Measuring Absolute Values of Modulus of Elasticity for ... · PDF fileMeasuring Absolute Values of Modulus of ... • New comprehensive suite of force curve analysis tools ... Values

Measuring Absolute Values of Modulus of Elasticity for Soft Materials with AFM Part I: Recent developments in PeakForce QNM and Force Volume mechanical property mapping. Bede Pittenger, Senior Applications Scientist December 19, 2012

A brief review of AFM imaging technology

• Mapping topography -> more information • Contact mode (1986)

• Tapping Mode (1992)

• Force-Volume Mapping (~1992)

• PeakForce Tapping (2009)

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Bruker’s PeakForce Tapping technology

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• PeakForce Tapping imaging • Sinusoidal Z ramping • Constant peak force feedback • Tip intermittently “taps” sample (~1kHz) • Best for soft samples, ultra-low forces

Note three essential features: • Sinusoidal ramping (not linear)

• Tip velocity approaches zero as the tip nears the sample surface

• Real feedback loop force control • Force control benefits from the results

of prior force curves

• Fast ramping • Faster images, even with more pixels

The Result: • Best force control • Fastest speed • Highest resolution • Greatest stability

Z motion

Deflection

Force Volume

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• Force-Volume Mode • Linear Z ramping • Discrete force triggers at each ramp • Tip intermittently “taps” sample

(<~0.01kHz) • Force control is ramp speed dependent

Force-Volume potential issues: • Linear ramping (not sinusoidal)

• Tip hits sample at full velocity • Abrupt turn-around at high speed ->

ringing, hysteresis

• Trigger monitored force control • Trigger monitors force and attempts to turn

around at trigger. At high speeds, it can’t reverse fast enough, so it overshoots.

The Result, three options: • Fast & high resolution, but poor

force control, poor z accuracy • Good force control & high

resolution, but slow imaging (>1h) • Fast & good force control, but low

resolution (few pixels)

Z motion

Deflection

PeakForce QNM Example Heat-sealed bag

Barrier and Tie layers are incompatible, so we expect a relatively abrupt interphase.

• Single scan line has a clear step in modulus over a distance of ~75nm.

• Lamella do not cross the interface, but grow epitaxially from the Barrier layer ~250nm into the Tie layer.

(a)

(b)

(a)

(c)

(b)

DMTModulus

Barrier layer Nylon Strength & gas impermeability

Tie layer ULDPE Preserves layer adhesion Sealant layer Metallocene PE/LDPE blend Adheres to itself when heated

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PeakForce QNM Example Heat-sealed bag

Tie and Sealant layers are more compatible, so we expect a wider interphase.

• Single scan line: the variation in modulus is dominated by individual lamella.

• Collectively: modulus varies over a much wider range ~250nm to ~1um.

• Lamella from Tie layer act as nucleation sites or penetrate into the Sealant layer resulting in a more ordered region up to ~1um from the interface.

(a)

(b)

(a)

(c)

(b)

DMTModulus

Barrier layer Nylon Strength & gas impermeability

Tie layer ULDPE Preserves layer adhesion Sealant layer Metallocene PE/LDPE blend Adheres to itself when heated

12/19/2012 6

PeakForce QNM calculates sample properties directly from force curves

(ii)

The complete force curve from every interaction between tip and sample is analyzed in real-time, allowing:

• Feedback based on the peak force, protecting the tip and sample. • Individual curves can be examined and analyzed offline (PeakForce

Capture) • Peak Force, Adhesion, Young’s Modulus, Deformation, Dissipation

mapped simultaneously with topography.

