An Alternative Approach to the Saturation Behavior of Adsorption Isotherms

Experimentally, adsorption is usually described by adsorption isotherms, which present a saturation effect at high enough concentration or pressure of the adsorbate fluid. This well-known saturation effect was first theoretically discussed by Langmuir, and it is commonly attributed to the finite number of adsorption sites on the substrate surface. Here, we propose an alternative approach to introduce saturation via a repulsive interaction potential, ϕ, among the adsorbate particles, in addition to the attractive potential between the adsorbate particles and the substrate. Using the proposed toy model for a semi-infinite sample, we calculate adsorption isotherms for a typical van der Waals interaction potential. The concentration profile of the adsorbate as a function of the distance from the surface is calculated for several bulk concentrations. The functional dependence of the saturation concentration on the strength of the repulsive inter-particle interaction is extracted by fitting numerical data. Our results are compared to those of the Langmuir model. No assumption of a finite predefined number of adsorption sites is required to obtain saturation.