explorinexploring_nanomechanical_propertiesg nanomechanical properties an085

8/9/2019 Explorinexploring_nanomechanical_propertiesg Nanomechanical Properties An085

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Application Note 085

Introduction

Atomic force microscopy (AFM) was introducedto perform high-resolution imaging of surfacesfor a broad range of materials [1]. Initially, thisfunction was realized using a microfabricatedcantilever with a sharp tip that scans a samplesurface in contact mode. The force interac-tions between the probe and the sample aremonitored by the deflection of the cantilever,and they are applied for profiling surface cor-rugations. Measurements of the tip-sampleforce interactions and their understandingbecome essential for the optimization of sur-face imaging [2] and, furthermore, for studies

of local mechanical properties of materials [3].Minimization of normal and lateral tip forcesreduces the damage to soft samples and lowersthe tip-sample contact area thus facilitating thehigh-resolution imaging of the topmost surfacestructures.

The most basic information about these in-teractions at a single location on a sample isobtained from force curves, which representthe dependence of the cantilever deflection onthe tip-sample separation (DvZ). The schematic

description of the DvZ curves and their practi-cal examples are presented in Figures 1a-c. As

Different aspects of probing local mechanical interactions in Atomic Force Microscopy (AFM) will be discussed anddemonstrated in this application note, using the practical examples obtained with the NEXT scanning probe microscope.The critical areas of study include the use of tip-sample force interactions in various modes for compositional imagingof heterogeneous materials and the quantitative examination of mechanical properties at small scales down to a fewnanometers.The application note consists of an introduction, three parts, which describe the force measurements in contact mode, inamplitude modulation (AM) mode, and in AFM-based nanoindentation, and, nally, the conclusions. The experimental

data are supported by their theoretical analysis, which is based on the description of the tip-sample interactions using theEuler-Bernoulli equation and the asymptotic solutions of the oscillatory tip behavior during its interactions with a sample.

• Force effects in Atomic ForceMicroscopy imaging andspectroscopy

• Contact resonance, phaseimaging, dissipation, andbimodal excitation

• Quantitative Atomic ForceMicroscopy - basednanoindentation

Exploring Nanomechanical Properties of

Materials with Atomic Force Microscopy

Sergei Magonov, NT-MDT Development



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the cantilever approaches a sample, attractiveforces cause downward bending of the cantile-ver and on further movement repulsive forcesstart to act and bend the cantilever upwards. A strong snap of the Si probe on a Si surface,which is seen during the probe retraction inFigure 1b, is typically caused by a meniscusforce originated from a water layer present onmany surfaces in air. This effect is eliminatedduring AFM studies under water [2]. The similarregion recorded in the force curve on a rub-ber sample, Figure 1c, looks quite different andsuch behavior is usually explained by adhesivetip-sample interactions. Generally, the measure-ments of force curves in AFM have features

common to force studies with a surface forceapparatus and indentation curves obtained withthe stylus indenters.

The use of force curves for studies of local me-chanical properties has substantially broadened AFM applications. The extreme force sensitivityof this technique has inspired a large number ofdeformation studies, in which pulling the probe,whose apex has been modified to stick to thesample surface, can stretch individual macro-

molecules. In addition to the unique force sensi-tivity, the small size of the probe was essentialin performing both indentation and molecularpulling experiments at the nanoscale. Typically,

in AFM-based nanoindentation the DvZ curvesare collected at rates in the 0.01-10 Hz range,which is well below the resonant frequency ofthe probes. In order to expand this single pointtechnique to mapping the surface, the forcecurves are collected in a mesh of points (up to128×128 points in an operation known as ForceVolume) over the examined surface area; yetthis procedure is t ime consuming and demandslow thermal drift of the microscope. The speedof this process can be dramatically increased ifonly few points of the DvZ curves are collectedfor determination of stiffness and adhesionmaps. There are also a number of dynamic ap-proaches, such as force modulation [4], contact

resonance or atomic force acoustic microscopy(AFAM) [5], which can be used for exploring thelocal mechanical properties in contact mode.These modes are typically applied for relativelystiff samples with an elastic modulus exceeding1 GPa.

Several problems of contact mode imagingwere overcome by the development of oscil-latory modes (AM and frequency modula-tion – FM), in which the force interactions of

the probe oscillating at its f lexural resonance(30 kHz-1 MHz) are employed for AFM stud-ies. Phase lag imaging, commonly call PhaseImaging in AM mode provides compositional

Figures 1a-c. (a) Sketch illustrating the recording of DvZ curves in AFM. In an approach (1-2-3) a sample is moved vertically by a piezoand it causes the probe upward bending in the response to the tip-force. On the way back (4-5-6) the probe reduces its bending andexercises an adhesion before leaving the sample. (b)-(c) The experimental force curves obtained, which were recorded on a Si surfaceand a rubber sample, emphasize the regions reecting the sample stiffness and adhesion.

