Wetting of prototypical one- and two-dimensional systems: thermodynamics and density functional theory

Consider a two-dimensional capped capillary pore formed by capping two parallel planar walls with a third wall orthogonal to the two planar walls. This system reduces to a slit pore sufficiently far from the capping wall and to a single planar wall when the side walls are far apart. Not surprisingly, wetting of capped capillaries is related to wetting of slit pores and planar walls. For example, the wetting temperature of the capped capillary provides the boundary between first-order and continuous transitions to condensation. We present a numerical investigation of adsorption in capped capillaries of mesoscopic widths based on density functional theory. The fluid-fluid and fluid-substrate interactions are given by the pairwise Lennard-Jones potential. We also perform a parametric study of wetting in capped capillaries by a liquid phase by varying the applied chemical potential, temperature, and pore width. This allows us to construct surface phase diagrams and investigate the complicated interplay of wetting mechanisms specific to each system, in particular, the dependence of capillary wetting temperature on the pore width.