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We show that to account for the full spectrum of surface fluctuations fromlow scattering vector qd << 1 (classical capillary wave theory) to high qd > 1(bulk-like fluctuations), one must take account of the interface's bendingrigidity at intermediate scattering vector qd = 1, where d is the moleculardiameter. A molecular model is presented to describe the bending correction tothe capillary wave model for short-ranged and long-ranged interactions betweenmolecules. We find that the bending rigidity is negative when the Gibbsequimolar surface is used to define the location of the fluctuating interfaceand that on approach to the critical point it vanishes proportionally to theinterfacial tension. Both features are in agreement with Monte Carlosimulations of a phase-separated colloid-polymer system.

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