Abstract
The study employed the formalism of the canonical ensemble to analyze adsorption equilibrium, assuming that linear association of molecules is the only type of attractive interaction in the mobile monolayer on a homogeneous solid adsorbent surface. The partition function of the canonical ensemble was related to the free energy and the chemical potential of the adsorbate. The initial model did not show the possibility of two-dimensional condensation of the adsorbate, confirming the analogy to the one-dimensional Ising model.
The generalization of the model, assuming a branched form of adsorbate-adsorbate associates, leads to a new adsorption equation that takes into account the number of centers favorable for association. The introduction of the concept of multidimensional association enabled the derivation of an adsorption equation, which was analyzed with respect to the critical point of the adsorption layer condensation. This analysis showed that condensation is possible if the number of such centers is greater than two. The critical values of the association constant and the degree of surface coverage are functions of the number of association centers. These results demonstrate that the formalism of the canonical ensemble is effective for describing adsorption equilibrium with linear association of molecules, and that generalizing the model to include branched associates leads to a new adsorption equation predicting two-dimensional condensation of the adsorbate under certain conditions.
The described model introduces new solutions in the use of sorbents in diving apparatus with a closed circuit and thus increasing their efficiency in military applications.