(a) (c)

(b)



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mapping of multi-component polymer materials,which is primarily based on dissimilarities of lo-cal mechanical and adhesive properties of theirconstituents [6]. Although the phase contrast isefficient in differentiating the rubbery, glassy,and inorganic components of polymer blends,block copolymers, and composites, its interpre-tation in terms of specific mechanical properties

is not feasible.

We will demonstrate the peculiarities of nano-mechanical analysis of force curves obtained onpolymer samples with AFM-based nanoindenta-tion, which is an extension of the studies of DvZcurves where the probe deforms a sample withdifferent loading levels.

This technique can be employed with high spa-tial and force resolution for local nanomechani-

cal studies of materials. Several related exam-ples will be discussed below. We will describedifferent types of nanoindentation curves andthe specifics of their quantitative analysis.

Tip-Sample Forces and Nanomechanical

Studies in Contact Mode

Contact mode, which was the original operationtechnique of the AFM, is characterized by thenormal and lateral forces that act between theprobe and the sample during imaging. Ideallythe height images reflect the sample topography

best when imaging is performed at the smallestpossible force. However in practice, this is notalways possible because capillary forces oftenstrongly attract the probe to the surface andsurface heterogeneities leading to t ip-sampleforce variations outside the control of the feed-back loop. The force effects in contact modecan lead to changes and irregularities in theheight images; many of these effects have beenrecognized [7].

A more pecul iar situation happens with theinfluence of lateral forces, as one sees fromthe following example. The images of a fewpentacene dendritic structures of the secondadlayers on top of a single pentacene layer ona Si substrate are shown in Figures 2a-d. These

Figures 2a-d. Contact mode images on the pentacene layer with a dendriticstructure atop. The height and lateral force images in (a)-(b) were obtained witha triangular Si3N4 probe scanning perpendicular to the probe main direction. Theheight image in (c) was obtained with the probe scanning along its main axis. Thecontrast covers the surface corrugations in the 0-5nm range in (a) and (c). Thecontrast in the lateral force image is in the relative units.

(a) (b)

(c)

Height Lateral Force

(d)

Height Height proles

3.5 µm

images were obtained using a tri-angular Si

3N

4 probe with a spring

constant of ~ 0.06 N/m. The heightand lateral force images in Figures2a-b were recorded with the probescanning perpendicular to the

main axis of the probe.

The lateral force image indicatesthat different parts of the dendriticstructures exhibit various contrastlevels compared to each otheras well as to the first pentacenelayer. As expected, the height pro-file of the entire dendritic structureis at the same level of 2 nm whichcorresponds to the single layer

thickness of the molecules stackedwith the molecular planes be-ing perpendicular, Figure 2d. Theheight image, which is obtainedwith the probe scanning alongits main axis, is quite different.Unexpectedly, part of the dendrite,which shows lower contrast in thelateral force image, appears 1-nmlower than the rest of the struc-ture, Figure 2d. This effect might

originate from variations of thelateral force that cause differentdegrees of probe buckling. Thelatter alters the apparent normal



4

force response and therefore the related heightprofile. The reason for the lateral force varia-tions can be different epitaxy between the partsof the top structure and the grain structure ofthe first layer that the dendrites cover [8].

An example of the dynamic mechanical stud-ies in the contact mode (the contact reso-

nance technique), which were performed on asurface of high-density polyethylene partiallycovered with a flake of graphite, is presented inFigures 3a-c. In this contact-resonance experi-ment a probe stays in the contact with a sampleand the amplitude-versus-frequency spectrumof the probe, which is driven by a shaker, ex-hibits one or more contact resonances. As theprobe scans over a sample surface the ampli-tude, phase or frequency of such resonancesvaries when the probe interacts with the loca-

tions of different stiffness. Basically the contactresonance shifts to higher frequency on stifferlocations.

This effect is pronounced in the amplitude andphase images shown in Figures 3b-c. An edgeof the graphite flake, which is recognized in thebottom part of the examined area (Figure 3a),shows the lower amplitude values and higherphase contrast as compared to the polymer inthe top region. This is consistent with the fact

that graphite (elastic modulus ~ 10 GPa) is stiff-er component at this location. Furthermore, thephase image also exhibits the contrast varia-tions on the polymer surface. This effect canbe attributed to local variations of either stiff-ness or adhesion and it demonstrates a highersensitivity of the phase response. A continuinginterest to the contact resonance studies is alsorelated with a possibility to explore the sample

viscoelastic behavior [9] and thus to enhancethe characterization of local mechanical proper-ties of materials.

Phase Imaging

The introduction of oscillatory AM mode sub-stantially expanded AFM applications to soft

materials such as polymers and biologicalspecimens. The short contact time during theprobe oscillation at the cantilever resonanceavoids the non-desirable, destructive shearingof the sample common in contact mode. Thetip-sample force interactions in AM are con-trolled by monitoring the amplitude of the probe,which is driven near or at its resonance, and bymaintaining its damping at the desired set-pointlevel during scanning. This operation is mostcommon for AFM applications under ambientconditions. Control of the frequency of the oscil-lating probe is performed in another oscillatorymode – FM, which was originally applied inUHV but recently expanded to studies in air andunder liquid.

