INTEGRAL-EQUATION THEORY OF BLOCK-COPOLYMER LIQUIDS .1. GENERAL FORMALISM AND ANALYTIC PREDICTIONS FOR SYMMETRICAL COPOLYMERS

The equilibrium properties of block copolymer liquids are studied using liquid state theory. We first present the formal extension of the, polymer reference interaction site model theory to treat block copolymers of general architectures, and then apply this to the symmetric block copolymer using the Gaussian thread model. Contact with Leibler mean field theory is made by employing the ''reference molecular mean spherical approximation'' closure within the thread idealization. A host of density and concentration fluctuation effects are studied using the ''reference molecular Percus-Yevick'' closure. In particular, the dependence of the effective chi-parameter and peak scattering intensity on density, chain length, temperature, composition, and spatial range of interactions is examined. Within the thread-polymer/effective incompressibility assumption the chain length dependence of the fluctuation stabilization in the vicinity of the mean field spinodal is found to be the same as in the Brazovskii-Fredrickson-Helfand theory. However, a rich dependence on the nonuniversal prefactors, and the enthalpic origin of the feedback mechanism, distinguishes these results from previous field theoretic work.