Finite size effects on the phase diagram of a binary mixture confined between competing walls

A symmetrical binary mixture AB that exhibits a critical temperature T-cb O f phase separation into an A- and a B-rich phase in the bulk is considered in a geometry confined between mio parallel plates a distance D apart, It i s assumed that one wall preferentially attracts A while the other wall pref erentially attracts B with the same strength (''competing walls"). In the l imit D --> infinity, one then may have a wetting transition of fiat-order a t a temperature T-w, from which prewetting Lines extend into the one phase region both of the A- and the B-rich phase. It is discussed how this phase diagram gets distorted due to the finiteness of D: the phase transition at T-cb immediately disappears for D < infinity due to finite size rounding, a nd the phase diagram instead exhibit two two-phase coexistence regions in a temperature range T-trip < T < T-e1 = T-c2. In the Limit D --> infinity T- c1, T-c2 become the prewetting critical points and T-trip --> T-w. For smal l enough D it may occur that at a tricritical value D-t the temperatures T- c1 = T-c2 and T-trip merge, and then for D < D-t there is a single unmixing critical point as in the bulk but with T-c(D) near T-w. As an example, for the experimentally relevant case of a polymer mixture a phase diagram with two unmixing critical points is calculated explicitly from self-consistent field methods. (C) 2000 Elsevier Science B.V. All rights reserved.