Dalia Yablon, Ph.D. and Bede Pittenger, Ph.D. Measuring ......Dalia Yablon, Ph.D. and Bede...

Measuring nanoscale viscoelastic properties with

AFM-based nano-DMA

Dalia Yablon, Ph.D. and Bede Pittenger, Ph.D.

AFM primed for nanomechanical measurements

Inherently mechanical interaction between probe and sample

Many ways to interact (resonant and non-resonant) and many observables to monitor

Different challenges for measuring properties on stiff (10 GPa +), softer materials (kPa – 1GPa),

and viscoelastic materials (frequency dependent, softer)

Stiff materials:

sensitivity, probe wear

Soft materials:

probe contamination, adhesion, contact mechanics model limitations

Viscoelastic materials:

problems for soft materials + frequency (measure and match)

surface

2

Measuring elastic and viscoelastic moduli

• Young’s modulus: E = s/e

• s = stress; e = strain

• Dynamic moduli – apply osc stress

• Modulus is complex for viscoelastic materials E=E’ + iE”

• Storage modulus: G’ or E’=(s0/e0)cosd

• Elastic component of response

• Energy stored per cycle

• In phase response

• E’ E if d=0

• Loss modulus: G” or E”=(s0/e0)sind

• Viscous component of response

• Energy lost/dissipated per cycle

• viscous dissipation of energy, out of phase component

• E” 0 if d=0

• Loss tangent: E”/E’

• Tand is a synonym for loss tangent

• Rubber ~1

• HDPE ~0.1

• Wood ~0.01

• Ceramics ~0.001

• Reduced Modulus

Courtesy of Jenny Hay, Nanomechanics Inc.

s Essentials of Polymer Sci and Eng, Painter and Coleman

n=Poissons ratio

i = indenter (tip)

s = sample

DMA measures bulk viscoelastic moduli

• Dynamic mechanical analysis (DMA) measures bulk viscoelastic moduli of solid samples

• Common tool in the polymer industry

• Apply sinusoidal stress and measure resulting strain

• Can vary temperature (-150C to 600C)

• Can vary frequency (.001Hz-200Hz) low freq is very slow

• But, don’t have to worry about adhesion

TA Instruments Pressure sensitive adhesive, TA instruments

Current status of nanomechical measurements with AFM

• Force spectroscopy (elastic modulus)

• Phase Imaging (convolution of elastic and viscoelastic properties)

• Contact resonance (viscoelastic moduli)

• PFQNM (elastic modulus)

• AFM-nDMA (viscoelastic moduli)

Dealing with adhesion in AFM world: contact mechanics models

JKR: adhesion within contact area

DMT: adhesion outside contact area h

(Indentation

Depth)

Figures from G. Haugstad

PF QNM (DMT model)

7/24/2017 7 Bruker Confidential

PP

PS

PE

DMT Modulus DMA and AFM modulus comparison at 2000Hz

PP PE PS PE:PP PS:PP

DMA 2.19 1.95 2.92 0.89 1.33

Avg. AFM 1.98 1.24 2.63 0.62 1.32

Stdev AFM 0.16 0.22 0.35 0.08 0.1

Other universal challenges

• All measurements require calibration of spring constant and lever sensitivity

• Variance formula allows estimation of error in DMT modulus

R=30nm

θ=50O

𝛿𝐸

𝐸

2

=1

4

𝛿𝑅

𝑅

2

+𝛿𝐾𝑐

𝐾𝑐

2

+9

41 +

𝐷

𝑑

2 𝛿Z

Z

2

+ 1 +3𝐷

2𝑑

2𝛿𝑆𝐷𝑆𝐷

2

+𝛿V

V

2

𝐸∗ =3𝐾𝑐

4 𝑅

𝐷

𝑑1.5

• Careful choice of probe & calibration

• Controlled tip radii=30 or 125nm, SEM measured

• Spring constant measured by highly accurate LDV

• Sensitivity still requires calibration

• No reference sample required

tip radius (R)

spring constant (Kc)

Z piezo extension; 𝑑 ~ 𝑍 − 𝑍0 − 𝐷 (D and d are deflection and indentation relative to pull − off) Deflection 𝐷 = 𝑆𝐷𝑉

deflection voltage (V), deflection sensitivity (Sd)

Challenges with current AFM-based methods for nanomechanical measurements

Modulus measured Frequency

Probe-sample interaction

Contact Mechanics

Models

Force spectroscopy E Low*: 1Hz + nonlinear Hertz, DMT,

JKR

Phase imaging convolution

High*: 10's to 100's of

kHz nonlinear none

Contact resonance** E', E", loss tangent high: 100's

of kHz + linear Hertz, JKR

PFQNM E Low*: <8kHz nonlinear DMT (others

available)

AFM-nDMA E', E", loss tangent low: 1Hz + linear JKR

Bulk DMA E', E", loss tangent 1-200Hz linear N/A

*estimated ** requires ref sample

to calibrate tip radius

Measuring nanoscale viscoelastic properties with AFM-based nano-DMA

Q: What can we do to improve the capabilities of AFM in measuring viscoelastic properties of materials?

