 20 and 350 nm stacked PS

rods are similar to those obtained for 20 nm ultrathin PS film4 and bulk4-5 when compared

as a function of jump size Tfo-Ta, whereas the induction times for 20 nm stacked PS rods

are slightly lower than 350 nm stacked PS rods, and 20 nm ultrathin and bulk PS films

when comapred at same aging temperatures which implies that the relaxation time is

slightly faster when comapard at same temperatures.

The times to reach equilibrium for both 20 and 350 nm stacked PS rods are

obtained from the Tf-Ta data close to equilibrium using the following equation:

𝑙𝑜𝑔𝑡∞ = 𝜏0 [𝑙𝑛 (𝑇𝑓𝑜 − 𝑇𝑎

𝑇𝑓∞ − 𝑇𝑎)]

1/𝛽

(

(7.7)

where relaxation time 𝜏0 and nonexponentiality paramater 𝛽 are the KWW

parameters. 𝑇𝑓𝑜 − 𝑇𝑎 is the initial departure from equilibrium temperature. The time to

reach equilibrium is defined as the time taken to reach 𝑇𝑓 − 𝑇𝑎 = 0.035 K, as reported in

other work.29 The time to reach equilibrium for 20 nm stacked PS rods is slightly faster

than 350 nm stacked PS rods at a jump size of 17 K; whereas, similar equilibrium times

were observed at a jump size of 7 K. When the time to reach equilibrium is compared at

the same aging temperature, Ta = 100.5 °C, the 20 nm stacked PS rods reach the

equilibrium faster than all other samples because of Ta’s proximity to Tfo. The time to


167

reach equilibrium can also be described as the same WLF temperature dependance as

average relaxation time; hence, they can be related as: 𝑙𝑜𝑔𝑡∞ = 𝑙𝑜𝑔𝜏 + 𝐴, where 𝐴 is the

shift factor from average relaxation time that is necessary to describe time to reach

equilibrium. The shifted average relxation time WLF fits to 𝑡∞ for 20 nm ultrathin film

and the bulk are shown in Figures 7.5.a and 7.5.b as short-dashed blue and red lines,

respectively. The same values of 𝐴, 3.53 and 1.95 , that are used to shift 20 nm ultrathin

film and the bulk also describe the 𝑡∞s for 20 and 350 nm stacked PS rods; the green

short-dashed line which is shifted by 3.53 from average relaxation times for 20 nm

stacked PS rods is shown in Figures 7.5.a.

In the previously discussed enthalpy recovery process for 20 nm stacked PS

nanorods when scanned to 30 °C, the recovery towards equilibrium is linear and

monotonic for aging temperatures between 50.5 to 110.5 °C, but Cangialosi and co-

workers report a non-monotonic, two-step recovery towards equilibrium in case of PS

stacked thin films14-15 and PS nanospheres12, where the second step was related to the

presence of a braod-low temperature endotherm. In the measurements by Cangialosi and

co-workers, the samples were cooled to – 90 °C post aging and heated back from the

same temperature to capture the aged scan; in addition, aging was also performed at

temperatures as low as – 90 °C (Tg – 140). Here, we report enthalpy recovery for 2D

stacked PS nanorods scanning to – 80 °C for aging temperatures -20.5, 20.5 and 80.5 °C.

The evolution of the low temperature endotherm with aging time can be clearly seen in

the Figures 7.6.a and 7.6.b which show the excess specific heats with respect to the

unaged heat flow as a function of aging time. Although the low-temperature endotherms

demonstrate similar behavior on aging as the enthalpy overhshoots at Tg, we have


168

observed the same low temperature endotherms for indium and gold samples. In addition,

the area of the low temperature endotherm is sample dependent for nominally the same

material, differing by as high as 300 % for a bulk PS film depending on whether it is

placed on the bare chip, on a layer of Krytox oil, or on a thin AAO template. Hence, we

have concluded that the low-temperature endotherm does not contain physics related to

the glassy material being studied but, rather, is related to the sample and chip sensor

configuration.

To verify the two-step recovery observed by Cangialosi and co-workers, we

deduced the fictive temperatures of the aged scans including the low temperature

endotherm for three different aging temperatures which have low, medium and high jump

sizes from the initial fictive temperature (Tfo). The fictive temperatures are calculated

using Equations 7.3 and 7.4 with the low temperature endotherm included. The decrease

in fictive temperature as a function of aging time is shown in Figure 7.7.a; the data is also

plotted as Tf - Ta as a function of aging time in Figure 7.7.b for the sake of comparison.

The recovery towards equilibrium for all aging temperatures with the inclusion of the low

temperature endotherm is still linear and monotonic unlike the two-step recovery reported

by Cangialosi and co-workers at similar jump sizes and characteristic lengths for PS thin

films14-15 and PS nanospheres12; in case of 230 nm 3D PS nanospheres, intermediate

plateaus were reported at time scales as small as 100 s at a jump size of 31 K.12 In case of

enthalpy recovery at 80.5 °C, Tf - Ta decreases from Tf0 - Ta = 27 K to – 50 K; i.e, 50 K

below the equilibrium value. The fact that the fictive temperature has recovered past the

aging temperature does not fit into the physics of enthalpy recovery and implies that the

low temperature endotherm is an artifact which occurs when scanned to ultra-low


169

temperatures. Additional evidence can also be observed from the enthalpy recovery at 20

°C, where a ~ 40 K change in fictive temperature is observed after aging for only 8 hours;

the change in fictive temperature is comparable to that obtained for a 20 Ma aged amber

(~43.6 K)30-31.

7.4 Conclusions

The enthalpy recovery of 20 and 350 nm stacked 2D polystyrene nanorods

dispersed in ionic liquid was studied using the Flash DSC. The enthalpy recovery

measurments for 20 and 350 nm stacked PS nanorods were perfromed at similar jump sizes

in the range of -4 to 127 K from Tfo for aging times ranging from 0.01 s to 8 hrs; the Tfos

are 107.5 ± 1.4 and 116.8 ± 2.0 °C for 20 and 350 nm stacked PS nanorods, respectively.

The enthalpy recovery behavior in both 20 and 350 nm stacked PS nanorods was linear and

monotonic at all jump sizes where enthalpy recovery was observed. The induction times

for both 20 and 350 nm stacked PS rods were similar and also in good agreement with the

induction times of 20 nm ultrathin film and bulk from previous studies in our laboratory

when comapared at similar distances from Tfo, whereas shorter induction times are

observed when comapred at same aging temperatures. In both 20 and 350 nm stacked rods,

the equilibrium was reached for jump sizes less than 17 K with similar enthalpy recovery

rates; on the other hand, enhanced enthalpy recovery rates were observed in case of 20 nm

stacked rods when compared to 350 nm stacked rods at jump sizes greater than 17 K. The

overall enthalpy recovery rate of 20 nm stacked PS nanorods was found to be similar to

that of 20 nm ultrathin film. Similar agreement in overall enthalpy recovery rate was also

observed for 350 nm stacked PS rods and bulk implying an insignificant effect of spatial

dimensionality on the enthalpy recovery behavior. The similarity in enthalpy recovery


170

behavior across spatial dimensionality is presumably due to the similar temperature

dependence of average relaxation times. Enthalpy recovery meaurements scanning to -80

°C also exhibited a linear and monotonic decrease in fictive temperature inspite of the

presence of broad low temeperature endotherms at all aging temperatures studied. In case

of enthalpy recovery measurements at an aging temperature of 80.5 °C, fictive temperature

was found to be 50 K below the aging temperature when the low temperature endotherm

was included in the enthalpy recovery. The abnormal decrease in fictive temperature

beyond aging temperature indicates that the low temperature endotherm is not a secondary

relaxation but an artifact presumably arising due to generated residual stresses when

scanned to ultra-low temperatures.


171

References



2753.





1549-1558.



146 (20), 203329.





Thermochim. Acta 2015, 603, 135-141.

