Theoretical studies of equilibrium structure and linear response in diblock copolymer melts

This thesis consists of three parts. In the first part, we apply the weak-segregation theory to the orthorhombic Fddd structure in diblock copolymer melts which is motivated by the numerical SCFT prediction of a stable Fddd phase in diblocks very close to the critical point, by Tyler and Morse (Phys. Rev. Lett., 2005). We consider an Fddd structure with the cell parameters satisfying the ratio of a : b : c = 1 : 2 : 23 as predicted by Tyler and Morse, and show that such a structure is a stable equilibrium structure in any weakly crystallized material. In case of diblock copolymer melts, the predictions of the analytical weak-segregation theory agree well with the numerical SCFT results.; In the second part we construct a formalism for studying the linear response behavior of the ordered phases in diblock copolymers. We devise a new numerical algorithm that is significantly more efficient than a previous implementation by Shi et al. (Phys. Rev. Lett., 1997; Macro-molecules, 1997). With our algorithm, we show the gyroid phase to be a locally stable structure for those parameters for which it is believed to be a global minimum, and thereby resolve a controversy regarding its stability.; In the third part, we perform numerical SCFT calculations to construct the phase diagram of a polydisperse diblock system with one block monodisperse and the other block polydisperse with a most-probable distribution.