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

技术概要：该奖项支持理论和计算研究，以及旨在超越自洽场理论的教育，该理论构成了当前对聚合物混合物和嵌段共聚物熔体的理解的基础，也是组成波动的无规相近似理论的基础。自洽场理论是准确的，在很长的聚合物的限制，但忽略了相关的影响，这是很重要的系统较短，更强的相互作用链，和强的组合物波动的影响附近的临界点的聚合物混合物或有序无序过渡的对称二嵌段共聚物熔体。PI和其他人已经开发了一个重整化的单圈理论，对自洽场论进行了修正，改进了早期的粗粒度理论。PI将扩展这种方法来计算修正的自洽场理论自由能的有序相的二嵌段共聚物熔体，并构建一个系统的理论，在这些系统中的波动诱导的一级转变。通过重整化单圈理论和通用Ising交叉函数的渐近匹配，研究了聚合物共混物中从经典到Ising临界行为的交叉。将开发和测试在简单模拟模型中独立确定自洽场理论中的可调参数的方法。粗粒模型的一组广泛的计算机模拟将测量聚合物共混物和二嵌段共聚物中的组成波动，对于几种不同的模型，使用上面讨论的方法来建立现象学参数的值。几个模型的使用将使我们能够测试结果的普遍性以及单回路理论的准确性。具有更真实化学键合相互作用的模型的模拟将测试单环理论是否可以用于外推短链的模拟结果，以预测较长聚合物的性质。作为对该领域计算基础设施的贡献，PI将开发，维护和编写两个可能对其他人有用的程序的广泛文档：用于计算嵌段共聚物和聚合物混合物相图的自洽场代码，以及Monte Carlo和分子动力学模拟的一般分子模拟。该奖项支持的研究涉及将理论发展与计算模拟相结合，以研究聚合物，大链状分子及其混合物的混合物的行为。 研究重点是特定类别的聚合物，这些聚合物作为散装材料显示出各种各样的结构，并且具有根本利益并用于工业。PI将专注于改进聚合物混合物的当前模型，使其能够处理组成的大幅波动，例如当系统接近不同相之间的过渡点时。广泛的模拟，以及比较不同模型数据的新方法，将提供一个确定的数据库，以检验理论。我们的目标是将这些液体中的波动效应理论提升到一个成熟的领域，在这个领域中，理论已经通过数值模拟得到了验证。作为对该领域计算基础设施的贡献，PI将为两个程序开发，维护和编写大量文档，这些程序将有助于聚合物研究社区和材料研究社区广泛使用的计算工具。

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.