Free-Energy Landscapes of Clathrate Hydrate Polymorphism

Clathrate hydrates exhibit polymorphism among distinct hydrogen-bonded water-framework topologies, yet the structure observed during formation or transformation need not be the thermodynamically stable polymorph. A structure-resolved free-energy framework is developed to distinguish stable single-polymorph states, equilibrium coexistence of compositionally distinct polymorphs, and kinetically retained metastable structures. Guest-induced cage stabilization is combined with the reference free energy of each water framework, while closed multicomponent systems are evaluated through a global convex-envelope construction. Cyclopropane provides a positive benchmark for temperature-driven sI−sII polymorphism, with the calculated lower coexistence pressure differing from the experimental four-phase value by 0.68%. Methane−ethane exhibits composition-driven re-entrant sI−sII−sI polymorphism; canonical reconstruction reveals strong structural−compositional partitioning, with the lower transition showing a polymorph-separation driving force approximately nine times larger than the upper transition. In methane−propane, experimentally retained sI states remain strongly on the sII-favored side of the calculated free-energy landscape, supporting kinetic polymorph selection rather than equilibrium coexistence. The resulting framework provides a thermodynamic reference for interpreting polymorph selection, coexistence, guest partitioning, and structural memory during clathrate crystallization.