Nanoscale Deformation and Nanomechanical Properties of Polydimethylsiloxane(PDMS)

Constantinos A. Charitidis*

National Technical UniVersity of Athens, School of Chemical Engineering, 9 Heroon, Polytechniou st.,Zografos, GR-157 80 Athens, Greece

In the present work, the zero-load plastic deformation of polydimethylsiloxane (PDMS) was examined usingthe nanoindentation technique. Although no load had been applied to the sample, there was an interactionbetween the tip and PDMS. An analysis using the power law P ) a ·hn was also performed and n valuesvaried from 0.6 to 1.3 until they reached 1.35 for bulk PDMS. The results were compared with those obtainedfrom the Oliver and Pharr analysis and were in good agreement. Both methods revealed the existence of asurface/near surface region (∼2500 nm) with enhanced elastic modulus values in comparison with thosecorresponding to greater penetration depths (bulk PDMS).

1. Introduction

Polydimethylsiloxane (PDMS), a clear elastomer, is a com-mon material used in many applications in bioengineering,electronics, and microelectromechanical systems because it isbiologically inert, gas permeable, insulating, and good for rapidprototyping of devices.1 The advantages of PDMS include itsgood electrical properties, low surface energy, and isotropic andhomogeneous properties.2 PDMS is also thermally stable andperforms well over a wide range of temperatures.3 The nano-mechanical properties of PDMS are of great interest in applica-tions involving pressure support or fluid manipulation. In suchapplications, nanomechanical properties have to be carefullyvalidated because exposure to chemicals and temperaturechanges may cause variation of the mechanical properties.

Nanoindentation is a technique that has been widely used tocharacterize the mechanical properties of materials at surfaceor subsurface. More specifically through the nanoindentationexperiment, the hardness (H), the elastic modulus (E), theyielding stress, and other mechanical properties can be deter-mined from very small volumes of materials. The applicationof nanoindentation to soft matter has increased over recent years.However, there are still critical issues associated with applyingnanoindentation to soft materials. Major sources of difficultyinclude evaluating the appropriateness of mechanical models,4

defining proper calibration materials,5 and eliminating othersources of experimental error in the measurements.6 It has beenshown that adhesion has a big influence on soft materials.7 Withnanoindentation of soft materials, it is often necessary to modifythe standard testing protocols for stiff materials to accuratelycalculate the surface position.8 Polymers are typically muchmore compliant compared to hard materials, with modulusranging from a few GPa for common glassy polymers to a fewMPa or lower for rubbery polymers.9 Adhesion forces betweenthe tip of the nanoindenter and the sample’s surface can add upto a significant percentage of the overall maximum load.Adhesion will thus cause an extra phase shift, which can havesignificant influence on the loss modulus.10 Moreover, softmaterials exhibit time-dependent or viscoelastic behavior. Theeffect of viscoelasticity which is most observed on nanoinden-tation is creep, or a sinking of the tip into the sample under aconstant load.11

In the current work, an atomic force microscopy (AFM) studywas carried out to investigate the surface nanotopography ofPDMS. Several characteristics of the sample’s surface werecalculated as well as the roughness of PDMS which was foundto be 19.79 nm.

Furthermore, the plastic deformation when no load had beenapplied to PDMS was examined. Although no load had beenapplied to the sample, there was an interaction between the tipand the sample. This phenomenon is frequently referred in theliterature as zero-load plastic deformation.12 The load-depthresults revealed an almost reversible feature, which indicatedelastic deformation. However, when the tip was pulled awayfrom the sample, the adhesive attraction deformed the softpolymer along the direction of the tip motion and caused anegative indentation (i.e., polymer extension under a tensilestress).

Moreover, nanoindentation technique was used to estimatethe E of PDMS. To analyze the nanoindentation results, theOliver and Pharr (O&P) method13 was used to estimate the Evalues using the unloading data of the load-unload curves. Ourresults revealed the heterogeneity of PDMS and providedquantitative information on the complex changes, namely theexistence of a surface/near surface region (∼2500 nm) withenhanced E values in comparison with those corresponding togreater penetration depths (bulk PDMS). In addition, the loadingdata of the load-unload curves had been fitted to the powerlaw function: P ) a ·hn, where P is the applied load, a is amaterial parameter, h is the displacement, and n is the index ofthe deformation (indentation index), to determine the depthoffset. In the PDMS specimens, n values varied from 0.6 to 1.3with the increase of the penetration depth until they reached1.35 for bulk PDMS. Deviations from the normal relationship(n ) 2) between load and depth during the indentation testingmay occur when (i) there is strain-rate hardening of the sample,(ii) there are viscoelastic effects, and (iii) the mechanicalproperties vary with depth due to a changing cross-linkingprofile.

