Derivation of a Non-Local Interfacial Hamiltonian for Short-Ranged Wetting II: General Diagrammatic Structure

Abstract

In our first paper, we showed how a non-local effective Hamiltionian for short-ranged wetting may be derived from an underlying Landau-Ginzburg-Wilson model. Here, we combine the Green's function method with standard perturbation theory to determine the general diagrammatic form of the binding potential functional beyond the double-parabola approximation for the Landau-Ginzburg-Wilson bulk potential. The main influence of cubic and quartic interactions is simply to alter the coefficients of the double parabola-like zig-zag diagrams and also to introduce curvature and tube-interaction corrections (also represented diagrammatically), which are of minor importance. Non-locality generates effective long-ranged many-body interfacial interactions due to the reflection of tube-like fluctuations from the wall. Alternative wall boundary conditions (with a surface field and enhancement) and the diagrammatic description of tricritical wetting are also discussed.

arXiv comment(14 pages, 2 figures) Submitted J. Phys. Condens. Matter

References in corpus (5)

• Morphological Thermodynamics of Fluids: Shape Dependence of Free Energies
• Filling transition for a wedge
• Non-locality and short-range wetting phenomena
• Three-dimensional wedge filling in ordered and disordered systems
• Quantal Andreev billiards: Semiclassical approach to mesoscale oscillations in the density of states

Cited by in corpus (16)

• On the spectrum of fluctuations of a liquid surface: From the molecular scale to the macroscopic scale
• Liquid drops on a surface: using density functional theory to calculate the binding potential and drop profiles and comparing with results from mesoscopic modelling
• Wetting Transition in the Two-Dimensional Blume-Capel Model: A Monte Carlo study
• Influence of the fluid structure on the binding potential: comparing liquid drop profiles from density functional theory with results from mesoscopic theory
• Pair correlation functions and the wavevector-dependent surface tension in a simple density functional treatment of the liquid-vapour interface
• Free-energy landscape of nucleation with an intermediate metastable phase studied using capillarity approximation
• Capillary Wave Theory of Adsorbed Liquid Films and the Structure of the Liquid-Vapor Interface
• Mesoscopic analysis of Gibbs' criterion for sessile nanodroplets on trapezoidal substrates
• Filling and wetting transitions on sinusoidal substrates: a mean-field study of the Landau-Ginzburg model
• Curvature corrections to the nonlocal interfacial model for short-ranged forces
• From density to interface fluctuations: the origin of wavelength dependence in surface tensions
• The Influence of Intermolecular Forces at Critical Point Wedge Filling
• Inhomogeneous surface tension of chemically active fluid interfaces
• Quantum wetting transitions in two dimensions: an alternative path to non-universal interfacial singularities
• Effective Hamiltonian for fluid membranes in the presence of long-ranged forces
• The influence of the Casimir effect on the binding potential for 3D wetting