The spectrum of experimentally accessible states for melting and freezing transitions in mesoporous materials

Structural disorder in mesoporous solids gives rise to complex phase behavior for materials confined within their pore spaces. As a result, a wide spectrum of possible phase configurations associated with spatial distributions of thermodynamic phases throughout the pore networks can be realized in experiments. Despite their importance, quantifying these states remains largely unaddressed. By considering solid-liquid equilibria as a representative example and using a simple random network model, we investigate the spectrum of such states accessible in real experiments and relate this spectrum to the structural characteristics of porous solids. We classify these states by their free energies and demonstrate how network effects break degeneracies for specific phase compositions and temperatures. Furthermore, we identify the experimental conditions that delineate boundary free energy states, differentiating accessible from inaccessible states. The insights from this study on solid-liquid equilibria are also equally applicable to gas-liquid equilibria in confined spaces and contribute to a deeper understanding of relaxation dynamics associated with hysteresis.