Thermodynamic modeling of equilibrium phase transitions in confined fluids

Phase transition of confined fluids in mesoporous materials deviates from that of bulk fluids owing to their interactions with the surrounding heterogeneity. For example, metal-organic frameworks (MOFs) create a strong heterogeneous field, hence adsorbed fluids in MOFs show atypical phase characteristics such as capillary condensation and higher-order phase transitions. This behavior is modeled by decoupling the host-guest and guest-guest interactions as a many-body problem in the presence of an external non-uniform field. We employ mean-field theory to approximate the guest-guest interactions and Mayer’s f-function for the host-guest interactions in a 3-dimensional unit cell. In accordance with Hill’s theory of nanothermodynamics, the smaller length scale and inhomogeneous nature of the problem give rise to an excess chemical potential. Furthermore, the phase transition is studied in canonical (NVT) and grand canonical (μVT) ensembles within the Ising framework. Employing this model, differential and integral intrinsic thermodynamic functions such as entropy, enthalpy, free energy, and pressure in the confined space are obtained. For fluid confined in larger pore sizes, we observe a first-order phase transition, whereas a higher-order phase transition is observed for fluid confined in smaller pore sizes. Finally, the integral thermodynamic functions are summarized in the form of a phase diagram, positing a first step of a more generalizable way to understand the phase of confined fluid.