Finite-temperature properties of the Frenkel-Kontorova model: Relation to tribological systems and fluid rheology

Abstract

The Frenkel-Kontorova model is a simple yet generic framework for the description of tribological phenomena and processes, including dry solid friction and the motion of adsorbed layers. As revealed in this work, it also reproduces qualitatively various features of complex liquids, such as, power-law subdiffusion between the ballistic and the diffusive regimes as well as a crossover from a non-Arrhenius to an Arrhenius dependence of the diffusion coefficient near the temperature, where the specific heat assumes its maximum. By systematically analyzing these thermal and kinetic properties, we also identify and clarify several misconceptions prevalent in the literature. Most notably, we show that the shear thinning with a shear-thinning exponent close to zero can be the natural consequence from enforced basin hopping: the energy drops caused by shear-induced instabilities dictate the friction-velocity dependence at medium shear rates rather than the way how shear forces reduce the free energy barriers for directed motion. Our findings thus demonstrate that even if the rheology is described by semiempirical theories such as the Eyring model, any agreement with experimental data, whether past, present, or future, may be purely coincidental.