Oscillating adhesive contacts between micron-scale tips and compliant polymers

Adhesion of micron-scale probes with model poly(dimethylsiloxane), PDMS, elastomers was studied with a depth-sensing nanoindenter under oscillatory loading conditions. For contacts between diamond indenters (radius R = 5 or 10 microm) and PDMS, force-displacement curves were highly reversible and consistent with Johnson-Kendall-Roberts (JKR) behavior. However, our experiments have revealed striking differences between the experimental measurements of tip-sample interaction stiffness and the theoretical JKR stiffness. The measured stiffness was always greater than zero, even in the reflex portion of the curve (between the maximum adhesive force and release), where the JKR stiffness is negative. This apparent paradox can be resolved by considering the effects of viscoelasticity of PDMS on an oscillating crack tip in a JKR contact. Under well described conditions determined by oscillation frequency, sample viscoelastic properties, and the Tabor parameter (with variables R, reduced elastic modulus, E*, and interfacial energy, deltagamma), an oscillating crack tip will neither advance nor recede. In that case, the contact size is fixed (like that of a flat punch) at any given point on the load-displacement cycle, and the experimentally measured stiffness is equal to the equivalent punch stiffness. For a fixed oscillation frequency, a transition between JKR and punch stiffness can be brought about by an increase in radius of the probe or a decrease in PDMS modulus. Additionally, varying the oscillation frequency for a fixed E*, R, and deltagamma also resulted in transition between JKR and punch stiffness in a predictable manner. Comparisons of experiments and theory for an oscillating viscoelastic JKR contact are presented. The storage modulus and surface energy from nanoscale JKR stiffness measurements were compared to calculated values and those measured with conventional nanoindentation and JKR force-displacement analyses.     

Evaluation of the adhesion properties of inorganic materials with high surface energies

With the aim of checking the validity of methods for characterizing the adhesion between inorganic materials with high surface energies, the properties of the adhesion between an inorganic material (indium tin oxide (ITO)) and model surfaces with various surface energies (Cl-, NH2-, CH(3)-, and CF3-functionalized surfaces) were evaluated using atomic force microscopy (AFM) and the Johnson-Kendall-Roberts (JKR) apparatus. For this purpose, the AFM tip and the JKR lens were modified with ITO using radio frequency (rf) magnetron sputtering. The work of adhesion between the ITO coating and each model surface was estimated using AFM and the JKR apparatus and compared with the result obtained from contact angle measurements. The adhesion forces determined from the force-displacement curves (AFM) were found to agree with the predictions of the Derjaguin-Muller-Toporov (DMT) theory. The JKR equation used in the interpretation of the JKR experiments was modified by taking into account the differences between the surface and bulk moduli of the ITO-coated poly(dimethylsiloxane) (PDMS) lens. The ratio of the surface modulus to the bulk modulus we used in this modified JKR equation was obtained by determining the slope of the attracting part of the force-displacement curve. The values of the work of adhesion calculated using the modified JKR equation were also found to agree with the values obtained from contact angle measurements. We conclude that the two methods using AFM and the JKR apparatus can be used in the evaluation of the work of adhesion between inorganic materials with high surface energies such as metal and metal oxide surfaces.     

Characterization of adhesion at solid surfaces: Development of an adhesion-testing device

A custom-built adhesion-testing device (ATD) is described in this paper, which was developed to study energetics of various solid (polymeric) interfaces. A review is also given of the main techniques of adhesion and adherence measurements, including non-destructive and destructive methods, with major emphasis on the evolution and applications of contact mechanics techniques. Using the Johnson-Kendall-Roberts (JKR) theory of contact mechanics in the elastic deformation regime, the interfacial energy of solid surfaces can be obtained by measuring the contact radius, loading force, and vertical displacement between an (elastic) sphere (lens) and a flat surface (one of which, or both, coated with the sample of interest). The parameters needed for JKR analyses were determined by our custom-built device. Based on the JKR theory, the values of work of adhesion, combined elastic modulus and interfacial energy were determined from the loading and unloading curves on poly(dimethylsiloxane)-poly(dimethylsiloxane) (PDMS) systems. Cumulative adhesion hysteresis and elastic modulus were also calculated. The results obtained agree well with literature data measured by different methods. These measurements on compliant PDMS-PDMS model systems can also serve as validation and verification of the adhesion-testing devices described in this study.     

