X-Ray Synchrotron Study of Liquid-Vapor Interfaces at Short Length Scales: Effect of Long-Range Forces and Bending Energies

We have investigated the small-scale structure of the liquid-vapor interface using synchrotron x-ray scattering for liquids with different molecular structures and interactions. The effective momentum-dependent surface energy first decreases from its macroscopic value due to the effect of long-range forces, and then increases with increasing wave vector. The results are analyzed using a recent density functional theory. The large wave-vector increase is attributed to a bending energy for which local and nonlocal contributions are equally important.

Figure 1

(a) OMCTS ($[({\mathrm{C}\mathrm{H}}_3{)}_2\mathrm{S}\mathrm{i}\mathrm{O}{]}_4$; black $=$ Si, black and white $=$ O, grey $=$ C, white $=$ H) is inert and of low polarity ($\mu \simeq 0.42\mathrm{D}$). The molecular diameter is $\simeq 0.75–0.85\mathrm{n}\mathrm{m}$ [12]. (b) Squalane (${\mathrm{C}}_{30}{\mathrm{H}}_{62}$) with 6 methyl groups symmetrically placed along a 24 carbon backbone is a soft sphere with gyration radius $\simeq 0.7\mathrm{n}\mathrm{m}$ [13].

Figure 2

Schematic view of the experiment. The Teflon trough (inner diameter $=330\mathrm{m}\mathrm{m}$) is mounted on an active antivibration system. The size of the incident beam is fixed by a $275\mu \mathrm{m}\times 250\mu \mathrm{m}$ ($H\times V$) slit. The horizontal resolution of the experiment is fixed by the slits $S_c$, $300\mu \mathrm{m}$ wide, and $S_d$, $545\mu \mathrm{m}$ wide, placed at $254$ and $882\mathrm{m}\mathrm{m}$ from the sample, respectively, as well as by the illuminated area seen by the detector (dark grey paralleogram). $\mathbf{q}$ is the wave-vector transfer whose in-plane component is ${\mathbf{q}}_{\parallel }$.

Figure 3

Signal recorded on the PSD for in-plane wave-vector transfers $q_y={10}^8{\mathrm{m}}^{-1}$ (○) and $q_y=4\times {10}^8{\mathrm{m}}^{-1}$ (△) for OMCTS. The solid line is the best fit [via $\gamma (q_{\parallel })$, ${\kappa }_T$, and $q_{\mathrm{m}\mathrm{a}\mathrm{x}}$] to Eq. (2); long and short dashed lines are, respectively, surface and bulk contributions as explained in the text.

Figure 4

$\gamma (q_{\parallel })/\gamma$ for OMCTS, carbon tetrachloride, squalane, water, and glycol. Lines are the best fits using Eq. (3). Dashed lines give the long-range forces contribution (excluding nonlocal bending energy). Bottom: Contribution of long-range forces, local bending energy, and nonlocal bending energy to the momentum dependent surface tension for OMCTS.