The intrinsic liquid–vapour interface

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Abstract
The steepness of the equilibrium transition density profile of a planar liquid–gas interface at a first-order phase transition has been attested to by several experiments, by numerous computer simulations, and by perhaps even more numerous approximate theories. It has also become reasonably clear on dynamical grounds that the observed profile should represent an average of capillary-wave distortions of some “intrinsic profile”. Here, the intrinsic profile is examined from two points of view. First, it is taken as representing a short-time mean normal density pattern with spatial origin chosen at some reference density. The long-term dynamics then consist of normal displacements as a function of transverse location. It is seen that the statistical mechanics of this pattern, weighted by surface tension energy, accounts for the predicted and observed free-interface long-range transverse correlations and softened density profile. In addition, it is consistent with the modification of one and two-point distributions as a hard wall is pushed into the interface. A second representation is as the characteristic profile of mean-field theory, in which fluctuations in the field of attractive interactions responsible for the liquid–gas condensation are neglected. This is identified with a zerothorder expansion of the Kac–Siegert potential ensemble representation, in which the next order brings in the required capillary waves.

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