Analytical methods to derive the elastic modulus of soft and adhesive materials from atomic force microcopy force measurements

We present new DMT‐based and JKR‐based methods to derive the elastic modulus of sample surfaces from an atomic force microscope force‐distance curve (DMT: Derjaguin‐Muller‐Toporov, JKR: Johnson–Kendall–Roberts). Application of the methods to the Maugis–Dugdale curves revealed that the JKR‐based method determines very accurate moduli for Maugis' transitional parameter λ > 0.3; however, the DMT‐based method generally estimates much less accurate moduli. The new JKR‐based method has advantages over the two‐point method, which has been often used for the JKR analysis, in capabilities to select the fitting range and to involve more than two points in curve fitting. Utilizing the advantages, for example, one can limit the fitting range to the attractive force zone to reduce the contact area of soft and adhesive materials. The method consists of algebraical calculation and optionally linear fitting; hence, the computational cost is low enough to be applicable to a real‐time JKR analysis method of fast force mapping. The detailed procedure of the method is explained using a force‐distance curve on a poly(dimethylsiloxane) surface. The advantages of the method are demonstrated using a force mapping data on a vulcanized rubber blend. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1279–1286     

Viscoelastic characterization of polymers using instrumented indentation. I. Quasi‐static testing*

The use of instrumented indentation to characterize the mechanical response of polymeric materials was studied. A model based on contact between a rigid probe and a linear viscoelastic material was used to calculate values for the creep compliance and stress relaxation modulus for two glassy polymeric materials, epoxy and poly(methyl methacrylate), and two poly(dimethyl siloxane) (PDMS) elastomers. Results from bulk rheometry studies were used for comparison with the indentation stress relaxation results. For the two glassy polymers, the use of sharp pyramidal tips produced responses that were considerably more compliant (less stiff) than the rheometry values. Additional study of the deformation remaining in epoxy after indentation creep testing as a function of the creep hold time revealed that a large portion of the creep displacement measured was due to postyield flow. Indentation creep measurements of the epoxy with a rounded conical tip also produced nonlinear responses, but the creep compliance values appeared to approach linear viscoelastic values with decreasing creep force. Responses measured for the unfilled PDMS were mainly linear elastic, with the filled PDMS exhibiting some time‐dependent and slight nonlinear responses in both rheometry and indentation measurements. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1794–1811, 2005     

General Equations Describing Elastic Indentation Depth and Normal Contact Stiffness versus Load

Continuum mechanics models describing the contact between two adhesive elastic spheres, such as the JKR and DMT models, provide a relationship between the elastic indentation depth and the normal load, but the general intermediate case between these two limiting cases requires a more complex analysis. The Maugis-Dugdale theory gives analytical solutions, but they are difficult to use when comparing to experimental data such as those obtained by scanning force microscopy. In this paper we propose a generalized equation between elastic indentation depth and load that approximates Maugis' solution very closely. If the normal contact stiffness can be described as the force gradient, that is the case of the force modulation microcopy, then a generalized equation between normal contact stiffness and load can be deduced. Both general equations can be easily fit to experimental data, and then interfacial energy and elastic modulus of the contact can be determined if the radius of the indenting sphere is known. Copyright 2000 Academic Press.     

Elastic properties of oriented polymers, blends and reinforced composites using the microindentation technique

The elastic behaviour of poly(ethylene terephthalate) (PET) and nylon 6 (PA6), their blends (1:1 by weight) and microfibrillar-reinforced composites of the previously mentioned homopolymers has been investigated by means of load-displacement analysis from indentation experiments. The dependence of the elastic modulus of the homopolymers upon the degree of crystallinity and the crystal size, as derived from indentation experiments, is discussed. A linear correlation between the elastic modulus anisotropy and the microindentation hardness anisotropy values is also found to apply for the oriented materials. The results reveal that the indentation modulus values of the PET/PA6 blends follow the parallel additivity model of the individual components. The use of the additivity law is also shown to provide a value, otherwise not accessible from direct measurements, of the modulus of the microfibrils within the microfibrillar-reinforced composites.     