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The new Nanomechanics Package greatly expands these capabilities

• The new Nanomechanics Package includes: • New expanded PeakForce QNM capabilities for soft samples:

• capture force curves at larger amplitudes • capture force curves at lower frequencies • addition of the Sneddon conical indenter model

• New PeakForce Capture feature to capture full PeakForce QNM data • New Quantitative Force-Volume Mapping with new analysis tools • New comprehensive suite of force curve analysis tools

• How do I get it? • Offline tools are available to everyone at no charge – just download

the latest version of Nanoscope Analysis v1.40r3 • Users of Dimension FastScan and Icon, Bioscope Catalyst, and

Multimode 8 can obtain a free upgrade to the latest version of Nanoscope v8.15r3

12/19/2012 8

See Nanoscale world SPM digest at http://nanoscaleworld.bruker-axs.com/nanoscaleworld/forums/p/1208/3315.aspx#3315

Expanded PeakForce QNM capabilities

• Can now choose Hertz/DMT (spherical) or Sneddon (conical) models • On very soft samples (e.g. cells, tissues, biomolecules), the tip often indents

well past the very tip, even with the best force control, so the Sneddon model is often a better model for biological samples.

• Softer samples often require larger force curve ramp sizes • PeakForce QNM can now support ramp sizes up to 4µm (Catalyst only) • In some cases lower PeakForce QNM modulation frequencies can be useful. You

can now choose among 250Hz, 500Hz, 1kHz and 2kHz (depending on system)

12/19/2012 9

Real AFM tip

Tip radius ~20nm

Tip half angle ~18°

New, more quantitative PeakForce QNM data using the Sneddon model

• PeakForce QNM image of E. coli bacteria using a standard DNP-A probe in fluid with 300nm modulation amplitude at 250 Hz. The Sneddon (conical) modulus model was used with the nominal 18˚ tip half angle. (Scan size 5µm) • Note that the dividing cell on the right is significantly softer than the cell on the left (~2MPa vs ~15MPa) • Much of the substrate is too stiff to accurately measure under the same conditions as the bacteria, but note

the presence of some softer components, including the bacterial flagella in the lower-right corner.

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Modulus data painted on 3D topography Sneddon modulus data channel

Sneddon model works well over the biologically relevant kPa-MPa range

• Agarose gels measured with PeakForce QNM (Sneddon model, MLCT-E probe)

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PeakForce Capture -Greater transparency and flexibility

• Capture a force curve at every pixel in PeakForce QNM images • QNM images still calculate and capture normally, as before • Additionally, force curves are captured to a separate file

• PeakForce Capture uses the Quantitative Force-Volume file format • Use the full Quantitative Force-Volume analysis tools on PeakForce

Capture data to generate modulus and adhesion maps • Can import the data into custom analysis software

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PeakForce Capture offline analysis

12/19/2012 13

New Quantitative Force-Volume Mapping

• Force-volume has been widely used for more than 15 years for mapping sample properties • Important reference technique to compare to new methods • Allows very low ramp rates for comparison to non-AFM material property

measurement techniques such as DMA

• The new Quantitative Force-Volume Mapping mode adds new real-time and offline analysis capabilities • Directly obtain modulus and adhesion maps from force-volume • Same indentation models (Sneddon & Hertz/DMT) as PFQNM • All force curves available for further offline processing

12/19/2012 14

Force-Volume example E. coli bacteria DNP-A probe in fluid

• Quantitative Force-Volume Mapping images of E. coli bacteria using a 600nm ramp size and different ramp rates • The Sneddon (conical) modulus model was used with the nominal 18˚ tip

half angle. (Scan size 5µm) • Modulus numbers vary only slightly for these ramp rates

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20Hz ramp rate, 64x64 pixels, 5µm scan 2Hz ramp rate, 64x64 pixels, 5µm scan 10Hz ramp rate, 64x64 pixels, 5µm scan

Good agreement between PeakForce QNM and Quantitative Force-Volume Mapping

• Agarose gel series was measured with both techniques

• Many more measurements with PeakForce QNM for better statistics • Force volume: 256 points (16x16) • QNM: 16.4k points (128x128)

• PeakForce QNM provides more measurements faster • QNM: ~11min for 16.4k points • Force-volume: ~4min for 256 points

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Comprehensive force curve analysis tools

• NanoScope Analysis now includes:

Modify Force Parameters: Update key parameters in captured files

Baseline Correction: Remove force curve baseline offset and/or tilt

Boxcar Filter: Apply moving average smoothing filter to data

Indentation Analysis: Fit indentation models to obtain modulus values

Batch Processing: Apply multiple functions to many curves at once

MATLAB Toolbox: Easy loading of data directly from Nanoscope data files

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Comprehensive force curve analysis tools

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• These functions all work with Run History for automation!

