Molecular simulation of excess isotherm and excess enthalpy change in gas-phase adsorption

We present a new approach to calculating excess isotherm and differential enthalpy of adsorption on surfaces or in confined spaces by the Monte Carlo molecular simulation method. The approach is very general and, most importantly, is unambiguous in its application to any configuration of solid structure (crystalline, graphite layer or disordered porous glass), to any type of fluid (simple or complex molecule), and to any operating conditions (subcritical or supercritical). The behavior of the adsorbed phase is studied using the partial molar energy of the simulation box. However, to characterize adsorption for comparison with experimental data, the isotherm is best described by the excess amount, and the enthalpy of adsorption is defined as the change in the total enthalpy of the simulation box with the change in the excess amount, keeping the total number (gas + adsorbed phases) constant. The excess quantities (capacity and energy) require a choice of a reference gaseous phase, which is defined as the adsorptive gas phase occupying the accessible volume and having a density equal to the bulk gas density. The accessible volume is defined as the mean volume space accessible to the center of mass of the adsorbate under consideration. With this choice, the excess isotherm passes through a maximum but always remains positive. This is in stark contrast to the literature where helium void volume is used (which is always greater than the accessible volume) and the resulting excess can be negative. Our definition of enthalpy change is equivalent to the difference between the partial molar enthalpy of the gas phase and the partial molar enthalpy of the adsorbed phase. There is no need to assume ideal gas or negligible molar volume of the adsorbed phase as is traditionally done in the literature. We illustrate this new approach with adsorption of argon, nitrogen, and carbon dioxide under subcritical and supercritical conditions.