INTERFACIAL PHASE-TRANSITIONS IN BLOCK COPOLYMER HOMOPOLYMER BLENDS

A theoretical treatment of A-B diblock copolymer aggregation in matrices of homopolymer A is developed. These aggregates, termed ''bulk' micelles when they form within a homogeneous matrix phase and 'surface'' micelles when they form at a surface or interface, can be pointlike (spherical), linear (cylindrical), or planar (lamellar). Bulk micelles set the limiting value of the copolymer chemical potential which can be obtained in a given system. Surface micelles will be formed at lower copolymer chemical potentials when the surface has a preferential affinity for the B repeat units which make up the micelle core. The interfacial properties are determined by the copolymer asymmetry g, the thermodynamic incompatibility chiN(c) between A and B copolymer blocks, the ratio N(h)/N(c) of the homopolymer and copolymer molecular weights, and a bare surface free energy difference gamma(a) - gamma(b) between A and B polymers. A scaling treatment valid for N(h)/N(c) greater-than-or-similar-to 1 is developed from a simple physical picture of the aggregation process. Phase transitions between different surface micellar geometries are predicted to occur for certain combinations of g and gamma(a) - gamma(b). The primary result of the scaling treatment is a surface phase diagram describing the transitions which can occur for different values of these parameters. A more quantitative self-consistent-field treatment based on the description of the polymer chain statistics by a set of chain-end distribution functions is also developed. The self-consistent-field predictions include the detailed structures of both bulk and surface micelles and give values for the copolymer chemical potential for bulk micelles which are in quantitative agreement with recent experiments. The self-consistent-field theory is used to illustrate the detailed nature of some surface phase transitions and is also applied to the segregation of an A/B diblock copolymer to the interface between immiscible A and C homopolymers.