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.     

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.     

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.     

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.     

Oscillatory loading of a viscoelastic adhesive contact

The cycle of loading and unloading of a spherically-tipped probe against an adhesive, viscoelastic plane specimen is studied by numerical integration of the relations between crack speed and apparent surface energy previously found for a linear 3-element viscoelastic solid with a Maugis-Dugdale law of force across the crack. It is found that even when the rate of loading is so slow that the loading and unloading curves almost coincide, suggesting purely elastic behaviour, the pull-off force can be appreciably greater than the elastic (JKR) value. When the normal force is modulated with a small amplitude sinusoidal variation during unloading--in order to find the contact stiffness--the contact radius barely changes, and the stiffness is close to that for a rigid flat punch instead of having the expected JKR value.     

Effect of large deformation and material nonlinearity on the JKR (Johnson–Kendall–Roberts) test of soft elastic materials

We study in detail the effect of large deformation and material nonlinearity on the JKR (Johnson–Kendall–Roberts) theory of adhesive contact for two systems. The first is a Neo‐Hookean hemisphere in adhesive contact with a smooth rigid substrate. The second is a smooth rigid spherical indenter in adhesive contact with a Neo‐Hookean half space. We show that our results are special cases of a general theory that models large deformation adhesive contact of spherical lenses. This theory shows that the solution of any large deformation JKR (LDJKR) problem can be obtained from the solution of a corresponding large deformation Hertz (LDH) problem. Using this theory, we extend the small strain JKR theory to the large deformation regime, the only restriction being that the materials are nonlinear elastic or hyperelastic. The adhesive contact problem for the two systems is solved using two methods. In method one, the LDJKR theory is obtained using finite element simulation results for a corresponding LDH problem; in method two, we solve the adhesive contact problems directly using a cohesive zone model to quantify adhesive interaction. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2912–2922, 2006     

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     

A comparison of JKR-based methods to analyze quasi-static and dynamic indentation force curves

The Johnson-Kendall-Roberts (JKR) theory of elastic contact, extended to take viscoelastic effects into account, is used to evaluate work of adhesion and modulus of elastomeric films. In this paper, we present a comparison of five approaches to analyze quasi-static and dynamic JKR force curve data obtained using instrumented indentation. The load-displacement experiments were performed using a 200-microm radius borosilicate glass sphere against poly(dimethyl siloxane) (PDMS). By applying a small oscillation to the tip during indentation, dynamic stiffness vs load data were also obtained for frequencies between 25 and 160 Hz. Direct curve fitting as well as simplified 2- and 3-point analysis methods were used to compare modulus values obtained from load-displacement and stiffness-load data. Fit methods not requiring determination of the initial point of tip-sample contact ("zero" displacement) provided modulus values closest to those obtained by direct curve fitting. The dynamic stiffness-load data revealed a frequency dependent modulus; load-displacement measurements obtained simultaneously were consistent with the relaxed, or low-frequency, modulus of the PDMS sample. These experiments demonstrate that both the frequency dependent and relaxed modulus can be obtained from a single experiment.     

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.     

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.     

Super-hydrophobic, highly adhesive, polydimethylsiloxane (PDMS) surfaces

Super-hydrophobic surfaces have been fabricated by casting polydimethylsiloxane (PDMS) on a textured substrate of known surface topography, and were characterized using contact angle, atomic force microscopy, surface free energy calculations, and adhesion measurements. The resulting PDMS has a micro-textured surface with a static contact angle of 153.5° and a hysteresis of 27° when using de-ionized water. Unlike many super-hydrophobic materials, the textured PDMS is highly adhesive, allowing water drops as large as 25.0 μL to be inverted. This high adhesion, super-hydrophobic behavior is an illustration of the "petal effect". This rapid, reproducible technique has promising applications in transport and analysis of microvolume samples.     

A generalized analytical model for the elastic deformation of an adhesive contact between a sphere and a flat surface

A new method to calculate the elastic deformation of a sphere on a flat surface is presented. The model considers the influence of short-range as well as long-range attractive forces both inside and outside the actual contact area. In contrast to earlier models, this theory describes the nature of these deformations in the intermediate regime between the so-called JKR and DMT limits by simple analytic expressions. Equations for the calculation of the contact radius, the deformation, and the pressure distribution are given. In all equations, the critical force that might vary between the limiting values found in the DMT and the JKR model acts as transition parameter.     