20 March 2019 10 Bruker Nano Surfaces

Imaging focused modes - not suited for quantifying viscoelasticity

• Probing sample impulsively

• Plunge-in and rip-out in each cycle, make-and-break contact

• Not a linear measurement

• Since it’s not linear, the nominal frequency is not the only frequency

• Cannot really quantify frequency dependence

• Tapping based methods introduce added constraints

• Frequencies fixed and 100,000x too high

• Challenge in quantifying load and adhesion


Start with time dependence Basic idea of AFM mode for rheology

• Approach: Preload the sample at known force

• In contact: Modulate at well-defined, rheological freq, low amp

• Low amplitude provides small perturbation in force: linear regime

• Cover 0.1Hz to 300Hz: single frequency or spectrum

• Retract: fit with contact mechanics model that includes adhesion (e.g. JKR) to obtain contact radius (ac)

• Need contact radius to extract moduli (E’, E”) from raw data


T. Igarashi, S. Fujinami, T. Nishi, N. Asao, and K. Nakajima, Macromolecules (2013)

AFM-nDMA theory

• Need to extract amplitude ratio (𝐷1 𝑍1 ) and phase shift (𝜑 − 𝜓) and do a little complex algebra to get stiffness = force/deformation

• 𝑆∗ = 𝑆′ + 𝑖𝑆" = 𝐾𝑐𝐷1𝑒𝑖𝜑 [𝑍1𝑒

𝑖𝜓 − 𝐷1𝑒𝑖𝜑 ]

• 𝑆′ =𝐾𝑐𝐷1

𝑍1

cos 𝜑−𝜓 −𝐷1 𝑍1

(cos 𝜑−𝜓 −𝐷1 𝑍1 )2+ (sin(𝜑−𝜓))2

• 𝑆" =𝐾𝑐𝐷1

𝑍1

sin 𝜑−𝜓

(cos 𝜑−𝜓 −𝐷1 𝑍1 )2+ (sin(𝜑−𝜓))2

• Loss tangent is then: tan 𝛿 = 𝑆"/𝑆′ =sin(𝜑−𝜓)

cos(𝜑−𝜓)−(𝐷1 𝑍1)


𝑍1 𝐷1

𝜑 − 𝜓

𝑧 𝑡 = 𝑍1 sin 𝜔𝑡 + 𝜓

𝑑 𝑡 = 𝐷1 sin(𝜔𝑡 + 𝜑)

Two modes quantify viscoelasticity E’, E’’, tan d at bulk DMA frequencies

• Mapping with Fast Force Volume

• Simple, single modulation segment embedded in force curve

• Spectroscopy with RampScripting

• measurements at multiple frequencies at a single point


AFM-nDMA storage

modulus map of

polymer blend

(100Hz)

With correlated,

frequency spectra at

selected locations

How are these spectra collected?

• An AFM-nDMA “RampScript” has segments that allow for control of preload, relaxation, modulation, and calculation of contact radius

• Low frequency segments use raw deflection for better filtering, while higher frequencies use lock-in based demodulation


Managing changes in contact radius

• To get moduli E’, E’’, we also need a contact mechanics model like JKR to estimate contact radius (ac)

• 𝐸′ =𝑆′

2𝑎𝑐; 𝐸"=

𝑆"

2𝑎𝑐

• Reference segments correct evolution of contact radius over time

• Measure S’(fref) and assume E’(fref) is constant during script


Setting up AFM-nDMA spectroscopy Efficient generation of scripts

• Quick set up with DMA focus

• Frequencies, preload, modulation amplitude

• Advanced parameters if wanted

• Log vs linear frequency distribution

• Frequency shuffle avoids artifacts

• Modify reference segments

• Change length of relaxation segment

• Adjust any ramp parameter

• Or edit segment-by-segment in general ramp scripting interface

• Maximum flexibility


New hardware for AFM-nDMA Installs at rear of Dimension Icon chuck

• Fast, low drift heater, RT to +250C

• Up to 2cm samples, prefer <1mm thin for fast equilibration

• High power, water cooled, 5x faster stabilization than Bruker’s std heater – in practice, stabilization time paced by sample

• 0.1Hz-300Hz frequencies available while heating

• High frequency sample actuator, expands frequency range to 20kHz at RT


Workflow for locating and navigating Optical → fast AFM maps → AFM-nDMA

• MIROView: Optical image is the canvas

• Start AFM with PeakForce QNM mapping

• Uses same tips as AFM-nDMA

• Fast, hi-res, elastic modulus, calibrated

• Resolve small domains, structure detail

• Then targeted rheological measurements

• Use PFQNM to ID ROI

• AFM-nDMA maps, arrays, vectors, points


Can a nanoscale measurement tie directly to bulk DMA?

