Phase separation of polymer blends in solution near adsorbing surface

In this paper, we consider a mixture of two polymers A and B of different chemical nature, dissolved in a common good solvent, in contact with an interacting surface. We start from a mixture of two incompatible homopolymers A and B in the molten state, and assume that the surface adsorbs strongly one or both polymer species at high temperature. It is assumed that this is a strong adsorption, so that chains cannot desorb once they are linked to the surface. This constrains the system to a quenched composition on the surface. Once the adsorption process is finished, a quantity of a good solvent is added to get a semi-dilute solution. We assume that demixing transition in the presence of solvent occurs at lower temperature. The purpose is to discuss the influence of the quenched surface fluctuations on the critical properties of the mixture. Within the framework of the so-called blob model, we determine the exact shape of the composition profile as a function of the distance z to the surface, for any value of the relevant parameters, namely, the temperature T, the molecular weight M, the monomer concentration c and the surface composition x(0) Our analysis reveals a universal character of the composition profile for D << z << xi (t), where the characteristic size D is some known length depending on the relevant parameters of the problem, and not on temperature, and xi (t) is the thermal correlation length. Near surface, for a << z << D (a is the monomer size), the profile is no longer universal, and in particular, it is sensitive to the boundary condition. Far from the surface, that is z >> xi (t), the profile tends exponentially to its bulk value. We show that the length D approaches its lowest value as the surface composition reaches its saturated value l. In this limit, we find that the profile shape is a characteristic of critical adsorption in simple binary fluid mixtures. Finally, this work must be regarded as a natural extension of a previous one, which was concerned with the same problem, but in the absence of solvent.