7. Boucher, V. M.; Cangialosi, D.; Alegría, A.; Colmenero, J., Enthalpy recovery in

nanometer to micrometer thick polystyrene films. Macromolecules 2012, 45 (12),

5296-5306.

8. Pye, J. E.; Rohald, K. A.; Baker, E. A.; Roth, C. B., Physical aging in ultrathin

polystyrene films: Evidence of a gradient in dynamics at the free surface and its

connection to the glass transition temperature reductions. Macromolecules 2010,

43 (19), 8296-8303.

9. Green, P. F.; Glynos, E.; Frieberg, B., Polymer films of nanoscale thickness: linear

chain and star-shaped macromolecular architectures. Mrs Communications 2015, 5

(3), 423-434.




11. Guo, Y.; Zhang, C.; Lai, C.; Priestley, R. D.; D’Acunzi, M.; Fytas, G., Structural

relaxation of polymer nanospheres under soft and hard confinement: isobaric versus

isochoric conditions. ACS nano 2011, 5 (7), 5365-5373.




172

13. Koh, Y. P.; Simon, S. L., Enthalpy recovery of polystyrene: does a long-term aging

plateau exist? Macromolecules 2013, 46 (14), 5815-5821.








095701.


polymers. PCCP 2018, 20 (18), 12356-12361.



134.



Thermochim. Acta 2018, 663, 157-164.




21. Tool, A. Q., Relation between inelastic deformability and thermal expansion of

glass in its annealing range. J. Am. Ceram. Soc. 1946, 29 (9), 240-253.



16.

23. Richardson, M.-J.; Savill, N., Derivation of accurate glass transition temperatures

by differential scanning calorimetry. Polymer 1975, 16 (10), 753-757.

24. Shamim, N.; Koh, Y. P.; Simon, S. L.; McKenna, G. B., The glass transition of

trinitrotoluene (TNT) by flash DSC. Thermochim. Acta 2015, 620, 36-39.




26. Gao, S. Y.; Koh, Y. P.; Simon, S. L., Calorimetric Glass Transition of Single



173

27. Williams, M. L.; Landel, R. F.; Ferry, J. D., The temperature dependence of

relaxation mechanisms in amorphous polymers and other glass-forming liquids. J.

Am. Chem. Soc. 1955, 77 (14), 3701-3707.

28. Hodge, I. M., Enthalpy relaxation and recovery in amorphous materials. J. Non-

Cryst. Solids 1994, 169 (3), 211-266.

29. Simon, S.; Sobieski, J.; Plazek, D., Volume and enthalpy recovery of polystyrene.

Polymer 2001, 42 (6), 2555-2567.





the super-Arrhenius behaviour of glass-forming systems. Nature communications

2013, 4, 1783.


174

Table 7.1 WLF parameters C1 and C2; fragility and activation Energy of 20 and 350 nm stacked PS

rods dispersed in ionic liquid*, 20 nm ultrathin PS films2, 4, and bulk25-26

Rod Diameter

(nm) Tfo

a (K) Tgrefb (K) C1 C2 (K) Ea/R (kK)

350* 389.9 373.2 ± 1.6 12.1 ± 0.6 34.4 ± 2.4 112.9 ± 9.4

20* 380.6 354.5 ± 2.0 13.6 ± 2.1 63.5 ± 5.0 62.0 ± 4.4

Film Thickness

(nm)

bulk 390.2 374.5 ± 0.2 19.7 ± 3.6 61 ± 13 104.9 ± 3.3

20 389.5 362.3 ± 0.3 10.6 ± 0.8 45 ± 5 70.5 ± 3.0

* current work

aTfo is the initial fictive temperature at a reference cooling rate q = 1000 K/s

aTg,ref is the glass transition temperature at a reference cooling rate q0 = 0.1 K/s


175

Figure 7.1 Flash DSC heating scans as a function of aging time for (a) 20 nm stacked

PS nanorods (green) after aging at Ta = 80.5 °C (b) 350 nm stacked SP nanorods (red)

after aging at Ta = 90.5 °C. The aging temperatures are at the same distance from

their respective Tfo obtained at a cooling rate of 1000 K/s.


176

Figure 7.2 Flash DSC heat flow scans for 20 nm stacked PS nanorods on heating

from -80 °C as function of aging time at aging temperatures (a) 80.5 °C and (b) -20.5

°C. The insets show the excess specific heats with respect to the unaged specific heat

(1000 K/s) as a function of aging temperature and aging time.


177

Figure 7.3 (a) Tf -Ta vs log ta for different jump sizes from Tfo for (a) 20 nm stacked

PS nanorods dispersed in ionic liquid (solid green left angled triangles) and 350 nm

stacked rods (solid red diamonds) (b) 20 and 350 nm stacked PS rods compared

with 20 nm ultrathin (solid blue squares) and bulk PS films (red diamonds) from

previous studies2-6.


178

Figure 7.4 Aging rate comparison at (a) similar aging temperatures and (b) similar

jump sizes for 20 and 350 nm stacked PS nanorods, 20 nm ultrathin PS film2, 4 and

bulk2, 4, 24


179

Figure 7.5 Relaxation time map including induction times (tind; diamonds), average

relaxation times (squares) and times to reach equilibrium (t∞, circles) as a function of

(a) T and (b) Tfo-T are shown for 20 (solid green symbols) and 350 nm (solid red

symbols) stacked PS rods along with 20 nm ultrathin PS film2, 4 (open blue symbols)

and bulk4-5, 25-26 (open orange symbols). The black dashed line is linear fit to all the

induction times. The colored solid lines (red, blue and green) are the WLF dependence

of average relaxation times obtained using the cooling rate dependence of Tg. The

colored short-dashed lines are the same WLF dependence data shifted by a constant.


180

Figure 7.6 Excess specific heat data versus temperature on heating from -80 °C as a

function of aging time for 20 nm stacked PS nanorods aged at (a) 80.5 °C and (b) -

20.5 °C.


181

Figure 7.7 (a) Tf and (b) Tf-Ta vs log ta for three different aging temperatures when

cooled to -80 °C.


182

CHAPTER 8

REACTION KINETICS OF LINEAR EPOXY POLYMERIZATION

IN CPG NANOPORES

8.1 Introduction

The effect of nanoconfinement on reaction kinetics of step-growth polymerization

has been well studied over the last decade.1-5 In general, accelerated cure kinetics are

observed under nanoconfinement, with the degree of acceleration increasing with

decreasing pore diameter.1-5 The acceleration is hypothesized to be due to an increase in

the local concentration of reactive species as a result of surface layering or ordering;3, 6-7

however, layering has been validated only in silanized nanopores where reactive

functional groups like hydroxyls are absent. In native nanopores, the underlying physics

to explain accelerated reaction kinetics is more complex due to the presence of surface

silanol groups. In the case of nanoconfined dicyanate ester polymerization,5, 8 a faster

degree of cure was observed in native nanopores when compared to silanized nanopores

and the acceleration in native pores was attributed to an additional catalytic effect of

available surface silanol groups. The catalytic effect of hydroxyl moieties has also been

observed in case of epoxy-amine polymerization, where accelerated cure was observed

when hydroxyl-functionalized particles were added to the curing mixture9-17; in addition,

the cure rate increased with increase in particle loading until aggregation was observed13-

14, 16-17. Recently, Tarnacka and co-workers2 studied the reaction kinetics of a linear

epoxy system in native anodic aluminum oxide (AAO) nanopores with surface hydroxyl

groups using FTIR and found acceleration in all of the pore sizes studied and specifically,

a 5-fold increase in 35 nm pores. Since it is well known that epoxy-amine polymerization


183

reactions are influenced by hydroxyl groups, the acceleration effect observed in the

native AAO nanopores may not be solely attributed to the confinement effect, rather it

could be a combination of both confinement and catalytic effect from hydroxyl groups or

a sole contribution from the catalytic effect of hydroxyl groups. To further investigate the

aforementioned possibilities, here we study a linear epoxy polymerization similar to that

investigated by Tarnacka et al.2 in a different nanopore matrix, specifically borosilicate

controlled pore glass (CPG), which has a lower density of surface hydroxyls when

compared to AAO nanopores, using differential scanning calorimetry.