The control of the set-point amplitude in AMmode defines whether it operates in the non-contact or intermittent contact regime. Thelatter is characterized by an elevated level oftip-sample interactions that gives raise to sub-stantial phase changes of the vibrating probe.

Phase imaging is extremely useful in studiesof multicomponent polymer materials due to itshigh sensitivity to variations of materials’ prop-erties, particularly, the nanomechanical andadhesive properties. However, interpretation ofthe phase contrast is a very complex problem.In many cases, it is impossible to establish adirect link between the phase variation and a

Figures 3a-c. An example of the contact resonance studies of surface of high-density polyethylene with a ake of graphite. Simultane -ously recorded height image (a), amplitude image (b) and phase image (c). The amplitude and phase images were collected at thecontact resonance frequency of 860 kHz for the probe with the spring constant of 4 N/m. The contrast covers the surface corrugationsin the 0-50 nm range in (a) and phase changes in the 0 – 50 degrees range. The contrast in the amplitude image (b) is in the rela-tive units.

(a) (b) (c)

Amplitude PhaseHeight

5 µm



5

corresponding variation in the chemical com-position or specific sample properties suchas adhesion, viscoelasticity, modulus, etc.Considerable difficulties for rational interpreta-tion of the phase changes result from severalfactors: (i) the abrupt transition (bifurcation)from an attractive force regime to strong re-pulsion which acts for a short moment of the

oscillation period, (ii) nanoscopic localizationof the tip-sample interaction, (iii) non-linearvariation of both attractive forces and mechani-cal compliance in the repulsive regime, and (iv)the interdependence of the material properties(viscoelasticity, adhesion, f riction) and scanningparameters (amplitude, frequency, cantileverposition). The interpretation of the phase andamplitude images becomes especially intricatefor viscoelastic polymers.

Despite the all of the complications, phaseimaging is practically important for the compo-sitional discrimination of multicomponent poly-mer materials. Several semi-empirical correla-tions between the phase contrast and nature ofindividual constituents in polymer and rubber

composites has been established. For example,when imaging is performed with a stiff probe(spring constant ~40 N/m) and elevated forceconditions ( A

0 = 50 nm, A

sp= 20 nm) the phase

contrast changes from darkest to brightest inthe following materials sequence: fillers, plas-tics, butyl rubber, EPDM rubber, styrene-buta-diene rubber, butadiene rubber, natural rubber,

oil. This succession of phase changes is validfor NEXT microscope, in which the initial phaseresponse changes from -90 to 90 degreespassing through zero at the probe resonance.Practical examples of the phase imaging arepresented in Figures 4-5.

The first example is taken from studies of a filmof an immiscible blend of polystyrene (PS) andlow density polyethylene (LDPE), Figures 4a-d.Phase imaging at elevated forces reveals the

phase separation in this blend at the microns’and sub-micro scales. In the large scale imag-es, Figures 4a-b, the matrix show fine features,which can be assigned to the lamellar struc-ture of LDPE, the round and extended blocksare smooth and, therefore, can be related to

Figures 4a-d. The height and phase images of a PS-LDPE blend at two dif-

ferent scales. The imaging was conducted in AM mode with a stiff AFM probe(k = 30 N/m) at elevated tip-force (Asp= 20 nm with A0 = 50 nm). The contrastcovers the height corrugations in the 0 - 250 nm range in (a) and in the 0-30 nmrange in (c). The contrast in the phase images is in the 0-95 degrees in (b) and inthe 0-65 degrees in (d).

(b)

(d

Phase

(a)

(c)

Height

Height

Phase

10 µm

1 µm

amorphous PS. This assignmentis further confirmed by the phasecontrast because a st iffer material(such as PS with elastic moduliin the 2-3 GPa range) typically

shows a darker contrast comparedto the softer (such as LDPE withelastic moduli in the 150-290 MParange). At the smaller scale,Figures 4c-d, the phase contrastclearly shows the nanoscaledomains of PS with a diameter inthe 20-100 nm range, and darkerlinear strips (~10 nm in width) thatcan be assigned to the individualLDPE lamellae embedded in thesofter amorphous matrix of thispolymer.

The second example, whichexplores the phase imagingof a binary blend of PS withpoly(butadiene) – PB with a 1:1ratio of the components,is muchmore complicated. The images ofthis blend at different scales areshown in Figures 5a-e. On thesurface of the sample, its morphol-

ogy is characterized by the raisedround-shaped PS blocks, whichare partially immersed in the PBmatrix, Figure 5a.