Continuous stiffness mode nanoindentation response of poly(methyl methacrylate) surfaces

Indentation is a comparatively simple and virtually nondestructive method of determining mechanical properties of material surfaces by means of an indenter inducing a localized deformation. The paper present experimental results of the load-displacement curves, the hardness and the elastic modulus data, and associated analysis for poly(methyl methacrylate) (PMMA) surfaces as a function of contact displacement. The experimental results include continuous stiffness indentations performed using constant loading rate and constant displacement rate experiments. The continuous stiffness indentation involves continuous calculation of a material stiffness, and hence hardness and elastic modulus of surfaces, during discrete loading-unloading cycles, as in a conventional indentation routine, and in a comparatively smaller time constant. The dependence of the compliance curves, the hardness, the elastic modulus and the plasticity index upon the imposed penetration depth, the applied normal load and the deformation rate are described. Tip area and load frame calibrations for the continuous stiffness indentation are also reported. The paper includes practical considerations encountered during indentation of polymers specifically at low penetration depths. The experimental results show a peculiarly harder response of PMMA surfaces at the submicron (near to surface) layers.     

The effects of pile-up,viscoelasticity and hydrostatic stress on polymer matrix nanoindentation

It is well known that a clear disparity exists between the elastic modulus determined using macroscopic tensile testing of polymers and those determined using nanoindentation, with indentation moduli generally overestimating the elastic modulus significantly. The effects of pile-up, viscoelasticity and hydrostatic stress on the indentation modulus of an epoxy matrix material are investigated. An analysis of residual impressions using scanning probe microscopy indicates that material pile-up is insignificant. Viscous effects are negated by increasing the time on the sample during the loading/hold segment phases of the indentation test, and by calculating the contact stiffness at a drift-insensitive point of the unloading curve. Removing the effects of viscous deformation reduces the modulus by 10–13%, while also significantly improving the non-liner curve fitting procedure of the Oliver and Pharr method. The effect of hydrostatic stress on the indentation modulus is characterised using relations from literature, reducing the measured property by 16%. Once viscous and hydrostatic stress effects are accounted for, the indentation modulus of the material compares very well with the bulk tensile modulus, and modifications to standard indentation protocols for polymers are proposed.     

RECENT PROGRESS OF NANO-MECHANICAL MAPPING

Nano-mechanical mapping by atomic force microscopy has been developed as an useful application to measure mechanical properties of soft materials at nanometer scale.To date,the Hertzian theory was used for analyzing force- distance curves as the simplest model among several contact mechanics between elastic bodies.However,the preexisting methods based on this theory do not consider the adhesive interaction in principle,which cannot be neglected in the ambient condition.A new analytical method was introdu...     

RECENT PROGRESS OF NANO-MECHANICAL MAPPING

 Nano-mechanical mapping by atomic force microscopy has been developed as an useful application to measure mechanical properties of soft materials at nanometer scale. To date, the Hertzian theory was used for analyzing force-distance curves as the simplest model among several contact mechanics between elastic bodies. However, the preexisting methods based on this theory do not consider the adhesive interaction in principle, which cannot be neglected in the ambient condition. A new analytical method was introduced to estimate the elasticity and the adhesive energy simultaneously by means of the JKR theory, describing adhesive contact between elastic materials. Poly(dimethylsiloxane) (PDMS) and isobutylene-co-isoprene rubber (IIR) were analyzed to verify the applicable limit of the JKR analysis. For elastic samples such as PDMS, the force-deformation plots obtained experimentally were consistent with JKR theoretical curves. Meanwhile, for viscoelastic samples, especially for IIR, the experimental plots revealed large deviations from JKR curves depending on scanning velocity and maximum loading force. Some nano-rheological arguments were employed based on the difference between these specimens.     

Using the adhesive interaction between atomic force microscopy tips and polymer surfaces to measure the elastic modulus of compliant samples

An atomic force microscope (AFM) method for measuring surface elasticity based on the adhesive interactions between an AFM tip and sample surfaces is introduced. The method is particularly useful when there is a large adhesion between the tip and soft samples, when the indentation method would be less accurate. For thin and soft samples, this method will have much less interference from the substrate than is found using the indentation method because there is only passive indentation induced by tip-sample adhesion; in contrast, a large indentation with a sharp tip in the sample may break its stress-strain linearity, or even make it fracture. For the case where it is difficult to accurately locate the tip-sample contact point, which is problematic for the indentation method, the method based on adhesive interactions is helpful because it does not require locating the tip-sample contact point when fitting the whole retraction force curve. The model is tested on PDMS polymers with different degrees of cross-linking.     