Adhesive Contact Deformation of a Single Microelastomeric Sphere

This paper reports on an experimental study of the adhesive contact of a single microscopic (about 300 μm) elastomer sphere compressed between two smooth parallel glass platens at small imposed deformations. An experimental arrangement that allows the simultaneous measurement of the compressive displacements and the reaction forces is described. A number of interesting phenomena, including the pull-off separation and the “jump” contact phenomena of the microsphere and the moving platen supported by a cantilever, are shown in the experimental force-displacement curve of a loading and unloading cycle. The pull-off forces are demonstrated to not depend upon the applied dimensionless approach (compressive displacement/initial particle diameter), while they increase with the increasing rate at which the interfaces are separated. The predictions of an established contact mechanical adhesive theory, Johnson–Kendall–Roberts (JKR) theory, in which the influence of the surface energy on the contact has been taken into account, are in good agreement with these experimental results. An application of the JKR analysis to the pull-off force provides a reasonable estimate of the interfacial free energy of the contact.     

An elastic-plastic hybrid adhesion model for contacting rough surfaces in the presence of molecularly thin lubricant

The study of adhesion has received considerable attention in recent years, partly due to advances in the design and fabrication of micro/nano devices. Many adhesion investigations are centered on single-spherical-contact models, which include the classic Johnson-Kendall-Roberts (JKR), improved Derjaguin-Muller-Toporov (IDMT), and Maugis-Dugdale (MD) models. Based on the IDMT single-asperity model, adhesive rough surface contact models have also been developed, which are valid for elastic and elastic-plastic contact conditions. A limitation of the IDMT-based models is that they are only valid for application cases with low adhesion parameter values. In this research, a contacting rough surface adhesion model was developed by combining an extended Maugis-Dugdale (EMD) model (which is only valid for elastic contacts) with an IDMT-based elastic-plastic adhesion model. The proposed model, termed the elastic-plastic hybrid adhesion model, is valid for the entire adhesion parameter range and also for elastic-plastic contacts. The proposed model gives results similar to the EMD rough surface model when the contact is primarily elastic. Moreover, the proposed model was compared to an IDMT-based model (ISBL model) and both gave similar results for contacts with low adhesion parameter values. With high adhesion parameter values, the ISBL model fails, whereas the proposed model correctly predicts higher adhesion. Last, based on the stiffness of the external force, the instability for adhesive rough surfaces in contact was also discussed, and it was postulated that a high peak value of the external force stiffness directly relates to the unstable contact process.     

Multiasperity contact adhesion model for universal asperity height and radius of curvature distributions

A new approach to the multiasperities contact interaction between two surfaces is presented. Each asperity is individually considered with its own different height and radius of curvature. Different materials, such as polyvinylchlorine (PVC) and stainless steel, are used as model systems. For each of the model materials, a set of asperities was generated using Monte Carlo method. Both asperity heights and radii were based on their statistical distributions experimentally obtained. Contact forces were determined for each asperity at a given distance between the two surfaces, while the deformation of each asperity was calculated according to the Johnson-Kendall-Roberts (JKR) or the Derjaguin-Muller-Toporov (DMT) model (depending on the material). The contribution of each asperity to the overall surface was summed, and the overall contact force was determined. The developed method was validated against contact force measurements obtained with atomic force microscopy (AFM).     

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.     

Mechanical and thermodynamic properties of surfactant aggregates at the solid-liquid interface

Surfactants are widely used to stabilize colloidal systems in a variety of industrial applications through the formation of self-assembled aggregates at the solid-liquid interface. Previous studies have reported that the control of surfactant-mediated slurry stability can be achieved through the manipulation of surfactant chain length and concentration. However, a fundamental understanding of the mechanical and energetic properties of these aggregates, which may aid in the molecular-level design of these systems, is still lacking. In this study, experimentally measured force/distance curves between an atomic force microscope (AFM) tip and self-assembled surfactant aggregates on mica or silica substrates at concentrations higher than the bulk critical micelle concentration (CMC) were used to determine their mechanical and thermodynamic properties. The experimental curves were fitted to a model which describes the interaction between a hard sphere (tip) and a soft substrate (surfactant structures) based on a modified Hertz theory for the case of a thin elastic layer on a rigid substrate. The calculated mechanical properties were found to be in the same order of magnitude as those reported for rubber-like materials (e.g., polydimethylsiloxane (PDMS)). By integrating the force/distance curves, the energy required for breaking the surface aggregates was also calculated. These values are close to those reported for bulk-micelle formation.     