2. Experimental Section

2.1. PDMS Sample Preparation. PDMS sample was pre-pared by mixing 30 g of siloxane base with 4.5 g of cross-linking agent. An increase in viscosity was observed during thepreparation of the sample. The addition of the cross-linking

* Tel.: 0030-210-772-4046. Fax: 0030-210-772-2339. E-mail:charitidis@chemeng.ntua.gr.

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10.1021/ie100099g 2011 American Chemical SocietyPublished on Web 06/02/2010

agent was followed by the addition of catalyst. Its final shape(3 mm thickness with smooth surface at top and rough surfaceat bottom) was due to the casting process in aluminum pot/pipkin, where the smooth surface was exposed to air and therough one was in contact with the bottom of the pot (vulcaniza-tion time about 24 h). The surfaces of the sample were cleanedwith water prior to testing to avoid contamination.

2.2. Instrumentation. The nanoindentation analysis in thiswork was performed using a Hysitron TriboLab nanomechanicaltest instrument allowing the application of loads from 1 to 10000µN and the recording of penetration depths as a function ofapplied loads with a high load resolution (1 nN) and a highdisplacement resolution. The TriboLab employed in this studywas equipped with a scanning probe microscope (SPM), inwhich a sharp probe tip moved in a raster scan pattern acrossa sample surface using a three-axis piezo position. In all depth-sensing tests a total of 10 indents were averaged to determinethe mean E values for statistical purposes, with a spacing of 50µm (relative humidity ∼45%, temperature 23 °C). After theindenter tip contacted the specimen surface, the indentation loadand displacement were recorded simultaneously.

AFM measurements were performed in intermittent contactmode with a Quesant Q-Scope 250 atomic force microscope(Quesant Instrument Co., U.S.A.) equipped with a 40 µm DualPZT scanner. The images were obtained in ambient conditionswith an NSC16 (W2C Si3N4) silicon cantilever. Imaging wasperformed on different scanning areas at a maximum scanningrate of 6 Hz and with image resolution 600 × 600 pixels inbroadband mode. The microscope was enclosed in an acoustic/thermal isolation unit.14

3. Results and Discussion

3.1. Surface Topography of PDMS. Control of the surfacetopography of PDMS is greatly desired as it can potentiallyaffect the functionality of the structure.15 An AFM study wascarried out to investigate the surface topography of a specificarea of the smooth surface of PDMS where the nanoindentationtechnique was also performed. Figure 1 shows a tapping-modetopographical image of PDMS in 2D (Figure 1a) and 3D (Figure1b) representation. It is obvious that the surface of the sampleis not perfectly smooth and exhibits irregularities that may havebeen produced during the preparation of the sample.

The surface parameters are given in Table 1. Zave is theaverage of the Z values within the given area, Rq (root-mean-square roughness) is the standard deviation of the height valuesof the surface structures in the z direction (Z value), within thegiven area and is calculated by the software provided by the AFMimage analysis data, Rp is the maximum height of the profile

roughness above the mean plane, while Rv is the lowest pointbelow the mean image plane and Rt is the sum total of themaximum peak and maximum valley measurements. Figure 2shows the height histogram of PDMS. It is obvious that it isalmost symmetric around the maximum surface roughness at90 nm.

3.2. Nanoscale Deformation. The plastic deformation whenno load had been applied to PDMS was examined in the presentwork. The dynamic load signal (dynamic contact stiffness) wasused to provide much greater sensitivity to surface contact andsurface stiffness in comparison with a change in quasi-staticforce or stiffness measurement. The dynamic load signal as thetip approached the surface snapped into contact because ofsurface forces and measured the increase in the surface stiffnesswith displacement.16 Figure 3 presents the load vs displacementplot into PDMS surface.17 Although no load had been appliedto the sample, there was an interaction between the tip and thesample. In the literature, this phenomenon is frequently referredto as zero-load plastic deformation.12 The point where theinteraction becomes attractive is assigned to be the point wherethe tip contacts the surface, as shown in Figure 3. From Figure

Figure 1. 2D (a) and 3D (b) AFM image of PDMS (8 × 8 µm2 scanned area) indicating the surface topography of the sample.

