Incorporating Material Flexibility Effects into Adsorption Modeling Using Nonlocal Density Functional Theory

We present a thermodynamically consistent framework to model adsorption in flexible nanoporous materials by coupling three-dimensional classical density functional theory (cDFT) based on the SAFT-VR-Mie equation of state with the osmotic ensemble formalism. This approach enables the treatment of fluid adsorption in deformable frameworks, overcoming the rigid-host limitation of conventional cDFT descriptions. The methodology is first validated on a simplified MIL-53-type model, where adsorption isotherms and grand potential trends are shown to be in good agreement with molecular simulation data. The analysis highlights how breathing transitions and hysteresis emerge from the interplay between the fluid grand potential and the host free-energy landscape, emphasizing the critical role of the relative stability of narrow- and large-pore states and of the associated energy barriers. The framework is then applied to methane adsorption in the flexible metal-organic framework MIL-53. After minimal calibration of the fluid-framework cross-interactions, the model reproduces experimental adsorption isotherms at 300 and 213 K and captures adsorption-induced structural transitions within the osmotic description. While quantitative prediction of hysteresis remains sensitive to the assumed host free-energy profile, the present osmotic SAFT-cDFT approach provides a computationally efficient and predictive tool for investigating adsorption-deformation coupling in responsive porous materials, opening perspectives for the screening and thermodynamic analysis of flexible metal-organic frameworks.