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.     

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.     

"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.     

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.     

Forced detachment of immersed elastic rubber beads

We investigate the strength of adhesion and the dynamics of detachment of elastic beads (Young's modulus E approximately 1 MPa) adhering to a horizontal solid surface in a viscous liquid. The beads are initially compressed on the surface. Their unbinding is imposed by fast vertical stretching (above a certain threshold value). The decrease in the contact radius is monitored by interferential microscopy. We find that the dynamics of detachment involves three steps: (i) fast elastic decompression, (ii) slow adhesive detachment, and (iii) catastrophic rupture. They can be interpreted by a transfer of the Johnson Kendall Roberts (JKR) energy toward viscous losses in the liquid wedge, near the rubber/solid/liquid (R/S/L) contact line.     

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.     

Colloidal aggregate micromechanics in the presence of divalent ions

Colloidal gels exhibit rheological properties, such as a yield stress and elasticity, which arise from the manner in which stress is transmitted through the microstructure. Insight into the mechanisms of stress transmission is critical in developing a full understanding of the mechanics of these materials. Paramount to this is a thorough knowledge of the interparticle interactions. In this work, we use optical trapping to study interactions between poly(methyl methacrylate) (PMMA) particles in adhesive contact by measuring the bending elasticity of directly assembled colloidal aggregates under various physicochemical conditions. The simplified geometry of the aggregate enables us determine the single-bond rigidity, which can then be related to the work of adhesion, W(SL), through the Johnson-Kendall-Roberts (JKR) theory of adhesion. We find that W(SL) is independent of ionic strength in flocculating monovalent salt solutions. However, more complex behavior is observed for divalent salts. Using zeta-potential measurements, we show that divalent cations adsorb to the particle surface. This results in the formation of ionic bridges between particles in adhesive contact. A model of the aggregate micromechanics that considers the divalent ion contribution to the surface energy provides a direct link between the interfacial properties of the particles, nanoscale contact interactions between particles, and the bulk gel modulus.     

Measurement of interfacial adhesion between glassy polymers using the JKR method

The surface and interfacial energies of polymers are measured using the JKR-type experiments. A novel method has been developed to prepare samples of glassy polymers for adhesion measurements. A thin layer of a polymer is coated on the surface of an O₂-plasma modified cross-linked poly(dimethylsiloxane) [PDMS] spherical cap resulting in the formation of a composite. Using the JKR theory, the surface energies of polystyrene [PS] and poly(methyl methacrylate) [PMMA] are determined from the measurements of the contact radius as a function of applied load. The results of the JKR-type experiments are compared to adhesion measurements done using the surface forces apparatus (SFA). Adhesion hysteresis was observed for PS-PS contact as well as PMMA-PMMA contact. However, no hysteresis was observed for PDMS-PDMS, PDMS-PS, and PDMS-PMMA contacts. The exact origin of the hysteresis is not clear at present. The current evidence suggests that hysteresis is due to rearrangement of the interface during contact.     

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.     

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.     

The mechanics of contact and adhesion of periodically rough surfaces

An analytical model based on the Johnson–Kendall–Roberts (JKR) theory of adhesion was used to study the contact mechanics and adhesion of periodically rough surfaces. The relation of the applied load to the contact area and the work of adhesion W was found in closed form for arbitrary surface profiles. Our analysis showed that when the parameter [where α* is a numerical constant of order one, β is the aspect ratio of a typical surface profile (or asperity), and ρ is the number of asperities per unit length], the surfaces will jump into contact with each other with no applied load, and the contact area will continue to expand until the two surfaces are in full contact. The theory was then extended to the non‐JKR regime in which the region where the surface forces act is no longer confined to a small region near the contact zone. Exact solution was also obtained for this case. An exact analysis of the effect of entrapped air on the mechanics of adhesion and contact was also enacted. The results showed that interaction between asperities should be taken into consideration in contact‐mechanics models of adhesion or friction. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 1195–1214, 2001     

Direct determination of interfacial energy between brittle and polymeric films

Very few analyses exist for determining the adhesion f thin brittle films in the micron range on low modulus polymeric substrates. A theoretical model and experimental means are developed to determine the adhesion for this situation using the concept of fracture mechanics and Griffith's energy criterion. An expression for the adhesion is derived in terms of the external loading, material constants, and thicknesses of the films. The model is compared with measurements of brittle films vacuum deposited onto polymeric substrates. Excellent agreement is obtained and interfacial energies are calculated. Since the moduli of thin films are very difficult to determine accurately, the effect of a variation in measurements of this material parameter on the adhesion is calculated. The effect of varying preparative conditions is also discussed.     

