Capillary waves and the mean field theory of interfaces

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Abstract
The relationship of the usual mean field molecular theory of planar interfaces to the capillary wave theory of interfaces is investigated. It is shown that the good agreement between the planar mean field theories and computer simulation of a liquid–vapor interface results from the smallness of the interfacial area chosen for simulation. For an interface of finite thickness, capillary waves lead, through a geometric effect, to a mean square dispersion that is larger than the sum of the intrinsic dispersion of a planar interface and the capillary wave dispersion of a surface. It is shown that the maximum wave vector introduced in capillary wave theory as an arbitrary cutoff parameter is predicted naturally by mean field theory. The implication of capillary wave theory on the possibility of ultralow tensions for fluids far from a critical point is discussed.

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