Quantifying Density Fluctuations in Water at a Hydrophobic Surface: Evidence for Critical Drying

Employing smart Monte Carlo sampling techniques within the grand canonical ensemble, we investigate the properties of water at a model hydrophobic substrate. By reducing the strength of substrate-water attraction, we find that fluctuations in the local number density, quantified by a rigorous definition of the local compressibility $\chi (z)$, increase rapidly for distances $z$ within one or two molecular diameters from the substrate as the degree of hydrophobicity, measured by the macroscopic contact angle $\theta$, increases. Our simulations provide evidence for a continuous (critical) drying transition as the substrate-water interaction becomes very weak: $\cos (\theta )\to -1$. We speculate that the existence of such a transition might account for earlier simulation observations of strongly enhanced density fluctuations.

Figure 1

(a) The measured forms of $p(\rho )$ for a selection of values of ${\epsilon }_{wf}$ spanning the range from wetting to drying; the contact angles $\theta$ are shown. The system size is $L=D=20\AA$. (b) A closeup of the region close to the drying transition. Note the continuous erosion of the liquid peak as ${\epsilon }_{wf}$ decreases. In (a) and (b), the dashed line is $p(\rho )$ for the periodic system with $L=20\AA$.

Figure 2

Estimates of $\cos (\theta )+1$ as a function of ${\epsilon }_{wf}$ spanning the region from wetting $\cos (\theta )=1$ to drying $\cos (\theta )=-1$. Statistical uncertainties are smaller than symbol sizes.

Figure 3

Normalized number density profiles $\rho (z)$ for various values of ${\epsilon }_{wf}$ in the hydrophobic regime. ${\rho }_b$ is the bulk liquid density at ${\mu }_{cx}$.

Figure 4

The normalized local compressibility $\chi (x)/{\chi }_b$ for a selection of values of ${\epsilon }_{wf}$. These correspond to the density profiles of Fig. 3.