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The phase images, which were recorded at lowand elevated forces (Figures 5b-c) show moreheterogeneities than expected. Besides theround-like domains, a large flat area in betweenthe domains exhibits the contrast similar to thatof the PS domains. At the smaller scale, thephase image obtained at elevated force showsfeatures with four different contrast levels. Aswe will see below, some of these structures canbe assigned to thin layers of PS residing on thePB matrix. This example demonstrates that thephase contrast is most likely sensitive not onlyto the spatial variations of the mechanical prop-erties but also to the vertical composition of the

sample. Therefore, in some cases the interpre-tation of phase images even of binary materialsis far from trivial.

The expanded capabilities of the NEXT mi-croscopes, which incorporate several lock-inamplifiers and generators, allow studies oflocal mechanical properties in different less-common modes like imaging with the excitationat first two flexural resonances. This approachwas described in [10]. We have performed

the similar examination of the heterogeneouspolymer samples including patches of meso-morphic poly(diethylsiloxane) - PDES, whichwere spread on a Si substrate by rubbing. Suchsamples were studied with AFM previously [11]

and the phase images recorded in the AM modeat elevated tip-sample forces have clear distin-guished the substrates locations, amorphousand crystalline parts of PDES. Furthermore, theimaging of this sample at the 2nd flexural mode,which is ~36 times stiffer than the 1st flexuralmode, made the amorphous polymer regions“invisible” in the height image due to the tippenetration through the soft material.

The examination of the PDES sample using thesimultaneous drive of the probe at the 1st and2nd flexural modes and surface tracking at the1st flexural mode is illustrated by height andphase images in Figure 6. These images show

the PDES patches, which are partially coveredthe substrate surfaces and aligned along therubbing direction from the left bottom cornerto the right top corner. A remarkable differencebetween the height and phase images is thatthe lamellar aggregates, which are embeddedinto amorphous surrounding, are exhibit muchbrighter phase contrast that the amorphouspolymer. The same lamellar structures arebarely seen in the height image.

A comparison of the phase images recordedin the 1st and 2nd flexural modes shows thatthe phase contrast in the 2nd mode is morepronounced yet this difference is not asstrong as one reported in [10]. The analytical

(b) (c)

(e)

Phase Phase

Phase

(a)

(d)

Height

Height

Figures 5a-e. AM height and phaseimages of a PS-PB blend at two scalesobtained with an AFM probe withk=30 N/m. The images in (d)-(e) wererecorded in an area marked with a

white dashed square in (a). The heightchanges are in the 0- 300 nm rangein (a) and in the 0-150 nm range in(c). The phase contrast is in the 0-55degrees in (b), in the 0-75 degrees in(d), and in the 0-45 degrees in (e).

15 µm

5 µm



7

consideration of the probe behavior when it isdriven at the 1st and 2nd flexural modes showsa substantial cross-talk between the modes. Although the double excitation brings noveldata this does not eliminate a need of a cor-rect model of the t ip-sample interactions for theextraction of specific mechanical properties.

The aforementioned complexity led to a strongmotivation to extend the capabilities of nano-mechanical studies beyond surface imaging.This inspired the development of theoreticaland practical approaches to examine the dis-sipative and viscoelastic behavior of polymersand other materials on small scales. Here wewill briefly consider the theoretical analysis ofthe probe behavior in AM mode. The amplitudeand phase of the interacting probe are relatedto the mechanical forces as the tip approaches

the sample and as the tip retreats from thesample ( F

a and F

r ) as stated by the following

equations [12]:

where A0 - the probe amplitude prior to its

engagement into tip-sample force interactions; Z c - an averaged position of the cantilever over

a surface during oscillations, and

(k and Q - spring constant and quality factor ofthe probe at 1st flexural resonance).

The essential parts of the equations are theintegrals

and

,

which can be connoted as the dissipative andconservation integrals, respectively. In the caseof conservative forces the dissipative integral isnullified and the first equation is simplified.

A pathway from oscillatory AFM measurementsto the extraction of specific material propertiesincludes the reconstruction of the tip-sampleforce from the probe variables (e.g. amplitudeand phase) and the calculation of the specificmaterials properties from the force-property

model or equation.

As we have already shown [13], this task isachievable for local tip-sample electrostaticmeasurements because the latter are conserva-tive and separable, in addition the electrostaticforce/surface potential, electrostatic force/di-electric permittivity relationships can be derivedand verified for various AFM tip-sample geom-etries with finite element analysis.

The main hurdle on the way to the extraction ofspecific mechanical properties from AM mea-surements is poor knowledge how F

a and F

r are

related to the fundamental mechanical proper-ties such as storage and loss modulus and workof adhesion. The use of conservative modelssuch as Hertz, Sneddon, JKR and DMT can be justi fied only for true non-dissipative measure-ments, which are quite rare in AFM studies ofpolymers.

Figures 6a-c. Height and phase images recorded in the amplitude modulation mode in which the Si probe (spring constant ~ 4 N/m)was driven at the 1st and 2nd exural modes at frequencies of 88.2 kHz and 558 kHz. The topography was examined in the 1 st exural

mode and the contrast of height image covers surface corrugations in the 0-400 nm range. The phase 1 (1 st exural mode) and phase 2

(2nd exural mode) exhibit the variations in the 0-50 degrees and 0-70 degrees ranges, respectively.

