How adsorbate-adsorbate interaction determines the functional shape of an adsorption isotherm is an important and challenging question. Many models for adsorption isotherm have been proposed to answer this question. However, a successful fitting of an isotherm on its own is insufficient for the correctness of the model assumptions. Instead, starting from the principles of statistical thermodynamics, we propose how adsorbate-adsorbate interactions can be quantified from an isotherm. This was made possible by extending the key tools of solution statistical thermodynamics to adsorbates in interface, namely, the Kirkwood-Buff and Macmillan-Mayer theories, as well as their relationship to the thermodynamic phase stability condition. When capillary condensation and interfacial phase transition are absent, adsorbate-adsorbate interactions can be quantified from an isotherm using the Kirkwood-Buff integrals, and virial coefficients can yield multiple-body interaction between adsorbates. Such quantities can be obtained directly from the fitting parameters for the well-known isotherm models (e.g., Langmuir, BET). The size of adsorbate cluster involved in capillary condensation and interfacial phase transition can also be evaluated from the isotherm, which was demonstrated by the adsorption isotherm of water on activated carbons of varying pore sizes from the literature. Signatures of the isotherm classifications by IUPAC have been characterized in terms of multiple-body interactions between adsorbates.
CORE (COnnecting REpositories)
CORE (COnnecting REpositories)