Roles of surface heterogeneity and lateral interactions on the isosteric heat of adsorption and adsorbed phase heat capacity

Analytical expressions are developed, based on a lattice statistics model incorporating the Bragg-Williams approximation and a random heterogeneous surface described by a uniform distribution of energies, for predicting the single-component isosteric heat of adsorption and differential adsorbed phase heat capacity as a function of temperature, surface coverage, lateral interactions, and adsorbent heterogeneity. A parametric study demonstrates that these four factors all affect the isosteric heat of adsorption but with different magnitudes at different conditions. The temperature dependence of the isosteric heat of adsorption is always related to, and accompanied by, the adsorbent surface heterogeneity. The differential adsorbed phase heat capacity has a very weak temperature dependence and is not directly affected by lateral interactions. The molar adsorbed phase heat capacity is in most cases higher than the gas phase heat capacity. The deviation between the molar adsorbed and gas phase heat capacities depend mostly on surface coverage and surface heterogeneity and weakly on the lateral interactions and temperature. The derived expressions are used also to predict the isosteric heat of adsorption and adsorbed phase heat capacity from regressed parameters obtained from experimental adsorption isotherm data in the literature. Comparisons show that the molar adsorbed phase heat capacity can sometimes exceed it by 20% or more, depending on the regressed value of the heterogeneity parameter. These results have significant implications for adsorption-process modeling.