A Consistent Thermodynamic Characterization of the Adsorption Process through the Calculation of Free Energy Contributions.

We apply in this study different methodologies based on thermodynamic integration (TI), free energy perturbation (FEP), and potential of mean force (PMF) to address the challenging issue of the calculation of the free energy of adsorption. A model system composed of a solid substrate, an adsorbate, and solvent particles is specifically designed to reduce the dependence of our free energy results on the sampling of the phase space and the choice of the pathway. The reliability and efficiency of these alchemical free energy simulations are established through the closure of a thermodynamic cycle describing the adsorption process in solution and in a vacuum. We complete this study by the calculation of free energy contributions related to phenomena of desorption of solvent molecules and desolvation of the adsorbate upon adsorption. This calculation relies on the work of adhesion, the interfacial tension of the liquid-vapor of the solvent, and the free energy of solvation of the substrate. The different ways of calculating the free energy of adsorption are in excellent agreement and could complete experiments in the field of adsorption by giving quantitative data on the different energy contributions involved in the process.