Non–monotonous crossover between capillary condensation and interface localisation/delocalisation transition in binary poly- mer blends

– Within self–consistent field theory we study the phase behaviour of a symmetric binary AB polymer blend confined into a thin film. The film surfaces interact with the monomers via short range potentials. One surface attracts the A component and the corresponding semi–infinite system exhibits a first order wetting transition. The surface interaction of the opposite surface is varied as to study the crossover from capillary condensation for symmetric surface fields to the interface localisation/delocalisation transition for antisymmetric surface fields. In the former case the phase diagram has a single critical point close to the bulk critical point. In the latter case the phase diagram exhibits two critical points which correspond to the prewetting critical points of the semi–infinite system. The crossover between these qualitatively different limiting behaviours occurs gradually, however, the critical temperature and the critical composition exhibit a non-monotonic dependence on the surface field. Introduction. – We study the phase behaviour of a symmetric binary mixture confined into a slit–like pore. The shift of the critical point for symmetric film surfaces[1] (capillary condensation) has been studied extensively. The unmixing transition approaches the critical temperature of the infinite system for thick films. Below the critical temperature the coexisting phases differ in their composition at the center of the film. More recently, novel types of phase transitions have been studied in the case of antisymmetric surface fields,[2-6] i.e., one surface attracts the A component of a symmetric mixture in exactly the same way the opposite surface attracts the B component. Close to the critical temperature in the bulk, enrichment layers of the components gradually form at the surfaces and stabilise an interface at the center of the film (soft–mode phase). It is only close to the temperature[3] of the second order wetting transition in the semi–infinite system that the symmetry is spontaneously broken and the interface is located at either surface. Upon increasing the film thickness the temperature of this interface localisation/delocalisation transition converges to the wetting temperature rather than the critical temperature of the bulk, and the interpretation of the transition in terms of Typeset using EURO-LaTEX 2 EUROPHYSICS LETTERS a thin film critical critical point or a wetting transition in the limit of large film thickness has been discussed.[7] The effect of an external field (i.e., gravity) has been explored.[8] Analytical approaches and simulations have considered systems with second order wetting transitions[3, 6] in the semi–infinite system or the behaviour at bulk coexistence[5, 9] only. This has excluded a possible interplay between phase behaviour and prewetting, which might alter the topology of the phase diagram in thin films,[10, 11] from consideration. In this Letter we revisit the interface localisation/delocalisation transition for a first order wetting transition in the corresponding semi–infinite system and explore the crossover from the interface localisation/delocalisation transition to capillary condensation upon varying the interaction Λ2 at one surface. The interaction Λ1 at the other surface is kept constant. This is the first systematic theoretical study of boundary conditions which are neither strictly symmetric nor antisymmetric. It is clearly pertinent to the interpretation of experiments as the idealized limiting cases are never strictly realized. Our calculations yield information about the range of asymmetry where the behaviour characteristic of the symmetric and antisymmetric boundary conditions is observable, and we explore the dependence of the topology of the phase diagrams on the surface interactions. Both the phase diagram as a function of the intensive variables incompatibility and chemical potential as well as the binodals are discussed. Self–consistent field calculations. – We calculate the phase behaviour of a confined AB mixture within the self-consistent field theory of Gaussian polymers.[12-14]Polymer mixtures in confined geometries are interesting for many applications (e.g., coating, lubrication), and consequentially have attracted abiding recent attention.[15] In these systems the soft mode phase mentioned above has been experimentally studied.[16] Thus we focus on these systems, although we believe that our results carry over to other confined mixtures at least qualitatively. We consider a film with volume V0 = ∆0×L×L. ∆0 denotes the film thickness, while L is the lateral extension of the film. The density at the film surfaces decreases to zero in a boundary region of width ∆w according to[17]