Bonding of a viscoelastic periodic rough surface to a rigid layer

A theoretical analysis is performed for the study of the bonding of a viscoelastic rough surface to a rigid substrate. The mechanics of contact and adhesion are studied with the Dugdale–Barenblatt model for surface interaction. Exact solutions are obtained for arbitrary surface profiles and loading histories. Detailed solutions are given for a power‐law viscoelastic material. This solution is used to determine the time for the self‐bonding of surfaces (solid sintering under zero load). The time to self‐bonding is shown to be extremely sensitive to the aspect ratio of the asperities. A closed form expression is derived for the time needed to achieve full contact when the surfaces are compressed with a load that increases linearly with time. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 545–561, 2002; DOI 10.1002/polb.10113     

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     

How does tack depend on time of contact and contact pressure?

The tack of polymer melts on rigid substrates under conditions of short contact times and low pressures is examined. The substrate is modeled as a random rough surface with a distribution of asperities heights. The true contact area between the adhesive and the substrate is calculated for a given total load and elastic modulus of the substrate. The dependence of tack on contact time is accounted for by introducing the relaxation of the adhesive through a time-dependent elastic modulus. For relatively high pressures the tack is predicted to scale with 1/E so that for short contact times, t_c, the tack is predicted to scale with (t_c/τ_e)^1/2, where τ_e is the entanglement time. For lower pressures this simple scaling law is no longer valid and we predict a complex variation of tack with contact time and molecular parameters. © 1996 John Wiley & Sons, Inc.     

Tack properties of pressure‐sensitive adhesives

Relevant experiments are essential to clearly understand the role of various molecular (chemical structure, surface energy, composition), experimental (contact time, contact pressure, temperature) or topological (sample roughness and thickness) parameters, on the tack properties of pressure sensitive adhesives (PSA). The “mechano‐optical tack tester” (MOTT) is a novel device that we have developed to provide accurate measurements of both the contact area and the tack strength. The MOTT is designed to apply controlled contact pressures by mean of a quartz prism probe, for determined contact times, onto the surface of PSA samples. The probe is then pulled up at controlled rates while the tearing force (tack strength) and the contact area are plotted versus time. The tack energy is then calculated. Using the MOTT, the influence of various parameters (contact pressure, contact area, sample thickness, …) on the tack properties of PSA samples has been studied. The main result lies in the strong dependence of the tack energy on the sample thickness. This points out that the release energy is close to the interface rather than in the bulk of the PSA films, and is a function of the contact area. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1201–1208, 2000     

Viscoelastic modeling of nanoindentation experiments: A multicurve method

Nanoindentation is an increasingly used method of extracting surface mechanical properties of viscoelastic materials, especially polymers. Recently, Hutcheson and McKenna used a viscoelastic contact mechanics model to analyze the contact problem between a nanosphere and polystyrene surface. In nanoindentation experiments, the ramp loading test is a similar problem to the particle embedment experiment except that the indentation load function differs. The motivation in this work is to expand the Hutcheson and McKenna analysis to the nanoindentation problem. In particular, we illustrate the limitations of analyzing only a single load‐indentation curve, which does not provide enough information to determine the full range of the viscoelastic response of a polymer, and we show that performing a test sequence that includes multiple loading rates or indentation rates spanning two or more orders of magnitude greatly improves the extracted viscoelastic properties. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 633–639     

Mechanics of contact and adhesion between viscoelastic spheres: An analysis of hysteresis during loading and unloading

Detailed finite element simulations are carried out to study the adhesive contact of viscoelastic spheres. The spheres are brought into contact by a compressive force that increases at a constant rate. Upon reaching a maximum load, the spheres are unloaded until they separate. We studied in detail the effect of loading and unloading rates on hysteresis and on the pull‐off force for a standard viscoelastic solid. The surface interaction is modeled by the Dugdale–Barenblatt model. Numerical results are compared with analytical models for bonding and debonding, including a recent theory proposed by Johnson. There is excellent agreement between analytical and finite element results for the bonding phase. However, for the debonding phase, current analytical models break down unless the loading and unloading rates are slow in comparison with the material relaxation time. Based on the finite element results, a simple approximate analytical model is proposed to quantify adhesive contact in the debonding phase. We also examine the dependence of hysteresis on interfacial parameters such as the cohesive strength and the intrinsic work of adhesion. Our results show that viscoelastic adhesive contact depends on the details of the surface interaction and cannot be determined solely by the work of adhesion. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 772–793, 2002     

Contact area between a viscoelastic solid and a hard, randomly rough, substrate

We study the time-dependent contact area as a viscoelastic solid is squeezed against a randomly rough substrate. Using a recently developed contact mechanics theory we study how the contact area depends on time and on the magnification zeta. Numerical results are presented for self-affine fractal surfaces, and applications to tack, rubber friction, and sealing are given.     

