ASYMPTOTIC DECAY OF LIQUID STRUCTURE - OSCILLATORY LIQUID-VAPOR DENSITY PROFILES AND THE FISHER-WIDOM LINE

Recent work has highlighted the existence of a unified theory for the asymptotic decay of the density profile rho(r) of an inhomogeneous flu id and of the bulk radial distribution function g(r). For a given shor t-ranged interatomic potential rho(r) decays into bulk in the same fas hion as g(r), i.e. with the same exponential decay length (alpha0(-1)) and, for sufficiently high bulk density (rho(b)) and/or temperature ( T), oscillatory wavelength (2pi/alpha1). The quantities alpha0 and alp ha1 are determined by a linear stability analysis of the bulk fluid; t hey depend on only the bulk direct correlation function. In this paper we reintroduce the concept of the Fisher-Widom (FW) line. This line w as originally introduced, in say the (rho(b), T) plane, as that which separates pure exponential from exponentially damped oscillatory decay of g(r). We explore the relevance of the FW line for the form of the density profile at a liquid-vapour interface. Using a weighted density approximation (WDA) density functional theory we locate the FW line f or the square-well model of an atomic fluid. We find that this line cr osses the liquid branch of the liquid-vapour coexistence curve at T/T( c); almost-equal-to 0.9, where T(c) is the critical temperature. Accor dingly, for T less than or similar to 0.9 T(c), very general statistic al mechanical theory predicts damped oscillatory decay of the liquid-v apour density profile into the bulk liquid. Since the amplitude of the oscillations is not determined by the linear analysis we have calcula ted explicit nonlinear numerical solutions of our WDA theory, using a high quality finite element method. Our results show that in a mean-fi eld treatment the amplitude of the oscillatory profile in the saturate d liquid tail is about 2% of rho(b) at temperatures approaching the tr iple point and decreases rapidly as T increases towards the FW line. T he predictions of the asymptotic profile decay theory are confirmed by our explicit results and the unified nature of the phenomena is illus trated by comparing results for the liquid-vapour profile with profile s calculated for attractive wall-liquid interfaces at the same bulk li quid state point. The effects of capillary-wave fluctuations on the os cillatory nature of liquid-vapour profiles, above the FW line, are dis cussed, and we argue that while incorporating such fluctuations should lead to a significant reduction in the amplitude of oscillations, in d = 3, at least, there should be no change to the period and decay len gth for the profile in the liquid tail. The implications of our result s for other interfacial properties, for computer simulations of the li quid-vapour interface, for studies of wetting transitions and for the nature of the solvation force that arises when a fluid is confined bet ween two planar walls are considered.