Undulation Theory and Analysis of Capillary Condensation in Cylindrical and Spherical Pores

The undulation theory, recently developed to explain the mechanism of the onset of condensation in an open end slit pore, is extended to investigate the effects of pore diameter, pore wall curvature, temperature, and surface strength on the condensation of argon in cylindrical and spherical pores. Using the concept of an undulating interface separating the adsorbed phase and the gas-like core, we can determine the mean thickness of the adsorbate phase and thus the mean radius of the gas-like core just before condensation. The radius of curvature of the core is used in the Cohan-Kelvin equation, modified to account for the contribution from the solid-fluid interaction (better known as the Derjaguin-Broekhoff-de Boer equation), to derive the interfacial energy parameter. For cylinders and spheres, this parameter is always greater than the bulk phase value, which is used in the unmodified Cohan-Kelvin equation but converges to the bulk value as the pore diameter is increased. For spheres, the energy parameter is smaller than in cylinders of the same diameter but is still higher than the bulk value for pore diameters less than 6 nm. This difference is attributed to packing effects in the 3D-confined spherical geometry. This shows the interesting interplay between packing effects in 3D-spherical confinement and the cohesiveness of the adsorbate enhanced by the solid-fluid interaction.