Saturating adsorption densities, match

There are many potential models that have been proposed in the Hterature. Among the popular ones that are currently enjoying widespread applications are the Lennard-Jones (LJ 12-6) equation and the Buckingham Exp-6 equation. The parameters of these equations are usually obtained by matching the theory (i.e., DFT) or simulation results (e.g., MC simulations) against various experimental properties, e.g., second virial coefficient, viscosity, vapor pressure, saturated liquid density, or surface tension, at the temperature at which the adsorption is carried out. 

Our method for the calculation of p(P,W) is a statistical mechanical approach known as mean-field theory (refs. 1 and 5). In this approach, the properties of the nitrogen within the graphite pore are obtained directly from the forces between the constituent molecules. The parameters of the intermolecular forces are determined by (a) ensuring that the saturation pressure and saturated liquid density of the model fluid are equal to the experimental values for nitrogen at its normal boiling point (77 K, which is the temperature at which the adsorption experiments are carried out) and (b) matching the model adsoq)tion on an isolated surface to the experimental t-curve of de Boer et al. (ref. 10). Having fixed the values for these parameters, the theory is then used to calculate model isotherms for pores of a variety of widths, which are then correlated (ref. 1) as a function of pressure and pore width to yield the individual pore isotherm p(P,W). Mean-field theory is known to become less accurate as the pore size is made very small (ref. 11) even for very small pores, however, this approach is more realistic than methods based on the Kelvin equation. 

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