Critical Behavior of Interfaces: Roughening and Wetting Phenomena
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CRITICAL BEHAVIOR OF INTERFACES: ROUGHENING AND WETTING PHENOMENA REINHARD LIPOWSKY, STEFAN GROTEHANS, and GOTZ J.0. SCHMIDT Institut M~r Festk6rperforschung,Forschungszentrum JAiich
Postlfach 1913, D-5170 Jiilich, Germany
ABSTRACT. The critical behavior of interfaces is discussed from a theoretical point of view. Two classes of critical phenomena will be considered: (i) Roughening phenomena related to changes in the interfacial morphology; and (ii) Wetting phenomena related to changes in the interfacial structure. In two dimensions, the critical behavior can be determined exactly for a variety of models. As a result, one obtains different universality classes depending on the nature of the intermolecular forces. 1. Introduction Critical phenomena at interfaces have been studied, both theoretically and experimentally, for many years. Here, we will discuss two classes of critical phenomena related to the reduced dimensionality of the interface.1
In some cases, the interface can simply be viewed as a planar 2-dimensional system. However, it can also 'bulge' into the third dimension and then attain nonplanar morphologies. This roughening .of the interface can be thermally excited or induced by frozen randomness. In addition, the interface has a certain depth profile and thus has itself a third dimension. This intrinsic thickness of the interface can become mesoscopic as in wetting phenomena; one then has a system which interpolates between two and three dimensions. This paper is organized as follows. First, the physics of roughening and wetting is briefly reviewed (Sect. 2). The corresponding critical behavior at roughening and wetting can be studied in the framework of effective interface models (Sect. 3). The last section focusses on the behavior in two dimensions: a variety of critical effects will be discussed arising from the behavior of 1-dimensional interfaces or domain boundaries. These effects should be accessible to experiments, for example in the context of Langmuir-Blogdett films. 2.
Roughening and Wetting Phenomena
2.1 Interfacial morphology and roughening An interface or domain wall represents the contact region between two bulk phases of matter. Its macroscopic shape is governed by the interfacial free energy or tension, IE, which is the work (per unit area) required to create new interfacial area. If the two bulk phases, say a and )3, are both isotropic fluids, E. is also isotropic, and a macroscopic chunk of 0 phase surrounded by a phase has a spherical shape (if one can ignore the effects of gravity). If one of the two phases is anisotropic, the tension E]is anisotropic as well and depends on the interfacial orientation. For crystalline phases, this anisotropy leads to the possibility of flat interfaces or facets. From the theoretical point of view, the equilibrium shape of crystals is completely determined, up to a scale factor, by the functional dependence of the interfacial (or surface) free energy, E2,on the interfacial orientation or normal vector, h. Now, assume that E = E(h) has a local m
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