Table 1. Surface Characteristics Obtained by the Analysis of theAFM Image

surface characteristics nm

Zave (average height) 88.51rms deviation 19.79Rp (max peak) 245.7Rv (max valley) 88.51Rt (max peak - valley) 334.2

Figure 2. Height histogram of PDMS.

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3, one can see that when the tip is pulled away from the sample(unloading), the adhesive attraction deforms the soft polymeralong the direction of the tip motion and causes a negativeindentation (i.e., polymer extension under a tensile stress). Atpoint “0”, where the tip is drawn into the sample surface becauseof the adhesive interaction, the stored elastic energy and thesurface energy are balanced. The indentation between the pointwhere the tip starts to contact the sample surface and point “0”is defined as the adhesion-induced indentation. The pull-offadhesion force (Padh in Figure 3) is determined as the differencebetween the minimum force value and the zero offset. Carilloet al.19 performed adhesion experiments in dry and aqueousconditions. The mean adhesion pull-off forces measured rangedfrom 93.1 to 43.6 µN with decreasing cross-linker concentration.The Padh calculated in the present study is 1.92 µN. Thedeviation from the values presented by Carillo et al. is probablycaused by the difference in the degree of cross-linking.

3.3. Nanomechanical Properties of PDMS. A typicalnanoindentation test provides load-depth data, which are thedeformation response of a material. Significant adhesion maybe observed while indenting PDMS. Figure 4 presents a typicalload-unload curve of the sample where the applied load isplotted in accordance with the displacement of the indenter. As

shown in Figure 4, negative load values may appear duringloading-unloading procedure in the load-displacement curve.In the first step of nanoindentation testing, the Berkovich tipsenses a negative load as it approaches the sample, such that aminimum force is seen on the loading curve prior to the appliedload increasing.18 It is reported in the literature19-22 that theadhesion effect during nanoindentation experiments of softpolymers leads to overestimation of the modulus when there issignificant tip-sample adhesion. At the largest starting depth,the calculated modulus is almost 5 times the actual value. Oneeffective method to ensure that the zero displacement positionis accurately determined is the correct determination of thecontact area between the indenter and the sample being tested.One method to define the surface position of soft materialscorrectly is to perform displacement controlled experiments asdescribed in Cao et al.6 Instead of using the software to locatethe surface, the tip is moved manually above the sample andthe Z location of the surface is found while lowering thenanoindenter tip on the finest motor speed.18 In the present work,the area for the nanoindentation testing was carefully chosenusing the SPM, to obtain low values of the surface roughnessof the sample, i.e., 3-4 nm. Thus, it was ensured that nonegative load values would appear in the load-displacementcurve. Figure 5 presents the load-unload curve of PDMS whenthe surface of the sample is determined correctly using a manualindentation method. No negative load values appear. Four modesof mechanical deformation are commonly observed duringindentation testing: elastic, plastic, viscous, and fracture. Byexamining the shape of the indentation load-displacementcurve, the active deformation mode during indentation testingcan be identified.23 From Figure 5, it is obvious that PDMSexhibits a fully elastic behavior, as the loading and the unloadingcurve are identical.

An analysis using the power law P ) a ·hn was performed.The power law P ) a ·hn, where P stands for the applied load,a is a constant depending on the geometry of the indenter tipand the properties of the material, h is the displacement, and nis the index of the deformation (indentation index), is based onthe loading obtained data excluding the unloading curve. Figure6 presents typical load curves of PDMS when four differentloads are applied to the sample, i.e., when the applied load is4, 8, 14, and 45 µN. A fitting analysis is also presented in Figure6 according to the method presented by Zeng and Chiu24 tocalculate the E. The load curves are fitted to the P ) a ·hn

equation and a comparison of the fitted curve with the actual

Figure 3. Load vs displacement as the tip approaches the surface and snapsinto contact because of surface forces in the surface of PDMS.17

Figure 4. Load-unload curves of PDMS when the surface between the tipand the sample is not properly determined and significant tip-sampleadhesion is observed as negative load values appear.

Figure 5. Load-unload curves of PDMS when the surface between the tipand the sample is correctly determined.

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P ) a ·h2 curve is presented. Deviations are observed due tothe viscoelastic effects. Figure 7 presents the indentation index,n, plotted in accordance with the displacement of the tip. Asshown in Figure 7, as the penetration depth increases, the nvalues also increase and vary from 0.6 to 1.3 with the increaseof the penetration depth until they reach a constant value (1.35)for displacement >2500 nm (bulk PDMS). Higher n values forPDMS imply higher resistance to indentation degree (higherapplied load needed for the tip to reach the same displacement).Higher resistance to indentation degree results in increase of Eof PDMS.

