Pore Size Distribution Analysis Using Developing Hysteresis of Nitrogen in the Cylindrical Pores of Silica

A new method of mesopore size analysis was developed for the cylindrical pores of silica using a developing hysteresis of nitrogen measured at liquid nitrogen temperature. The method is based on the semimacroscopic approach of a modified Bonnet-Wolf model that deals with the grand potential of a vapor bubble in the cylindrical pore. It is capable of assessing correctly the pore structures of mesoporous materials with cylindrical pores using the narrow hysteresis loop of the developing hysteresis. When the mesoporous materials possess cylindrical pores of minor imperfections, two pore size distributions (PSDs) from the adsorption and desorption branches overlap. On the other hand, for cylindrical pores with an enhanced amplitude of pore corrugations and/or constrictions, PSD from the desorption branch is shifted to smaller pore sizes compared to the one from the adsorption branch, and at the same time, both the PSDs evaluated are shifted to lower pore sizes compared to the actual ones. The actual PSD can be assessed from the reversible isotherm measured at a hysteresis critical temperature. In principle, the present method may enable the determination of the PSDs from the adsorption hysteresis measured at any given temperature for mesoporous materials with cylindrical pores.