Young's modulus and loss tangent measurement of polydimethylsiloxane using an optical lever

In this article, the Young's modulus and the loss tangent of polydimethylsiloxane (PDMS) is obtained in the frequency range between 10 and 1500 Hz using an optical technique. The first three mechanical modes of vibrating PDMS beams are detected by measuring the tip rotational displacement using an optical lever. The experiments are carried out for 10:1 and 20:1 volume mixing ratios between the polymer base and the curing agent. The experimental results show that the Young's modulus varies between 1 and 2.6 MPa for 10:1 while its values are between 0.6 and 1.1 MPa for 20:1. The loss tangent is between 0.2 and 0.4 for 10:1 and 0.2 and 0.5 for 20:1. However, the measured values of the loss tangent are greater than the values reported in ref. 13. We also found that if the PDMS is not cured properly, its mechanical properties are time dependent. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 747–751     

"Contact" of nanoscale stiff films

We investigated the contact behaviors of a nanoscopic stiff thin film bonded to a compliant substrate and derived an analytical solution for determining the elastic modulus of thin films. Microscopic contact deformations of the gold and polydopamine thin films (<200 nm) coated on polydimethylsiloxane elastomers were measured by indenting a soft tip and analyzed in the framework of the classical plate theory and Johnson-Kendall-Roberts (JKR) contact mechanics. The analysis of this thin film contact mechanics focused on the bending and stretching resistance of thin films and is fundamentally different from conventional indentation measurements where the focus is on the fracture and compression of the films. The analytical solution of the elastic modulus of nanoscopic thin films was validated experimentally using 50 and 100 nm gold thin films coated on polydimethylsiloxane elastomers. The technical application of this analysis was further demonstrated by measuring the elastic modulus of thin films of polydopamine, a recently discovered biomimetic universal coating material. Furthermore, the method presented here is able to quantify the contact behaviors of nanoscopic thin films, effectively providing fundamental design parameters, the elastic modulus, and the work of adhesion, crucial for transferring them effectively into practical applications.     

Nanoscale hydrophobic recovery: A chemical force microscopy study of UV/ozone-treated cross-linked poly(dimethylsiloxane)

Chemical force microscopy (CFM) in water was used to map the surface hydrophobicity of UV/ozone-treated poly(dimethylsiloxane) (PDMS; Sylgard 184) as a function of the storage/recovery time. In addition to CFM pull-off force mapping, we applied indentation mapping to probe the changes in the normalized modulus. These experiments were complemented by results on surface properties assessed on the micrometer scale by X-ray photoelectron spectroscopy and water contact-angle measurements. Exposure times of < or = 30 min resulted in laterally homogeneously oxidized surfaces, which are characterized by an increased modulus and a high segmental mobility of PDMS. As detected on a sub-50-nm level, the subsequent "hydrophobic recovery" was characterized by a gradual increase in the pull-off forces and a decrease in the normalized modulus, approaching the values of unexposed PDMS after 8-50 days. Lateral imaging on briefly exposed PDMS showed the appearance of liquid PDMS in the form of droplets with an increasing recovery time. Longer exposure times (60 min) led to the formation of a hydrophilic silica-like surface layer. Under these conditions, a gradual surface reconstruction within the silica-like layer occurred with time after exposure, where a hydrophilic SiOx-enriched phase formed < 100-nm-sized domains, surrounded by a more hydrophobic matrix with lower normalized modulus. These results provide new insights into the lateral homogeneity of oxidized PDMS with a resolution in the sub-50-nm range.     

Measurement of residual stresses in polymeric parts by indentation method

An indentation method was studied as a means of measuring the residual stress in an injection molded polymeric specimen because destructive methods restrict the reuse of measured parts and it is not possible to apply them to small and complicated parts. The load-displacement curve was measured for indentation at stressed and non-stressed positions. Residual stress distribution of the injection molded part was calculated by comparing the load-displacement curve results with respect to the indentation depth. The residual stresses measured by the indentation method were reliable because they were in good agreement with numerical results and those measured by the hole drilling method. The indentation method can be utilized to measure the residual stresses in polymeric parts for practical applications, particularly for small or complicated parts.     