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.     

Effects of flame treatment on the interfacial energy of polyethylene assessed by contact mechanics

The effects of flame treatment of low-density polyethylene (LDPE) on the work of adhesion (W) and energy release rate (G) were assessed by a custom-built adhesion testing device (ATD). The contact area and the vertical displacement between planar LDPE films and PDMS lenses (untreated and UV/ozone treated) were varied as a function of the applied load, P. The adhesion and pull-off forces between the extracted PDMS lenses and the LDPE films were studied as a function of the duration of the flame treatment expressed in treatment numbers. A fracture mechanics approach was used to relate the applied load and the radius of the contact area to the energy release rate (G). The difference between the energy release rate and the thermodynamic work of adhesion, defined as the adhesion hysteresis (G - W), increased systematically with increasing treatment numbers for both lens types. In addition, the adhesion hysteresis appeared to be dependent on the contact time. Finally, the origin of the adhesion hysteresis was discussed. It was concluded that bonding by surface functional groups may be the dominating mechanisms for the changes in the observed hysteresis.     

Some aspects of AFM nanomechanical probing of surface polymer films

We analyzed how the approach developed for the microindentation of non-uniform elastic solids can be adapted to analyze the atomic force microscopy (AFM) probing of ultrathin (1-100 nm thick) polymer films on a solid substrate, as well as polymer films with a multilayered structure. We suggested that recent Johnson's modification of the contact mechanics model that included a viscoelastic contribution could also be utilized to analyze rate-dependent loading data for polymer surfaces. The graded model proposed for microindentation experiments was modified allowing to account not only for variable elastic moduli within different layers but also for the gradient of properties between layers within a transition zone. Two examples of a recent application of this model for molecularly thick hyperbranched polymer monolayers (<3 nm thick) and tri-layered polymer films (20-40 nm thick) tethered to a solid substrate were presented and discussed. In both cases, complex shapes of both loading curves and elastic modulus depth profiles obtained from experimental AFM data were successfully fitted by the graded model with realistic structural parameters.     

Correlations between adhesion hysteresis and friction at molecular scales

Correlations between adhesion hysteresis and local friction are theoretically and experimentally investigated. The model is based on the classical theory of adhesional friction, contact mechanics, capillary hysteresis, and nanoscale roughness. Adhesion hysteresis was found to scale with friction through the scaling factor containing a varying ratio of adhesion energy over the reduced Young's modulus. Capillary forces can offset the relationship between adhesion hysteresis and friction. Measurements on a wide range of engineering samples with varying adhesive and elastic properties confirm the model. Adhesion hysteresis is investigated under controlled, low humidity atmosphere via ultrasonic force microscopy. Friction is measured by the friction force microscopy.     

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     

Determination of solid surface tension from particle-substrate pull-off forces measured with the atomic force microscope

Atomic force microscopy (AFM) is capable of solid surface characterization at the microscopic and submicroscopic scales. It can also be used for the determination of surface tension of solids (gamma) from pull-off force (F) measurements, followed by analysis of the measured F values using contact mechanics theoretical models. Although a majority of the literature gamma results was obtained using either Johnson-Kendall-Roberts (JKR) or Derjaguin-Muller-Toporov (DMT) models, re-analysis of the published experimental data presented in this paper indicates that these models are regularly misused. Additional complication in determination of gamma values using the AFM technique is that the measured pull-off forces have poor reproducibility. Reproducible and meaningful F values can be obtained with strict control over AFM experimental conditions during the pull-off force measurements (low humidity level, controlled and known loads) for high quality substrates and probes (surfaces should be free of heterogeneity, roughness, and contamination). Any probe or substrate imperfections complicate the interpretation of experimental results and often reduce the quality of the generated data. In this review, surface imperfection in terms of roughness and heterogeneity that influence the pull-off force are analyzed based upon the contact mechanics models. Simple correlations are proposed that could guide in selection and preparation of AFM probes and substrates for gamma determination and selection of loading conditions during the pull-off force measurements. Finally, the possibility of AFM measurements of solid surface tension using materials with rough surfaces is discussed.