Molecular thermodynamics of binary mixture adsorption: A scaled particle theory approach

Abstract

We examine the thermodynamic properties of two-dimensional fluid mixtures of hard convex particles using scaled particle theory (SPT). Analytic expressions are obtained for the excess area, Gibbs free energy, and excess entropy of a binary mixture. For typical fluid densities and for a range of area and perimeter ratios of the two species the fluid mixtures exhibit small negative deviations from ideality. The excess quantities are smaller than the corresponding bulk (three dimensional) mixtures which offers some explanation for the success of the ideal adsorbed solution (IAS) theory. According to the SPT, binary mixtures of hard particles are stable for all compositions and no fluid-fluid demixing transition is possible. The SPT equations are used to examine the adsorption equilibrium between an ideal bulk phase and an adsorbed phase. Adsorption isotherms and selectivities are computed for a range of area and perimeter ratios, equilibrium constant ratio, and bulk mole fraction. Unlike the widely used multicomponent Langmuir equations, the selectivity computed from the SPT isotherms exhibits strong sensitivity to these parameters. The selectivity of the smaller species always increases with increasing bulk pressure which may lead to a selectivity reversal. Finally, we discuss systems where the adsorbed molecules can adopt various orientations with respect to the surface normal.