Using the calibration function is suggested to increase the accuracy of approximate equations in the lattice-gas model at calculating various concentration dependences of equilibrium characteristics for nonideal adsorption systems in the vicinity of the critical point. This function should provide a shift of the approximate result to the exact one, when the lattice-gas model equations are used in the quality of the interpolation tool between the exact solutions. A comparison of approximate equations with Onsager's exact solution preferrably allows a use of the quasi-chemical approximation as the interpolation procedure and the exact information on the critical point. The modified lattice-gas model takes into account next the molecular properties of the Lennard-Jones fluid:  the long-range potential of adsorbate−adsorbate, an excluded volume of the adsorption site, and a contribution of the triple interactions, as well as a softness of the lattice structure. The modified lattice-gas model with the calibration function is used for the phase diagram descriptions for argon adsorption on the homogeneous (111) CdCl2 face (two-dimensional systems) and for methane adsorption in carbon slitlike pores (three-dimensional system) as well as the other equilibrium characteristics of mentioned systems.

The equilibrium distribution and the concentration dependence of the local and average self-diffusion coefficients for pure fluid and binary mixture components in narrow slitlike pores were analyzed. The coefficients were calculated using the lattice gas model in the quasi-chemical approximation on the assumption of a spherical shape and approximately equal sizes of the components. For the pure adsorbate, these calculations were compared with molecular dynamics simulations. Both methods gave similar concentration profile changes and dynamic characteristics of interlayer particle redistributions in strong nonuniform adsorption fields for dense fluids. A satisfactory agreement was obtained for the temperature dependences of the self-diffusion coefficients along the pore axis. The influence of the molecule-wall potential and of intermolecular interaction were considered. The self-diffusion coefficients of the adsorbate were shown to strongly depend on the density of the mixture and the distance from pore walls.

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