Linear response and stability of ordered phases of block copolymer melts

An efficient pseudo-spectral numerical method is introduced for calculating a self-consistent field (SCF) approximation for the linear susceptibility of ordered phases in block copolymer melts (sometimes referred to as the random phase approximation). Our method is significantly more efficient than that used in the first calculations of this quantity by Shi and Laradji and co-workers, allowing for the study of more strongly segregated structures. We have re-examined the stability of several phases of diblock copolymer melts and find that some conclusions of Laradji et al. regarding the stability of the gyroid phase were the result of insufficient spatial resolution. We find that an epitaxial (k = 0) instability of the gyroid phase with respect to the hexagonal phase that was considered previously by Matsen competes extremely closely with an instability that occurs at a nonzero crystal wavevector k.