Critical Drying of Liquids

We report a detailed simulation and classical density functional theory study of the drying transition in a realistic model fluid at a smooth substrate. This transition (in which the contact angle $\theta \to 180°$) is shown to be critical for both short-ranged and long-ranged substrate-fluid interaction potentials. In the latter case critical drying occurs at exactly zero attractive substrate strength. This observation permits the accurate elucidation of the character of the transition via a finite-size scaling analysis of the density probability function. We find that the critical exponent ${\nu }_{\parallel }$ that controls the parallel correlation length, i.e., the extent of vapor bubbles at the wall, is over twice as large as predicted by mean field and renormalization group calculations. We suggest a reason for the discrepancy. Our findings shed new light on fluctuation phenomena in fluids near hydrophobic and solvophobic interfaces.

Figure 1

Left: GCMC results for $\cos (\theta )+1$ versus $\epsilon$ for the SR and LR wall potential at $T=0.775T_c$, for $L=15\sigma$, $D=30\sigma$. For the LR case a FSS analysis of the GCMC data yields critical drying at ${\epsilon }_c=0$, as predicted by theory while for the SR case a FSS analysis gives critical drying at ${\epsilon }_c=0.52(2)$ and critical wetting at ${\epsilon }_c=4.25(5)$. Right: corresponding DFT results.

Figure 2

GCMC results for $p(\rho )$ for the LR wall potential for $D=30\sigma$ and various $L$ at a selection of near-critical values of $\epsilon$. Note that at small $\rho$ capillary evaporation occurs, manifest as a vaporlike peak in $p(\rho )$ as shown in the inset for $\epsilon =0.05$, $L=15\sigma$.

Figure 3

GCMC measurements of the scaling of the peak in $\chi (z)/{\chi }_b$ with wall-fluid potential well depth $\epsilon$ for the LR wall-fluid potential. ${\chi }_b$ is the bulk liquid phase compressibility. The system size is $L=50\sigma$, $D=30\sigma$. Inset: DFT results for $\chi (z)/{\chi }_b$ for a single wall, showing the divergence as $\epsilon \to 0$. This occurs in the way binding potential arguments predict, i.e., $\ln (\chi (l))\sim l$ with $l$ the drying layer thickness and $\chi (l)\sim {\xi }_{\parallel }^2$; see Fig. S1 of [19].

Figure 4

The scaling of ${\epsilon }_c(L)$, i.e., the wall strength at which a peak appears in $p(\rho )$, as a function of $L$ for the LR wall-fluid potential. Data are shown for two subcritical temperatures. Inset: simulation snapshot for a system with $L=40\sigma$, $\epsilon =0.2$. Particles are color coded according to their distance from the wall at $z=0$. A large correlation length is manifest in the vapor close to the wall; see the Supplemental Material [19].