In general, traditional mechanical property parameters, suchas E, can be determined through nanoindentation. Attention hasbeen paid to analyzing the unloading curve to obtain contactarea for the determination of E. Most analyses are based on theO&P method,13 which determines the contact area using the

unloading tangent together with the known area function. The O&Pmethod is based on the first segment (30%) of the unloading data,where the elastic theory takes the linearity of the curve for granted.It is believed that the contact area between the tip and the samplebeing tested is underestimated when it is calculated by the O&Pmethod for most ductile metals and soft polymers.25 O&Pderived expressions for calculating the elastic modulus fromindentation experiments based on Sneddon’s26 elastic contacttheory:

where S is the unloading stiffness and is taken to be the initialslope of the unloading load-displacement curve at the maxi-mum depth of penetration (or peak load), Ac is the projectedcontact area between the tip and the substrate at peak load, and� is a constant that depends on the geometry of the indenter(� ) 1.167 for Berkovich tip). The contact area can be calculatedusing the ideal geometric area function:

where hc is the contact depth at peak load which is estimatedby:

where hm is the total penetration depth of the indenter at peakload, Pm is the peak load at the indenter displacement depthhm, and ε is an indenter geometry constant. The O&P methodincorrectly assumes that the contact area remains constant duringthe initial unloading of the material. Also, this method doesnot take into account the viscoelastic behavior of PDMS, whichaffects the shape of the unloading curve, and the viscoelastic

Figure 6. Typical load curves obtained for applied loads of 4, 8, 14, and 45 µN, respectively, presented with the appropriate fitting analysis. The values ofa and n are also presented.

Figure 7. Indentation index vs displacement.

Er )S√π

2�√Ac

(2)

Ac ) π(2Rhc - hc2) (3)

hc ) hm - εPm

Sm(4)

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creep which increases the initial slope of the unloading curve.27

Both of these factors affect the determination of the stiffness S.Creep effects usually occur during nanoindentation. In creepsituations, the unloading curve exhibits a nose meaning that theindenter continues to sink into the specimen even though theload is decreasing.

In Figure 8, the elastic moduli E obtained from the twodifferent methods, i.e., the power-law fitting and the O&Panalysis,28 are plotted in accordance to the displacement of thetip. The E values were calculated from the power-law analysisaccording to the method presented by Zeng and Chiu.24

The results obtained from the two different methods are ingood agreement although those calculated from the power-lawfitting are slightly higher. Also, the results obtained from thetwo methods reveal the heterogeneity of PDMS and providequantitative information on the complex changes, namely theexistence of a surface/near surface region (∼2500 nm) withenhanced E values (from the O&P analysis the E value is 24.4MPa, whereas from the power-law analysis E is 29 MPa) incomparison with those corresponding to greater penetrationdepths (bulk PDMS) (from the O&P analysis the E value is 2.5MPa whereas from the power-law analysis the E value is 3.4MPa). Comparing the two methods, the limits of each regionof PDMS, i.e., surface/near surface and bulk region, are foundto be almost identical. Higher E values in the surface area arecaused probably by higher cross-link density in the lowdisplacement range (combined with exposure of the PDMSsamples in atmospheric air). Wahl et al.32 confirmed the increasein elastic modulus of PDMS with higher cross-linking agentconcentrations due to polymerization degree decrease (E ) 8.7MPa). Several studies on PDMS samples via nanoindentationhave revealed various nanomechanical properties.16,29-33 Houet al.30 investigated PDMS samples (surface E ) 19 MPa, bulkregion E ) 8 MPa) with average roughness ∼15 nm. Shen etal.33 applied O&P analysis and obtained E values of PDMS(E ) 3.02 MPa). Carillo et al.19 used the nanoindentationtechnique to characterize the E of PDMS with different degreesof cross-linking (E ) 3.64 MPa for 10:1 concentration). Ourresults are in good agreement with those presented in theliterature.

It is interesting to speculate whether the increase in E insurface/near surface region is an indentation size effect, or

represents a change in the mechanical properties of the surface/near surface region due to being enhanced crystalline-like(higher amount of cross-linking in the surface). On polymerswhich strain-rate harden, increasing surface/near surface E hasbeen attributed to a strain-rate effect. In a load-controlled(constant velocity) indentation the strain rate will decrease withincreasing indentation depth, which is thought to be responsiblefor the apparent decrease in E with depth. On PDMS, however,which does not strain-rate harden; the explanation must be morecomplex. Several factors can effect whether the normal relation-ship between load and depth during an indentation (P ) a ·hn,n ) 2) holds. Deviations from this (i.e., n < 2) can occur when(i) there is strain-rate hardening, (ii) there are viscoelastic effects,and (iii) the mechanical properties vary with depth due to achanging cross-linking profile. It is clear that viscoelastic effectsare important for PDMS.

