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

Parry, A. O.
Rascon, C.
Bernardino, N. R.
Romero-Enrique, J. M.
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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.
Comment: (14 pages, 2 figures) Submitted J. Phys. Condens. Matter
Condensed Matter - Statistical Mechanics, Condensed Matter - Soft Condensed Matter