8.2 Experimental

8.2.1 Methodology

Differential scanning calorimetry

The curing was followed using a Mettler Toledo DSC 823 with a Freon

intercooler maintained at -80 °C and a nitrogen gas purge of 50 ml/min. Hermetic pans

(20 µl; PerkinElmer, Inc.) were used to study both bulk and nanoconfined reactions. For

the bulk samples, 3-5 mg was loaded into the pan; for nanoconfined samples, 3-6 mg of

CPG was loaded followed by the monomer mixture whose weight was chosen such that it

fills 70-85 % of the pore volume of respective pore diameter. Imbibement occurred

spontaneously and the pans were immediately sealed under a nitrogen blanket to

minimize adventitious water. The pans with CPG samples were immediately stored on

dry ice (-78 °C) to prevent cure during storage. The conversion during storage or prior to

the DSC measurements was estimated to be less than 5 %; the conversion was estimated

using DiBenedetto equation18 which relates the glass transition temperature of partially

cured mixture (Tg,12) with conversion (x):


184

Tg,12 − T𝑔𝑜

Tg∞ − T𝑔𝑜=

λx

1 − (1 − λ)x

(8.1)

where Tg,12 is the glass transition temperature of a partially cured sample, Tgo (= -40.8 ±

2.4 °C) is the glass transition temperature of the uncured sample, Tg∞ (= 88.5 ± 3.4 °C) is

the glass transition temperature of a fully cured sample, and λ = 0.6619 is a structure-

dependent parameter. The glass transition temperatures were captured in the temperature

range of -70 to -20 °C for Tg0 and Tg,12, and 30 to 160 or 210 °C for Tg∞ on heating at 10

K/min after cooling at the same rate. The limiting fictive temperature (Tfˈ) is calculated

from the captured data on heating using the Moynihan’s method20 and is approximately

equal to Tg (~ 1 K) when measured on cooling at the same rate21; hence, it will be

addressed as Tg in the forthcoming sections.

Dynamic DSC experiments were performed to monitor the evolution of the curing

process in the DSC at various heating rates in the range of 1-30 K/min for both bulk and

nanoconfined samples; three samples were measured for repeatability. Heat flow

calibration was performed using indium; temperature calibration was performed using

indium and octane. In addition, sample weight measurements made before and after the

DSC scans indicated that weight losses were less than 2 %.

8.3 Results

Representative reaction exotherms of DGEBA and aniline polymerization in bulk

and 55 nm CPG nanopores for five different heating rates are shown in Figures 8.1.a and

8.1.b. The heat flow for the reaction at different heating rates is normalized by the factor

of β/βref for the sake of comparison, where β is the heating rate and βref is 5 K/min. The


185

reaction exotherms shift to higher temperatures with increasing heating rate for both bulk

and 55 nm CPG because of the reduced reaction time at a given temperature as heating

rate increases. In 55 nm CPG, the polymerization reaction occurs at a significantly lower

temperature when compared with the bulk at a given heating rate. The shifts in the

reaction qualitatively in agreement with the results from Tarnacka et al.2 for the same

reaction in AAO nanopores. The average heat of reaction (∆𝐻𝑏𝑢𝑙𝑘) obtained from the

areas under the exotherms are 437.8 ± 8.6 J/g and 427.7 ± 9.5 J/g for bulk and 55 nm

CPG, respectively. The average heats of reaction are independent of heating rate and

confinement and are in good agreement with the literature (∆𝐻𝑏𝑢𝑙𝑘 = 426 J/g).22 We will

perform a more quantitative comparison using the reaction kinetics.

To study the kinetics of the reaction in the bulk and nanopores, the temperature-

dependent heat flow data is converted to temperature-dependent conversion data using

Equation 8.2:

𝑥 =∫ ��𝑑𝑡

𝑡

0

∫ ��𝑑𝑡𝑡∞

0

(8.2)

where x is the conversion at a given time t, and t∞ is the total reaction time, and �� is heat

flow in J/g. The conversion, x, in equation 8.2 is defined as the ratio of exotherm area at

time t to the total exotherm area.

The conversion versus temperature data for the reaction in the bulk are shown in

Figure 8.2 and are well described by a second order autocatalytic model:


186

𝑑𝑥

𝑑𝑇=

1

𝛽𝑘0𝑒𝑥𝑝 [−

𝐸𝑎

𝑅[1

𝑇−

1

𝑇𝑟𝑒𝑓]] (1 − 𝑥)2(𝑥 + 𝑏)

(8.3)

where 𝑘0 is the rate constant at the reference temperature (𝑇𝑟𝑒𝑓 = 353.15 K), 𝛽 is the

heating rate, 𝐸𝑎 is the activation energy of the reaction, and 𝑏 is a constant that is related

to the hydroxyl groups that catalyze the reaction initially.23-25 The parameters 𝑘0, 𝐸𝑎 and

𝑏 for bulk were obtained by 𝜒2 minimization and are summarized in Table 8.1. The

activation energy, 𝐸𝑎= 55.1 kJ/mol, obtained from the second order autocatalytic model

for the bulk data is in good agreement with previous studies2, 22 on the same system and

other crosslinked epoxy systems.1, 10-11, 13-14, 16-17, 22, 24-30

For the nanoconfined reaction in 55 nm CPG pores, the fitting was done by

assuming that activation energy (𝐸𝑎) is unaffected under nanoconfinement and the

parameter 𝑘0 and 𝑏 were varied. The second order autocatalytic model with values 𝐸𝑎=

55.1 kJ/mol, 𝑘0= 1.0 x 10-4 s-1, and b = 8.60 well describe the nanoconfined reaction in

55 nm CPG pores, but the value of 𝑏 is dramatically higher as compared to the bulk. The

parameter 𝑏 is a quantitative measure of the autocatalytic behavior in the polymerizing

system. The higher value of 𝑏 suggests that the initial concentration of hydroxyl groups

catalyzing the epoxy polymerization in the CPG nanopores is higher when compared to

the bulk, presumably due to the silanol groups on the nanopore surface. Further, the fact

that 𝑏 ≫ 𝑥 implies that the autocatalytic behavior is suppressed in CPG nanopores.

Similarly, suppressed autocatalytic behavior was also reported by Tarnacka et al.2 for the

same epoxy system in AAO nanopores.


187

To test the weakened autocatalytic behavior in CPG nanopores, a non-

autocatalytic, second order reaction model was fitted to the nanoconfined reaction data

from 55 nm CPG, as shown in Figure 8.3. The non-autocatalytic reaction model is a

simple second order expression:

𝑑𝑥

𝑑𝑇=

1

𝛽𝑘0𝑒𝑥𝑝 [−

𝐸𝑎

𝑅[1

𝑇−

1

𝑇𝑟𝑒𝑓]] (1 − 𝑥)2

(8.4)

where the activation energy 𝐸𝑎 is again assumed to be similar to the bulk and the rate

constant 𝑘0 is taken as a fitting parameter which is 9.7 x 10-4 s-1. The model describes the

experimental data well, indicating that autocatalytic behavior is indeed negligible in CPG

nanopores.

The epoxy polymerization kinetics is also compared as a function of pore size; the

dynamic heating scans of the reaction at 5 K/min in 55 and 7.5 nm CPG nanopores along

with the bulk are shown in Figure 8.4.a. The epoxy polymerization in the nanopores is

accelerated when compared to the bulk and is faster as the pore size decreases. The

acceleration is evident from the decrease in the reaction onset temperature from 141.71

±0.86 °C for the bulk to 51.5 ± 2.3 and 25.5 ± 1.4 °C for 55 and 7.5 nm CPG, respectively.

The magnitude of the decrease in reaction onset temperatures for 55 and 7.5 nm CPG are

approximately 90 and 116 K, respectively.

