Generalized Statistical Isotherm for Modeling Adsorption Equilibria in Stimuli-Responsive Framework Materials

Designing large-scale adsorption-based separation units requires a multiscale understanding of material behavior, from molecular interactions to process-level performance. An underpinning challenge is the development of predictive multicomponent adsorption equilibrium models for systems departing from the classic type I isotherm for microporous adsorbents. Adsorbents that undergo adsorption-induced transitions (flexible adsorbents) belong to this category and are a class of framework materials that exhibit unique features such as sigmoidal equilibrium isotherms and intrinsic thermal management capabilities. Despite their promise for practical applications, flexible adsorbents remain underexplored at the process scale due to the lack of a suitable equilibrium isotherm model that mechanistically captures their adsorption-induced structural transitions. Here, we present a simplified statistical isotherm model for transition materials (SSI-T) as a generalized approach to parametrize─using a combination of sorbate-dependent and -independent physical parameters─the adsorption equilibria in flexible adsorbents that exhibit a broad range of structural and configurational transitions upon adsorption. We have validated the model using unary and binary equilibrium data for gate-opening, breathing, and configurational transitions in multiple adsorbent-adsorbate systems. Our formulation represents the first continuous, differentiable, and explicit isotherm model in the literature capable of accurately describing unary adsorption and desorption isotherms in flexible adsorbents, and predicting binary equilibria for multiple types of adsorption-induced transitions without any additional parameters. Because SSI-T is an explicit function of state variables, it can be seamlessly integrated into process-scale simulators, enabling the design and optimization of adsorption-based technologies that use flexible adsorbents.