Effect of dispersion forces on the capillary-wave fluctuations of liquid surfaces

Structure of liquid-vapor interfaces: Perspectives from liquid state theory, large-scale simulations, and potential grazing-incidence x-ray diffraction

Grazing-incidence x-ray diffraction (GIXRD) is a scattering technique that allows one to characterize the structure of fluid interfaces down to the molecular scale, including the measurement of surface tension and interface roughness. However, the corresponding standard data analysis at nonzero wave numbers has been criticized as to be inconclusive because the scattering intensity is polluted by the unavoidable scattering from the bulk. Here, we overcome this ambiguity by proposing a physically consistent model of the bulk contribution based on a minimal set of assumptions of experimental relevance. To this end, we derive an explicit integral expression for the background scattering, which can be determined numerically from the static structure factors of the coexisting bulk phases as independent input. Concerning the interpretation of GIXRD data inferred from computer simulations, we extend the model to account also for the finite sizes of the bulk phases, which are unavoidable in simulations. The corresponding leading-order correction beyond the dominant contribution to the scattered intensity is revealed by asymptotic analysis, which is characterized by the competition between the linear system size and the x-ray penetration depth in the case of simulations. Specifically, we have calculated the expected GIXRD intensity for scattering at the planar liquid-vapor interface of Lennard-Jones fluids with truncated pair interactions via extensive, high-precision computer simulations. The reported data cover interfacial and bulk properties of fluid states along the whole liquid-vapor coexistence line. A sensitivity analysis shows that our findings are robust with respect to the detailed definition of the mean interface position. We conclude that previous claims of an enhanced surface tension at mesoscopic scales are amenable to unambiguous tests via scattering experiments.

Thermal capillary waves on bounded nanoscale thin films

The effect of confining walls on the fluctuation of a nanoscale thin film's free surface is studied using stochastic thin-film equations (STFEs). Two canonical boundary conditions are employed to reveal the influence of the confinement: (1) an imposed contact angle and (2) a pinned contact line. A linear stability analysis provides the wave eigenmodes, after which thermal-capillary-wave theory predicts the wave fluctuation amplitudes. Molecular dynamics (MD) simulations are performed to test the predictions, and a Langevin diffusion model is proposed to capture oscillations of the contact lines observed in MD simulations. Good agreement between the theoretical predictions and the MD simulation results is recovered, and it is discovered that confinement can influence the entire film. Notably, a constraint on the length scale of wave modes is found to affect fluctuation amplitudes from our theoretical model, especially for 3D films. This opens up challenges and future lines of inquiry.

Surface reconstruction amendment to the intrinsic sampling method

The intrinsic sampling method (ISM) is a powerful tool that allows the exploration of interfacial properties from molecular simulations by fitting a function that represents the local boundary between two phases. However, owing to the non-physical nature of an "intrinsic" surface, there remains an ambiguity surrounding the comparison of theoretical properties with the physical world. It is therefore important that the ISM remains internally consistent when reproducing simulated properties which match experiments, such as the surface tension or interfacial density distribution. We show that the current ISM procedure causes an over-fitting of the surface to molecules in the interface region, leading to a biased distribution of curvature at these molecular coordinates. We assert that this biased distribution is a cause of the disparity between predicted interfacial densities upon convolution to a laboratory frame, an artefact which has been known to exist since the development of the ISM. We present an improvement to the fitting procedure of the ISM in an attempt to alleviate the ambiguity surrounding the true nature of an intrinsic surface. Our "surface reconstruction" method is able to amend the shape of the interface so as to reproduce the global curvature distribution at all sampled molecular coordinates. We present the effects that this method has on the ISM predicted structure of a simulated Lennard-Jones fluid air-liquid interface. Additionally, we report an unexpected relationship between surface thermodynamic predictions of our reconstructed ISM surfaces and those of extended capillary wave theory, which is of current interest.

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

We present Molecular Dynamics (MD) simulations of liquid-vapor surfaces, and their Intrinsic Sampling Method analysis, to get a quantitative test for the theoretical prediction of the capillary wave (CW) effects on density correlation done by Bedeaux and Weeks (BW) in 1985. The results are contrasted with Wertheim's proposal which is the first term in BW series and are complemented with a (formally defined and computational accessible) proposal for the background of non-CW fluctuations. Our conclusion is that BW theory is both accurate and needed since it may differ significantly from Wertheim's proposal. We discuss the implications for the analysis of experimental X-ray surface diffraction data and MD simulations.

Capillary waves as eigenmodes of the density correlation at liquid surfaces

We analyze the density correlations in a liquid-vapor surface to establish a quantitative connection between the Density Functional (DF) formalism, Molecular Dynamic (MD) simulations, and the Capillary Wave (CW) theory. Instead of the integrated structure factor, we identify the CW fluctuations as eigenmodes of the correlation function. The square-gradient DF approximation appears as fully consistent with the use of the thermodynamic surface tension to describe the surface fluctuations for any wavevector because it misses the upper cutoff in the surface Hamiltonian from the merging of the CW mode with the non-CW band. This mesoscopic cutoff may be accurately predicted from the main peak in the structure factor of the bulk liquid. We explore the difference between the full density-density correlation mode and the bare CW that represents the correlation between the corrugation of the intrinsic surface and the density at the interfacial region. The non-local decay of the CW effects, predicted from DF analysis and observed in MD simulations with the intrinsic sampling method, is found to characterize the bare CW fluctuations, which also require a wavevector-dependent surface tension.

