  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 > 1
(bulk-like fluctuations), one must take account of the interface's bending
rigidity at intermediate scattering vector qd = 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.
