Microscopic model for spreading of a two-dimensional monolayer

We study the behavior of a monolayer, which occupies initially a bounded region on an ideal crystalline surface and then evolves in time due to random hopping of the monolayer particles. In the case when the initially occupied region is the half-plane X less than or equal to 0, we determine explicitly, in terms of an analytically solvable mean-field-type approximation, the mean displacement X(t) of the monolayer edge. We find that X(t) approximate to A root D(0)t, in which law D-0 denotes the bare diffusion coefficient and the prefactor A is a function of the temperature and of the particle-particle interactions parameters. We show that A can be greater, equal or less than zero, and specify the critical parameter which distinguishes between the regimes of spreading (A > 0), partial wetting (A = 0) and dewetting (A < 0). (C) 1998 Elsevier Science B.V.