Elastic Interactions and Instability Transitions

Abstract

The study in Chap. 9 assumed that the lateral corrugation of the adsorbate-substrate interaction potential was so weak that the adsorbate layer could fluidize as a result of the shear force stemming from the external force acting on the block. For this case we have argued that the kinetic frictional force at low sliding velocities is likely to involve the formation and fluidization of solid structures. But in many cases the corrugation of the adsorbate-substrate potential energy surface is so strong that no fluidization of the adsorbate layer can occur. This often seems to be the case when fatty acids are used as boundary lubricants: the polar heads of fatty acid molecules bind strongly to specific sites on many metal oxides and the sliding occurs now between the inert hydrocarbon tails as indicated schematically in Fig. 2.5. In Sect. 10.1 we discuss some simple models which illustrate the fundamental origin of the friction force when no fluidization can occur. As will be shown below, if the corrugated substrate potential is large enough compared with the local elasticity, an elastic instability will occur, which will result in a kinetic friction force which remains finite as the sliding velocity v → 0 (we assume zero temperature, so that no thermally activated creep motion occurs). In Sect. 10.2 the elastic coherence length ξ is introduced and calculated for a semi-infinite elastic solid exposed to a random surface stress.