4. Conclusions

In the present study, the surface topography of PDMS wasinvestigated by AFM. The root-mean-square (rms) roughnesswas found to be 19.79 nm and the height histogram was almostsymmetric around the maximum surface roughness at 90 nm.Moreover, it was found that when the indenter tip was pulledaway from the sample, the adhesive attraction deformed the softpolymer along the direction of the tip motion and caused anegative indentation. The current study attempted also to usenanoindentation technique to calculate the elastic modulus ofPDMS using two different methods for the fitting of the obtainedload-unload curves, i.e., the power-law analysis based on theloading data and the O&P method based on the first segment(30%) of the unloading data. The surface of the sample wasdefined manuallysinstead of using the softwaresto avoid thepresence of negative load values in the load-displacementcurve. The E values calculated from the two methods werecompared and were found to be in good agreement as the limitsof the regions (surface/near surface and bulk region) of thesample were almost identical.

Acknowledgment

I thank Dr. E. Sarantopoulou for providing the AFM imagesand acknowledge Mrs. V. Tsikourkitoudi for her contributionin realizing this work.

Literature Cited

(1) Mills, K. L.; Zhu, X.; Takayama, S.; Thouless, M. D. The mechanicalproperties of a surface-modified layer on poly(dimethylsiloxane). J. Mater.Res. 2008, 23, 37.

(2) Kikuchi, T.; Nishimura, S.; Nagao, M.; Izumi, K.; Kubota, Y.; Sakata,M. Survey on the Use of Non-Ceramic Composite Insulators. IEEE Trans.Elect. Insul. 1999, 6, 548.

(3) Meincken, M.; Berhane, T. A.; Mallon, P. E. Tracking the hydro-phobicity recovery of PDMS compounds using the adhesive force deter-mined by AFM force distance measurements. Polymer 2005, 46, 203.

(4) Cheng, L.; Xia, X.; Scriven, L. E.; Gerberich, W. W. Spherical-TipIndentation of Viscoelastic Material. Mech. Mater. 2005, 37, 213.

(5) Oyen, M. L. Spherical indentation creep following ramp loading. J.Mater. Res. 2005, 20, 2094.

(6) Cao, Y.; Yang, D.; Soboyejoy, W. Nanoindentation method fordetermining the initial contact and adhesion characteristics of soft poly-dimethylsiloxane. J. Mater. Res. 2005, 20, 2004.

(7) Wahl, K. J.; Ebenstein, D. M. A comparison of JKR-based methodsto analyze quasi-static and dynamic indentation force curves. J. ColloidInterface Sci. 2006, 298, 652.

(8) Hayes, S. A.; Goruppa, A. A.; Jones, F. R. Dynamic nanoindentationas a tool for examination of polymeric materials. J. Mater. Res. 2004, 19,3298.

Figure 8. Elastic modulus calculated from the two different methods usedvs displacement.

Ind. Eng. Chem. Res., Vol. 50, No. 2, 2011 569

(9) VanLandingham, M. R. Review of Instrumented Indentation. J. Res.Natl. Inst. Stand. Technol. 2003, 108, 249.

(10) Franke, O.; Goken, M.; Hodge, M. H. The Nanoindentation of SoftTissue: Current and Developing Approaches. J. Miner, Met. Mater. Soc.2008, 60, 49.

(11) Ebenstein, D. M.; Pruitt, L. A. Nanoindentation of biologicalmaterials. Nanotoday 2006, 1, 26.

(12) Kim, K. S.; Lin, Z.; Shrotriya, P.; Sundararajan, S.; Zou, Q. Iterativecontrol approach to high-speed force-distance curve measurement usingAFM: time-dependent response of PDMS example. Ultramicroscopy 2008,108, 911.

(13) Oliver, W. C.; Pharr, G. M. An improved technique for determininghardness and elastic modulus using load and displacement sensing indenta-tion experiments. J. Mater. Res. 1992, 7, 1564.

