Capillary waves and the decay of density correlations at liquid surfaces

Abstract

Wertheim predicted strong density-density correlations at free liquid surfaces, produced by capillary wave fluctuations of the interface [M. S. Wertheim, J. Chem. Phys. 65, 2377 (1976)JCPSA60021-960610.1063/1.433352]. That prediction has been used to search for a link between capillary wave (CW) theory and density functional (DF) formalism for classical fluids. In particular, Parry et al. have recently analyzed the decaying tails of these CW effects moving away from the interface as a clue for the extended CW theory [A. O. Parry et al., J. Phys.: Condens. Matter 28, 244013 (2016)JCOMEL0953-898410.1088/0953-8984/28/24/244013], beyond the strict long-wavelength limit studied by Wertheim. Some apparently fundamental inconsistencies between the CW and the DF theoretical views of the fluid interfaces arose from the asymptotic analysis of the CW signal. In this paper we revisit the problem of the CW asymptotic decay with a separation of local non-CW surface correlation effects from those that are a truly nonlocal propagation of the CW fluctuations from the surface towards the liquid bulk.

Vapor−Liquid Interface of the Lennard-Jones Truncated and Shifted Fluid: Comparison of Molecular Simulation, Density Gradient Theory, and Density Functional Theory

“…The pressure and density profiles obtained with the three methods are reported for temperatures covering the range between the triple point and the critical point. Also, an empirical correlation for the density profiles is used -mainly for the curve deconvolution (see below) -that was adopted from Vrabec et al 28 A second focus of this work lies in the investigation of the oscillatory layering structure 43,44 on the liquid side of the vapor-liquid density profiles, which has been investigated in the literature by integral equation theory, 40,43,[45][46][47][48][49][50][51] density functional theory, 20,40,41,52 and molecular simulations [46][47][48][49] for some model fluids. The vapor phase of a vapor-liquid interface can be regarded as an external field 40 that causes a structuring of the molecules in the liquid phase -similar to what is observed at wall-liquid interfaces.…”

Density correlation in liquid surfaces: Bedeaux-Weeks high order terms and non capillary wave background

“…The third rows in Figs. 2 and 3 show the bare CW contribution (21), taking the non-CW background out of the full density correlation G. In the LJ surface (Fig. 2), the round CW peak in G(z, z ; q) is perfectly well reproduced by ∆G(z, z ; q) and the diagonal oscillatory tail, from the dense liquid correlations, is eliminated.…”

“…Over the last two decades, there has been an important effort to extract γ(q) from X-ray diffraction experiments, [5][6][7][8] DF theories, [9][10][11][12][13][14][15] and computer simulations 12,16,17 based on Wertheim's prediction. The results have been confusing and puzzling, with very different predictions for γ(q) depending on the assumptions made to represent the "regular" contributions, 4,[11][12][13][14][15][16][18][19][20][21] except for their consensus for the thermodynamic limit γ(0) = γ o .…”

Correlation-function structure in square-gradient models of the liquid-gas interface: Exact results and reliable approximations

“…This capillary wave model of the interface, which regards it as a drumskin under tension, is an excellent description of the interfacial region for wavelengths much larger than the bulk liquid correlation length, and has been successfully used to understand fundamental interfacial phase transitions such as roughnening and wetting [9][10][11]. However, the question of how density-density correlations behave at shorter lengthscales, comparable with the bulk correlation length, has proved considerably more difficult to answer [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. For instance, plausible attempts to extend the capillary wave description by introducing a scale-dependent surface tension have run into numerous difficulties and have failed to connect with detailed simulation studies of the correlation function G and its integral, the structure factor S [21].…”