Contact mechanics with adhesion: Interfacial separation and contact area

We study the adhesive contact between elastic solids with randomly rough, self affine fractal surfaces. We present molecular dynamics (MD) simulation results for the interfacial stress distribution and the wall-wall separation. We compare the MD results for the relative contact area and the average interfacial separation, with the prediction of the contact mechanics theory of Persson. We find good agreement between theory and the simulation results. We apply the theory to the system studied by Benz et al. involving polymer in contact with polymer, but in this case the adhesion gives only a small modification of the interfacial separation as a function of the squeezing pressure.Comment: 5 pages, 4 figure

Influence of surface roughness on superhydrophobicity

Superhydrophobic surfaces, with liquid contact angle theta greater than 150 degree, have important practical applications ranging from self-cleaning window glasses, paints, and fabrics to low-friction surfaces. Many biological surfaces, such as the lotus leaf, have hierarchically structured surface roughness which is optimized for superhydrophobicity through natural selection. Here we present a molecular dynamics study of liquid droplets in contact with self-affine fractal surfaces. Our results indicate that the contact angle for nanodroplets depends strongly on the root-mean-square surface roughness amplitude but is nearly independent of the fractal dimension D_f of the surface.Comment: 5 Pages, 6 figures. Minimal changes with respect to the previous versio

Fluid flow at the interface between elastic solids with randomly rough surfaces

I study fluid flow at the interface between elastic solids with randomly rough surfaces. I use the contact mechanics model of Persson to take into account the elastic interaction between the solid walls and the Bruggeman effective medium theory to account for the influence of the disorder on the fluid flow. I calculate the flow tensor which determines the pressure flow factor and, e.g., the leak-rate of static seals. I show how the perturbation treatment of Tripp can be extended to arbitrary order in the ratio between the root-mean-square roughness amplitude and the average interfacial surface separation. I introduce a matrix D(Zeta), determined by the surface roughness power spectrum, which can be used to describe the anisotropy of the surface at any magnification Zeta. I present results for the asymmetry factor Gamma(Zeta) (generalized Peklenik number) for grinded steel and sandblasted PMMA surfaces.Comment: 16 pages, 14 figure

Molecular dynamics study of contact mechanics: contact area and interfacial separation from small to full contact

We report a molecular dynamics study of the contact between a rigid solid with a randomly rough surface and an elastic block with a flat surface. We study the contact area and the interfacial separation from small contact (low load) to full contact (high load). For small load the contact area varies linearly with the load and the interfacial separation depends logarithmically on the load. For high load the contact area approaches to the nominal contact area (i.e., complete contact), and the interfacial separation approaches to zero. The present results may be very important for soft solids, e.g., rubber, or for very smooth surfaces, where complete contact can be reached at moderate high loads without plastic deformation of the solids.Comment: 4 pages,5 figure

Interfacial separation between elastic solids with randomly rough surfaces: comparison of experiment with theory

We study the average separation between an elastic solid and a hard solid with a nominal flat but randomly rough surface, as a function of the squeezing pressure. We present experimental results for a silicon rubber (PDMS) block with a flat surface squeezed against an asphalt road surface. The theory shows that an effective repulse pressure act between the surfaces of the form p proportional to exp(-u/u0), where u is the average separation between the surfaces and u0 a constant of order the root-mean-square roughness, in good agreement with the experimental results.Comment: 6 pages, 10 figure

Transverse thermal depinning and nonlinear sliding friction of an adsorbed monolayer

We study the response of an adsorbed monolayer under a driving force as a model of sliding friction phenomena between two crystalline surfaces with a boundary lubrication layer. Using Langevin-dynamics simulation, we determine the nonlinear response in the direction transverse to a high symmetry direction along which the layer is already sliding. We find that below a finite transition temperature, there exist a critical depinning force and hysteresis effects in the transverse response in the dynamical state when the adlayer is sliding smoothly along the longitudinal direction.Comment: 4 pages, 4 figures, to appear in Phys. Rev. Let

Dynamical transitions and sliding friction in the two-dimensional Frenkel-Kontorova model

The nonlinear response of an adsorbed layer on a periodic substrate to an external force is studied via a two dimensional uniaxial Frenkel-Kontorova model. The nonequlibrium properties of the model are simulated by Brownian molecular dynamics. Dynamical phase transitions between pinned solid, sliding commensurate and incommensurate solids and hysteresis effects are found that are qualitatively similar to the results for a Lennard-Jones model, thus demonstrating the universal nature of these features.Comment: 11 pages, 12 figures, to appear in Phys. Rev.

Elastic contact between self-affine surfaces: Comparison of numerical stress and contact correlation functions with analytic predictions

Contact between an elastic manifold and a rigid substrate with a self-affine fractal surface is reinvestigated with Green's function molecular dynamics. Stress and contact autocorrelation functions (ACFs) are found to decrease algebraically. A rationale is provided for the observed similarity in the exponents for stress and contact ACFs. Both exponents differ substantially from analytic predictions over the range of Hurst roughness exponents studied. The effect of increasing the range of interactions from a hard sphere repulsion to exponential decay is analyzed. Results for exponential interactions are accurately described by recent systematic corrections to Persson's contact mechanics theory. The relation between the area of simply connected contact patches and the normal force is also studied. Below a threshold size the contact area and force are consistent with Hertzian contact mechanics, while area and force are linearly related in larger contact patches.Comment: 12 pages, 9 figure

Friction Laws for Elastic Nano-Scale Contacts

The effect of surface curvature on the law relating frictional forces F with normal load L is investigated by molecular dynamics simulations as a function of surface symmetry, adhesion, and contamination. Curved, non-adhering, dry, commensurate surfaces show a linear dependency, F proportional to L, similar to dry flat commensurate or amorphous surfaces and macroscopic surfaces. In contrast, curved, non-adhering, dry, amorphous surfaces show F proportional to L^(2/3) similar to friction force microscopes. In our model, adhesive effects are most adequately described by the Hertz plus offset model, as the simulations are confined to small contact radii. Curved lubricated or contaminated surfaces show again different behavior; details depend on how much of the contaminant gets squeezed out of the contact. Also, it is seen that the friction force in the lubricated case is mainly due to atoms at the entrance of the tip.Comment: 7 pages, 5 figures, submitted to Europhys. Let