The conversion versus temperature for reactions in bulk and nanopores at a

heating rate of 5 K/min are compared in Figure 8.4.b. Similar to the reaction in 55 nm

CPG nanopores, the reaction kinetics of epoxy reaction in 7.5 nm CPG nanopores is well


188

described by a simple second order model demonstrating the weakened autocatalytic

nature in the nanopores. In addition, the unchanged activation energy of 𝐸𝑎 = 55.1

kJ/mol well describes the reaction in 8 nm CPG pores with a 5-fold increase in 𝑘0 when

compared with that of 55 nm CPG nanopores. The activation energy for the reaction in

CPG nanopores is also in good agreement with similar polymerization reaction

previously studied by Tarnacka et al. in AAO nanopores.2

The apparent activation energy of the reaction can be obtained from the

conversion versus temperature data using a model-free isoconversion method without the

need for a kinetic model. The present work uses the Kissinger-Akahira-Sunose method31-

32 based on the recommendation from International Confederation for Thermal analysis

and Calorimetry (ICTAC)33 and is defined as equation 8.5:

ln𝛽𝑖

𝑇𝑥,𝑖2 =

−𝐸𝑎

𝑅𝑇𝑥,𝑖+ 𝐶

(8.5)

where 𝑇𝑥,𝑖 is the temperature at which a particular conversion is reached for given heating

rate 𝛽𝑖 and C is a constant independent of conversion and temperature. The apparent

activation energy (𝐸𝑎) is obtained from the slope of natural logarithm of (𝛽𝑖 𝑇𝑥,𝑖2⁄ )

versus (1 𝑇𝑥,𝑖⁄ ) at constant conversion; the plots and the linear fits for each conversion

are shown for the bulk data in Figure 8.5.a, and the apparent activation energies as a

function of conversion for the reaction in bulk, 55 and 7.5 nm CPG nanopores are shown

in Figure 8.5.b. The apparent activation energy of the bulk reaction decreases with

increase in conversion, and has an average value of 53.3 ± 1.2 kJ/mol which is in good

agreement with that obtained from the second order autocatalytic model (55.1 kJ/mol)


189

and with previous studies on linear polymerization of DGEBA + aniline;2, 22, 28 however,

the apparent activation energies of the reaction in 55 and 7.5 nm CPG nanopores from the

KAS isoconversion method are 48.3 ± 1.1 and 49.1 ± 1.1 kJ/mol, respectively; they are

approximately 10 % lower than the activation energies obtained from second order model

for reaction in 55 and 7.5 nm CPG pores.

The linear epoxy synthesized in the bulk and nanopores is also characterized for

glass transition temperature post curing; the specific heat capacity versus temperature

data for bulk, 55, and 7.5 nm CPG nanopores are shown in Figure 8.6. The average glass

transition temperature (Tg) for the cured bulk epoxy is 86.9 ± 1.8 °C with a step change in

heat capacity (ΔCp) at Tg of 0.46 ± 0.02 Jg-1K-1, respectively. Our values are consistent

with those reported in the literature, where reported Tg values range from 85 to 95 °C,

and ΔCp values range from 0.45 to 0.51 Jg-1K-1;22, 28 we note that the relatively large

breadth of the literature data is presumably due to minor variations in the stoichiometric

ratio which can have a profound effect on the properties.

The epoxy polymer that was synthesized inside the nanopores exhibits two Tgs in

both nanopore sizes, one within the vicinity of the bulk and the second one higher than

the bulk, as shown in Figure 8.6. In the case of the 55 nm CPG pores, the average Tg1 is

86.1 ± 2.4 °C, which is similar to the Tg of bulk epoxy polymer, and the associated

average ΔCp1 is 0.39 ± 0.01 Jg-1K-1; the Tg2 value is approximately 30 K higher than Tg1

with an average value of 116.5 ± 3.7 °C with an associated ΔCp2 of 0.07 ± 0.01 Jg-1K-1. In

the 7.5 nm CPG pores the average Tg1 is 90.5 ± 3.1 °C, which is slightly higher but

within the range of bulk values, with ΔCp1 being 0.42 ± 0.01 Jg-1K-1 which is slightly

higher than that observed in 55 nm CPG pores. The average Tg2 value in 7.5 nm CPG


190

nanopores is 172.4 ± 4.5 °C, which is approximately 80 K higher than Tg1, with ΔCp2 of

0.05 ± 0.01 Jg-1K-1.

The double glass transition phenomenon in the CPG nanopores has been

explained by a two-layer model34-35 comprising of a core and a less mobile shell closer to

the surface of the nanopore. The primary Tg1 is usually associated with the material in

center of the nanopore and the secondary Tg2, which is elevated, is associated with the

shell; i.e., the less mobile surface layer. The thickness of the less mobile shell can be

obtained by assuming that the step changes in heat capacity at the primary and secondary

Tgs are proportional to the volume fraction of the material associated with the respective

transition. In addition, it is assumed that the density is unchanged for the two layers, and

the CPG nanopores have cylindrical geometry:

√Δ𝐶𝑝1

Δ𝐶𝑝𝑇= 1 −

𝑙

𝑟

(8.6)

where Δ𝐶𝑝1 is the step change in heat capacity associated with Tg1, Δ𝐶𝑝𝑇 is the total

change in heat capacity (Δ𝐶𝑝1 + Δ𝐶𝑝2), 𝑟 is the nanopore radius, and 𝑙 is the shell layer

thickness. The shell layer thickness obtained from Equation 6 for both nanopores sizes

are shown in Table 8.2; the shell layer thickness increases with increase in CPG nanopore

diameter. The occurrence of two Tgs for polymers synthesized in CPG nanopores has

been previously observed in our lab for polycyanurates3, 5, 8, 36 confined in CPG, but for

those materials Tg1 is lower than the bulk and only Tg2 was higher. In addition, the

magnitude of the elevated Tgs for epoxy polymer synthesized in 55 and 7.5 nm CPG


191

nanopores are significantly higher when compared to that observed for polycyanurates,3-5,

7-8, 36-38 presumably due to the strong interfacial effect of the hydroxyl groups on the

surface layer formed in CPG nanopores.

8.4 Discussion

The epoxy-amine reaction kinetics is accelerated under nanoconfinement for the

bulk and nanopores as indicated by the decrease in the temperature at the onset of the

reactrion exotherm. We can then quantify the acceleration by comparing the initial

reaction rate, obtained from the reaction model Equations 8.3 and 8.4 at x = 0

(𝑑𝑥 𝑑𝑡⁄ |x=0); the initial reaction rates for the second order autocatalytic and non-

autocatalytic models are equal to 𝑘0𝑏 and 𝑘0, respectively. A comparison of

nanoconfined and bulk initial reaction rates reveals that initial reaction rates in 55 and 7.5

nm CPG nanopores are accelerated over the bulk by 240 and 1280 times, respectively;

however, only a 5-fold acceleration is observed when the initial reaction rates of 55 and

7.5 nm CPG nanopores are compared. The initial reaction rate is also estimated from the

work of Tarnacka et al., where they used the Avrami model to describe the reaction

kinetics;2 we calculated their initial reaction rates for bulk and 35 nm AAO pores to be

1.5 x 10-4 and 7.5 x 10-4 s-1, respectively.2 Thus, in the work of Tarnacka et al., the initial

reaction rate accelerated five times in 35 nm AAO pores, considerably lower than the

magnitude observed in our work. In addition, the bulk initial reaction rate is 40-fold faster

in case of Tarnacka et al.’s study2 and 6-fold faster in case of Wise et al.’s22 study when

compared to our work; future studies will be performed to address the differences. On the

other hand, the initial reaction rate is 1.3 times slower in 35 nm AAO pores2 when

compared to that in 55 nm CPG pores a somewhat surprising finding, given the smaller


192

pore diameter and higher density of hydroxyl groups (4 OH/nm2 in CPG39 vs 19 OH/nm2

in AAO40) in AAO nanopores. The result suggests that the reaction rate is not directly

proportional to the density of hydroxyl groups. The reason for higher reaction rates in

CPG nanopores when compared to that in AAO nanopores is not clear at this point and

will be addressed in future studies.

