Sorption Hysteresis Is a Deformation Problem: An Atomistic Free-Energy Perspective

Gas sorption hysteresis in flexible amorphous materials plays an important role in a plethora of engineering applications, yet its mechanistic origin remains unresolved. Here, we develop a stepwise hybrid grand canonical Monte Carlo/molecular dynamics (GCMC/MD) framework that follows a continuous adsorption-desorption cycle in a fully deformable microporous carbonaceous matrix under equilibrium conditions, eliminating diffusion-rate artifacts. We show that hysteresis arises from adsorption-induced swelling and persistent micromechanical rearrangements of the host: at identical chemical potentials, the pore volume, pore size distributions (PSDs), and connectivity remain systematically larger on the desorption branch, revealing irreversible structural evolution. To quantify this effect, we introduce a two-route alchemical free energy perturbation (FEP) protocol that isolates the reversible work associated with host deformation. The resulting deformation free energy density is consistently higher on desorption than on adsorption, demonstrating that contraction of the metastably swollen framework requires more work than its expansion. This branch-asymmetric deformation free energy provides a fundamental thermodynamic explanation for sorption hysteresis in flexible amorphous microporous solids. These findings highlight the need to incorporate sorption-induced deformation and metastable free energy states into predictive models of gas production, storage, and separations in deformable porous materials.