Derivation of a non-local interfacial Hamiltonian for short-ranged wetting: I. Double-parabola approximation

Abstract

We derive a non-local effective interfacial Hamiltonian model for short-ranged wetting phenomena using a Green's function method. The Hamiltonian is characterized by a binding potential functional and is accurate to exponentially small order in the radii of curvature of the interface and the bounding wall. The functional has an elegant diagrammatic representation in terms of planar graphs which represent different classes of tube-like fluctuations connecting the interface and wall. For the particular cases of planar, spherical and cylindrical interfacial (and wall) configurations, the binding potential functional can be evaluated exactly. More generally, the non-local functional naturally explains the origin of the effective position-dependent stiffness coefficient in the smallgradient limit.

Capillary wave spectrum at adsorbed liquid films

“…From layer to layer, the dependence on the film thickness is given by the same exponential decay, ∼e −λξ IS , as the potential (ξ IS ), where the decay constant λ is the inverse correlation length in the bulk liquid. The dependence on q fits well into the form (ξ IS ) + q 2 γ w (0)e −λξ IS used in the RG analysis by Fisher and Jin, 3 but the nonlocal effects pointed out by Parry et al 4,5 appear to be strong and clear in the contribution γ LV (q), independent of ξ IS , which gives the free liquid surface limit for thick films. In this respect, our method to extract the CW fluctuations from the molecular positions gives a quantitative and testable link between the molecular and the mesoscopic descriptions of wetting films.…”

“…3(b) and the theoretical framework suggests that the enhanced (or subdamped) CW fluctuations that create the oscillatory behavior of γ (q,ξ IS ) could be spurious or irrelevant in the RG flux. The present procedure may also be applied to the study of wetting layers on structured substrates where nonlocal effects could be more relevant to contrast with the predictions of Fisher and Jin 3 and Parry et al 4,5 Work addressing these questions is in progress and will be reported in the future.…”

“…In the second proposal the nonlocal effects are included in the interaction between the substrate and the liquidvapor interface, i.e., in the effective interface potential. 4,5 In the latter model the nonlocal effects are due to a self-interaction arising from two-body interfacial forces between particles on the interface and also are presented for free liquid-vapor interfaces. 6 Although these Hamiltonians have been broadly used in the study of the criticality for short-range wetting transitions, the quantitative identification of these nonlocal effects in realistic models of wetting films has proven to be difficult.…”

“…This is the aim of the present work: to study the dependence of surface fluctuations on the thickness of the adsorbed liquid film and to analyze possible nonlocal effects. This is a very delicate question because previous studies 4,5 have confirmed the validity of the simplest mean-field (MF)-like Hamiltonian until the film layer is rather thin, and then the theoretical assumptions, based on a smooth density profile at the external edge of the film, may be questioned.…”

3D Short-Range Wetting and Nonlocality

“…Progress has recently been made towards resolving problems in the theory of three-dimensional (3D) shortranged wetting [1-3] from analysis of a nonlocal (NL) interfacial Hamiltonian [4 -6]. Starting from a LandauGinzburg-Wilson (LGW) model, it can be shown that the interfacial binding potential contains two-body interfacial interactions and also has a simple diagrammatic representation [5,6]. The latter allows one to visualize the binding potential as arising from tubelike fluctuations that zigzag between the surfaces.…”