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Register a new userKinetic Friction and Atomistic Instabilities in Boundary-Lubricated Systems
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The contribution of sliding-induced, atomic-scale instabilities to the kinetic friction force is investigated by molecular dynamics. For this purpose, we derive a relationship between the kinetic friction force $F_{rm k}$ and the non-equilibrium velocity distribution $P(v)$ of the lubricant particles. $P(v)$ typically shows exponential tails, which cannot be described in terms of an effective temperature. It is investigated which parameters control the existence of instabilities and how they affect $P(v)$ and hence $F_{rm k}$. The effects of the interfaces dimensionality, lubricant coverage, and internal degrees of freedom of lubricant particles on $F_{rm k}$ are studied explicitly. Among other results we find that the kinetic friction between commensurate surfaces is much more susceptible to changes in $(i)$ lubricant coverage, $(ii)$ sliding velocity, and $(iii)$ bond length of lubricant molecules than incommensurate surfaces.
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The understanding of sliding friction for wet, patterned surfaces from first principles is challenging. While emerging applications have sought design principles from biology, a general framework is lacking because soft interfaces experience a multiphysics coupling between solid deformation and fluid dissipation. We investigate the elastohydrodynamic sliding of >50 patterned sliding pairs comprising elastomers, thermosets, and hydrogels, and discover that texturing induces a critical transition in the macroscopic friction coefficient. This critical friction scales universally, without any fitting parameters, with the reduced elastic modulus and the pattern geometry. To capture the frictional dissipation, we separate the flow curve into two regimes and account for the contributions of shear and normal forces applied by the fluid on the patterns. Our model combines Reynolds equations and elastic deformation to provide physical insights that allow engineering of the elastohydrodynamic friction in a class of soft tribopairs using pattern geometry, material elasticity, and fluid properties.
A theoretical account is given of the microscopic basis of the rate- and state-dependent friction (RSF) law. The RSF law describes rock friction quantitatively and therefore it is commonly used to model earthquakes and the related phenomena. But the RSF law is rather empirical and the theoretical basis has not been very clear. Here we derive the RSF law starting from constitutive laws for asperities, and give the atomistic expressions for the empirical RSF parameters. In particular, we show that both the length constant and the state variable are given as the 0th weighted power means of the corresponding microscopic quantities: a linear dimension and the contact duration of each asperity. As a result, evolution laws for the state variable can be derived systematically. We demonstrate that the aging and the slip laws can be derived and clarify the approximations behind these two major evolution laws. Additionally, the scaling properties of the length constant are clarified for fractal distribution of asperities.
A new contribution to friction is predicted to occur in systems with magnetic correlations: Tangential relative motion of two Ising spin systems pumps energy into the magnetic degrees of freedom. This leads to a friction force proportional to the area of contact. The velocity and temperature dependence of this force are investigated. Magnetic friction is strongest near the critical temperature, below which the spin systems order spontaneously. Antiferromagnetic coupling leads to stronger friction than ferromagnetic coupling with the same exchange constant. The basic dissipation mechanism is explained. If the coupling of the spin system to the heat bath is weak, a surprising effect is observed in the ordered phase: The relative motion acts like a heat pump cooling the spins in the vicinity of the friction surface.
We present a study of the magnetic order and the structural stability of two-dimensional quantum spin systems in the presence of spin-lattice coupling. For a square lattice it is shown that the plaquette formation is the most favourable form of static two-dimensional dimerization. We also demonstrate that such distortions may coexist with long range magnetic order, in contrast to the one-dimensional case. Similarly, the coupling to Einstein phonons is found to reduce, but not to eliminate the staggered magnetic moment. In addition, we consider the renormalization of the square lattice phonon spectrum due to spin-phonon coupling in the adiabatic approximation. Towards low temperatures significant softening mainly of zone boundary phonons is found, especially around the $(pi,0)$ point of the Brillouin zone. This result is compatible with the tendency to plaquette formation in the static limit. We also point out the importance of a magnetic pressure on the lattice due to spin-phonon coupling. At low temperatures, this results in a tendency towards shear instabilities of the lattice.
Avalanching systems are treated analytically using the renormalization group (in the self-organized-criticality regime) or mean-field approximation, respectively. The latter describes the state in terms of the mean number of active and passive sites, without addressing the inhomogeneity in their distribution. This paper goes one step further by proposing a kinetic description of avalanching systems making use of the distribution function for clusters of active sites. We illustrate application of the kinetic formalism to a model proposed for the description of the avalanching processes in the reconnecting current sheet of the Earth magnetosphere.
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