(d) (e) (f)

Phase 1 Phase 2Height

20 µm

[ ] ydy y x Z F F N

cr a cos)cos(1

cos0

+−−= ∫π

θ {

[ ]00

sin)cos(1

sin A

A ydy y x Z F F

N

p s

cr a ++−= ∫π

θ

Q

k A N 0π

=

[ ] ydy y x Z F F I cr a sin)cos(0

sin +−= ∫π

[ ] ydy y x Z F F I cr a cos)cos(0

cos +−= ∫π

sp



8

7a-d. In these images, which were obtainedat elevated forces ( A

sp= 0.5 A

0, A

0= 80 nm), the

contrast of the phase, dissipation and tand probe

channels looks quite similar.

AFM-Based Nanoindentation

The use of DvZ curves for probing of local me-chanical properties in AFM was proposed morethan 20 years ago [3]. Below we consider theessential elements of nanomechanical studieswith AFM and present a number of illustrativeexamples.

The extraction of quantitative nanomechanicaldata from AFM measurements is a challengingtask that can be achieved for a number of ma-terials under the assumptions that a researchercan accomplish a number of requirements.The first one is related to the characterizationof the AFM probe that includes the evaluation

of the cantilever spring constant and shape ofthe tip as well as detection of the probe’s opti-cal sensitivity on a hard surface. The springconstant of the probe is typically determined

using its thermal excitation and the calculationsintroduced by J. Sader and coworkers [15]. Theshape of the tip is best estimated from electronmicroscopy micrographs [16]. It can be alsoverified by imaging latex spheres as shownelsewhere [17-18]. The conversion of DvZ datainto load-versus-penetration (PvH) curves canbe accomplished by subtraction of the slope ofthe calibration DvZ curve obtained on hard sub-strate, such as the one shown in Figure 1b.

Prior to AFM-based indentation, it is quite desir-able to examine the surface morphology andto choose particular locations of the sample.The imaging is accomplished in AM mode toavoid possible modification or damage of thetip and sample. For homogeneous samples,indents performed in different locations arenecessary to collect sufficient DvZ curves foraveraging. For heterogeneous materials prelimi-nary imaging will allow indenting the individual

components or specific locations for furthercomparison of their properties. It is also impor-tant to perform the measurements at differentforce levels by triggering the maximal probe

Recently [14], there was an at-tempt to approach studies of thenon-dissipative response of poly-mer samples using the ratio ofthe dissipative and conservativeintegrals as follows:

Obviously, this tand probe

is not di-rectly related to tand

samp le, which is

the ratio of loss and storage mod-uli determined in macroscopic dy-namic mechanical measurements.Therefore, exploring the possiblecorrelation between tand

probe and

tand samp le

needs complete practicalverification, which is not trivial due

to many reasons including the dif-ferences in frequencies of macro-scopic and nanoscale mechanicaltesting.With regards to the expansion ofphase imaging by addition of thedissipative and tand

probe channels,

the situation does not look verypromising. The relevant images ofa sample of a binary PS/PB blend,in which the components’ disper-

sion was improved by ultrasonicagitation, are presented in Figures

Figures 7a-d. The height, phase, dissipation and tand images of a PS-PB blend.The imaging was conducted in AM mode with stiff AFM probe (k=30 N/m) atelevated tip-force (Asp=40 nm, with A0=80 nm). The contrast covers the height cor-rugations in (a) in the 0-300 nm range in (a). The contrast in the phase image (b)is in the 0-55 degrees range. The contrast in the tand and dissipation images is in

arbitrary units.

(b)

(d)

Dissipation

(a)

(c)

Height

Tan d

Phase

10 µm

θ

θ

δ cos

sin

tan 0

cos

sin

−

== A

A

I

I probe

sp



9

deflection. Such measurements can be invalu-able for separation of the elastic and plasticcontributions to the force curves, which will sim-plify their quantitative analysis. After the forcecurves are collected it is worth re-examiningthe same locations to visualize the possibleindents left and to measure their shapes anddimensions.

The additional information, such as visualizationof the possible pile-ups around the indents, willbe invaluable in the analysis of the local me-chanical properties. Finally, one should choosethe appropriate deformation model for dataanalysis and extraction of the elastic modu-lus and work of adhesion. Unfortunately, mostof the indentation data are analyzed with theconservative solid deformation models (Hertz,Sneddon, JKR, DMT) that discard the time-de-

pendent (viscoelastic) effects. In some instanc-es it can be wise to record the force curves atdifferent rates or to follow an indents’ recoveryby continuous imaging in order to determine ifsuch effects are present.The practical examples, which illustrate themethodology of AFM-based nanoindentation,were obtained on several polymer materialswith the elastic modulus in the 600 kPa – 3 GParange.

