THERMODYNAMICALLY CONSISTENT EQUILIBRIUM ADSORPTION-ISOTHERMS FOR MIXTURES OF DIFFERENT-SIZE MOLECULES

Simple and general differential criteria are derived for testing equil ibrium adsorption isotherms for consistency with the laws of thermodyn amics. The generalized Langmuir isotherm (L-model) for binary solutes of different sizes or adsorption capacities fails the test, as previou sly noted. A consistent isotherm is derived for the first time, by usi ng the framework of the ideal adsorbed solution (IAS) theory of Myers and Prausnitz (AIChE J. 1965, 11, 121). The scaled particle theory iso therms 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 adso rbed solution predict that at high coverages the larger molecules (tho se with smaller adsorption capacity) are substantially depleted from t he surface for steric and entropic reasons. With increasing concentrat ion, the models predict selectivity reversals in cases where the large r molecules are not much more surface active than the smaller molecule s.