An approximate model for the adhesive contact of rough viscoelastic surfaces

Surface roughness is known to easily suppress the adhesion of elastic surfaces. Here, a simple model for the contact of viscoelastic rough surfaces with significant levels of adhesion is presented. This approach is derived from our previous model (Barthel, E.; Haiat, G. Langmuir 2002, 18, 9362) for the adhesive contact of viscoelastic spheres. For simplicity, a simple loading/unloading history (infinitely fast loading and constant pull-out velocity) is assumed. The model provides approximate analytical expressions for the asperity response and exhibits the full viscoelastic adhesive contact phenomenology such as stress relaxation inside the contact zone and creep at the contact edges. Combining this model with a Greenwood-Williamson statistical modeling of rough surfaces, we propose a quantitative assessment of the adhesion to rough viscoelastic surfaces. We show that moderate viscoelasticity efficiently restores adhesion on rough surfaces over a wide dynamic range.     

Interplay between bulk viscoelasticity and surface energy in autohesive tack of rubber‐tackifier blends

The effects of change in surface energy and bulk viscoelastic properties on the autohesive tack strength of brominated isobutylene‐co‐p‐methylstyrene (BIMS) rubber have been investigated by the addition of hydrocarbon resin (HCR) tackifier and maleated hydrocarbon resin (MA‐g‐HCR) tackifier. The addition of compatible HCR tackifier results in a reasonable increment in the tack strength of BIMS rubber by modifying only the bulk viscoelastic properties (compliance, entanglement molecular weight, relaxation time, self‐diffusion, and monomer friction coefficient values) of BIMS rubber to perform better during the course of bonding and debonding steps of the peel test. Incorporation of MA‐g‐HCR tackifier (containing 5–20 wt % of grafted maleic anhydride) steadily increases the tack strength of BIMS rubber further by precisely modifying both the surface energy and bulk viscoelastic properties to perform much better in the bonding and debonding steps. However, beyond 20 wt % of grafted maleic anhydride in the HCR tackifier, the tack strength starts decreasing due to the incompatibility between the blend components, and hence, the bulk viscoelastic properties required for bond formation are severely retarded by the interrelated reinforcing effect and the phase separation effect of the brittle MA‐g‐HCR tackifier in the BIMS rubber. Hence, the polar groups in a tackifier will contribute to significant enhancement of autohesive tack strength only if the bulk viscoelastic property of the rubber‐tackifier blend is favorable for bond formation and bond separation. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 972–982, 2010     

Effect of surface tension on the relaxation of a viscoelastic half-space perturbed by a point load

We study the effect of surface tension on the flattening of a surface perturbed by a point load subsequent to its removal. The surface bounds an infinite isotropic linear viscoelastic incompressible half space. The point load is initially applied for a sufficiently long time so that the half space is fully relaxed before the load removal. An exact solution is obtained assuming small deformation. We then specialize our theory to the case of a standard viscoelastic solid. There is an initial reduction of the surface displacement immediately after load removal that is found to be directly proportional to the ratio of applied load to surface tension. This is followed by a temporal decay of the surface profile that depends only on the relaxation time and the long and short time moduli of the viscoelastic solid. Our work also provides the Green's function for a suddenly applied point load on the surface of a viscoelastic half space. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016, 54, 274–280     

Viscoelastic, mechanical, and dielectric measurements on complex samples with the quartz crystal microbalance

Piezoelectric resonators have been in use as mass-sensing devices for almost half a century. More recently it was recognized that shifts in frequency and bandwidth can come about by a diverse variety of interactions with the sample. The classical "load" consists of a thin film, which shifts the resonance frequency due to its inertia. Other types of loading include semi-infinite viscoelastic media, rough objects contacting the crystal via isolated asperities, mechanically nonlinear contacts, and dielectric films. All these interactions can be analyzed within the small-load approximation. The small-load approximation provides a unified frame for interpretation and thereby opens the way to new applications of the QCM.     

