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

## TL;DR

This paper introduces a new method using classical density functional theory to calculate enthalpies of adsorption for mixtures in a thermodynamically consistent way.

## Contribution

The paper presents a novel framework for calculating mixture adsorption enthalpies using cDFT with thermodynamic consistency.

## Key findings

- A thermodynamically consistent model for adsorption enthalpy calculation is developed using cDFT.
- Expressions for adsorption enthalpy are derived and demonstrated for pure and mixed gases.
- The framework is validated using the PC-SAFT Helmholtz energy model in slit pores.

## Abstract

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.