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 sub-diffusion between the ballistic and the diffusive regimes as well as a cross-over from a non-Arrhenius to an Arrhenius dependence of the diffusion coefficient near the temperature, where the specific heat assumes its maximum. The study of these and related thermal and kinetic properties highlights several misconceptions prevalent in the literature. Most notably, 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. Thus, even if the rheology is described by semi-empirical theories such as the Eyring model, any agreement with experimental data, whether past, present, or future, may be purely coincidental.