Upload
others
View
6
Download
0
Embed Size (px)
Citation preview
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
20 March 2019 11 Bruker Nano Surfaces
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
20 March 2019 12 Bruker Nano Surfaces
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)
20 March 2019 13 Bruker Nano Surfaces
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
20 March 2019 14 Bruker Nano Surfaces
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
20 March 2019 15 Bruker Nano Surfaces
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
20 March 2019 16 Bruker Nano Surfaces
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
20 March 2019 17 Bruker Nano Surfaces
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
20 March 2019 18 Bruker Nano Surfaces
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
20 March 2019 19 Bruker Nano Surfaces
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
20 March 2019 20 Bruker Nano Surfaces
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
20 March 2019 27 Bruker Nano Surfaces
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?
20 March 2019 28 Bruker Nano Surfaces
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
20 March 2019 29 Bruker Nano Surfaces
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
20 March 2019 30 Bruker Nano Surfaces
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
20 March 2019 31 Bruker Nano Surfaces
QUESTIONS?
Dalia Yablon, Ph.D. and Bede Pittenger, Ph.D.