Thermodynamically Consistent Equilibrium Adsorption Isotherms for Mixtures of Different-Size Molecules

Simple and general differential criteria are derived for testing equilibrium adsorption isotherms for consistency with the laws of thermodynamics. The generalized Langmuir isotherm (L-model) for binary solutes of different sizes or adsorption capacities fails the test, as previously noted. A consistent isotherm is derived for the first time, by using the framework of the ideal adsorbed solution (IAS) theory of Myers and Prausnitz (AIChE J. 1965, 11, 121). The scaled particle theory isotherms for circular disks are shown to be thermodynamically consistent and to lead to almost identical predictions as an IAS model based on a modified Langmuir isotherm. All models with ideal mixing in the adsorbed solution predict that at high coverages the larger molecules (those with smaller adsorption capacity) are substantially depleted from the surface for steric and entropic reasons. With increasing concentration, the models predict selectivity reversals in cases where the larger molecules are not much more surface active than the smaller molecules.