A statistical theory of polydisperse block copolymer systems under weak supercrystallization

A statistical theory of conjugated macro- and microphase separation in flexile polydisperse block copolymer systems with a given arbitrary molecular structural distribution is developed in the mean field approximation. A special attention is paid to recognizing and calculating all terms having the least order of magnitude to be taken into account. To this end a special procedure is elaborated enabling to distinguish between strongly and weakly fluctuating order parameters characterizing polydisperse systems and to construct explicitly a one-field parametrization of the free energy of the systems under investigation. The contribution of so-called higher harmonics and effect of a redistribution of macromolecules among coexisting phases are taken into account therewith by a proper renormalization of the fourth vertex of the corresponding effective hamiltonian. In order to compare the presented approach and other existing theories phase diagrams of molten polydisperse diblock copolymer are built numerically in approximations corresponding to different theories. It is shown that our rigorous approach results in phase diagrams qualitatively different from the conventional ones. In particular, we predict the existence of one-phase region having a quasicrystal symmetry and regions of coexistence of this phase with disordered phase and one having the symmetry of the body-centered-oubic lattice as well as a considerable shrinking of the region of the existence of the lamellar phase.