Harmonic corrections to the mean-field phase diagram for block copolymers

Allowance is made for harmonic corrections within mean-field theory for weakly segregated block copolymers. The theory of Marques and Cates [C. M. Marques and M. E. Cates, Europhys. Lett. 13, 267 (1990)] for the stability of phases near the ordering transition is applied to diblock copolymer melts. A wave-vector dependence of the coefficients in the Landau mean-field free energy is included. We find that the face centered cubic (fcc) and square phases predicted by Marques and Cates to be stable near the ordering transition depending on the structure factor for the system are not stable for diblock copolymers. In addition, hexagonal close packed (hcp) and ordered bicontinuous double diamond (OBDD) structures are found to be unstable with respect to the classical lamellar, cylinder, and body centered cubic phases. The hexagonal intermediate phases and complex bicontinuous structures recently observed near the order-disorder transition are not accounted for in this theory.