Binding site models of friction due to the formation and rupture of bonds: state-function formalism, force-velocity relations, response to slip velocity transients, and slip stability.

We present a model describing friction due to the thermally activated formation and rupture of molecular bonds between two surfaces, with long molecules on one surface attaching to discrete or continuous binding sites on the other. The physical assumptions underlying this model are formalized using a continuum approximation resulting in a class of master-equation-like partial differential equations that is a generalization of a friction model due to Persson [Phys. Rev. B 51, 13568 (1995)] and is identical to the equations used to describe muscle contraction, first proposed by A. F. Huxley. We examine the properties of this friction model in the continuous binding site limit noting that this model is capable of producing both monotonically increasing and an increasing-decreasing force dependence on slip velocity. When monotonically increasing, the force dependence on velocity is (asymptotically) logarithmic. The model produces a transient increase in friction in response to a sudden velocity increase, whether or not the steady-state friction force is a decreasing or increasing function of steady slip velocity. The model also exhibits both stable steady slip and stick-slip-like oscillatory behavior, in the presence of compliance in the loading machine, even when the steady-state friction force is a decreasing function of steady-state slip velocity.