| Dense polymer liquids are well described by the self consistent field theory (SCFT), which assumes that chains are random walks and that the interactions between monomers are local. Attempts to go beyond the mean-field treatment of the SCFT, however, have been marred by a recurrent problem of divergent corrections. The corrections are divergent due to short length-scale interactions, which the model was never designed to correctly describe. The goal of the thesis is to demonstrate that despite this, a coarse-grained phenomenological theory of polymer liquids can be used to make nontrivial physical predictions. This work presents a theory for both blends of homopolymers and melts of diblock copolymers. A loop expansion of the structure factor is used, and the one loop corrections to the intramolecular and intermolecular components of the structure factor are shown to be divergent, or equivalently, strongly cutoff dependent. To deal with this obstacle, a renormalization procedure is applied. It is shown that the divergent contributions to both collective and intramolecular correlation functions can be absorbed into redefinitions of the phenomenological parameters of the theory. This is true for both homopolymer blends and diblock copolymer melts, and the required redefinitions of parameters are identical in blends and copolymer melts of the same composition. Having dealt with the divergences, the theory can be employed to make quantitative predictions by subtracting the divergent terms in the numerical calculations. Single-chain and collective correlation functions are calculated for diblock copolymer melts near the order-disorder transition (ODT). The shift near the ODT in the wavenumber q* at which the collective correlation function (or scattering intensity) reaches maximum, is shown to be primarily a result of intermolecular correlations, rather than of changes in single-chain correlations. |
