Van der Waals model of adsorption

Abstract

A statistical-mechanical model for physical adsorption of a gas on a solid substrate is developed, based on Van der Waals' concept of dividing the interaction potential between a pair of molecules into a hard-sphere repulsive part and an infinitely weak and long-range attractive part. The interaction between the substrate and gas molecules is similarly modeled by a hard-wall repulsive potential with long-range attractive tail. For a specific choice of the intermolecular and wall-molecule attractive terms, an explicit solution is obtained for the model. This solution shows that three different classes of adsorption isotherm are possible: in class I, the adsorption is infinite in the limit that the gas pressure approaches the saturated vapor pressure, in class II the adsorption remains finite in the limit, while in class III the adsorption becomes negative in the limit. If the temperature of crossover between different classes is plotted as a function of $\frac{{\ensuremath{\epsilon}}_{w}}{\ensuremath{\alpha}}$, where ${\ensuremath{\epsilon}}_{w}$ and $\ensuremath{\alpha}$ are respectively the minimum of the wall-molecule potential and the integrated strength of intermolecular attractions, then the resulting curve has the same shape as the bulk phase coexistence curve. The model shows agreement with experimental results for the adsorption of argon, krypton, and xenon on graphite, and for argon adsorbed on xenon, as well as with recent computer-simulation results for argon adsorbed on carbon dioxide.