Statistical Thermodynamics Models for Multicomponent Isothermal Diphasic Equilibria

We propose in this paper a whole family of models for isothermal diphasic equilibrium, which generalize the classical Langmuir isotherm. The main tool to obtain these models is a fine modeling of each phase, which states various constraints on the equilibrium. By writing down the Gibbs conditions of thermodynamical equilibrium for both phases, we are led to a constrained minimization problem, which is solved through the Lagrange multipliers. If one of the phases is an ideal solution, we can solve explicitly the equations, and obtain an analytic model. In the most general case, we have implicit formulas, and the models are computed numerically. The models of multicomponent isotherm we obtain in this paper are designed for chromatography, but can be adapted mutatis mutandis to other cases.