Edge contact angle and modified Kelvin equation for condensation in open pores
AbstractWe 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 pcc(L;H) at which condensation occurs and show that the two menisci are characterized by an edge contact angle θe 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 θe≈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 Tw we find very good agreement for slit pores of widths of just a few tens of molecular diameters, while above Tw the modified Kelvin equation only becomes accurate for much larger systems.