Ensemble inequivalence in the design of mixtures with super-Gibbs phase coexistence
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912904770486272 |
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| author | Thewes, Filipe C. Sollich, Peter |
| author_facet | Thewes, Filipe C. Sollich, Peter |
| contents | Designing the phase behavior of multicomponent mixtures is a rich area with many potential applications. One key question is how more than $M+1$ phases, as would normally be allowed by Gibbs' phase rule at generic temperature in a mixture of $M$ molecular species, can be made to coexist in equilibrium. In the grandcanonical ensemble, such super-Gibbs phase equilibria can be realized by tuning the interactions among the $M$ species. This introduces $\sim M^2$ additional degrees of freedom and hence a superlinear number of phases that can coexist. We show that, surprisingly, there is no straightforward equivalence to the situation in the experimentally relevant canonical ensemble: here only a subset of the grandcanonical phases will generically be realized. This subset is determined by interfacial tensions in addition to bulk free energies. Using a graph-theoretical approach, we determine a sufficient set of inequalities for the interfacial tensions for which all grandcanonical phases are realized so that equivalence of ensembles is effectively restored. We illustrate the design method for a two-component mixture with four coexisting phases and point out the route for generalizing this to a higher number of components. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07734 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ensemble inequivalence in the design of mixtures with super-Gibbs phase coexistence Thewes, Filipe C. Sollich, Peter Statistical Mechanics Soft Condensed Matter Designing the phase behavior of multicomponent mixtures is a rich area with many potential applications. One key question is how more than $M+1$ phases, as would normally be allowed by Gibbs' phase rule at generic temperature in a mixture of $M$ molecular species, can be made to coexist in equilibrium. In the grandcanonical ensemble, such super-Gibbs phase equilibria can be realized by tuning the interactions among the $M$ species. This introduces $\sim M^2$ additional degrees of freedom and hence a superlinear number of phases that can coexist. We show that, surprisingly, there is no straightforward equivalence to the situation in the experimentally relevant canonical ensemble: here only a subset of the grandcanonical phases will generically be realized. This subset is determined by interfacial tensions in addition to bulk free energies. Using a graph-theoretical approach, we determine a sufficient set of inequalities for the interfacial tensions for which all grandcanonical phases are realized so that equivalence of ensembles is effectively restored. We illustrate the design method for a two-component mixture with four coexisting phases and point out the route for generalizing this to a higher number of components. |
| title | Ensemble inequivalence in the design of mixtures with super-Gibbs phase coexistence |
| topic | Statistical Mechanics Soft Condensed Matter |
| url | https://arxiv.org/abs/2501.07734 |