Thermodynamically Consistent Enthalpies of Adsorption of Mixtures from Classical Density Functional Theory

Classical density functional theory (cDFT) has been established as an efficient and robust framework for predicting adsorption isotherms. Moreover, the mathematical form of cDFT─an optimization instead of the more widely used molecular simulations─opens up additional opportunities based on calculating noise-free derivatives of interfacial properties. One of these opportunities is the rapid, consistent calculation of thermodynamic properties, such as the enthalpy of adsorption. This work showcases cDFT as a thermodynamically fully consistent model for fluids that describes all homogeneous and adsorbed phases with a single model, providing access to phase equilibria, density profiles, enthalpies, and more. Because the enthalpy of adsorption of a mixture is difficult to measure experimentally and is rarely discussed in modeling approaches, we first revisit its definition from an energy balance perspective and in the context of the Clausius-Clapeyron relation, independent of specific model assumptions. We follow this up by deriving expressions for the enthalpy of adsorption suitable for cDFT. The resulting framework is demonstrated using the PC-SAFT Helmholtz energy model for the adsorption of real gases in a model slit pore for a pure fluid, a binary mixture, and a multicomponent system.