Revisiting the Nature of Adsorption and Desorption Branches: Temperature Dependence of Adsorption Hysteresis in Ordered Mesoporous Silica

To gain a deeper understanding as to the nature of the adsorption hysteresis due to capillary condensation of nitrogen in ordered mesoporous silicas, we calculated the temperature dependences of the activated condensation, equilibrium transition, and activated desorption pressures for nitrogen in spherical and cylindrical silica pores with several different pore sizes on the basis of semimacroscopic continuum models. The results clearly indicate that the models capture the exact nature of capillary condensation and evaporation phenomena of a fluid in cagelike and cylindrical mesopores. The temperature dependences of the adsorption hysteresis of nitrogen measured confirm previous theoretical predictions for cylindrical pores: for the ordered mesoporous silicas with cylindrical mesopores at least greater than ∼7 nm in diameter, the capillary condensation takes place via a nucleation process followed by a growth process of a bridging meniscus at pressures higher than the equilibrium transition, while the capillary evaporation takes place via a receding meniscus from pore ends at the equilibrium. For SBA-15 and MCM-41 with smaller mesopore sizes, on the other hand, the capillary condensation takes place close to the equilibrium transition pressures, while the capillary evaporation takes place at pressures lower than the equilibrium, owing to single pore blocking due to corrugation of the cylindrical pores. We discuss the effect of curvature on surface tension in capillary condensation, as well as the relation between a change in the mechanisms of adsorption and desorption and the pore corrugation in the cylindrical pores.