Modeling the contact mechanics of hydrogels

A computationally lean model for the coarse-grained description of contact mechanics of hydrogels is proposed and characterized. It consists of a simple bead-spring model for the interaction within a chain, potentials describing the interaction between monomers and mold or confining walls, and a coarse-grained potential reflecting the solvent-mediated effective repulsion between non-bonded monomers. Moreover, crosslinking only takes place after the polymers have equilibrated in their mold. As such, the model is able to reflect the density, solvent quality, and the mold hydrophobicity that existed during the crosslinking of the polymers. Finally, such produced hydrogels are exposed to sinusoidal indenters. The simulations reveal a wavevector-dependent effective modulus E*(q) with the following properties: (i) stiffening under mechanical pressure, and a sensitivity of E*(q) on (ii) the degree of crosslinking at large wavelengths, (iii) the solvent quality, and (iv) the hydrophobicity of the mold in which the polymers were crosslinked. Finally, the simulations provide evidence that the elastic heterogeneity inherent to hydrogels can suffice to pin a compressed hydrogel to a microscopically frictionless wall that is undulated at a mesoscopic length scale. Although the model and simulations of this feasibility study are only two-dimensional, its generalization to three dimensions can be achieved in a straightforward fashion. © 2019 by the authors

The spectral problem for the dispersionless Camassa-Holm equation

We present a spectral and inverse spectral theory for the zero dispersion spectral problem associated with the Camassa-Holm equation. This is an alternative approach to that in [10] by Eckhardt and Teschl

Single layer graphene induces load-bearing molecular layering at the hexadecane-steel interface

The influence of a single layer graphene on the interface between a polished steel surface and the model lubricant hexadecane is explored by high-resolution force microscopy. Nanometer-scale friction is reduced by a factor of three on graphene compared to the steel substrate, with an ordered layer of hexadecane adsorbed on the graphene. Graphene furthermore induces a molecular ordering in the confined lubricant with an average range of 4-5 layers and with a strongly increased load-bearing capacity compared to the lubricant on the bare steel substrate. © 2019 IOP Publishing Ltd

Distance dependence of force and dissipation in non-contact atomic force microscopy on Cu(100) and Al(111)

The dynamic characteristics of a tip oscillating in the nc-AFM mode in close vicinity to a Cu(100)-surface are investigated by means of phase variation experiments in the constant amplitude mode. The change of the quality factor upon approaching the surface deduced from both frequency shift and excitation versus phase curves yield to consistent values. The optimum phase is found to be independent of distance. The dependence of the quality factor on distance is related to 'true' damping, because artefacts related to phase misadjustment can be excluded. The experimental results, as well as on-resonance measurements at different bias voltages on an Al(111) surface, are compared to Joule dissipation and to a model of dissipation in which long-range forces lead to viscoelastic deformations

Ageing of a Microscopic Sliding Gold Contact at Low Temperatures

Nanometer-scale friction measurements on a Au(111) surface have been performed at temperatures between 30 and 300 K by means of atomic force microscopy. Stable stick slip with atomic periodicity is observed at all temperatures, showing only weak dependence on temperature between 300 and 170 K. Below 170 K, friction increases with time and a distortion of the stick-slip characteristic is observed. Low friction and periodic stick slip can be reestablished by pulling the tip out of contact and subsequently restoring the contact. A comparison with molecular dynamics simulations indicates that plastic deformation within a growing gold junction leads to the observed frictional behavior at low temperatures. The regular stick slip with atomic periodicity observed at room temperature is the result of a dynamic equilibrium shape of the contact, as microscopic wear damage is observed to heal in the sliding contact

Atomic structure of alkali halide surfaces

The atomic structure of surfaces of alkali halide crystals has been revealed by means of high-resolution dynamic force microscopy. True atomic resolution is demonstrated both on steps surrounding islands or pits, and on a chemically mixed crystal. We have directly observed the enhanced interaction at low-coordinated sites by force microscopy. The growth of NaCl films on metal surfaces and radiation damage in a KBr surface is discussed based on force microscopy results. The damping of the tip oscillation in dynamic force microscopy might provide insight into dissipation processes on the atomic scale. Finally, we present atomically resolved images of wear debris found after scratching a KBr surfac

Role of friction-induced torque in stick-slip motion

We present a minimal quasistatic 1D model describing the kinematics of the transition from static friction to stick-slip motion of a linear elastic block on a rigid plane. We show how the kinematics of both the precursors to frictional sliding and the periodic stick-slip motion are controlled by the amount of friction-induced torque at the interface. Our model provides a general framework to understand and relate a series of recent experimental observations, in particular the nucleation location of micro-slip instabilities and the build up of an asymmetric field of real contact area.Comment: 6 pages, 5 figure

Inverse Scattering Transform for the Camassa-Holm equation

An Inverse Scattering Method is developed for the Camassa-Holm equation. As an illustration of our approach the solutions corresponding to the reflectionless potentials are explicitly constructed in terms of the scattering data. The main difference with respect to the standard Inverse Scattering Transform lies in the fact that we have a weighted spectral problem. We therefore have to develop different asymptotic expansions.Comment: 17 pages, LaTe