8.5 Conclusions

The reaction kinetics of linear epoxy polymerization in bulk and in 55 and 7.5 nm

CPG nanopores were investigated using differential scanning calorimetry in dynamic

mode. The polymerization reaction is found to be accelerated in the nanopores, as

evidenced by a decrease in the onset temperature for the nanoconfined reaction exotherm.

A second order autocatalytic reaction model describes both bulk and nanoconfined data

well, but autocatalytic behavior is weaker in the nanopores and well described by a

simple non-autocatalytic second order model. Two Tgs were observed in both 55 and 7.5

nm CPG nanopores. Tg1s were in good agreement with the bulk values, and Tg2s were

found to be elevated by 30 and 80 K in 55 and 7.5 nm CPG nanopores, respectively. The

initial reaction rates were accelerated by 240 and 1280 times in 55 and 7.5 nm CPG

pores, presumably due to silanol groups on the CPG nanopore surface.


193

References

1. Sanz, B.; Ballard, N.; Marcos-Fernández, Á.; Asua, J. M.; Mijangos, C.,

Confinement effects in the step-growth polymerization within AAO templates and

modeling. Polymer 2018, 140, 131-139.





3. Lopez, E.; Simon, S. L., Trimerization Reaction Kinetics and T g Depression of

Polycyanurate under Nanoconfinement. Macromolecules 2015, 48 (13), 4692-

4701.

4. Li; Simon, S. L., Curing of Bisphenol M Dicyanate Ester under Nanoscale

Constraint. Macromolecules 2008, 41 (4), 1310-1317.

5. Li, Q.; Simon, S. L., Surface Chemistry Effects on the Reactivity and Properties of

Nanoconfined Bisphenol M Dicyanate Ester in Controlled Pore Glass.

Macromolecules 2009, 42 (10), 3573-3579.

6. Malvaldi, M.; Bruzzone, S.; Picchioni, F., Confinement Effect in Diffusion-

Controlled Stepwise Polymerization by Monte Carlo Simulation. The Journal of


7. Koh, Y. P.; Simon, S. L., Kinetic Study of Trimerization of Monocyanate Ester in

Nanopores. J. Phys. Chem. B 2011, 115 (5), 925-932.

8. Li, Q.; Simon, S. L., Curing of bisphenol M dicyanate ester under nanoscale

constraint. Macromolecules 2008, 41 (4), 1310-1317.

9. Ryu, S. H.; Sin, J.; Shanmugharaj, A., Study on the effect of hexamethylene

diamine functionalized graphene oxide on the curing kinetics of epoxy

nanocomposites. Eur. Polym. J. 2014, 52, 88-97.

10. Zabihi, O.; Hooshafza, A.; Moztarzadeh, F.; Payravand, H.; Afshar, A.; Alizadeh,

R., Isothermal curing behavior and thermo-physical properties of epoxy-based

thermoset nanocomposites reinforced with Fe2O3 nanoparticles. Thermochim.

Acta 2012, 527, 190-198.

11. Rajabi, L.; Kaihani, S.; Kurdian, A.; Rezai, N., Dynamic cure kinetics of

epoxy/TiO2 nanocomposites. Science of Advanced Materials 2010, 2 (2), 200-209.

12. Rosso, P.; Ye, L., Epoxy/Silica Nanocomposites: Nanoparticle‐Induced Cure

Kinetics and Microstructure. Macromol. Rapid Commun. 2007, 28 (1), 121-126.


194

13. Sanctuary, R.; Baller, J.; Zielinski, B.; Becker, N.; Krüger, J.; Philipp, M.; Müller,

U.; Ziehmer, M., Influence of Al2O3 nanoparticles on the isothermal cure of an

epoxy resin. J. Phys.: Condens. Matter 2008, 21 (3), 035118.

14. Baller, J.; Thomassey, M.; Ziehmer, M.; Sanctuary, R., The catalytic influence of

alumina nanoparticles on epoxy curing. Thermochim. Acta 2011, 517 (1-2), 34-39.

15. Choi, S.; Janisse, A. P.; Liu, C.; Douglas, E. P., Effect of water addition on the cure

kinetics of an epoxy‐amine thermoset. J. Polym. Sci., Part A: Polym. Chem. 2011,

49 (21), 4650-4659.

16. Ghaemy, M.; Nasab, S. A.; Barghamadi, M., Nonisothermal cure kinetics of

diglycidylether of bisphenol‐A/amine system reinforced with nanosilica particles.

J. Appl. Polym. Sci. 2007, 104 (6), 3855-3863.

17. Ghaemy, M.; Bazzar, M.; Mighani, H., Effect of nanosilica on the kinetics of cure

reaction and thermal degradation of epoxy resin. Chin. J. Polym. Sci. 2011, 29 (2),

141-148.

18. DiBenedetto, A., Prediction of the glass transition temperature of polymers: a

model based on the principle of corresponding states. J. Polym. Sci., Part B: Polym.

Phys. 1987, 25 (9), 1949-1969.

19. Min, B.-G.; Stachurski, Z.; Hodgkin, J., Cure kinetics of elementary reactions of a

DGEBA/DDS epoxy resin: 1. Glass transition temperature versus conversion.

Polymer 1993, 34 (23), 4908-4912.



16.

21. Badrinarayanan, P.; Zheng, W.; Li, Q.; Simon, S. L., The glass transition

temperature versus the fictive temperature. J. Non-Cryst. Solids 2007, 353 (26),

2603-2612.

22. Wise, C. W.; Cook, W. D.; Goodwin, A. A., Chemico-diffusion kinetics of model

epoxy-amine resins. Polymer 1997, 38 (13), 3251-3261.

23. Horie, K.; Hiura, H.; Sawada, M.; Mita, I.; Kambe, H., Calorimetric investigation

of polymerization reactions. III. Curing reaction of epoxides with amines. J. Polym.

Sci., Part A: Polym. Chem. 1970, 8 (6), 1357-1372.

24. Wisanrakkit, G.; Gillham, J., The glass transition temperature (Tg) as an index of

chemical conversion for a high‐Tg amine/epoxy system: chemical and diffusion‐

controlled reaction kinetics. J. Appl. Polym. Sci. 1990, 41 (11‐12), 2885-2929.


195

25. Wisanrakkit, G.; Gillham, J.; Enns, J., The glass transition temperature (Tg) as a

parameter for monitoring the cure of an amine/epoxy system at constant heating

rates. J. Appl. Polym. Sci. 1990, 41 (7‐8), 1895-1912.

26. Wisanrakkit, G.; Gillham, J. K., Continuous heating transformation (CHT) cure

diagram of an aromatic amine/epoxy system at constant heating rates. J. Appl.

Polym. Sci. 1991, 42 (9), 2453-2463.

27. Gupta, S. K.; Kumar, A., Reaction engineering of step growth polymerization.

Springer Science & Business Media: 2012.

28. Swier, S.; Van Assche, G.; Van Mele, B., Reaction kinetics modeling and thermal

properties of epoxy–amines as measured by modulated‐temperature DSC. I. Linear

step‐growth polymerization of DGEBA+ aniline. J. Appl. Polym. Sci. 2004, 91 (5),

2798-2813.

29. Pascault, J.-P.; Williams, R. J., Epoxy polymers: new materials and innovations.

John Wiley & Sons: 2009.

30. May, C., Epoxy resins: chemistry and technology. CRC press: 1987.

31. Kissinger, H. E., Reaction kinetics in differential thermal analysis. Anal. Chem.

1957, 29 (11), 1702-1706.

32. Akahira, T.; Sunose, T., Method of determining activation deterioration constant of

electrical insulating materials. Res. Rep. Chiba Inst. Technol.(Sci. Technol.) 1971,

16, 22-31.

