Theoretical understanding of the surface and bulk thermodynamic properties of nonlinear macromolecules is desirable with rapid advances in the synthesis and application of polymers with complex architectures. This thesis focuses on the study of the surface and bulk in polymeric systems containing nonlinear species as two individual topics. Polymers with nonlinear architectures, such as branched or cyclic polymers, can segregate to both surfaces and interfaces when blended with linear polymer. A self-consistent field theory (SCFT) was developed to understand the segregation of blends of a linear polymer with various nonlinear polymer molecules, and was carried out in close collaboration with experiments on a series of nonlinear molecules with exquisitely controlled architectures. The theory predicts how the composition density profiles vary with the architecture of the nonlinear species and the volume fraction of two components, as well as the total density. The dependence on composition of the total surface excess of nonlinear species is compared with both linear response theory and experimentally determined surface excesses of star, branched, comb and ring polymers. The comparison between experiments and theories indicates that SCFT can capture the effects of the branch points, the lengths of side branches and the topologies on the surface enrichment in those blends containing nonlinear and linear polymers. As the second topic, the bulk conformations of nonlinear polymers are studied using a novel two-chain SCFT developed in this thesis. The two-chain theory is designed to capture the intra- and intermolecular correlations in melts and solutions of linear and branched polymers that are not present in conventional SCFT. The intra- and intermolecular density correlations are calculated using SCFT by breaking translational symmetry and holding a given monomer fixed. The two-chain theory is shown to be capable of describing the crossover from self-avoiding walk at short distances, to screened random walk at long distance in a semi-dilute solution or melt of linear and branched molecules, and to predict dependence on the excluded volume parameter. End-branched polymers varying in branch functionality and length are studied by SCFT, and indicate that the branching architectures enhance the swelling of polymers in melts, and show stretching effects at short distances from the core. The mean field Helmholtz free energy can be evaluated in both canonical and grand-canonical ensemble within the two-chain theory. The effective Flory interaction parameter in the two-chain SCFT is obtained from an approximate evaluation of the mixing free energy, which is dependent on excluded volume. The calculations show qualitative agreement with the Gaussian field theory by Fredrickson and co-workers and with neutron scattering experiments. In summary, my original contributions to the knowledge in this field are: 1) SCFT studies of surface segregation in blends of new branched and linear polymers. 2) SCFT studies of surface segregation in blends of linear and cyclic polymers, and tests of linear response theory predictions. 3) Numerical algorithms to handle a variety of complex architectures for SCFT. 4) Development of a novel two-chain SCFT for various branched polymers to capture bulk intra- and intermolecular correlations, with application to stars, end-branched and pom-pom molecules. 5) Evaluation of the mixing free energy for homogeneous polymer blends containing complex branched architectures by two-chain SCFT. Most importantly, close collaboration with experimentalists has proven that SCFT can give good agreement with experiments on both surface and bulk thermodynamics. Therefore, the theory provides an efficient and useful tool in directing future experiments and hopefully the commercialization of nonlinear polymers.
Copyright of the original work is retained by the author.
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