### 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 degreeS 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.

Original language | English |
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Article number | 012144 |

Number of pages | 19 |

Journal | Physical Review. E, Statistical, Nonlinear and Soft Matter Physics |

Volume | 90 |

Issue number | 1 |

DOIs | |

Publication status | Published - 31 Jul 2014 |

### Keywords

- capillary condensation
- mesoporous silica
- phase-transitions
- porous materials
- ising-model
- Bethe lattice
- spin-glasses
- systems
- fluids
- MCM-41

## Cite this

*Physical Review. E, Statistical, Nonlinear and Soft Matter Physics*,

*90*(1), [012144]. https://doi.org/10.1103/PhysRevE.90.012144