THEORY OF ANISOTROPIC FLUCTUATIONS IN ORDERED BLOCK-COPOLYMER PHASES

A general theoretical framework for the study of anisotropic compositi on fluctuations about an ordered block copolymer phase is developed. T he approach is based on the idea that, in order to study the effects o f fluctuations around an ordered broken symmetry phase, the theory mus t be formulated as a self-consistent expansion around the mean-field s olution of this ordered state. A random phase approximation treatment- of the theory leads to anisotropic correlation functions for the syste m. It is shown that the calculation of the polymer correlation functio ns in an ordered phase is equivalent to the calculation of the energy bands and eigenfunctions for an electron in a periodic potential. This general method is applied to the lamellar phase of block copolymers. The calculated anisotropic scattering intensity captures the main feat ures observed experimentally, including the secondary peaks due to flu ctuations with hexagonal symmetry. The origin of the anisotropic fluct uations can be traced to the formation of ''energy'' bands, similar to electronic states in solids.