Effective interface models for ternary amphiphilic systems: thin–thick, first-order and continuous wetting transitions

We carefully derive an effective interface model for fluctuating membranes from an underlying Ginzburg–Landau theory. Unlike classical phenomenological approaches our model contains position-dependent rigidity and stiffness coefficients and furthermore allows the inclusion of external surfaces while, for the first time, accurately incorporating the corresponding boundary conditions. Using this model we investigate potential wetting or unbinding phenomena in ternary mixtures of oil, water and amphiphile in the presence of a wall. In particular, we find that the water phase can wet the wall–microemulsion interface resulting in both first-order and continuous wetting transitions, with in some cases the unbinding being preceded by a thin–thick transition. The stiffness and the rigidity coefficients are calculated and their importance for fluctuation effects is discussed in detail. Finally, we address the application of our model to experimental systems and to other interface behaviour in ternary mixtures.