Comprehensive Modeling of Capillary Condensation in Open-Ended Nanopores: Equilibrium, Metastability, and Spinodal

Capillary condensation within open-ended cylindrical nanopores is modeled thermodynamically and kinetically, in order to provide reasonable estimates of both the equilibrium phase transition pressure and capillary condensation pressure from a metastable state. The thermodynamic model is established by adding to the conventional Derjaguin–Broekhoff–de Boer model the effects of curvature on the fluid–solid interaction potentials and surface tension at the vapor–liquid interface. The equilibrium vapor–liquid phase transition pressure estimated via the thermodynamic model is in close agreement with that from the nonlocal density functional theory. In contrast to the equilibrium phase transition, capillary condensation from a metastable state cannot be estimated by the conventional thermodynamic models, because it inherently includes an activated process. To overcome this challenge, we propose a kinetic model of metastable capillary condensation for the first time. The model is based on the finding in our previous molecular simulation study, that metastable capillary condensation occurs when the corresponding rate constant reaches a critical value. The proposed kinetic model allows us to quantitatively reproduce the experimental capillary condensation pressures over a wide range of temperatures and mesopore sizes without computationally expensive molecular simulations.