阵列凹坑结构分布与水滴黏附性质的关系

以新鲜玫瑰花花瓣正面为模板, 采用模板印刷法制备具有微米级阵列凹坑和纳米级沟壑结构的聚二甲基硅氧烷(PDMS)薄膜, 通过对该薄膜逐级拉伸改变其微观结构的分布; 采用场发射扫描电子显微镜(SEM)和原子力显微镜(AFM)观察了不同拉伸程度下薄膜表面微观结构的变化, 采用高敏感性微电力学天平测试了样品表面微观结构变化过程中水滴的黏附力, 分析了其微观结构分布与水滴黏附性质的关系; 采用接触角测量仪表征不同拉伸条件下薄膜的浸润性. 结果表明, 随着PDMS薄膜被逐次拉伸, 单位面积内的凹坑结构数目减少, 且凹坑逐渐分离, 凹坑的深度逐渐降低, 水滴更容易浸入到凹坑结构中, 因此水滴与薄膜的黏附力急剧增大; 随着薄膜进一步拉伸, 纳米级沟壑结构会随着凹坑的拉伸而不断伸展, 纳米级沟壑结构的面积增加, 纳米沟壑结构诱捕的空气量逐渐上升, 导致水滴与薄膜表面的接触面积降低, 使得水滴与薄膜的黏附力下降; 继续拉伸PDMS薄膜, 纳米级沟壑结构进一步伸展, 水滴逐渐浸入纳米级沟壑结构中, 水滴与薄膜的黏附力缓慢增大, 当水滴完全进入到纳米级沟壑中时, 水滴与薄膜的黏附力达到极大值, 此时继续拉伸PDMS薄膜, 纳米级沟壑结构随着拉伸程度的增加继续伸展, 水滴与薄膜的接触面积稍有减少, 黏附力将有所下降, 直至薄膜被完全破坏. 由此可见, 微米级凹坑结构和纳米级褶皱结构的分布是影响PDMS薄膜对水滴黏附性质的主要因素.     

Comparison of the adhesion forces in single and double-layer coatings on the MEMS surfaces by JKR and DMT models

In many medical and industrial applications, some strategies are needed to control the adhesion forces between the materials, because surface forces can activate or hinder the function of the device. All actual surfaces present some levels of roughness and the contact between two surfaces is transferred by the asperities on the surfaces. The force of the adhesion, which depends on the operating situations, can be influenced by the contact region. The aim of the present study is to predict the adhesion force in MEMS surfaces using the JKR and DMT models. The surfaces of the coating material in this research consisted of the single-layer coating of Gold and Silver, and the double-layer coating of TiO₂/Gold and TiO₂/Silver on the silicon (100) substrates. The depositing was done by the thermal evaporation method. The results showed that the double-layer coating developed by the new deposition method helped the reduction of the adhesion forces between the probe tip and the specimen surface. The predicted adhesion forces between the probe and the specimens with DMT and JKR models were compared with the experimental results. For all specimens, the simulated data by applying the JKR theory were in a good agreement with the adhesion force experimental values.     

超疏水性聚二甲基硅氧烷膜的制备及其表面吸附性研究

采用简单的激光刻蚀方法制备了具有类“菜花”状多级结构的粗糙聚二甲基硅氧烷(PDMS)膜, 并用CCD与高敏感性微电力学天平观察和测量PDMS表面对水的吸附情况. 结果表明, 该膜表面具有超疏水性, 同时对水滴具有超低的吸附力. 还对其表面特殊多级结构产生的机理进行了分析, 并探讨了在化学组成和表面结构对超疏水性以及吸附性产生的影响.