On the spectrum of fluctuations of a liquid surface: from the molecular scale to the macroscopic scale

We show that to account for the full spectrum of surface fluctuations from low scattering vector qd<<1 (classical capillary wave theory) to high qd approximately > 1 (bulklike fluctuations), one must take account of the interface's bending rigidity at intermediate scattering vector qd approximately < 1, where d is the molecular diameter. A molecular model is presented to describe the bending correction to the capillary wave model for short-ranged and long-ranged interactions between molecules. We find that the bending rigidity is negative when the Gibbs equimolar surface is used to define the location of the fluctuating interface and that on approach to the critical point it vanishes proportionally to the interfacial tension. Both features are in agreement with Monte Carlo simulations of a phase-separated colloid-polymer system.