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The lattice gas model of condensation in a heterogeneous pore system,represented by a random graph of cells, is studied using an exact analyticalsolution. A binary mixture of pore cells with different coordination numbers isshown to exhibit two phase transitions as a function of chemical potential in acertain temperature range. Heterogeneity in interaction strengths isdemonstrated to reduce the critical temperature and, for large enough degree ofdisorder, divides the cells into ones which are either on average occupied orunoccupied. Despite treating the pore space loops in a simplified manner, therandom-graph model provides a good description of condensation in porousstructures containing loops. This is illustrated by considering capillarycondensation in a structural model of mesoporous silica SBA-15.

Effect of disorder on condensation in the lattice gas model on a random graph