33. Vyazovkin, S.; Chrissafis, K.; Di Lorenzo, M. L.; Koga, N.; Pijolat, M.; Roduit, B.;

Sbirrazzuoli, N.; Sunol, J. J., ICTAC Kinetics Committee recommendations for

collecting experimental thermal analysis data for kinetic computations.


34. Mel’nichenko, Y. B.; Schüller, J.; Richert, R.; Ewen, B.; Loong, C. K., Dynamics

of hydrogen‐bonded liquids confined to mesopores: A dielectric and neutron

spectroscopy study. The Journal of chemical physics 1995, 103 (6), 2016-2024.

35. Arndt, M.; Stannarius, R.; Gorbatschow, W.; Kremer, F., Dielectric investigations

of the dynamic glass transition in nanopores. Physical Review E 1996, 54 (5), 5377.

36. Koh, Y. P.; Li, Q.; Simon, S. L., T g and reactivity at the nanoscale. Thermochim.

Acta 2009, 492 (1), 45-50.

37. Koh, Y. P.; Simon, S. L., Crystallization and Vitrification of a Cyanurate Trimer in

Nanopores. J. Phys. Chem. B 2012, 116 (26), 7754-7761.

38. Koh, Y. P.; Simon, S. L., Kinetic Study of Trimerization of Monocyanate Ester in

Nanopores (vol 115, pg 925, 2011). J. Phys. Chem. B 2012, 116 (1), 731-731.


196

39. Zhuravlev, L., Concentration of hydroxyl groups on the surface of amorphous

silicas. Langmuir 1987, 3 (3), 316-318.

40. Tsyganenko, A. A.; Mardilovich, P. P., Structure of alumina surfaces. J. Chem.

Soc., Faraday Trans. 1996, 92 (23), 4843-4852.


197

Table 8.1 Kinetic parameters from the autocatalytic model for bulk. Kinetic

Parameters from the second order model for 55 and 7.5 nm CPG.

Bulk 55 nm CPG 7.5 nm CPG

Heat of Reaction (J/g) 437.8 ± 8.6 427.7 ± 9.5 433.2 ± 13.5

Activation Energy (Ea)

kJ/mol 55.12

Rate Constant (k0) 1/s

Tref = 353.15 K 4.6 x 10-4 9.7 x 10-4 5.0 x 10-3

b 8.4 x 10-3 NA NA

dx/dt|x=0 = k0b 3.9 x 10-6 9.7 x 10-4 5.0 x 10-3


198

Table 8.2 Summary of glass transition temperature, step change in heat capacities

for epoxy polymer synthesized in bulk, 55 and 7.5 nm CPG.

Pore Diameter (nm) Bulk 55 7.5

Tg1 (°C) 86.9 ± 1.8 86.1 ± 2.4 90.5 ± 3.1

Tg2 (°C) 116.5 ± 3.7 172.4 ± 3.1

ΔCp1 (Jg-1K-1) 0.46 ± 0.02 0.39 ± 0.01 0.42 ± 0.01

ΔCp2 (Jg-1K-1) 0.07 ± 0.01 0.05 ± 0.01

ΔCpT (Jg-1K-1) 0.46 ± 0.02 0.46 ± 0.01 0.47 ± 0.01

Surface layer thickness (nm) 2.23 ± 0.18 0.22 ± 0.07

volume fraction of upper Tg material 0.18 ± 0.01 0.13 ± 0.01


199

Figure 8.1 Representative reaction exotherms of epoxy polymerization in the (a)

bulk and (b) 55 nm CPG nanopores at various heating rates.


200

Figure 8.2 Conversion x as a function of temperature for the bulk reaction. The black

lines are the best fits from the second order autocatalytic model.


201

Figure 8.3 Conversion x as a function of temperature for reaction in 55 nm CPG

nanopores. The black solid line is the best fit from the second order reaction model.


202

Figure 8.4 (a) Comparison of representative reaction exotherms in bulk, 55 and 7. 5

nm CPG nanopores (b) conversion versus temperature of reactions in bulk, 55 and

7.5 nm CPG nanopores. The black solid line for the bulk is the best fit to the second

order autocatalytic model and the black solid lines for 55 and 7.5 nm CPG pores are

the best fits to the second order model.


203

Figure 8.5 (a) Isoconversional analysis of the bulk data at different heating rates. (b)

Apparent activation energies of the epoxy reaction in bulk, 55 and 7.5 nm CPG as a

function of conversion from KAS isoconversion method. (the error bars for the

activation energy at a given conversion was obtained from the standard error of the

linear fit)


204

Figure 8.6 Glass transition temperatures obtained on heating at 10 K/min after

cooling at the same rate for bulk, 55 nm CPG and 7.5 nm CPG.


205

CHAPTER 9

CONCLUSIONS

In this dissertation, the effect of nanoconfinement on melting, glass transition,

structural recovery, and step-growth polymerization kinetics was investigated. In

addition, the origin of low-temperature endotherms and their relationship to two-step

structural recovery was also investigated. To study the effect of nanoconfinement on

melting, glass transition and structural recovery, and to investigate the origin of low-

temperature endotherms, Flash differential scanning calorimetry was used; a conventional

DSC was used to study the effect of nanoconfinement on step-growth polymerization

kinetics.

Nanoconfinement effects on the melting and solid-solid transitions of n-

hexadecane (C16H34) and n-nonadecane (C19H40) were studied in an anodic aluminum

oxide (AAO) nanoporous membrane with pore diameters of 20 and 55 nm. The major

findings are:

• AAO nanopore membranes can be used on the Flash DSC to study the

nanoconfinement effects in 2D space.

• Nanoconfined melting of n-hexadecane results in a melting point depression (∆Tm) of

4.20 ± 0.60 °C in 55 nm AAO pores and 6.01 ± 0.24 °C in 20 nm AAO pores.

• Nanoconfined melting of n-nonadecane(C19) results in a melting point depression of

2.46 ± 0.40 °C and 4.2 ± 0.51 °C in 55 and 20 nm AAO pores, whereas its solid-solid


206

transition was found to be depressed by 1.94 ± 0.15 °C and 3.01 ± 0.29 °C in 55 and

20 nm AAO pores, respectively.

• Interestingly, the size-dependent melting behavior (∆Tm vs 1/d) for both C16 and C19

does not extrapolate to the bulk melting point at infinite pore size, indicating that a

different crystal structure, perhaps a nematocrystalline state may be formed in AAO

nanopores, as backed up by X-ray diffraction.

The glass transition behavior of AAO supported and stacked polystyrene (PS)

nanorods (2D) for diameters in the range of 20-350 nm was studied using Flash

differential scanning calorimetry over four decades of cooling rates, from 0.1 – 1000 K/s.

Major findings are:

• Tg depressions of 20.1 ± 2.2 and 8.8 ± 0.7 K are observed in case of 20 and 55 nm

stacked PS nanorods dispersed in ionic liquid, whereas bulk-like behavior is observed

in the case of 350 nm PS nanorods.

• An effect of spatial dimensionality is found; the Tg depression for 20 nm 2D stacked

PS nanorods is 8 K larger when compared to that of 20 nm 1D ultrathin PS film from

previous studies.

• The size-dependent glass transition behavior of 2D stacked PS nanorods compares

well with our group’s previous studies on 1D ultrathin PS films when scaled using the

volume to surface ratio.

• In the case of AAO supported PS nanorods bulk-like behavior is observed

irrespective of confinement diameter; the behavior is consistent with similar studies

in the literature.


207

Enthalpy recovery of 2D stacked polystyrene nanorods dispersed in ionic liquid was

studied for two different rod diameters, 20 and 350 nm, using Flash Differential scanning

calorimetry. The major findings are:

• The enthalpy recovery towards equilibrium is found to be linear and monotonic for

jump sizes where structural recovery is observed (7 K to 87 K), unlike the two-step

recovery reported in the literature at aging time scales within the range used in this

work.

