Three-Phase Fluid Coexistence in Heterogenous Slits

We study the competition between local (bridging) and global condensation of fluid in a chemically heterogeneous capillary slit made from two parallel adjacent walls each patterned with a single stripe. Using a mesoscopic modified Kelvin equation, which determines the shape of the menisci pinned at the stripe edges in the bridge phase, we determine the conditions under which the local bridging transition precedes capillary condensation as the pressure (or chemical potential) is increased. Provided the contact angle of the stripe is less than that of the outer wall we show that triple points, where evaporated, locally condensed, and globally condensed states all coexist are possible depending on the value of the aspect ratio $a=L/H$, where $H$ is the stripe width and $L$ the wall separation. In particular, for a capillary made from completely dry walls patterned with completely wet stripes the condition for the triple point occurs when the aspect ratio takes its maximum possible value $8/\pi$. These predictions are tested using a fully microscopic classical density functional theory and shown to be remarkably accurate even for molecularly narrow slits. The qualitative differences with local and global condensation in heterogeneous cylindrical pores are also highlighted.

Figure 1

Illustration of (a) gaslike, (b) locally condensed bridgelike, and (c) liquidlike states in a chemically heterogenous slit. Possible configurations depend on $\mu$.

Figure 2

DFT results for the grand potential as a function of the chemical potential (both in units of $ϵ$) for the maximum contrast slit with ${\theta }_p=0$ and $\theta =\pi$ and $H=10\sigma$. Three values of $L$ are shown corresponding to the aspect ratios (a) $a=2.3$ for which bridging precedes the global capillary condensation, (b) $a=2.6$ our best estimate of the triple point, and (c) $a=2.8$ where only single capillary condensation transition is stable and the bridge configurations are always metastable. Our estimate to the triple point $a=2.6$ is very close to the predicted value $a_T$ as given by (5).

Figure 3

Predicted triple-point aspect ratios for the heterogenous slit and the pore geometries for the completely wet patch ${\theta }_p$ as a function of the contact angle $\theta$ of the outer wall.