Vapour adsorption kinetics: statistical rate theory and zeta adsorption isotherm approach

The equilibrium zeta adsorption isotherm for vapours indicates the amount adsorbed is finite for vapour-phase pressures approaching the saturation value, and is strongly supported by experimental measurements for a number of different vapour-solid surface systems. This isotherm assumes the adsorbate consists of differently sized molecular clusters in local equilibrium rather than the adsorbate being in layers. We use the local-equilibrium approximation and develop a method to determine the expression for chemical potential of the adsorbate in terms of the amount adsorbed, n^A(t). This allows us to apply statistical rate theory to calculate n^A(t) at five different vapour-phase pressures, x^V (≡P^V/P_sat), in terms of a parameter, r^e. Statistical rate theory indicates that r^e describes the dynamics of a given isolated system under equilibrium conditions. We consider two methods for determining the value of r^e that give the best agreement with the measurements performed at each of five values of x^V. In one method, we assume, r^e, is a function of both temperature, T, and pressure, x^V, and determine the five best-fit values of r^e. In the experiments, x^V changes by a factor of more than two, but the standard deviation in the r^e values is 6%. In the second method, we assume r^e is a function only of T; and find that the value of r^e is not changed significantly. In all cases, the calculated n^A(t) agree with the measurements.