Solution of an associating lattice gas model with density anomaly on a Husimi lattice

Abstract

We study a model of a lattice gas with orientational degrees of freedom which resemble the formation of hydrogen bonds between the molecules. In this model, which is the simplified version of the Henriques-Barbosa model, no distinction is made between donors and acceptors in the bonding arms. We solve the model in the grand-canonical ensemble on a Husimi lattice built with hexagonal plaquettes with a central site. The ground-state of the model, which was originally defined on the triangular lattice, is exactly reproduced by the solution on this Husimi lattice. In the phase diagram, one gas and two liquid (high density-HDL and low density-LDL) phases are present. All phase transitions (GAS-LDL, GAS-HDL, and LDL-HDL) are discontinuous, and the three phases coexist at a triple point. A line of temperatures of maximum density (TMD) in the isobars is found in the metastable GAS phase, as well as another line of temperatures of minimum density (TmD) appears in the LDL phase, part of it in the stable region and another in the metastable region of this phase. These findings are at variance with simulational results for the same model on the triangular lattice, which suggested a phase diagram with two critical points. However, our results show very good quantitative agreement with the simulations, both for the coexistence loci and the densities of particles and of hydrogen bonds. We discuss the comparison of the simulations with our results.

12 pages, 5 figures

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• Order-disorder transition in a two-dimensional associating lattice gas
• Thermodynamic behavior of binary mixtures of hard spheres: Semianalytical solutions on a Husimi lattice built with cubes
• Solution of semi-flexible self-avoiding trails on a Husimi lattice built with squares
• Fluid-fluid demixing and density anomaly in a ternary mixture of hard spheres
• Phase diagram and critical properties of a two-dimensional associating lattice gas
• Entropy of fully-packed rigid rods on generalized Husimi trees: a route to the square lattice limit
• Semianalytical solutions of Ising-like and Potts-like magnetic polymers on the Bethe lattice