The polymer samples include ~1 mm thickblocks of polystyrene (PS), polycarbonate(PC), Nylon 6, linear low-density polyethylene(LDPE), a blend of PS and PB, and the de-scribed earlier 4-μm-thick films of semiconduc-tor dielectric resin SiLK™ [16] and polydimeth-ylsiloxanes (Dow Corning) with different degreeof polymerization between cross-links (PDMS8,PDMS60 and PDMS130) on Si substrate [17].

These measurements were performed with a Siprobe, which has a spring constant of 42.5 N/m.The tip radius, which was estimated on a latexsample [18, 19], is approximately 33 nm, whichis close to the radius size (30 nm) given by theprobe manufacturer.

Typical DvZ curves recorded on rubbery sam-

ples are shown in Figures 8a-b. The approachand retreat curves obtained on rubbery samplesof PDMS8 and PDMS130 are practically identi-cal, and this is direct evidence of complete re-covery of the sample deformation. These curveswere practically the same at low and high loads.The force curves, which were recorded in 9 dif-ferent locations, show remarkable consistency.Prior to the analysis of these curves they havebeen transformed into FvH plots, which are notmuch different from the DvZ plots for soft mate-

rials. Due to the conservative character of thedeformation, the analysis of the force curves ofPDMS8, PDMS60 and PDMS130 samples canbe performed using the elasto-adhesive JKRmodel.

This is one of the models, which are implement-ed in our LabVIEW-based analysis programthat was applied for the t reatment of the forcecurves described in this note. The elastic modu-lus and work of adhesion data for three rubbery

samples are presented in Table 1 together withthe results of the macroscopic studies [18]. Acomparison of these data shows a good quan-titative match between elastic moduli and workof adhesion, which were obtained in the macro-scopic measurements and AFM-based nanoin-dentation results. These findings are consistentwith the earlier observations [17, 20].

Figures 8a-b. (a) Force curves (DvZ) obtained on lms of PDMS8, PDMS60 and PDMS130. (b) A set of 9 DvZ curves, which were

measured in different locations of PDMS8 sample. The red curves correspond to the loading traces and blue curves correspond to theunloading traces.

(a) (b)

PDMS8 PDMS8

PDMS60

PDMS130



10

The next group of polymer samples includesPS, PC and SiLK – the amorphous materials,which are in the glassy state at room tempera-ture, and semicrystalline LDPE and Nylon 6.

We will use the force curves (DvZ and FvH)obtained on PS at different loads as a repre-sentative case, Figures 9a-b. In the contrastto the force curves of the rubber samples, theDvZ plots obtained on PS show the discrepan-cies between the approach (loading) and retreat(unloading) traces, which become more pro-nounced at high load.

This behavior points out a dissipative deforma-tion process and makes challenging the extrac-

tion of the quantitative mechanical properties.One of the problems of the analysis is properchoice of either a loading or unloading partsof the force curves. From one side, an initialpart of the loading curve, which is often usedin macroscopic experiments for an extractionof elastic modulus, in AFM measurement mightbe influenced by surface roughness effects orsurface contamination. From the other side, theuse of high loads might cause a change of poly-mer material under the probe and, therefore,the modulus will be estimated for the deformedmaterial.

Therefore, the use of moderate loads mightbe optimal for AFM-based nanoindentation

experiments. This suggestion is justified by theresults of analysis of the FvH curves of PS, PC,LDPE and SiLK samples, which were recordedat different loads. In this analysis we neglected

the dissipative character of such curves andtreated them in terms of Hertz model.

The elastic moduli of the materials calculatedfrom the force curves and, particularly, at thebeginning of the unloading trace in cases ofmoderate loads, show a reasonable correla-tion with the elastic modulus values recordedin macroscopic mechanical measurements,Table 2. When the load is increased the dis-sipative character of the curves becomes more

pronounced and this might be one reason thatthe use of the solid state deformation models,which do not account for materials plasticity andviscoelasticity, does not usually provide rationalresults. In many cases, however, the analysisof FvH curves obtained at high loads showedreasonable elastic moduli when the unloadingtraces were treated in terms of Sneddon modelwith plastic correlation [16].

The important feature of AFM-based nanoin-dentation is that the indented locations can bevisualized with high special resolution in theresultant images. The surface areas of PS, PC,SiLK and HDPE with the indentation marks,which we left by the AFM probe that deformed

PolymerMaterial

Elastic Modulus Work of Adhesion

Macro AFM Macro AFM

PDMS-8 13.4 MPa 13.9 MPa 49 J/m2 32 J/m2

PDMS-60 1.61 MPa 1.74 MPa 58 J/m2 52.2 J/m2

PDMS-130 0.74 MPa 0.66 MPa 47 - 58 J/m2 42.1 J/m2

Table 1. Elastic Modulus and Work of Adhesion of Rubber Films

Figures 9a-b. DFL curves (solid lines) and FvH curves (dashed lines) obtained on PS surface at two different loading forces: (a) 300 nNand (b) 1.2 mN. The red-color traces correspond to the loading curves and the blue-color traces to the unloading curves.