(14) Sarantopoulou, E.; Kollia, Z.; Cefalas, A. C.; Siokou, A. E.; Argitis,P.; Bellas, V.; Kobe, S. Surface modification of polyhedral oligomericsilsesquioxane block copolymer films by 157 nm laser light. J. Appl. Phys.2009, 105, 114305.

(15) Tsougeni, K.; Boulousis, G.; Gogolides, E.; Tserepi, A. Orientedspontaneously formed nano-structures on poly(dimethylsiloxane) films andstamps treated in O2 plasmas. Microelectron. Eng. 2008, 85, 1233.

(16) White, C. C.; Vanlandingham, M. R.; Drzal, P. L.; Chang, N. K.;Chang, S. H. J. Viscoelastic characterization of polymers using instrumentedindentation. II. Dynamic testing. Polym. Sci. 2005, 43, 1812.

(17) Pethica, J. B.; Oliver, W. C. Tip Surface Interaction in STM andAFM. Phys. Scr. T. 1987, 19, 61.

(18) Kaufman, J. D.; Klapperich, C. M. Surface detection errors causeoverestimation of the modulus in nanoindentation on soft materials. J. Mech.BehaV. Biomed. Mater. 2009, 2, 312.

(19) Carrillo, F.; Gupta, S.; Balooch, M.; Marshall, S. J.; Marshall,G. W.; Pruitt, L.; Puttlitz, C. M. Nanoindentation of polydimethylsiloxaneelastomers: Effect of crosslinking, work of adhesion, and fluid environmenton elastic modulus. J. Mater. Res. 2005, 20, 2820.

(20) Klapperich, K.; Komvopoulos, K.; Pruitt, L. NanomechanicalProperties of Polymers Determined From Nanoindentation Experiments. J.Tribol. - Trans. ASME 2001, 123, 624.

(21) Grunlan, J. C.; Xia, X.; Rowenhorst, D.; Gerberich, W. W.Preparation of tungsten tips for nanoindentation and comparison withdiamond on soft materials. ReV. Sci. Instrum. 2001, 72, 2804.

(22) Carrillo, F.; Gupta, S.; Balooch, M.; Marshall, S. J.; Marshall,G. W.; Pruitt, L.; Puttlitz, C. M. Erratum: “Nanoindentation of polydim-ethylsiloxane elastomers: Effect of crosslinking, work of adhesion, and fluidenvironment on elastic modulus”. J. Mater. Res. 2006, 21, 535.

(23) Oyen, M. L.; Cook, R. F. A practical guide to nanoindentation data.J. Mech. BehaV. Biomed. Mater. 2009, 2, 396.

(24) Zeng, K.; Chiu, C.-H. An Analysis of load-penetration curves frominstrumented indentation. Acta Mater. 2001, 49, 3539.

(25) Sakai, M. The Meyer hardness: a measure for plasticity. J. Mater.Res. 1999, 14, 3630.

(26) Sneddon, I. N. The relation between load and penetration in theaxisymmetric boussinesq problem for a punch of arbitrary profile. Int. J.Eng. Sci. 1956, 3, 47.

(27) VanLandingham, M. R.; Villarubia, J. S.; Guthrie, W. F.; Meyers, G. F.Nanoindentation of Polymers: An Overview. Macromol. Symp. 2001, 167, 15.

(28) Charitidis, C. A.; Koumoulos, E. Nanoindentation of nanocom-posites polydimethylsiloxane elastomers. Submitted to Mater. Sci. Eng. B.

(29) Sirghi, L.; Rossi, F. Adhesion and elasticity in nanoscale indentation.Appl. Phys. Lett. 2006, 89, 243118.

(30) Hou, H. Y., Chang, N. K., Chang, S. H., Chuang, T. J., Eds.Nanomechanics of Materials and Structures; Springer: New York, 2006.

(31) Deuschle, K. J.; Buerki, G.; Deuschle, H. M.; Enders, S.; Michler,J.; Arzt, E. J. In situ indentation testing of elastomers. Acta Mater. 2008,56, 4390.

(32) Wahl, K. J.; Asif, S. A. S.; Greenwoodc, J. A.; Johnson, K. L.Oscillating adhesive contacts between micron-scale tips and compliantpolymers. J. Colloid Interface Sci. 2006, 296, 178.

(33) Shen, Y. X.; Wei, P. J.; Lin, J. F. Initial and adhesive contactbetween a diamond indenter and polydimethylsiloxane. J. ReV. Sci. Instrum.2008, 79, 096106.

ReceiVed for reView January 15, 2010ReVised manuscript receiVed May 10, 2010

Accepted May 19, 2010

IE100099G

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