Polymer mixtures in confined geometries: Model systems to explore phase transitions

While binary (A,B) symmetric polymer mixtures ind = 3 dimensions have an unmixing critical point that belongs to the 3d Ising universality class and crosses over to mean field behavior for very long chains, the critical behavior of mixtures confined into thin film geometry falls in the 2d Ising class irrespective of chain length. The critical temperature always scales linearly with chain length, except for strictly two-dimensional chains confined to a plane, for whichT _c ∝N ^5/8 (this unusual exponent describes the fractal contact line between segregated chains in dense melts in two spatial dimensions,d = 2). When the walls of the thin film are not neutral, but preferentially attract one species, complex phase diagrams occur due to the interplay between capillary condensation and wetting phenomena. For ‘competing walls’ (one wall prefers A, the other prefers B) particularly interesting interface localization-delocalization transitions occur, while analogous phenomena in wedges are related to the ‘filling transition’.