Condensation in a Capped Capillary is a Continuous Critical Phenomenon

We show that condensation in a capped capillary slit is a continuous interfacial critical phenomenon, related intimately to several other surface phase transitions. In three dimensions, the adsorption and desorption branches correspond to the unbinding of the meniscus from the cap and opening, respectively, and are equivalent to 2D-like complete-wetting transitions. For dispersion forces, the singularities on the two branches are distinct, owing to the different interplay of geometry and intermolecular forces. In two dimensions we establish precise connection, or covariance, with 2D critical-wetting and wedge-filling transitions: i.e., we establish that certain interfacial properties in very different geometries are identical. Our predictions of universal scaling and covariance in finite capillaries are supported by extensive Ising model simulation studies in two and three dimensions.

Figure 1

Schematic cross section of a capped capillary of depth $D$ and width $L$ illustrating the local interfacial height $\ell (\mathbf{x})$. The slit is infinitely long in the $y$ direction. A typical adsorption isotherm is also sketched showing the rapid but continuous rise in the midpoint height near CC [$p\approx p_{\mathrm{co}}(L)$] and the complete wetting as saturation is approached.

Figure 2

Representative Monte Carlo simulation results (points) for the midpoint magnetization profile in 2D and 3D capped capillaries compared with theoretical predictions (8, 9) (curves). The temperatures, $T=0.741T_c^{\mathrm{bulk}}$ (2D) and $T=0.830T_c^{\mathrm{bulk}}$, respectively, were chosen to avoid the bulk critical region and also the roughening transition (3D).