Book/Report

FZJ-2018-03934

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Kritisches Verhalten von Grenzflächen und Membranen

Grotehans, S. (Corresponding author)FZJ*

1992
Forschungszentrum Jülich GmbH Zentralbibliothek, Verlag Jülich

Please use a persistent id in citations: http://hdl.handle.net/2128/19227

Report No.: Juel-2672

Abstract: The phase transition of a manifold from a state bound to a surface to an unbound state is considered in this work. The manifold feels an effective external potential which is motivated by the respective physical System. A general classification scheme, based on renormalization group calculations, of this unbinding transition is presented. Within this scheme the phase transition depends on the external potential and on the lateral dimension of the manifold. In the framework of an approximate renormalization calculation one can treat membranes, whose confoLinations are governed by the curvature energy, and interfaces with a finite surface tension simultaneously. The only parameters are the lateral dimension and the roughness of the respective manifold. Two classes of potentials were investigated. Potentials of the first dass contain a hand wall. This hard wall prevents the use of perturbation or linearization methods. However, the approximate renormalization group is nonlinear and the conditions of a hard wall can be considered. lt turns out that the Limit d $\rightarrow$ 3 for interfaces is nonanalytic, since the renormalization group has no fixed points at d = 3 anymore where d = 3 is just the dimension in which the interface is marginal i. e. logarthrnically rough. In d > 3 one expects mean field behaviour of the phase transition. In contrast to bulk critical phenomena one finds a nonanalytic behaviour of the renormalization group when the upper critical dimension is reached. This shows up in a complex bifurcation structure of the fixed points. This Limit is studied in detail for wetting and adhesion phenomena, leading to the concept of 'drifting fixed points'. Symmetrical potentials are the second dass which are considered. The order of the phase transition for this Blass is also investigated. Motivated by the calculations for potentials with a hard wall the Limit d $\rightarrow$ 3 is again studied. An analog bifurcation structure as for unbinding is found, but now one can use linearized methods to derive exact results. A starting point for the investigation of the symmetrie potentials is an exact transfer matrix calculation in d = 1 + 1 which serves also as a Lest for the approximate renormalization group.

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Contributing Institute(s):

1. Publikationen vor 2000 (PRE-2000)

Research Program(s):

1. 899 - ohne Topic (POF3-899) (POF3-899)

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Database coverage:

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