### 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

**Effect of disorder on condensation in the lattice gas model on a random graph.** / Handford, Thomas P.; Dear, Alexander; Perez-Reche, Francisco J.; Taraskin, Sergei N.

Research output: Contribution to journal › Article

*Physical Review. E, Statistical, Nonlinear and Soft Matter Physics*, vol. 90, no. 1, 012144. https://doi.org/10.1103/PhysRevE.90.012144

}

TY - JOUR

T1 - Effect of disorder on condensation in the lattice gas model on a random graph

AU - Handford, Thomas P.

AU - Dear, Alexander

AU - Perez-Reche, Francisco J.

AU - Taraskin, Sergei N.

PY - 2014/7/31

Y1 - 2014/7/31

N2 - 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.

AB - 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.

KW - capillary condensation

KW - mesoporous silica

KW - phase-transitions

KW - porous materials

KW - ising-model

KW - Bethe lattice

KW - spin-glasses

KW - systems

KW - fluids

KW - MCM-41

U2 - 10.1103/PhysRevE.90.012144

DO - 10.1103/PhysRevE.90.012144

M3 - Article

VL - 90

JO - Physical Review. E, Statistical, Nonlinear and Soft Matter Physics

JF - Physical Review. E, Statistical, Nonlinear and Soft Matter Physics

SN - 1539-3755

IS - 1

M1 - 012144

ER -