Use of the JKR model for calculating adhesion between rough surfaces

A simple method for using the JKR model to determine interfacial adhesion between two ideal rough surfaces is demonstrated for individual asperity-asperity and asperity-flat contacts both in air and in water. The model takes into account the effect of a modified contact area at separation due to viscoelastic effects. The equilibrium version of the model significantly underestimates the measured adhesion, whereas the viscoelastic version of the model is much closer to the measured data. The asperity-flat geometry used with the viscoelastic version of the model seems to fit the experimental results best. This was thought to be due to the unlikely occurrence of direct asperity-asperity contacts. Instead, it would seem that the asperities have a far higher chance of fitting between each other on opposing surfaces, leading to correspondingly higher pull-off forces measured on separation. Many possible extensions to the roughness model described here may be made, allowing a much-improved understanding of the contact mechanics between two rough surfaces.     

Criteria for entrapped gas under a drop on an ultrahydrophobic surface

Ultrahydrophobicity of a rough surface is mainly attributed to the entrapped gas under a drop. Two criteria were proposed for the entrapped gas: an intruding angle criterion and an intruding depth criterion. These two criteria are that the intruding angle must be less than the maximum asperity slope angle and the intruding depth must be less than the height of the asperities. The intruding angle is determined by the true contact angle, the surface geometry, and the drop size. The intruding angle is directly proportional to the true contact angle, and it increases with an increase of the fractional area of the liquid-gas interface under the drop and with a decrease of the linear dimension of the three-phase contact line on the asperities. The effect of the drop size on the intruding angle is induced by Laplace and hydrostatic pressures. The intruding depth increases with an increase of the intruding angle and the distance between the asperities. The proposed criteria were evaluated using experiment data from the literature. Comparison between the experiment and calculation results showed that the experiment data supported the theory.     

Flat‐punch indentation of viscoelastic material

The indentation of standard viscoelastic solids, that is, the three‐element viscoelastic material, by an axisymmetric, flat‐ended indenter has been investigated theoretically. Under the boundary conditions of flat‐punch indentation of a viscoelastic half‐space, the solutions of the equations of viscoelastic deformation are derived for the standard viscoelastic material. Their generality resides in their inclusion of compressible as well as incompressible solids. They cover the two transient situations: flat‐punch creep test and load‐relaxation test. In experimental tests of their applicability, nanoindentation and microindentation probes under creep and relaxation conditions yielded a modulus from 0.1 to 1.1 GPa and viscosity from 1 to 37 Gpa · s for a crosslinked glassy polyurethane coatings. For bulk polystyrene, the values vary from 1 to 2 GPa and from 20 to 40 Gpa · s, respectively. The analysis here provides a fundamental basis for probing elastic and viscous properties of coatings with nanoindentation or microindentation tests. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 10–22, 2000     

Mean-field theory of liquid droplets on roughened solid surfaces: application to superhydrophobicity

We present calculations of the density distributions and contact angles of liquid droplets on roughened solid surfaces for a lattice gas model solved in a mean-field approximation. For the case of a smooth surface, this approach yields contact angles that are well described by Young's equation. We consider rough surfaces created by placing an ordered array of pillars on a surface, modeling so-called superhydrophobic surfaces, and we have made calculations for a range of pillar heights. The apparent contact angle follows two regimes as the pillar height increases. In the first regime, the liquid penetrates the interpillar volume, and the contact angle increases with pillar height before reaching a constant value. This behavior is similar to that described by the Wenzel equation for contact angles on rough surfaces, although the contact angles are underestimated. In the second regime, the liquid does not penetrate the interpillar volume substantially, and the contact angle is independent of the pillar height. This situation is similar to that envisaged in the Cassie-Baxter equation for contact angles on heterogeneous surfaces, but the contact angles are overestimated by this equation. For larger pillar heights, two states of the droplet can be observed, one Wenzel-like and the other Cassie-like.     

Microscopic interpretation of the dependence of the contact angle on roughness

The macroscopic contact angle theta(m) of a liquid drop on a rough solid surface in the presence of a gas is calculated microscopically on the basis of a variational minimization of the total potential energy of the drop. Two limiting cases are considered: the liquid penetrates into the space between asperities (Wenzel regime) and the liquid resides on the top of asperities (Cassie-Baxter regime). Long-range as well as short-range interactions between the molecules of liquid, solid, and gas are taken into account. It was also assumed that small portions of insoluble gas are accumulated near the edges of the asperities during the formation of the droplet. The contact angle depends on several parameters involved in the microscopic interactions as well as on the fractions of solid surface between asperities, and of the surface of the asperities themselves, that are in contact with the liquid. It is shown that the theory can explain the nonlinear dependence of cos theta(m) on roughness observed by Krupenkin et al. [Krupenkin, T. N.; Taylor, J. A.; Schneider, T. M.; Yang, S. Langmuir 2004, 20, 3824].(1).     

