Capillary wave fluctuations and intrinsic widths of coupled fluid-fluid interfaces: An x-ray scattering study of a wetting film on bulk liquid

An x-ray specular reflectivity (XR) and off-specular diffuse scattering (XDS) study of the coupled thermal capillary fluctuations and the intrinsic profiles of two interacting fluid-fluid interfaces is presented. The measurements are carried out on complete wetting films of perfluoromethylcyclohexane (PFMC) on the surface of bulk liquid eicosane (C20), as a function of film thickness 30 < D < 160 angstrom. In order to facilitate the analysis and interpretation of the data with minimal complexity, approximate methods for calculating scattering intensities are developed to take into account the subtleties of thermal diffuse scattering from layered liquid surfaces. With these methods, the calculations of XR/XDS intensities are reduced to a single numerical integration of simple functions in real space. In addition, an analytic expression is derived for small-angle XR that contains Debye-Waller-like factors with effective capillary roughness and takes into account the partial correlations of the two interfaces. The expression for the XR is quantitatively accurate so long as the reflection angle is small enough that the scattering from interfaces is distinguishable from bulk scattering. The results of the XR and XDS data analysis indicate that the capillary fluctuations at the two interfaces of the wetting films are partially correlated and their coupling is consistent with the van der Waals interactions. The relatively large intrinsic width (4 similar to 6 angstrom) of the liquid-liquid interface observed for thicker films (D greater than or similar to 50 angstrom) is comparable to the value expected for the bulk liquid-liquid interface (D ->infinity), determined by either the radius of gyration (5.3 angstrom) or the bulk correlation length (4.8 angstrom) of the alkane C20. The intrinsic liquid-vapor interfacial width is sharper (similar to 2 angstrom) and remains essentially constant over the entire probed range of D.