MATLAB Toolbox

• MatLab calls DLL to access Nanoscope data files directly

• No more concerns regarding file parsing or format changes over time

• No need to ASCII export: better automation

• Frees researchers to focus on modeling and results

12/19/2012 19

Overview of the techniques available with the new Nanomechanics Package

12/19/2012 20

• Recalculate with different parameters • Recalculate with different models • Inspect curve anywhere on image

• Real-time calculation of Sneddon Modulus as well as all the usual PF-QNM channels

• Real-time calculation of DMT Modulus, Sneddon Modulus, Adhesion, Peak Force

• Recalculate with different parameters • Recalculate with different models

• Tools allow correction of force curves • Analysis allows inspection of model

fitting • Tools can be automated • MATLAB toolbox allows additional

models

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© Copyright Bruker Corporation. All rights reserved.

Measuring AbsoluteValues of Modulus of

Elasticity for SoftMaterials with AFM

Igor SokolovDepartment of Physics, Nanoengineering and Biotechnology Laboratories Center

(NABLAB), Clarkson University

After Jan.15, 2013: Dept. of ME and BME, Tufts University

Bruker Webinar, Dec. 19, 2012

Post-docs:Dr. Maxim DokukinDr. Shajesh Palantavida

Graduate Students:Vivekanand KalaparthiNataliia Guz

Undergrad. Students:A. Cardin, M. Kreshchuk

$UPPORT:

AcknowledgementsAcknowledgements

Here we test how quantitative AFM is inmeasuring the elastic moduli at the

nanoscale

Results in short: YES, it is quantitative,but one has to be accurate in usingappropriate models and probes..

OutlineOutline

How we test itHow we test it

The idea: to take a homogeneous polymer andmeasure its elastic modulus (the Young’s modulus)using existing methods:Ø Macro DMAØ Nanoindenterto compare with the AFM Force-Volume andPeakForce QNM modes

Assumption: the macro- and nanoscale moduli should be close(homogeneous material down to nanoscale; no surface effects -tested by comparing to a fresh cleavage of the sample bulk).

Note: Ramping speed was kept similar in all methods (exceptPeakForce QNM).

Here we use polystyrene and polyurethane.

http://www.perkinelmer.com/CMSResources/Images/44-74431BRO_DMA8000.pdf

Sample

http://www.tainstruments.com/

Compression

Bending

130Mpa

60Mpa

Stress-strain relation becomes essentially non-linear

Large range of stresses Small stresses

Micron scale modulus: NanoindenterMicron scale modulus: Nanoindenter

Summary table

polyurethane polystyrene Contactdiameter Depth

Macro DMA 0.65±0.15 2.68±0.23 ~5 mm n/a

All modulus values are in GPa

Micron scale: Nanoindenter-based DMAMicron scale: Nanoindenter-based DMA

http://www.hysitron.com/resources/core-techniques/hysitrons-patented-transducer

Spherical indenter Berkovich indenter

Micron scale modulus: NanoindenterMicron scale modulus: Nanoindenter

Berkovich indenter Spherical indenter: 108um

Macroscopic moduli

Linearity limits

polystyrene

polystyrene

polyurethanepolyurethane

polystyrene

polyurethane

polyurethane

polystyrene

M. Dokukin, Igor Sokolov, Langmuir, 2012, 28 (46) pp 16060–16071

Summary table


Macro DMA 0.65±0.15 2.68±0.23 ~5 mm n/a

Nanoindenter:Berkovich 0.91±0.02 <3.4** max force >15 µm >1500nm

Nanoindenter:Conosphere 0.60±0.02 >1.6** max force >15 µm >400nm

All modulus values are in GPa

Nano scale modulus: AFMNano scale modulus: AFM

2. Well defined geometry of the probe is a must: tip-check scanning method

Things to be careful about:

