Three-dimensional wedge filling in ordered and disordered systems

Abstract

We investigate interfacial structural and fluctuation effects occurring at continuous filling transitions in 3D wedge geometries. We show that fluctuation-induced wedge covariance relations that have been reported recently for 2D filling and wetting have mean-field or classical analogues that apply to higher-dimensional systems. Classical wedge covariance emerges from analysis of filling in shallow wedges based on a simple interfacial Hamiltonian model and is supported by detailed numerical investigations of filling within a more microscopic Landau-like density functional theory. For sufficiently short-ranged forces mean-field predictions for the filling critical exponents and covariance are destroyed by pseudo-one-dimensional interfacial fluctuations. In this filling fluctuation regime we argue that the critical exponents describing the divergence of lengthscales are related to values of the interfacial wandering exponent $\zeta (d)$ defined for planar interfaces in (bulk) two-dimensional ($d=2$) and three-dimensional ($d=3$) systems, recovering the known results for pure (thermal disorder) systems and predicting universal critical exponents for the case of random-bond disorder. Finally we revisit the transfer matrix theory of three-dimensional filling based on an effective interfacial Hamiltonian model and discuss the interplay between breather, tilt and torsional interfacial fluctuations.

30 pages, 9 figures, submitted to J. Phys.: Condens. Matter

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• Tricritical wedge filling transitions with short-ranged forces
• Interfacial structure at a two-dimensional wedge filling transition: exact results and a renormalization group study
• Filling and wetting transitions on sinusoidal substrates: a mean-field study of the Landau-Ginzburg model
• Capillary-wave models and the effective average action scheme of functional renormalization group
• Observation of a tricritical wedge filling transition in the 3D Ising model
• Capillary condensation in a pore-like geometry