Interfacial structure at a two-dimensional wedge filling transition: Exact results and a renormalization group study

Abstract

Interfacial structure and correlation functions near a two-dimensional wedge filling transition are studied using effective interfacial Hamiltonian models. An exact solution for short range binding potentials and results for Kratzer binding potentials show that sufficiently close to the filling transition a new length scale emerges and controls the decay of the interfacial profile relative to the substrate and the correlations between interfacial positions above different positions. This new length scale is much larger than the intrinsic interfacial correlation length, and it is related geometrically to the average value of the interfacial position above the wedge midpoint. The interfacial behavior is consistent with a breather mode fluctuation picture, which is shown to emerge from an exact decimation functional renormalization group scheme that keeps the geometry invariant.

Thermal fluctuations of an interface near a contact line

“…In fact, previous studies of the model defined by Eqs. (36) and (37) have typically considered R → ∞ (or, alternatively, employed periodic boundary conditions), thereby disregarding the behavior near the contact line [80,92,117,118]. The characteristic behavior of the average profile h(x) R is illustrated in Fig.…”

“…(55). Forx ≫ 1, instead, the probability becomes that is a distribution function completely unrelated to the outer problem [80]. Consequently, forx ≫ 1 the profile is localized near the wall, as a manifestation of the presence of the precursor film.…”

“…In the case of a one-dimensional interface, the solution can be obtained via a mapping to a quantum mechanical eigenvalue problem, whereas, for two-dimensional interfaces, field theoretical methods have to be employed. In many analytical investigations of the shapes of wedges of droplets, however, contact lines are either taken to be fixed [23,72,[82][83][84][85], or a mesoscopic precursor film is supposed in front of the wedge [21,29,30,80]. Due to the entropic repulsion effect, such a film would necessarily have a finite thickness.…”

Kratzer’s molecular potential in quantum mechanics with a generalized uncertainty principle

“…This potential is one of the most important model interaction in quantum physics; it has been first introduced to describe the vibration-rotation spectra of diatomic molecules [43,44]. Nowadays, KP appears in various fields of physics and chemistry such as molecular physics [45], nuclear physics [46], Liquid-solid interfaces and thermodynamics [47], chemical physics [48], and quantum chemistry [49][50][51][52][53]. From a more formal viewpoint, KP provides a good example for illustrating diverse methods used to solve the Schrödinger equation, such as the Fourier integral representation [54], the algebraic approach [55], the supersymmetry [53], the Nikiforov-Uvarov [49], the asymptotic iteration method [56], and the method of self-adjoint extensions [57], which is used when the coupling constant g 1 is such as 2µg 1 / 2 ≤ −1/4 (µ is the particle mass), where the corresponding Hamiltonian operator is not self-adjoint [57].…”

An interpretation of covariance relations for wetting and wedge filling transitions

“…The differences are as follows: First, the order of the wedge filling transition may be different to the order of the wetting transition. 22,[31][32][33][34][35][36] Alternatively, one can consider the transition only at mean-field level by ignoring fluctuation effects altogether. 25 Second, owing to the anisotropy of fluctuations in directions along and across a three-dimensional wedge, interfacial wandering effects and critical singularities are far more pronounced than at wetting transitions at planar substrates.…”