A phenomenology of boundary lubrication: the lumped junction model

We propose a phenomenological model of boundary lubricated junctions consisting of a few layers of small molecules which describes the rheological properties of these systems both in the static, frozen, and sliding, molten, states as well as the dynamical transition between them. Two dynamical regimes can be distinguished, according to the level of internal damping of the junction, which depends on its thickness and on the normal load. In the overdamped regime, under driving at constant velocity v through an external spring, the motion evolves continuously from "atomic stick-slip" to modulated sliding. Underdamped systems exhibit, under given external stress, a range of dynamic bistability where the sheared static state coexists with a steadily sliding one. The frictional dynamics under shear driving is analyzed in detail, it provides a complete account of the qualitative dynamical scenarios observed by Israelashvili et al., and yields semiquantitative agreement with experimental data. A few complementary experimental tests of the model are suggested.