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

Abstract

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.

Nanocapillarity and Liquid Bridge-Mediated Force between Colloidal Nanoparticles

“…The good agreement that is found here for a prewetting film is in line with previous results obtained from computer simulations for two related systems 21,22 and with a statistical mechanical theory proposed recently. 23…”

“…Instead, we recall that ξ e is a measure of the interface width. 23 Accordingly, we can obtain this parameter ab initio from the results of the liquid–vapor interface profile of the TIP3P model used in the simulations. 78,79 Using fits from ref (79) for the interface profile for the TIP3P model precisely at the temperature of interest T = 300 K, we find γ lv = 49.5 mJ/m 2 and ρ l ξ e 2 = 2.3 nm –1 a.…”

“…This serves, nevertheless, to highlight that the order of magnitude of the fitting parameter ξ e is indeed dictated by the interface width as expected from the theoretical considerations. 21−23 We can also estimate γ(Γ) employing Π(Γ; R ) instead of Π(Γ) in eq 13, using now a corrected value for ρ l ξ e 2 that is obtained from the average ratio of Π( h )/Π(Γ; R ). The results shown in the figure also provide a very good agreement for the observed film height-dependent surface tension γ(Γ).…”

“…However, we have found that an accurate agreement with eq 3 can only be recovered if we accept a film height-dependent surface tension, γ( h ), which becomes equal to γ lv for sufficiently large γ( h ). 16,21−23 In fact, we have argued and shown empirically that decay of γ( h ) toward γ lv is given in terms of disjoining pressure as 16,21−23 where ξ e is a parameter describing the width of the liquid–vapor interface. This result is consistent with previous unexplained computer simulation results 15 and with theoretical results for simplified models.…”

Molecular simulation of thin liquid films: Thermal fluctuations and instability

“…[24,27], but the derivation provided here is potentially more intuitive. We note that, from capillary wave theory, the average magnitude of each mode of waves can be determined from equipartition theorem [21,39]. Here is the interface energy related with disjoining pressure by φ = −∂ /∂h.…”