Application of the JKR Method to the Measurement of Adhesion to Langmuir-Blodgett Cellulose Surfaces

The JKR method has been applied for studying adhesion between poly(dimethylsiloxane) (PDMS) caps and Langmuir–Blodgett cellulose surfaces including the substrate, hydrophobized mica, and two flat mineral surfaces, bare mica and glass. The self-adhesion of PDMS caps and oxidized PDMS caps are included as a reference to compare with literature data. The results of the measurements have been compared with previous studies using the surface force apparatus and similar systems. A satisfactory agreement is obtained for simple systems showing no, or very limited, hysteresis between loading and unloading curves. In several cases, however, a large hysteresis is found between loading and unloading curves, with a larger adhesion measured from the pull-off force than from the JKR-curve determined on loading. This is, for instance, the case for PDMS against cellulose. The situation is analogous to that found in wetting studies showing a large hysteresis between advancing and receding contact angles.     

Quantitative lateral force microscopy study of the dolomite (104)-water interface

The friction and lateral stiffness of the contact between an atomic force microscopy (AFM) probe tip and an atomically flat dolomite (104) surface were investigated in contact with two aqueous solutions that were in equilibrium and supersaturated with respect to dolomite, respectively. The two aqueous solutions yielded negligible differences in friction at the native dolomite-water interface. However, the growth of a Ca-rich film from the supersaturated solution, revealed by X-ray reflectivity measurements, altered the probe-dolomite contact region sufficiently to observe distinct friction forces on the native dolomite and the film-covered surface regions. Quantitative friction-load relationships demonstrated three physically distinct load regimes for applied loads up to 200 nN. Similar friction forces were observed on both surfaces below 50 nN load and above 100 nN load. The friction forces on the two surfaces diverged at intermediate loads. Quantitative measurements of dynamic friction forces at low load were consistent with the estimated energy necessary to dehydrate the surface ions, whereas differences in mechanical properties of the Ca-rich film and dolomite surfaces were evidently important above 50 nN load. Attempts to fit the quantitative stiffness-load data using a Hertzian contact mechanical model based on bulk material properties yielded physically unrealistic fitting coefficients, suggesting that the interfacial contact region must be explicitly considered in describing the static and dynamic contact mechanics of this and similar systems.     

Forces between a stiff and a soft surface

The contact between a sphere and a planar half space, one being rigid and the other elastic (or between two elastic spheres), can be described by the JKR theory of Johnson, Kendall and Roberts (Proc. R. Soc. Lond. A 1971, 324, 301). One assumption of JKR theory is that the characteristic length scale L ≈ w/E is much smaller than the radius R of the sphere; where w is the work of adhesion and E is the Young's modulus of the soft, elastic body. Relative deformations for a mechanical contact increase with increasing L and decreasing particle size R. Experiments show that up to at least L/R = 0.2, JKR theory predicts the correct dependencies between the contact radius, the indentation and the load. However, when R ≫ L is no longer satisfied, the change in total free surface area due to deformation needs to be considered. Then, elastocapillary effects start playing a significant role. In addition to discussing theory and experiments of pure solid contacts, the effect of elastic deformation on capillary and hydrodynamic forces is discussed. Finally, we consider the interaction of hollow capsules as one example of a deformable body that is still formed from a stiff material.     

Porosity‐dependent Young's modulus of membranes from polyetherether ketone

The porosity‐dependent Young's modulus for PEEK membranes was determined and the data compared to several empirical and semiempirical equations often applied to porous systems. The Spriggs equation, Wang's approximation, Sudduth's equation, and the foam modulus‐density relationship were all tested against the data. The relatively wide range of porosities tested in these experiments shows the Spriggs equation to be inadequate to fitting the data, especially above 50% porosity where the Young's modulus decreases rapidly. Wang's approximation to second order fitted the data well, and the porosity‐modulus relations had non‐negative coefficients as required and consistent with the ceramic data obtained by others. The data also fitted Sudduth's equations, usually applied to sintered ceramics, but equivalently good fits were obtained with nonunique fitting parameters. The foam modulus‐density relationship fitted the data for foamlike membranes but fitted less well to nonfoam morphology membranes. Finally, the data were used to determine the range of porosities and hollow fiber dimensions necessary for microfiltration and composite membrane application. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1168–1174, 2003