(a) (b)



11

the samples with ~ 3 µN load, are shown inFigures 10a-d. The cross-section profiles, whichwere drawn in the vertical direction along thecentral row of the indents, are shown togetherwith the height images.

One can notice that high pile-ups are formedaround the indents left in PS sample due to

its plasticity, and they are practically absent incase of LDPE. Regarding the indent depth, it isthe largest for the softer LDPE and the smallestfor SiLK. The latter fact indicates a fast recov-ery of tip-induced deformation in this dielectricresin.Therefore, time-dependent effects shouldbe taken into consideration during analysis ofmechanical response of SiLK sample.

The comparison of the indents made in differ-ent polymers shows that we can learn muchabout local mechanical properties of polymersin addition to the measurements of elasticmodulus and adhesion. This statement is fur-ther supported by the indenting results, whichwere obtained a surface of an ultrathin film ofa binary blend of PS and poly(vinyl acetate) -

PVAC, Figures11a-b, and on lamellar structureof high-density polyethylene (HDPE), Figures11c-d. Two grids of 9 indents are seen on theround-shape domain of PVAC and surroundingmatrix of PS. Although, at room temperaturethese components are in glassy state and elas-tic modulus of PS is slightly larger than that ofPVAC the phase image shows a darker contraston the PVAC domains.

The contrast is difficult to interpret because of

an additional complication related to the factthat a rigid substrate might influence the localthicknessof such 70-nm thick film. A comparisonof the indents appearance and the cross-sec-tions, which are presented in Figure 10c, pointsout that the matrix material is more plasticwhereas the PVAC indents are smaller mostlikely due to their faster recovery.

PolymerMaterial

Elastic Modulus

Macro Macro

LDPE 152 - 290 MPa 204 MPa

PC 1.79 - 3.24 GPa 2.30 GPa

PS 3.0 - 3.5 GPa 2.99 GPa

SiLK 2.45 GPa 2.25 GPa

Table 2. A comparison of elastic moduli of polymer materials ob-tained in the macroscopic studies and in AFM nanoindentation

Figures 10a-d. Height images of the indents left on surfaces of different polymers: PS (a), PC (b), LDPE (c) and SiLK (d) with the probe(spring constant 42.5 N/m, tip radius of 33 nm) acting at 1.2 µN force.The cross-section proles, which were taken along the indents of

the central columns, are shown in between the images.

(c) (d)

HeightHeight

3 µm

(a) (e) (b)

HeightHeight

1 µm

(e)

700 nm

600 nm



12

Another example is taken from studies of HDPEsample, whose surface exhibits developedlamellar structures with the individual lamel-lae being flat or edge-on oriented, Figure 11d.Several indents were made on flat-lying lamel-lae, and the remaining indents of 6-7 nm indepth are shown in Figure 11e.

These values are close to the thickness of indi-vidual lamellae that was most likely penetratedby the tip. The loading and unloading tracesrecorded during the indenting of the lamel-lae (Figure 11f) are rather complicated. At thebeginning of the loading path, which is indicatedwith a blue arrow, the deformation is elasticand it transforms into a small plastic part beforeclimbing further.

The initial deformation is quite similar to one

that was reported in the indenting of the flatlamellae of the ultra-long alkane C390

H782

[21].The unloading portion looks more typical for

deformation of semi-crystalline polymers. Theestimates of the elastic modulus for the loadingand unloading paths in the regions indicatedwith the arrows showed that the elastic modulusof the initial deformation at least 50% higher.This can be expected because the polymerchains are oriented vertically in the flat-lyinglamellae and exhibit higher modulus comparedto the bulk material with random orientation of

polymer molecules.This example demonstratesthe unique ability of AFM in studies of mechani-cal properties of the confined nanostructures.

The variety of 2D and 3D morphologies ofpolymer materials is enormous and some ofthem are non-trivial for characterization. Evenin binary blends their constituents can appear instructures of different size and shape as shownin phase image of PS/PB blend, Figure 12a.

As we learned earlier (see the description ofFigures 5), the bright domains of the phaseimage can be assigned to PS structures

Figures 11a-f. (a)-(b) Height and phase images of a lm of binary blend PS/PVAC with two grids of the indents made with the regular

Si probe (spring constant 40 N/m). The cross-sections along the indents, which were taken along the directions marked with the whitedashed lines in (a) and (b), are presented in (c). (d)-(e) Height images of the lamellar structures of HDPE with the smaller image takenat the location where a at-lying lamellae was indented in a 2´3 grid. The cross-section along two indents in a direction marked with a

white dashed line is shown in the insert in (e). The force curve (DvZ) recorded during one of the indentation event is shown in (f). The

red curve corresponds to the loading trace and the blue curve – to the unloading trace. The blue arrows indicate the parts of loadingand unloading curves, which were used for the estimation of elastic moduli.