1. Stresses should be below the limit of linearity

3. Use appropriate cantilever length (do not over-bend – can easily be seenin the calibration sensitivity plot)


M. Dokukin, and I. Sokolov, Macromolecules, 2012, 45(10) pp 4277-4288

Oliver-Pharr model used. Note strong “Skin-effect”

Dull probe R~803nmSharp probe R=22nm

130MPaLinearity limits

Macroscopic moduli

Summary table


Macro DMA 0.65±0.15 2.68±0.23 ~5 mm n/a



AFM-indenter FV:Oliver dull 0.50±0.06 <1.6 180-250nm >10nm

AFM-indenter FV:Oliver sharp 0.99±0.13 2.23±0.21 110-140nm 50-60nm

M. Dokukin, and I. Sokolov, Macromolecules, 2012, 45(10) pp 4277-4288M. Dokukin, Igor Sokolov, Langmuir, 2012, 28 (46) pp 16060–16071



Dull probe R~803nm

130MPaLinearity limits

Macroscopic moduli

OK for small depthOK for small depth



Maugis parameter

>0.9 in our case

Both DMT and JKR models look good: no skineffect, no large non-linearity.. But which one is theright one?

JKR!

Summary table


Macro DMA 0.65±0.15 2.68±0.23 ~5 mm n/a





AFM-indenter FV:dull DMT 0.74 ± 0.14 1.82 ± 0.28 100nm ~2nm

AFM-indenter FV:dull JKR

0.96 ± 0.21 2.75 ± 0.30 120nm ~2nm


Can we compare AFM FV and PeakForce QNM?


Strictly speaking no, because the ramping (loading/unloading) speeds are quite different.BUT, we should expect the same results

if the elastic modulus is not frequency dependent.It is the case for the polymers considered here

Polyurethane

Polystyrene

Force-Volume

Quantitative PeakForce QNM


Polyurethane

Polystyrene

Summary table


Macro DMA 0.65±0.15 2.68±0.23 ~5 mm n/a





AFM-indenter FV:dull DMT 0.74 ± 0.14 1.82 ± 0.28 100nm ~2nm

AFM-indenter FV:dull JKR

0.96 ± 0.21 2.75 ± 0.30 120nm ~2nm

AFM PeakForceQNM (dull probe,JKR model)

0.98±0.22 2.70±0.50 50nm 3nm


Where is the limit of spatial resolution?Where is the limit of spatial resolution?

Radius of the probe to have max stress < the limit of linearity:

*2 *2 3 2 *4max max*

2 3max

6 6 6p sp s

+ +> adh L adhw E E F w E

RmaxLF

maxs

adhw adhesion energy (per unit area)maximum shear stressmaximal load


* 200 300> -R nmFor our materials:

One see the elastic modulus starting from2-3nm vertical deformations and ~50nm contact diameter.

BUT! It might be just “sure bet”. This was derivation was based on“classical” macroscopic theory of elasticity extrapolated to the nanoscale.Materials at the nanoscale can withstand much higher stresses withoutplastic deformation (just calculate the stress during contact modeimaging!). Thus, we need to continue studying the limits. It is what we aredoing these days.

ConclusionConclusion

To obtain the elastic modulus at the nanoscale for

soft material, one needs:1. Use either Force-Volume or PeakForce QNM modes.

2. Watch for the linearity in stress-strain relation.

3. Take into account adhesion.

More reading: Macromolecules, 2012, 45(10) pp 4277-4288; Langmuir, 2012, 28 (46) pp 16060–16071

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Measuring Absolute Values of Modulus of Elasticity for ... · PDF fileMeasuring Absolute Values of Modulus of ... • New comprehensive suite of force curve analysis tools ... Values