• Enhanced enthalpy recovery rates are observed for 20 nm stacked PS nanorods when

compared to 350 nm stacked PS nanorods at jump sizes greater than 17 K, whereas

similar enthalpy recovery rates are observed when compared at jump sizes smaller

than 17 K.

• The importance of comparing enthalpy recovery at similar jump sizes is also

highlighted, based on induction times, which are similar for stacked rods and ultrathin

films from previous studies when compared at similar jump sizes, but shorter

induction times are observed in case of 20 nm stacked PS rods when compared at

similar aging temperatures.

• The effect of spatial dimensionality on enthalpy recovery rates is found to be

insignificant when overall enthalpy recovery rates of 20 and 350 nm stacked PS

nanorods are compared with 20 nm ultrathin and bulk PS films from previous studies.

The similarity in enthalpy recovery rates is attributed to similar temperature

dependence of their respective average relaxation times.

The origin of low temperature endotherms was investigated using Flash differential

scanning calorimetry for micronsale PS thinfilms, 2D stacked PS rods, 2D AAO


208

supported PS rods, and metals, with a conclusion that the low temperature endotherms do

not exhibit physics related to the segmental or a secondary relaxation in glassy materials.

Rather, the low temperature endotherm is related to the sample and chip configuration.

Findings that lead to the aforementioned conclusion are:

• Broad low-temperature endotherms are observed for both micron-scale PS films and

20 nm stacked PS rods which were both cooling rate dependent and aging time

dependent and were found to be sample dependent for nominally the same material

investigated. For example, the areas of the low temperature endotherms decreased by

in the order of micron-scale PS film on bare chip > Krytox oil > 350 nm AAO > 55

nm AAO. In addition, a similar decrease in the low temperature endotherm area is

observed for 20 nm PS stacked nanorods dispersed ionic liquid versus the same

sample on bare chip.

• In addition to glassy polymers, the low temperature endotherms are also observed for

crystalline metals, indium and vapor-deposited gold, neither of which have

relaxations in the temperature range of interest (-80 to 110 °C).

• When enthalpy recovery of 20 nm stacked PS rods was studied with the inclusion of

the low temperature endotherm at aging temperatures -20.5, 20.5 and 80.5 °C, no

evidence of a two-step recovery was observed at timescales reported for 3D PS

nanospheres in the literature.

The reaction kinetics of linear epoxy polymerization in bulk, 55, and 7.5 nm

native controlled pore glass (CPG) nanopores was investigated using dynamic differential

scanning calorimetry (DSC). The major findings are:


209

• Polymerization is found to be accelerated in the nanopores, as indicated by a 90 and

116 K decrease in the onset temperatures of the reaction exotherm in 55 and 7.5 nm

CPG nanopores, respectively.

• The acceleration in the nanopores is quantified by initial reaction rates which are 240

and 1280 times faster in 55 and 7.5 nm CPG nanopores than in the bulk.

• The autocatalytic behavior which is observed in the bulk is found to be weakened in

the nanopores; hence, a simple second order model is used to model the nanoconfined

reaction kinetics.

• Two Tgs are observed in both 55 and 7.5 nm CPG nanopores. Tg1s are in good

agreement with the bulk values, and Tg2s are found to be elevated by 30 and 80 K in

55 and 7.5 nm CPG nanopores, respectively.

• The enhanced initial reaction rates, the weakened autocatalytic character, and elevated

Tg2s in native CPG nanopores are attributed to the surface silanol groups.


210

CHAPTER 10

FUTURE WORK

In this dissertation, Flash differential scanning calorimetry has been

predominantly used to study the nanoconfinement effects on melting, the glass transition,

and structural recovery. The ability of the Flash DSC to handle ultra-low sample masses

aided in characterizing stacked and AAO supported nanorods and previous studies on

ultrathin PS films. In addition, the main advantage of the Flash DSC is its ability to

achieve rapid scanning rates which are useful in creating high fictive temperature glasses;

and also, to suppress time sensitive processes like decomposition and crystallization. The

instruments extreme sensitivity at smaller time scales also helps in studying the enthalpy

recovery of polymers effectively. To expand the applicability of Flash DSC’s advantages,

some recommendations for future work are suggested in 10.1,10.2 and 10.3. In 10.4, a

future extension to the work described in chapter 8 is suggested.

10.1 Glass transition behavior and structural recovery of polynorbornene thin films

using Flash differential scanning calorimetry

The norbornene class of polymers are high Tg (>613 K)1-2 and high free volume3

polymers with excellent applications as membranes in butanol-water separations and gas

separations.4-5 Depending on the operating temperature the polymer is prone to physical

aging over time and may lose permeability;6 hence, studying the aging behavior of

norbornene class of polymers is relevant. Lewis and Vogt7 studied the structural

relaxation of thin films (60 nm to 2.3 µm) of a random copolymer of poly(butyl


211

norbornene) and poly(hexafluoroisopropyl norbornene) using ellipsometry and observed

structural relaxation even at 303 K (Tg -300 K) In addition, the aging rates decreased with

decreasing film thickness and increasing aging temperatures. This somewhat surprising

result warrants enthalpy recovery studies on the same norbornene copolymer for various

film thicknesses using Flash DSC. In addition, the use of Flash DSC will also help in

suppressing the side reactions that prevent annealing above Tg by employing ultra-fast

heating rates (1000 K/s) which have been successfully used in suppressing the

degradation of silk fibroin proteins8-9 and sucrose10. In addition to the enthalpy recovery

studies, the study of the size-dependent glass transition behavior of nanoscale thin films

of a polynorbornene copolymer is also interesting. Interestingly, previous studies on a

similar norbornene polymer did not result in any Tg depression because of the presence of

s rigid bicyclic backbone11 Generally, lack of Tg depression in nanoscale films implies

bulk-like mobility, which means the structural recovery process is expected to be size

independent which is contrary to Vogt and co-workers’7 finding, thus making the

investigation of structural recovery kinetics of norbornene polymers more interesting.

10.2 Glass transition behavior and enthalpy relaxation of thermoplastic epoxy

reinforced with multi-walled carbon nanotubes using Flash DSC

In general epoxy polymers are good insulators, but due to their excellent

mechanical properties they are preferred as a polymer matrix in thermal interface

materials (TIM) which are used in microelectronic packaging to plug voids in heat sinks

for efficient heat transfer.12 Since the epoxy polymer matrix has insulating properties,

thermally conductive fillers like carbon nanotubes are used to significantly enhance the

thermal conductivity; at optimum loadings (5-6 vol %)13of carbon nanotubes a 200 %


212

increase in thermal conductivity has been observed.12, 14-16 Recently, thermoplastic epoxy

polymers are being used as a polymer matrix in thermal interface materials owing to the

relative ease in impregnating fillers into the matrix.17 Since thermal interface materials

operate at temperatures where physical aging is relevant, the study of glass transition and

related behavior for a model thermoplastic epoxy polymer reinforced with multi-walled

carbon nanotubes (MWCNTs) is important; generally, an increase in the glass transition

temperature has been reported for MWCNT filled epoxy polymer18, but most studies lack

direct impregnation of MWCNTs into the polymer, rather, MWCNTs are dispersed into

the epoxy resin before curing. The objective of this suggested future study is to

investigate the glass transition behavior and enthalpy relaxation of thermoplastic epoxy

(DGEBA + Aniline) reinforced with multi-walled carbon nanotubes, where the carbon

nanotube reinforced thermoplastic epoxy will be prepared by first dissolving a chosen

weight percent of neat epoxy polymer in HPLC grade THF solvent, and then MWCNTs

will be dispersed into the dissolved solution by ultrasonication. The polymer solution

with dispersed MWCNTs will be spin coated into thin films. The glass transition and

enthalpy relaxation behavior will be studied as function of MWCNT loading in the

thermoplastic epoxy film.

