Role of substrate geometry in sliding friction

Via a Frenkel-Kontorova (FK) model approach, we study, in the context of solid friction phenomena, the role of the substrate potential geometry on the underdamped dynamics of a chain of interacting atoms. The choice of an on-site potential defined by the sum of two sinusoidal functions with different periodicity allows us to simulate microscopic sliding over simply periodic, multiple-well periodic and quasiperiodic substrates. We analyse the mobility-force characteristics and the related static friction, commenting on the nature of the particle dynamics in the vicinity of the pinning-depinning transition point and considering the role played by the coverage variable on the depinning mechanism. For the quasiperiodic cases, we also examine the hysteretic behaviour of the chain mobility as a function of the adiabatically varying force at zero temperature. For multiple-well periodic potentials, we observe the possible formation of commensurate dynamical structures during sliding.