A New Modeling Approach for the Adsorption Isotherm of Pure Components on Nonporous Surfaces

For the modeling of adsorption on the molecular level, density functional theory (DFT) is a suitable tool. Within the DFT different approaches (local (LDFT) or nonlocal (NLDFT)) can be applied, which differ in the numerical effort for the minimization of the grand thermodynamic potential to calculate the density profile of the confined fluid. We propose an alternative method combining the numerical advantages of the LDFT with the more realistic density profiles usually obtained with the NLDFT. The basic idea of the alternative consists of the incorporation of a square gradient term, known from density gradient theory, into the grand thermodynamic potential describing a confined fluid. The gradient term leads to the elimination of the unphysical jumps in the density profile at the liquid-gas phase transition and, consequently, to the elimination of the unphysical kinks in the adsorption isotherm. The new method was utilized to model the adsorption isotherms of nitrogen, methane, ethane, ethylene, and carbon dioxide on a nonporous carbon surface at different temperatures, where the fluid properties were described using the Perturbed Chain Polar-Statistical Associated Fluid Theory (PCP-SAFT). It was found that the influence parameter of the gradient term already known from the calculation of surface tension can not be transferred to the adsorption isotherm, because the value for the adsorption isotherm must be 1 order of magnitude smaller than for the calculation of the surface tension of the free fluid. The solid-fluid interaction energy depends slightly in a linear way on temperature. The obtained adsorption isotherms were compared to experimental data taken from the literature. The new model allows an excellent description of the adsorption isotherms of different fluids at low pressure, where only gas is present, and at high pressure, where only liquid is present. However, at pressures where the phase transition takes place, slight deviations occur.