Phase transitions in a cylindrical pore: Grand canonical Monte Carlo, mean field theory and the Kelvin equation

We report adsorption isotherms for a Lennard-Jones fluid confined in a cylindrical pore with attractive walls at temperatures above the wetting temperature. A low temperature isotherm exhibited two branches with metastable states and hysteresis. The grand potential of the system was calculated and the thermodynamic transition between the two branches of the isotherm was found. This transition is shifted to lower pressures than the bulk transition; the Kelvin equation was found not to predict accurately the shift. A higher temperature isotherm, still below the bulk critical point, was continuous and reversible and no hysteresis was found. This confirms the existence of a capillary critical point for the confined fluid. The mean field density functional theory which has been used to study confined fluids is found to give the correct qualitative features of the phase behaviour, in agreement with other studies.