Analytic results for wetting transitions in the presence of van der Waals tails

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Abstract
We present a systematic study of the wetting behavior of a one-component fluid at a wall and of interfacial wetting in binary liquid mixtures by taking into account all aspects of the long-range character of the van der Waals interactions between the particles. The corresponding effective interface potential is expressed in terms of those free interfacial profiles that emerge as a consequence of the wetting phenomena. This approach goes beyond previous ones, because we take into account the van der Waals tails of these interfaces, and in the one-component case the structure of the emerging wall-liquid interface. In addition, we discuss the distortion of the actual interface profile—compared with the corresponding free one—caused by a finite thickness of the wetting film. The analytic results allow us to draw conclusions about both the value of the wetting transition temperature for second-order wetting transitions and the size of the critical region for such a transition as well as about the onset of critical adsorption. We also present the exact expressions for the leading van der Waals tails of the liquid-gas, wall-liquid, and wall-gas interfaces in a one-component system as well as for interfaces in binary liquid mixtures. We find that at a critical wetting transition of the wall-gas interfaces, the wall-liquid interface profile undergoes a qualitative structural change.