1.4 Absolute Values Solving Absolute Value Equations By putting into one of 3 categories.
Measuring Absolute Values of Modulus of Elasticity for ... · PDF fileMeasuring Absolute...
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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.
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(b)
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(c)
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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.
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(b)
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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 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
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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)
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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
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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
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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
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Overview of the techniques available with the new Nanomechanics Package
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• 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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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 nano- scale 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
polyurethane polystyrene Contactdiameter Depth
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)
Nano scale modulus: AFMNano scale modulus: AFM
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
polyurethane polystyrene Contactdiameter Depth
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
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
Nano scale modulus: AFMNano scale modulus: AFM
M. Dokukin, and I. Sokolov, Macromolecules, 2012, 45(10) pp 4277-4288
Dull probe R~803nm
130MPaLinearity limits
Macroscopic moduli
OK for small depthOK for small depth
Nano scale modulus: AFMNano scale modulus: AFM
M. Dokukin, and I. Sokolov, Macromolecules, 2012, 45(10) pp 4277-4288
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
polyurethane polystyrene Contactdiameter Depth
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
AFM-indenter FV:Oliver dull 0.60±0.06 <1.6 180-250nm >10nm
AFM-indenter FV:Oliver sharp 0.99±0.13 2.23±0.21 110-140nm 50-60nm
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
M. Dokukin, and I. Sokolov, Macromolecules, 2012, 45(10) pp 4277-4288M. Dokukin, Igor Sokolov, Langmuir, 2012, 28 (46) pp 16060–16071
Can we compare AFM FV and PeakForce QNM?
M. Dokukin, Igor Sokolov, Langmuir, 2012, 28 (46) pp 16060–16071
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
M. Dokukin, Igor Sokolov, Langmuir, 2012, 28 (46) pp 16060–16071
Polyurethane
Polystyrene
Summary table
polyurethane polystyrene Contactdiameter Depth
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
AFM-indenter FV:Oliver dull 0.60±0.06 <1.6 180-250nm >10nm
AFM-indenter FV:Oliver sharp 0.99±0.13 2.23±0.21 110-140nm 50-60nm
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
M. Dokukin, and I. Sokolov, Macromolecules, 2012, 45(10) pp 4277-4288M. Dokukin, Igor Sokolov, Langmuir, 2012, 28 (46) pp 16060–16071
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
M. Dokukin, Igor Sokolov, Langmuir, 2012, 28 (46) pp 16060–16071
* 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