10.3 Obtaining three Kovacs’ signatures of structural recovery for 20 nm stacked

PS rods and 20 nm ultrathin PS film, and modeling with the modified TNM model

In chapter 7 of this dissertation, we have performed enthalpy recovery

measurements on 20 nm stacked PS nanorods. An interesting finding in that work is that

similar enthalpy recovery rates were observed for 20 nm stacked PS nanorods and 20 nm

ultrathin PS film. In order to better understand the kinetics of structural recovery of 2D


213

20 nm stacked rods and 1D 20 nm ultrathin film, one of the recommendations for future

work is to extend the enthalpy recovery experiments to obtain Kovacs’19 other signatures

of structural recovery, asymmetry of approach and memory effect. As a second

recommendation, the modeling of enthalpy recovery data of 20 nm stacked PS rods and

20 nm ultrathin film using Grassia and Simon’s modified TNM model20-21 is suggested.

The applicability of modified TNM model for nanoconfined data can also be elucidated

in this suggested study. The modified TNM model uses an odd symmetric function of

WLF equation to extend the temperature range of relaxation times to incorporate both

non-equilibrium glassy states and equilibrium liquid states,20-21 and the modified TNM

model requires only the fit of two parameters along with the WLF parameters obtained

from cooling rate dependent experiments.20-21

10.4 Reaction kinetics of alumina and silica filled epoxy polymerization

The reaction kinetics of epoxy polymerization in bulk, 55 and 7.5 nm CPG

nanopores have been discussed in Chapter 8, where accelerated initial reaction rates were

observed in 55 and 7.5 nm CPG nanopores when compared to the bulk. The magnitudes

of acceleration were found to be 240 and 1280 times in 55 and 7.5 nm CPG nanopores,

respectively; in addition, the acceleration factor was found to be higher in the case of

reaction in 55 nm CPG nanopores than that observed by Tarnacka and co-workers22 for

the same epoxy polymerization reaction in 35 nm AAO nanopores despite presumably

having lower a density of hydroxy groups on the nanopore surface (4 OH/nm2 in CPG23

versus 19 OH/nm2 in AAO24) and larger nanopore diameter. The enhanced reaction

kinetics under nanoconfinement is generally understood to be due to a combination of

nanoconfinement and surface effects. In the study reported in chapter 8 and the study by


214

Tarnacka and co-workers, native nanopores with surface hydroxyl groups were used,

resulting in an enhanced reaction rate of epoxy polymerization in addition to the

nanoconfinement effect. In order to understand the exact reason for enhanced reaction

kinetics in CPG nanopores when compared to AAO nanopores, separating the

nanoconfinement effect and surface effect is important. Attempt to study the

nanoconfinement effect alone using silianized CPG nanopores (trimethylsilyl groups)

was not successful because of poor wetting and plug formation of DGEBA + Aniline

liquid mixture in silanized CPG nanopores. Therefore, future recommendation is to study

the surface effect or the influence of hydroxyl groups and types of hydroxyl groups (Si-

OH and Al-OH) on the reaction kinetics of DGEBA + Aniline polymerization by adding

silica and alumina nanoparticles as fillers. The future study has two objectives: 1) To

compare the reaction kinetics with silica and alumina nano particles as a function of

hydroxyl concentration. 2) To compare the reaction kinetics of silica nanoparticles and

CPG nanopores at similar hydroxyl concentrations. In addition, to ensure homogenous

dispersion of particles ultrasonication method may be used.


215

References

1. Henschke, O.; Köller, F.; Arnold, M., Polyolefins with high glass transition

temperatures. Macromol. Rapid Commun. 1997, 18 (7), 617-623.

2. Bergström, C. H.; Seppälä, J. V., Effects of polymerization conditions when

making norbornene‐ethylene copolymers using the metallocene catalyst ethylene

bis (indenyl) zirconium dichloride and MAO to obtain high glass transition

temperatures. J. Appl. Polym. Sci. 1997, 63 (8), 1063-1070.

3. Wilks, B. R.; Chung, W. J.; Ludovice, P. J.; Rezac, M. R.; Meakin, P.; Hill, A. J.,

Impact of average free‐volume element size on transport in stereoisomers of

polynorbornene. I. Properties at 35° C. J. Polym. Sci., Part B: Polym. Phys. 2003,

41 (18), 2185-2199.

4. Kim, D.-G.; Takigawa, T.; Kashino, T.; Burtovyy, O.; Bell, A.; Register, R. A.,

Hydroxyhexafluoroisopropylnorbornene block and random copolymers via vinyl

addition polymerization and their application as biobutanol pervaporation

membranes. Chem. Mater. 2015, 27 (19), 6791-6801.

5. Knapp, B.; Elce, E.; Bedwell, B.; Langsdorf, L. J.; Wilks, R., Polynorbornene

pervaporation membrane films, preparation and use thereof. Google Patents: 2012.

6. Yin, H.; Chapala, P.; Bermeshev, M.; Schonhals, A.; Bohning, M., Molecular

mobility and physical aging of a highly permeable glassy polynorbornene as

revealed by dielectric spectroscopy. ACS Macro Letters 2017, 6 (8), 813-818.

7. Lewis, E. A.; Vogt, B. D., Thickness dependence of structural relaxation in spin‐

cast polynorbornene films with high glass transition temperatures (> 613 K). J.

Polym. Sci., Part B: Polym. Phys. 2018, 56 (1), 53-61.



3.







11. Torres, J. M.; Wang, C.; Coughlin, E. B.; Bishop, J. P.; Register, R. A.; Riggleman,

R. A.; Stafford, C. M.; Vogt, B. D., Influence of chain stiffness on thermal and

mechanical properties of polymer thin films. Macromolecules 2011, 44 (22), 9040-

9045.


216

12. Biercuk, M.; Llaguno, M. C.; Radosavljevic, M.; Hyun, J.; Johnson, A. T.; Fischer,

J. E., Carbon nanotube composites for thermal management. Appl. Phys. Lett. 2002,

80 (15), 2767-2769.

13. Yu, A.; Ramesh, P.; Itkis, M. E.; Bekyarova, E.; Haddon, R. C., Graphite

nanoplatelet− epoxy composite thermal interface materials. The Journal of Physical

Chemistry C 2007, 111 (21), 7565-7569.

14. Han, Z.; Fina, A., Thermal conductivity of carbon nanotubes and their polymer

nanocomposites: A review. Prog. Polym. Sci. 2011, 36 (7), 914-944.

15. Saw, W. S.; Mariatti, M., Properties of synthetic diamond and graphene

nanoplatelet-filled epoxy thin film composites for electronic applications. Journal

of Materials Science: Materials in Electronics 2012, 23 (4), 817-824.

16. Xu, X.; Thwe, M. M.; Shearwood, C.; Liao, K., Mechanical properties and

interfacial characteristics of carbon-nanotube-reinforced epoxy thin films. Appl.

Phys. Lett. 2002, 81 (15), 2833-2835.

17. Imanishi, T., In-situ polymerizable thermoplastic epoxy resin and high performance

FRTP using it and fiber fabrics. Proceedings of 16th ICCM, 2007 2007, 1, 194-195.

18. Thakre, P. R.; Bisrat, Y.; Lagoudas, D. C., Electrical and mechanical properties of

carbon nanotube‐epoxy nanocomposites. J. Appl. Polym. Sci. 2010, 116 (1), 191-

202.

19. Kovacs, A. J.; Aklonis, J. J.; Hutchinson, J. M.; Ramos, A. R., Isobaric volume and

enthalpy recovery of glasses. II. A transparent multiparameter theory. Journal of

Polymer Science: Polymer Physics Edition 1979, 17 (7), 1097-1162.



1549-1558.



Thermochim. Acta 2015, 603, 135-141.





23. Zhuravlev, L., Concentration of hydroxyl groups on the surface of amorphous

silicas. Langmuir 1987, 3 (3), 316-318.

24. Tsyganenko, A. A.; Mardilovich, P. P., Structure of alumina surfaces. J. Chem.

Soc., Faraday Trans. 1996, 92 (23), 4843-4852.

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Texas Tech University, Madhusudhan R. Pallaka, December 2019