Roughness models for particle adhesion

The effects of different surface roughness models on a previously developed van der Waals adhesion model were examined. The van der Waals adhesion model represented surface roughness with a distribution of hemispherical asperities. It was found that the constraints used to define the asperity distribution on the surface, which were determined from AFM scans, varied with scan size and thus were not constant for all surfaces examined. The greatest variation in these parameters occurred with materials that had large asperities or with materials where a large fraction of the surface was covered by asperities. These rough surfaces were modeled with fractals and also with a fast Fourier transform algorithm. When the model surfaces generated using the Fourier transforms are used in the adhesion model, the model accurately predicts the experimentally observed adhesion forces measured with the AFM.     

Scratching behavior of elastomeric poly(dimethylsiloxane) coatings

Scratch testing has been performed on elastomeric poly(dimethylsiloxane) (PDMS) coatings on stainless steel with a spherical indenter. The friction coefficient (horizontal‐to‐normal force ratio) during scratching decreases with increasing normal load. This result can be explained by assuming that during scratching the contact area is determined by elastic deformation and the horizontal force is proportional to the contact area. With increasing driving speed, the friction coefficient increases, but the rate of increase decreases; this suggests that the scratching of the PDMS coating is a rate process and that the viscoelastic property of the coating influences its frictional behavior. Below a critical normal load, which increases with the coating thickness, the PDMS coating recovers elastically after being scratched so that there are no scratch marks left behind. Above the critical normal load, the coating is damaged by a combination of delamination at the coating/substrate interface and through‐thickness cracking. When the coating is damaged, there is an increase in the friction coefficient, and the friction force displays significant fluctuations. Furthermore, the critical normal load increases with the driving speed; this implies that time is needed to nucleate damage. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1530–1537, 2002     

Scaling properties of contact area of pressure-sensitive adhesives

Two new devices were developed to provide accurate measurements of both the contact area and the tack strength of pressure-sensitive adhesives (PSAs). The first one is the "mechano-optical tack tester" (MOTT), which was designed to apply controlled contact pressure by means of a quartz prism probe, for determined contact times, onto the surfaces of PSA samples. The contact area is measured by the reflection of light at the quartz probe surface, which is in contact with the adhesive. The second device is an "acoustic contact tester" (ACT) that measures the tack strength and the contact area between a silicate glass and an adhesive by the reflection of an acoustic wave. Two ultrasonic sensors of different acoustic wavelengths have been built in order to study the scaling effects of the contact kinetics between an adhesive and the probe. MOTT and ACT experiments on a commercial PSA show that the contact area is the main parameter that governs the tack properties of the PSA. The experiments and the modeling point out that the contact area depends on the compression stress, the roughness, the thickness, and the Young's modulus of the PSA. However, comparison of contact kinetics from MOTT and ACT experiments show that the contact area is a subjective parameter that depends on the wavelength of the reflected beam used for its measurement.     

Water wetting transition parameters of perfluorinated substrates with periodically distributed flat-top microscale obstacles

Superhydrophobicity is obtained on photolithographically structured silicon surfaces consisting of flat-top pillars after a perfluorosilanization treatment. Systematic static contact angle measurements were carried out on these surfaces as a function of pillar parameters that geometrically determine the surface roughness, including pillar height, diameter, top perimeter, overall filling factor, and disposition. In line with thermodynamics models, two regimes of static contact angles are observed varying each parameter independently: the "Cassie" regime, in which the water drop sits suspended on top of the pillars (referred to as composite), corresponding to experimental contact angles greater than 140-150 degrees, and the "Wenzel" regime, in which water completely wets the asperities (referred to as wetted), corresponding to lower experimental contact angles. A transition between the Cassie and Wenzel regimes corresponds to a set of well-defined parameters. By smoothly depositing water drops on the surfaces, this transition is observed for surface parameter values far from the calculated ones for the thermodynamic transition, therefore offering evidence for the existence of metastable composite states. For all studied parameters, the position of the experimental transition correlates well with a rough estimation of the energy barrier to be overcome from a composite metastable state in order to reach the thermodynamically favored Wenzel state. This energy barrier is estimated as the surface energy variation between the Cassie state and the hypothetical composite state with complete filling of the surface asperities by water, keeping the contact angle constant.