Analytical equation for the mesopore size distribution function of open cylindrical capillaries

For the characterization of porous structures, besides the specific surface area, the pore size distribution is of special interest. In this paper, the pore size distribution of mesoporous structures is calculated from the adsorption branch of the hysteresis loop, whereby only loops of type H1 are considered. The modeling is done only for cylindrical capillaries and the calculation of the pore size distribution is done by a combination of the percolation theory and the theory of capillary condensation. By applying percolation theory to the adsorption process, the pressure dependence of pore filling during capillary condensation is described. Because of a lack of strictly theoretically based equations for the adsorption process by capillary condensation, a mathematical adaptation to measured data is done by the Bernoulli equation. This is proposed by the authors for the first time for a description of adsorption–desorption processes. Thus a new, strictly thermodynamic method to calculate the mesopore size distribution is gained. As an example, the pore size distribution is calculated. The results coincide well with other evaluation methods