Capillary Condensation and Evaporation in Irregular Channels: Sorption Isotherm for Serially Connected Pore Model

Geometrical disorder can strongly impact phase equilibria of fluids in mesoporous solids. There is insufficient knowledge of how the structural disorder results in the emergence of the cooperativity effects in phase transitions. To tackle this problem, understanding of the complex interplay between nucleation and phase growth and the pore space morphology is needed. We use statistically disordered chains of serially connected single pores with varying pore sizes to mimic geometric disorder and solve the problem using a statistical thermodynamics approach. As the main result, we derive the exact solution for the average phase composition at any thermodynamic condition including all states within the hysteresis region, i.e., the entire family of the sorption isotherms including the scanning isotherms. We show that our approach correctly reproduces the results of computational modeling using the mean field theory of lattice gas in irregular model pores. The theory developed is directly applicable to the analysis of phase equilibria in materials with tubular pores, such as MCM-41 and SBA-15, but can also be used to gain deeper insight into phase behavior in mesoporous solids with random pore networks.