Self-Consistent Field Theory within Hildebrand Approximation: Microphase Separation in Gradient Copolymers

To provide a faster calculation of the block copolymer phase diagrams a simplified version of the self-consistent field theory (SCFT) is proposed. Multi-component block copolymers with interactions between repeated units described by the -parameters satisfying the Hildebrand conditions are studied. This case is shown to correspond to a degeneration within the framework of the general SCFT approach. Remarkably, the degenerated thus multi-component block copolymers admit two-component only SCFT description. The procedure presented is applied to gradient copolymers considered as a limiting case of multi-component copolymers obeying Hildebrand conditions, the lengths of the blocks vanishing and the number of different kinds of repeated monomers tending to infinity. Finally, a melt of symmetric triblock copolymers blurred into a gradient copolymer is studied and corresponding phase diagrams are calculated.