• Nanoscale AFM-nDMA results show excellent agreement with

• micrometer scale Hysitron Nanoindenter

• millimeter scale Bulk DMA

• Consistent results across labs and operators (no reference samples)

• Directly cover bulk frequencies and extend to 20kHz with external actuator


E’

E’’

TO DALIA

Localized viscoelastic measurements on heterogeneous samples

21

PeakForce QNM AFM-nDMA 100Hz

Image then “point and frequency sweep”

Add temperature as a variable to frequency sweep measurements

22 Can be used to pinpoint thermal and structural transitions

25C 110C 170C 175C 160C

Sto

rag

e M

od

ulu

s

(10

0H

z)

Ta

n d

elt

a

(10

0H

z)

COC

PP

Quantitative comparison with bulk DMA Loss tangent

23

0

0.05

0.1

0.15

0.2

0.25

0.3

0.001 0.01 0.1 1 10 100 1000

Loss

Tan

gen

t

Frequency (Hz)

LLDPE tand AFM-nDMA

LLDPE, tan d DMA

elastomer, tan d, AFM-nDMA

elastomer, tan d, DMA

Comparison with bulk DMA: E’ and E”

24

0

100

200

300

400

500

600

700

800

900

0.001 0.01 0.1 1 10 100 1000

E;

Frequency (Hz)

LLDPE E' AFM-nDMA

LLDPE E' DMA

Elastomer E' AFM-nDMA

Elastomer E' DMA

0

20

40

60

80

100

120

0.001 0.01 0.1 1 10 100 1000

E”

Frequency (Hz)

LLDPE E" AFM-nDMA

LLDPE E" DMA

elastomer E" AFM-nDMA

elastomer E" DMA

Storage Modulus (E’)

Loss Modulus (E”)

Compare with bulk DMA: loss tangent as a function of temperature of plastomer

25

0

0.05

0.1

0.15

0.2

0.25

0.3

0.001 0.01 0.1 1 10 100 1000

Loss

Tan

gen

t

Frequency (Hz)

RT average

50C average

80C average

DMA DATA

Plastomer as a real-world sample

Capturing complex behavior as a function of temperature

High resolution measurements

• Not a huge difference in resolution despite larger tip • ~25nm for RTESPA150-30 at 30nN • <50nm for RTESPA300-125 at 100nN

• Significantly better SNR for larger 125nm tip 26

LLDPE Elastomer

RTESPA150-30 RTESPA300-125

2um 5um

LLDPE Elastomer

Time Temperature Superposition

• Collecting frequency spectra at several temperatures enables a more complete analysis

• TTS principle: near glass transition, raised temperature is equivalent to lowered frequency and vice versa

• Master curve: single curve resulting from shifting data measured at different temperatures

• Shift factors: can be parameterized via either WLF or Arrhenius model.

• Arrhenius equation gives activation energy from temperature dependence of a rate – energy needed to kick off a mechanical relaxation process


Activation energy analysis for a polymer

Arrhenius: ln(aT) = - Ea/R (1/T – 1/To)

TTS master curve construction

Temperature dependence for fluorinated ethylene propylene

• Qualitatively shows expected behavior

• Glass transition apparent in storage modulus and loss tangent

• Expected frequency dependence

• How well does it match bulk?


Full TTS from AFM data Compared to bulk DMA on same sample

• Master curves from AFM-nDMA data match bulk DMA reasonably well including glass transition temperature and the strong change in properties there

• Arrhenius analysis of TTS shift factors from AFM data also agrees with bulk


WLF Loss Tangent Mastercurve

DMA: Ea = 489 kJ/mol

AFM: Ea = 490 kJ/mol

Arrhenius Activation Energy Analysis

Correlating changes in nanomechanical properties with microstructural changes

• Temperature controlled measurements of PEEK with AFM-nDMA spectra

• AFM-nDMA in agreement with bulk measurements

• Irreversible change as sample crystallizes

• Strong tan-d peak at 150C, disappears on ramp down

• AFM-nDMA provides both quantitative modulus data and correlated high-resolution structural information


Before After 142C 160C

Bulk DMA (Perkin Elmer)

AFM-nDMA

Summary Viscoelastic analysis of polymers with the spatial resolution of AFM

• AFM-nDMA measures E’, E”, tan(d) directly at rheological frequencies

• Linear measurement, corrected for intrinsic creep effects

• Results match well with Hysitron & bulk DMA

• AFM data allows for full TTS analysis

• Spatial resolution of better than 50nm


QUESTIONS?

Dalia Yablon, Ph.D. and Bede Pittenger, Ph.D.

Dalia Yablon, Ph.D. and Bede Pittenger, Ph.D. Measuring ......Dalia Yablon, Ph.D. and Bede...

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