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

TL;DR

This paper presents an exact analytical study of condensation in a lattice gas model on a random graph, revealing how heterogeneity and disorder influence phase transitions and pore occupancy in porous materials.

Contribution

It introduces an exact solution for a lattice gas on a random graph, analyzing the effects of heterogeneity and disorder on condensation and phase transitions.

Findings

Binary mixture exhibits two phase transitions with changing chemical potential.

Heterogeneity reduces critical temperature and causes pore occupancy segregation.

Model accurately describes condensation in porous structures with loops, exemplified by mesoporous silica SBA-15.

Abstract

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