On the approach to complete wetting by gas at a liquid-wall interface

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Abstract
We study the approach to complete wetting by gas at the interface between a repulsive wall and dense liquid, paying particular attention to the basic model consisting of a hard-wall system approaching bulk liquid-vapour coexistence. This class of wetting phenomena is of special interest from the point of view of the compressibility route to interfacial statistical mechanics and for its suitability to direct observation by computer simulation. On the theoretical side, there exists a battery of exact sum rules that are of direct relevance to the problem and it is possible to make use of capillary wave fluctuation theory in almost the same form as has been developed for the study of liquid-vapour interfaces. The main conclusion of our study is that in the approach to complete wetting the capillary wave fluctuations of the developing liquid-vapour interface continue to manifest themselves at the wall, even when the liquid is separated from the wall by a macroscopic layer of gas. This implies a diverging transverse correlation length, ζ‖, determined by the surface tension and the limiting gradient of the density profile near the wall. When combined with the fluctuation theory result for the surface compressibility sum rule, linking ζ‖ to the behaviour of the adsorption, one can derive the complete wetting exponents and corresponding amplitudes, purely from the form of the density profile. The results are directly analogous to the predictions of lattice models and Landau theory; for example, for three-dimensional systems with short-range interparticle interactions we confirm that gaussian fluctuations do not alter the complete wetting exponents from their meanfield values. To confirm the dramatic theoretical predictions for the pair distribution function near the wall, we undertook an extensive computer simulation study of the approach to complete wetting by gas at the interface between squarewell liquid and a hard wall. Density profiles and pressure tensors were measured at points along a particular isotherm, in order to obtain a full thermodynamic description of the wetting region. One particular system, close to bulk liquid-vapour coexistence, was chosen for further study in which the transverse surface structure factor was calculated as a function of wavelength and position, and the pair distribution function for particles on the wall was determined. We find the simulation results to be unambiguously in agreement with theory. A remarkably successful measurement of the capillary wave pair correlations is obtained, because the low density next to the wall results in essentially weak-gas short-range correlations that are virtually decoupled from the long-range fluctuation contribution. Here, the effects of finite wall area are put to good use.