Title: Edge contact angle and modified Kelvin equation for condensation in open pores,
Abstract: We consider capillary condensation transitions occurring in open slits of
width $L$ and finite height $H$ immersed in a reservoir of vapour. In this case
the pressure at which condensation occurs is closer to saturation compared to
that occurring in an infinite slit ($H=\infty$) due to the presence of two
menisci which 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 characterised by an edge
contact angle $\theta_e$ which is always larger than the equilibrium contact
angle $\theta$, only equal to it in the limit of macroscopic $H$. For walls
which are completely wet ($\theta=0$) the edge contact angle depends only on
the aspect ratio of the capillary and is well described by $\theta_e\approx
\sqrt{\pi L/2H}$ for large $H$. Similar results apply for condensation in
cylindrical pores of finite length. We have tested these predictions against
numerical results obtained using a microscopic density functional model where
the presence of an edge contact angle characterising 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.