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.