Self-consistent calculations of block copolymer solution phase behavior

We present a theoretical study of the influence of solvent on ordered block copolymer solutions. The phase behavior is examined as a function of solvent selectivity, temperature, copolymer concentration, composition, and molecular weight. Phase maps are constructed using self-consistent mean-field (SCMF) theory, via the relative stability of the "classical" phases, lamellae (L), hexagonally packed cylinders (C), and a body-centered cubic array of spheres (S). Solvent selectivity and polymer concentration strongly influence phase transitions in copolymer solutions. When a neutral good solvent is added to a symmetric block copolymer, a direct (lyotropic) transition from L to disordered (D) is expected, analogous to the (thermotropic) L --> D transition in melts. Indeed for neutral good solvents the dilution approximation is followed: the phase map is equivalent to that in the melt, once the interaction parameter is multiplied by the copolymer volume fraction. In contrast, for a symmetric block copolymer in the presence of a slightly selective solvent, the progression L -->C -->S -->micelles -->D is expected, although the micellar phase is not treated here. For asymmetric copolymers more elaborate sequences are anticipated, such as the progression C-B -->L -->C-A -->S-A --> micelles -->D. The stability limit of a homogeneous block copolymer solution is also examined via the random phase approximation (RPA) method. The effect of polymer concentration on the spinodal instability falls into two regimes. When the solvent is not very selective, the stable microphase separation region is reduced as polymer concentration decreases, whereas for very selective solvents, whereas for very selective solvents decreasing polymer concentration broadens the region of stable ordered microstructures.