Surface fluctuations at the liquid-liquid interface

Within the capillary-wave model (CWM), the liquid-vapor interface is a hypothetical two-dimensional surface whose deviations from planarity are represented as long wavelength capillary waves. We modify the CWM for liquid-liquid interfaces and treat them as two harmonically interacting surfaces (model 1). Corrections to the model are proposed to prevent the usual divergence of the capillary- wave broadening in the thermodynamic limit by introducing a surface-bulk coupling (model 2) and to incorporate the curvature of the two surfaces (model 3). Expressions for the capillary- wave contribution to the surface tension of the interface are obtained. Molecular dynamics simulations are performed for two series of water-hydrocarbon interfacial systems (a) n-pentane, 2-methyl pentane, and 2,2,4-trimethyl pentane (constant chain length) and (b) n-octane, 2-methyl heptane, and 2,2,4- trimethyl pentane (constant molecular mass). A simple procedure to identify the molecular sites at the surface is utilized for a molecular representation of the surface. The distribution of these surface sites as well as the wave-vector dependence of surface fluctuations are analyzed in order to extract the parameters required for model 2. A small length scale is identified above which surface fluctuations correspond to capillary-wave fluctuations thereby connecting the molecular and mesoscopic scales. This approach is applied to all interfacial systems studied here and predictions based on the parameters found to be in good agreement with independent simulation results for surface tension and interfacial widths. Hydrocarbon branching has a small effect on model parameters.