Benetzungsübergänge und Adhäsionsübergänge 1. Ordnung

Both interfaces and membranes show unbinding transitions, at which a fluctuating surface unbinds from a wall. At the wetting transition of an interface the energy of the interface fluctuations is governed by the surface tension, whereas the bending rigidity gives the essential contribution at the adhesion transition of a membrane. In this work first-order unbinding transitions are considered, i. e. transitions showing a discontinuous detachment of the surface. In the mean-field approximation the semi-infinite Ising model in three dimensions is expected to show second order wetting transitions for a certain range of parameters. But a comparison of Monte-Carlo data for the Ising model and predictions for a effective interface model (derived from the Ising model) show discrepancies for the scaling properties at the phase transition. To solve the contradiction, some additional terms have been introduced in the effective model recently. Of special relevance is a surface tension, which depends on the location of the interface and which is expected to generate first-order transitions. In this thesis, the nature of this wetting transition is studied by Monte-Carlo simulations and finite-size scaling, which clearly indicates a discontinuous transition. Results of functional renormalization group calculations suggest that for a membrane in a short-range potential no first-order adhesion transition should occur. But on the other hand, a simple Landau-Peierls argument predictssuch discontinuous transitions. To study the possibility of first order transitions, Monte-Carlo simulations of a membrane in a double-well potential are considered. As a result, one finds a phase diagram which is similar to the corresponding phase diagram of an interface in a double-well potential: a line of first-order transitions ending at a critical point. In addition, this critical point of the membrane model belongs to the same universality class as the critical point of the 2-dimensional Ising model. Finally, for a short-ranged adhesion potential the decay times of a metastable bound state were observed by Monte-Carlo simulations indicating a discontinuous transition