(629e) Virial Coefficient Theory for Adsorption of Gas Mixtures

Reliable prediction of the properties of mixtures in the presence of adsorbents is a key capability for the design of adsorption processes. Molecular-based approaches are needed to include the key physical considerations to perform predictive modeling, and several such approaches are available. These include classical density functional theory, integral equation theories, and molecular simulation. Each of these methods has advantages and disadvantages relating to the complexity of physical features that can included in the treatment, as well as computational cost and suitability for analysis. Among this field of considerations a special place is held by methods based on a virial treatment of the properties. Such methods can incorporate almost any level of detail in the molecular model, including molecular flexibility, quantum effects, multibody interactions, etc., and (unlike molecular simulation) yield an analytic equation for the behavior. On the other hand, the range of application of the treatment is limited to low-density phases, which nevertheless are still of practical interest.

   Virial-based methods are well established for bulk fluids, where the approach has classically provided capabilities somewhere between thermodynamic models and molecular simulations. This powerful, systematic method can be applied to inhomogeneous systems as well. Even though the treatment of the general imperfect gas can easily extended to the present problem, the study of gas-surface system is far less well developed. The theory was developed by the 1962 papers by Bellemans, who then formulated a Mayer-cluster theory of an inhomogeneous system and showed a unique way to separate the surface terms proportional to the surface area

   In the present work, the virial coefficient theory is applied to the gas-surface system. We report a study of gas mixtures adsorbed on solid surface using inhomogeneous virial coefficients. The relevant surface variables for gas-surface system are directly expressed in terms of interactions between molecules themselves, and these molecules with the surface. The Mayer-sampling Monte Carlo (MSMC) method is applied to calculate the cluster integrals which contain surface contributions. We first report the results of calculation of “surface” virial coefficients of a mixture evaluated by using MSMC. Thermodynamic properties such as pressure, isosteric heat of adsorption are calculated by a virial expansion. Also we examine the selectivity at the limit of zero pressure which is directly related to the intermolecular forces.  Comparison with molecular simulation demonstrates the range of applicability of the virial treatment.