Precursors to Molecular Slip on Smooth Hydrophobic Surfaces

Experiments and simulations suggest that simple liquids may experience slip while flowing near a smooth, hydrophobic surface. Here we show how precursors to molecular slip can be observed in the complex response of a liquid to oscillatory shear. We measure both the change in frequency and bandwidth of a quartz crystal microbalance during the growth of a single drop of water immersed in an ambient liquid. By varying the hydrophobicity of the surface using self-assembled monolayers, our results show little or no slip for water on all surfaces. However, we observe excess transverse motion near hydrophobic surfaces due to weak binding in the corrugated surface potential, an essential precursor to slip. We also show how this effect can be easily missed in simulations utilizing finite-ranged interaction potentials.

Figure 1

(a) Diagram of the experimental setup. The QCM is immersed in a temperature-controlled bath of undecane as a water drop is slowly grown and imaged on the surface. (b),(c) The QCM emits a decaying shear wave which penetrates a characteristic distance $\delta \approx 200\mathrm{nm}$ into the liquid. (d) The hydrophobicity of the QCM surface is modified by oxygen plasma cleaning and/or coating with self-assembled monolayers. (e) The liquid’s interaction with the surface adds inertia and damping to the crystal’s motion, which decreases the resonant frequency by $\mathrm{\Delta }f$ and increases the half-bandwidth by $\mathrm{\Delta }\mathrm{\Gamma }$.

Figure 2

(a) $\mathrm{\Delta }f$ scales linearly with $A_{\text{drop}}$ on ${\mathrm{SiO}}_2$ surfaces (blue), and gold and gold-SAM surfaces (red). (b) The slip length $b$ is defined by extrapolating the linear velocity profile at the surface. The dashed lines in (a) represent $b_w=\pm 2\mathrm{nm}$, assuming $b_u=0$. (c) Differential slip length between water and undecane from Eq. (4) versus advancing contact angle of the water. The dashed line is a theoretical prediction [17], as described in the text. Symbol shapes correspond to different surface chemistries, and symbol fills indicate different experiments for a given surface. Error bars represent variations from multiple experiments, linear fitting of the data, and optical contact area measurements.

Figure 3

(a) $\mathrm{\Delta }\mathrm{\Gamma }$ increases linearly with $A_{\text{drop}}$ on ${\mathrm{SiO}}_2$ surfaces (blue), and on gold and gold-SAM surfaces (red). (b) Schematic showing a larger amplitude of motion in the liquid in comparison to the solid surface. (c) Difference in motional amplitude between the water and undecane at the solid surface, normalized by the amplitude of the solid, versus the advancing contact angle of the water drop in undecane. Symbol shapes correspond to different surface chemistries, and symbol fills indicate different experiments for a given surface. Error bars represent variations from multiple experiments, linear fitting of the data, and optical contact area measurements.

Figure 4

(a) One-dimensional model showing a liquid molecule moving in the transverse potential during left and right oscillatory motion of the surface. The excess amplitude of the liquid is $D_l-D_s$. (b) Illustration of a fcc lattice of dimensions $w\times w\times w/2$ and a liquid molecule at a center-to-center distance $h$ above the top surface molecular plane. (c) Local peak-to-peak variation in potential, $V_{pp}$, normalized by the interaction energy, versus $h$. The local potential depends on the size of the lattice, as well as the cutoff radius $r_0$ used for the pair potential. Unless specified, $r_0=\infty$.