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

技术摘要：该奖项支持理论和计算研究以及教育，目的是超越自洽场理论，该理论是目前理解聚合物混合物和嵌段共聚熔体的基础，也是组成波动的随机相近似理论的基础。自洽场理论在超长聚合物的极限范围内是准确的，但忽略了在具有更短、更强相互作用链的系统中重要的关联效应，以及聚合物混合物临界点附近强烈的组成涨落或对称的两嵌段共聚物熔体的有序-无序转变的影响。PI和其他人发展了一种重整化的单圈修正理论，对自洽场理论进行了修正，改进了早期的粗粒度理论。PI将把这一方法推广到计算两嵌段共聚物熔体有序相的自洽场理论自由能的修正，并建立一个系统的关于这些体系中涨落诱导的一级相变的理论。通过重整化单环理论和普适伊辛交叉函数的渐近匹配，研究了聚合物共混物从经典到伊辛临界行为的交叉。提出了一种在简单模拟模型中独立确定自洽场理论中可调参数的方法，并进行了验证。一组广泛的粗粒模型的计算机模拟将测量聚合物共混物和两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唯象参数的值。使用几个模型将使我们能够检验结果的普遍性以及单圈理论的准确性。对具有更接近化学现实的成键相互作用的模型的模拟将测试单环理论是否可以用于推断短链模拟的结果，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将为两个可能对其他人有用的程序开发、维护和编写大量文档：用于计算嵌段共聚物和聚合物混合物相图的自洽场程序，以及用于蒙特卡洛和分子动力学模拟的通用分子模拟。非技术总结本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行为。这项研究集中在特定类别的聚合物上，这些聚合物作为一种块状材料表现出不同的结构，既具有基本的兴趣，又在工业上使用。PI将专注于改进目前的聚合物混合物模型，使其能够处理组成的巨大波动，例如当体系接近不同相之间的转换点时。广泛的模拟，以及比较来自不同模型的数据的新方法，将提供可以检验该理论的确定的数据体。目标是将这些液体中的涨落效应理论提升到一个成熟的领域，在那里理论已经得到了数值模拟的验证。作为对该领域计算基础设施的贡献，PI将为两个程序开发、维护和编写广泛的文档，这两个程序将有助于在聚合物研究社区和更广泛的材料研究社区中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.