Fractal dimension of microporous carbon on the basis of the Polanyi-Dubinin theory of adsorption. Part 3: Adsorption and adsorption thermodynamics in the micropores of fractal carbons

Abstract

Fundamental thermodynamic relations are formulated based on the equation of physical adsorption on microporous fractal solids, proposed previously and derived from the Polanyi-Dubinin theory of volume filling of micropores. A new adsorption isotherm and corresponding adsorption heat equations are verified using the experimental data published by Dubinin and Polstyanov of benzene and cyclohexane adsorption and adsorption heat on three microporous carbons. The obtained average correlation coefficients are compared with those from the original Dubinin-Astakhov (DA) equation. The correlation between the theoretical and experimental data is satisfactory, especially in the range of relative adsorptive pressures for which, following Stoeckli, the potential theory is accepted as appropriate. It is shown that, for nearly all the cases, micropore volumes are similar to those obtained from the original DA equation. Fractal dimensions calculated from adsorption data of both sorbates on the same carbon are practically equal and can be treated as constants that characterize the micropores of a solid. Average pore diameters, calculated from the obtained fractal dimensions, and also minimal and maximal pore widths are similar to those determined by the methods proposed by other authors, especially those obtained using the equation of McEnaney, developed from the analysis of SAXS data. The explanation of why the approximate adsorption isotherm equation proposed by Avnir and Jaroniec cannot be applied for the correct determination of a micropore fractal dimension is given.