Statistical modeling of equilibrium phase transition in confined fluids

The phase transition of confined fluids in mesoporous materials deviates from that of bulk fluids due to the interactions with the surrounding heterogeneous structure. For example, adsorbed fluids in metal-organic-frameworks (MOFs) have atypical phase characteristics such as capillary condensation and higher-order phase transitions due to a strong heterogeneous field. Considering a many-body problem in the presence of a nonuniform external field, we model the host-guest and guest-guest interactions in MOFs. To solve the three-dimensional Ising model, we use the mean-field theory to approximate the guest-guest interactions and Mayer's f-functions to describe the host-guest interactions in a unit cell. Later, using Hill's theory of nanothermodynamics, we define differential thermodynamic functions to understand the distribution of intensive properties and integral thermodynamic functions to explain the phase transition in confined fluids. The investigation reveals a distinct behavior where fluids confined in larger pores undergo a discontinuous (first-order) phase transition, whereas those confined in smaller pores experience a continuous (higher-order) phase transition. Furthermore, the results indicate that the free-energy barrier for phase transitions is lower in confined fluids than in bulk fluids giving rise to a lower condensation pressure relative to the bulk saturation pressure. Finally, the integral thermodynamic functions are succinctly presented in the form of a phase diagram, marking an initial step toward a more practical approach for understanding the phase behavior of confined fluids.