Theory and Simulation of Correlations in Polymer Liquids: Beyond the Self-Consistent Field Approximation

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TECHNICAL SUMMARY: This award supports theoretical and computational research, and education with the aim of advancing beyond the self-consistent field theory that forms the basis for current understanding of polymer mixtures and block copolymer melts, and is also the basis of the random phase approximation theory of composition fluctuations. Self-consistent field theory is accurate in the limit of very long polymers, but neglects correlation effects that are important in systems of shorter, more strongly interacting chains, and the effects of strong composition fluctuations near the critical point of a polymer mixture or the order-disorder transition of a symmetric diblock copolymer melt. The PI and others have developed a renormalized one-loop theory of corrections to the self-consistent field theory that improves on earlier coarse-grained theories. The PI will extend this approach to calculate corrections to the self-consistent field theory free energy of ordered phases of diblock copolymer melts, and to construct a systematic theory of the fluctuation induced first order transition in these systems. The crossover from classical to Ising critical behavior in polymer blends will also be studied, by asymptotic matching of the renormalized one-loop theory and the universal Ising crossover function. A method of independently determining the adjustable parameters in self-consistent field theory in simple simulation models will be developed and tested. An extensive set of computer simulations of coarse grained models will measure composition fluctuations in polymer blends and diblock copolymers, for several different models, using the method discussed above to establish values for phenomenological parameters. The use of several models will allow us to test the universality of the results as well as the accuracy of the one-loop theory. Simulations of models with more chemically realistic bonded interactions will test whether the one-loop theory can be used to extrapolate the results of simulations of short chains to predict properties for longer polymers. As a contribution to the computational infrastructure of the field, the PI will develop, maintain, and write extensive documentation for two programs that are likely to be useful to others: a self-consistent-field code used for calculating phase diagrams of block copolymers and polymer mixtures and a general molecular simulation for Monte Carlo and molecular dynamics simulations. NONTECHNICAL SUMMARY The research supported under this award involves combining theoretical development with computational simulations to study the behavior of mixtures of polymers, large chain-like molecules, and their mixtures. The research focuses on particular classes of polymers which show a diverse range of structures as a bulk material and are of both fundamental interest and are used in industry. The PI will focus on improving current models for polymer mixtures to enable them to handle large fluctuations in composition such as when the system is near a transition point between different phases. Extensive simulations, and new methods of comparing data from different models, will provide a definitive body of data against which the theory can be tested. The goal will be to elevate the theory of fluctuation effects in these liquids to a mature field where theory has been validated using numerical simulations. As a contribution to the computational infrastructure of the field, the PI will develop, maintain, and write extensive documentation for two programs that will contribute to the computational tools widely used in the polymer research community and materials research community more broadly.