Nanocapillarity and Liquid Bridge-Mediated Force between Colloidal Nanoparticles

In this work, we probe the concept of interface tension for ultrathin adsorbed liquid films on the nanoscale by studying the surface fluctuations of films down to the monolayer. Our results show that the spectrum of film height fluctuations of a liquid-vapor surface may be extended to ultrathin films provided we take into account the interactions of the substrate with the surface. Global fluctuations of the film height are described in terms of disjoining pressure, whereas surface deformations that are proportional to the interface area are accounted for by a film thickness-dependent surface tension. As a proof of concept, we model the capillary forces between colloidal nanoparticles held together by liquid bridges. Our results indicate that the classical equations for capillarity follow very precisely down to the nanoscale provided we account for the film height dependence of the surface tension.

Capillary wave theory of adsorbed liquid films and the structure of the liquid-vapor interface

In this paper we try to work out in detail the implications of a microscopic theory for capillary waves under the assumption that the density is given along lines normal to the interface. Within this approximation, which may be justified in terms of symmetry arguments, the Fisk-Widom scaling of the density profile holds for frozen realizations of the interface profile. Upon thermal averaging of capillary wave fluctuations, the resulting density profile yields results consistent with renormalization group calculations in the one-loop approximation. The thermal average over capillary waves may be expressed in terms of a modified convolution approximation where normals to the interface are Gaussian distributed. In the absence of an external field we show that the phenomenological density profile applied to the square-gradient free energy functional recovers the capillary wave Hamiltonian exactly. We extend the theory to the case of liquid films adsorbed on a substrate. For systems with short-range forces, we recover an effective interface Hamiltonian with a film height dependent surface tension that stems from the distortion of the liquid-vapor interface by the substrate, in agreement with the Fisher-Jin theory of short-range wetting. In the presence of long-range interactions, the surface tension picks up an explicit dependence on the external field and recovers the wave vector dependent logarithmic contribution observed by Napiorkowski and Dietrich. Using an error function for the intrinsic density profile, we obtain closed expressions for the surface tension and the interface width. We show the external field contribution to the surface tension may be given in terms of the film's disjoining pressure. From literature values of the Hamaker constant, it is found that the fluid-substrate forces may be able to double the surface tension for films in the nanometer range. The film height dependence of the surface tension described here is in full agreement with results of the capillary wave spectrum obtained recently in computer simulations, and the predicted translation mode of surface fluctuations reproduces to linear order in field strength an exact solution of the density correlation function for the Landau-Ginzburg-Wilson Hamiltonian in an external field.

Capillary wave Hamiltonian for the Landau-Ginzburg-Wilson density functional

We study the link between the density functional (DF) formalism and the capillary wave theory (CWT) for liquid surfaces, focused on the Landau-Ginzburg-Wilson (LGW) model, or square gradient DF expansion, with a symmetric double parabola free energy, which has been extensively used in theoretical studies of this problem. We show the equivalence between the non-local DF results of Parry and coworkers and the direct evaluation of the mean square fluctuations of the intrinsic surface, as is done in the intrinsic sampling method for computer simulations. The definition of effective wave-vector dependent surface tensions is reviewed and we obtain new proposals for the LGW model. The surface weight proposed by Blokhuis and the surface mode analysis proposed by Stecki provide consistent and optimal effective definitions for the extended CWT Hamiltonian associated to the DF model. A non-local, or coarse-grained, definition of the intrinsic surface provides the missing element to get the mesoscopic surface Hamiltonian from the molecular DF description, as had been proposed a long time ago by Dietrich and coworkers.

The local structure factor near an interface; beyond extended capillary-wave models

We investigate the local structure factor S (z;q) at a free liquid-gas interface in systems with short-ranged intermolecular forces and determine the corrections to the leading-order, capillary-wave-like, Goldstone mode divergence of S (z;q) known to occur for parallel (i.e. measured along the interface) wavevectors [Formula: see text]. We show from explicit solution of the inhomogeneous Ornstein-Zernike equation that for distances z far from the interface, where the profile decays exponentially, S (z;q) splits unambiguously into bulk and interfacial contributions. On each side of the interface, the interfacial contributions can be characterised by distinct liquid and gas wavevector dependent surface tensions, [Formula: see text] and [Formula: see text], which are determined solely by the bulk two-body and three-body direct correlation functions. At high temperatures, the wavevector dependence simplifies and is determined almost entirely by the appropriate bulk structure factor, leading to positive rigidity coefficients. Our predictions are confirmed by explicit calculation of S (z;q) within square-gradient theory and the Sullivan model. The results for the latter predict a striking temperature dependence for [Formula: see text] and [Formula: see text], and have implications for fluctuation effects. Our results account quantitatively for the findings of a recent very extensive simulation study by Höfling and Dietrich of the total structure factor in the interfacial region, in a system with a cut-off Lennard-Jones potential, in sharp contrast to extended capillary-wave models which failed completely to describe the simulation results.

Mesoscopic Hamiltonian for the fluctuations of adsorbed Lennard-Jones liquid films

We use Monte Carlo simulations of a Lennard-Jones fluid adsorbed on a short-range planar wall substrate to study the fluctuations in the thickness of the wetting layer, and we get a quantitative and consistent characterization of their mesoscopic Hamiltonian, H[ξ]. We have observed important finite-size effects, which were hampering the analysis of previous results obtained with smaller systems. The results presented here support an appealing simple functional form for H[ξ], close but not exactly equal to the theoretical nonlocal proposal made on the basis a generic density-functional analysis by Parry and coworkers. We have analyzed systems under different wetting conditions, as a proof of principle for a method that provides a quantitative bridge between the molecular interactions and the phenomenology of wetting films at mesoscopic scales.