Influence of intermolecular forces at critical-point wedge filling

We use microscopic density functional theory to study filling transitions in systems with long-ranged wall-fluid and short-ranged fluid-fluid forces occurring in a right-angle wedge. By changing the strength of the wall-fluid interaction we can induce both wetting and filling transitions over a wide range of temperatures and study the order of these transitions. At low temperatures we find that both wetting and filling transitions are first order in keeping with predictions of simple local effective Hamiltonian models. However close to the bulk critical point the filling transition is observed to be continuous even though the wetting transition remains first order and the wetting binding potential still exhibits a small activation barrier. The critical singularities for adsorption for the continuous filling transitions depend on whether retarded or nonretarded wall-fluid forces are present and are in excellent agreement with predictions of effective Hamiltonian theory even though the change in the order of the transition was not anticipated.

Figure 1

Schematic illustration of the meniscus height $\ell \left(t\right)$ in a linear wedge with a tilt angle $\alpha$ with ${\ell }_w$ the equilibrium midpoint height measured above the apex. Inset shows the qualitative shape of the binding potential $W\left(\ell \right)$ for wetting at a planar wall for the cases of first-order wetting (solid line) and continuous (dashed line) wetting transitions.

Figure 2

Temperature dependence of the contact angle for two different wall strengths ${\varepsilon }_w=2\varepsilon$ and ${\varepsilon }_w=2.5\varepsilon$. The bulk critical temperature is located at $k_B{T}_c/\varepsilon =1.41$. The intersection of $\theta \left(T\right)$ with the dashed line at $\theta ={45}^{\circ }$ is the thermodynamic prediction for $T_{\mathrm{fill}}$. In the inset is shown a log-log plot illustrating the vanishing of $\theta$ in the vicinity of each $T_{\mathrm{wet}}$; both fitted straight lines have slope equal to $1/2$ consistent with the expected first-order singularity $\theta \left(T\right)\sim {(T_{\mathrm{wet}}-T)}^{\frac{1}{2}}$.

Figure 3

Coexisting density profiles near a first-order filling transition for wall strength ${\varepsilon }_w=2.5\varepsilon$ (corresponding to $k_B{T}_{\mathrm{fill}}/\varepsilon =1.05$). The upper panel shows the microscopic configuration in which the interface is tightly bound to the apex. The lower panel shows the macroscopic configuration in which the meniscus is far from the wall and meets each wall at the contact angle $\theta =\pi /4$ in line with the macroscopic condition (1).

Figure 4

Sequence of density profiles for the wedge with weaker strength (${\varepsilon }_w=2\varepsilon$) showing a continuous increase in the adsorption of liquid as $T$ is increased to the filling transition occurring at $k_b{T}_{\mathrm{fill}}/\varepsilon =1.3693$. From top left to bottom right $k_{b}T/\varepsilon =1.367,1.368,1.369$, and $1.3692$.

Figure 5

Plot of the adsorption (in reduced units) as a function of temperature for the wedge with weaker wall strength ${\varepsilon }_w=2\varepsilon$. Inset is a log-log plot and comparison with the prediction for continuous filling with retarded van der Waals interactions $\mathrm{\Gamma }\sim {(T_{\mathrm{fill}}-T)}^{-\frac{2}{3}}$.

Figure 6

Plot of the numerically determined binding potential for wetting at a planar wall with ${\varepsilon }_w=2\varepsilon$ at $k_{B}T/\varepsilon =1.393$ close to the filling temperature $T_{\mathrm{fill}}$. Notice that $W\left(\ell \right)$ shows a very small activation barrier near $\ell \approx 16\sigma$.