Theoretical modeling of adsorption isotherms and isosteric heat of associating and non-associating fluids using the two-dimensional SAFT-VR Mie approach

In this work, the two-dimensional Statistical Associating Fluid Theory for fluids interacting via Mie pair potentials (2D-SAFT-VR Mie) is applied to model adsorption isotherms and isosteric heat of adsorption for both associating and non-associating fluids on solid surfaces. First, we derive analytical expressions for the first- and second-order perturbation terms of the Helmholtz free energy in the 2D system, based on the radial distribution function of a hard-disk system. Next, we develop an adsorption model that accounts for the interactions between the adsorbed and bulk phases, incorporating the Mie pair potential as a function of repulsive and attractive exponents. The theoretical approach is validated against Gibbs ensemble Monte Carlo simulations for the adsorption isotherms of associating and non-associating fluids, showing excellent agreement. Finally, the 2D-SAFT-VR Mie approach is applied to describe the adsorption isotherms and isosteric heat of adsorption of methane, nitrogen, carbon dioxide, sulfur dioxide, and water on carbonaceous materials, including dry activated carbon, zeolites, and metal-organic frameworks (MOFs). The energy depth of the surface-particle potential (ɛw) and the specific surface area (as) are free molecular parameters determined by fitting to experimental adsorption isotherms. The obtained ɛw and as values are consistent with the experimental values of isosteric heat of adsorption at zero coverage and Brunauer-Emmett-Teller surface area, respectively. In all cases, the calculated adsorption behavior exhibits excellent agreement with experimental data. These findings provide valuable theoretical insights into the design and optimization of efficient fluid storage, separation, and purification systems in complex materials.