(a)

(d)

Height Phase

(e)

(b)

(f)

HeightHeight

3 µm

1,2 µm 600 nm

(c)



13

embedded into PB matrix. Several locations,which are marked with small circles of differentcolors, were chosen for the indentation experi-ments, and the phase image obtained afterthe experiments is presented in Figure 12b.Surprisingly, the DvZ curves obtained at the“blue” and “green” locations, which are as-signed to PS and PB materials, are the same,

Figure 12c. The loading and unloading pathsshow mostly strong adhesion. The phase im-age in Figure 12b, which shows a circle of PBat the former “blue” location, allows us to sug-gest that the PS domain was quite thin and wasdestroyed by the tip, which was attracted to thesample because of its relatively large size. TheDvZ curves, which were obtained at small andlarge round-shaped islands of PS, have differ-ent shapes, Figures 12d-e.

The curve obtained on the small island has twostages (Figure 12d) and this might correlatewith a partial damage of the island as seenfrom the phase image in Figure 12b. The curve,which was collected on the black-colored loca-tion of the big island, looks common to thosecollected on the blocks of PS and other amor-phous polymers. This example of the sample

complexity shows that a comprehensive studyof multicomponent materials can be quite dif-ficult and likely requires the interplay betweendifferent methods and approaches.

In further development of the nanoscale me-chanical measurements with AFM techniquesthere is a novel trend in data analysis - a tran-

sition from non-dissipative models to moresophisticated approaches accounting for visco-elasticity effects. As we mentioned before, thetime-dependent effects strongly manifest them-selves in the recovery of the indents [22-23].

This effect is illustrated by imaging of the in-dents, which were left on a surface of a blockprepared from a binary blend of polyethyleneswith different degree of octene branching. Theconstituents of the blend have different densi-

ties (0.92 g/cm-3 and 0.86 g/cm-3) and crystal-linity. The surface of the sample is enriched inlow-density material and does not show lamellarmorphology.

The sub-surface morphology might be verydifferent and can exhibit itself in the nanoin-dentation experiments, and particularly, in the

indent recovery pattern. This isdemonstrated in the height im-ages and the related graph in

Figures 13a-d. The first two im-ages were recorded 5 and 20minutes after the indentationexperiment, in which a grid of 9surface imprints was made. Theimprints disappeared slowly andbecame almost invisible in theheight image (Figure 13c), whichwas recorded 10 hours after theimage in Figure 13b. The analysisof the images shows the different

recovery kinetics for the imprints,with the slowest for the indent inthe center, Figure 13d. The timechanges of the imprint profile hintat the affine character of the re-covery similar to the finding in theexperiments on styrene-butadienecopolymers [24]. In the same pa-per, it was shown that the depth ofthe imprint follows the variationsof the corresponding homoge-neous creep-recovery experiment.Therefore, by imaging the imprintone can obtain the variations ofthe polymer compliance function.This example shows that local

Figures 12a-e. The phase images of the surface of a lm of PB/PS blend are

shown prior the indentation probing in several locations marked with the colorcircles (a) and after the indentations (b). DvZ curves, which were recorded duringindentation of the color-coded locations, are presented in (c) – (e).

(a)

(b)

Height DvZ

(e)

(b)

DvZ

DvZ

Height

5 µm

(d)

(c)



14

nanomechanical data that for some polymermaterials can be used for extracting the quanti-tative elastic modulus and work of adhesion.

However, broader acceptance of this methodis limited by the restrictions for the solid-state,non-dissipative models used for data analysis.

Several time-dependent effects in local mechan-ical studies were presented to underline theneed for their serious consideration. A develop-ment of novel models accounting the plastic andviscoelastic behavior of polymers is essentialfor the further progress of AFM nanomechanicalstudies.

Figures 13a-d. Height images of the location of a binary polyethylene blendwith the components having densities of 0.92g/cm-3 and 0.86g/cm-3 with theindentation imprints. The image in (a) was obtained 5 minutes after the indenta-tion procedure, the image in (b) was recorded 20 minutes after the image in (a)and the image in (c) – 10 hours after the image in (b). (d) Cross-sectional traces

(black, red, dark blue and light blue) across the central imprint were taken in theimages, which were recordedrespectively 5, 25, 40 minutes and 10.5 hours afterthe indentation.

(b)

(d)

(a)

(c)

Height

Height

Height

600 nm

mechanical properties of poly-mers and other materials can beexamined in different AFM-basedexperiments with the choice of themost appropriate mode.

Conclusions

The tip-force mechanical interac-tions are the core of AFM and theymanifest themselves in differentmodes and operation conditions.Therefore, knowledge of the tip-force effects is indispensable forthe correct interpretation of AFMdata and for their use for the ex-ploring local mechanical propertiesof materials.

Several techniques for probingof sample’s stiffness and adhe-sion were illustrated on practicalexamples obtained with the NEXTmicroscope, which is equippedwith most of the common modesfor studies of mechanical proper-ties. The differences in mechani-cal properties of the materials areemployed for compositional imag-ing of multi-component samples

in contact resonance mode andfor phase imaging in AM mode. AFM nanoindentation is a tech-nique that provides the local

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