Cooperative adsorption kinetics: Upper bound using activity series.

Abstract

We use the model of the adsorption of gas molecules to a surface treated as a two-dimensional Ising lattice gas to illustrate the use of equilibrium statistical mechanics (specifically, equilibrium activity series) to construct the kinetics of the adsorption in the limit that surface diffusion is rapid with respect to the rate of adsorption (assumption of internal equilibrium). These conditions generally give an upper bound to the rate of relaxation relative to a system with a finite or zero rate of diffusion on the surface. For the plane-square lattice and special choices of the kinetic parameters one can use known 15-term equilibrium activity series to give 15 terms of the power series in the time, or the inverse of this function. At the critical point the relaxation is extremely slow, varying as ${\mathit{t}}^{\mathrm{\ensuremath{-}}1/14}$. We find that if one expresses the kinetics in terms of a time-dependent activity the resulting series are much better behaved than the corresponding density series.