Edge contact angle and modified Kelvin equation for condensation in open pores

We consider capillary condensation transitions occurring in open slits of width L and finite height H immersed in a reservoir of vapor. In this case the pressure at which condensation occurs is closer to saturation compared to that occurring in an infinite slit (H=∞) due to the presence of two menisci that are pinned near the open ends. Using macroscopic arguments, we derive a modified Kelvin equation for the pressure p_{cc}(L;H) at which condensation occurs and show that the two menisci are characterized by an edge contact angle θ_{e} that is always larger than the equilibrium contact angle θ, only equal to it in the limit of macroscopic H. For walls that are completely wet (θ=0) the edge contact angle depends only on the aspect ratio of the capillary and is well described by θ_{e}≈sqrt[πL/2H] for large H. Similar results apply for condensation in cylindrical pores of finite length. We test these predictions against numerical results obtained using a microscopic density-functional model where the presence of an edge contact angle characterizing the shape of the menisci is clearly visible from the density profiles. Below the wetting temperature T_{w} we find very good agreement for slit pores of widths of just a few tens of molecular diameters, while above T_{w} the modified Kelvin equation only becomes accurate for much larger systems.