Brownian motion of particles near a free surface: Desorption from a monolayer

A simple model for desorption from a monolayer is presented based on the Smoluchowski equation for the Brownian motion of a particle in a potential well located in the liquid–vapor interfacial region. For a simple square-well potential of depth Q we find an analytic expression for the probability p (t) that the particle will remain at the surface after time t. The relaxation time for desorption is shown to be proportional to exp(2Q). At short time p (o) -p (t) ∝t1/2 whereas for very long times p (t) ∝t−1/2. Interactions between molecules in the monolayer are taken into account by using a mean field approximation to the pair interaction. In its simplest form the theory reduces to solving the Smoluchowski equation for a time-dependent square well. Comparison is made to published experimental data, and additional experiments are suggested which will adequately test the theory.