Engineering Free-Energy Landscape of Thermally Responsive Flexible MOFs: From Enthalpy-Entropy Competition to Predictive Design.

Thermally responsive structural transitions in flexible metal-organic frameworks (FMOFs) play a vital role in gas separation, energy storage, and sensing. Unlike pressure or guest adsorption, temperature governs phase stability by modulating the balance between enthalpic and entropic contributions. This review establishes a unified free-energy landscape (FEL) framework to rationalize thermally induced breathing across diverse FMOF systems. Key structural degrees of freedom, including ligand conformational flexibility, metal-ligand (M-L) bond dynamics, and framework topology, are evaluated for their roles in shaping the FEL. A thermodynamic phase diagram with enthalpy change (ΔH) and entropy change (ΔS) as axes partitions FMOFs into four characteristic regimes: closed-pore dominant, open-pore dominant, bistable, and hysteresis-governed. The topology of the FEL-encompassing the depth and connectivity of its minima and the kinetic barriers (ΔG‡) between them-determines whether breathing is abrupt, continuous, or stepwise. Regulation strategies including ligand functionalization, metal substitution, defect engineering, and nanoconfinement are interpreted as systematic movements on the ΔH-ΔS diagram. This review provides a mechanistic foundation and a predictive roadmap for designing thermally responsive FMOFs with tailored transition temperatures, hysteresis width, and breathing amplitude.