Theoretical Studies of Inhomogeneous Polymers

对非均相聚合物的平衡性质进行了全面的理论和计算研究。该研究将建立在PI及其同事在场论计算机模拟（FTS）方法上的最新进展的基础上，该方法可以对聚合物和复杂流体的场论模型进行数值研究，而无需任何简化假设，如平均场近似。本研究将包括以下内容：(1)FTS方法的基础：这将包括改进求解复杂扩散方程的算法的发展，这是该方法的核心，以及开发用于实现化学势场更新的复杂朗之万方程的时间积分的有效数值格式。实空间重整化群论也将应用于隔离晶格切断效应和使系统的粗粒化的聚合物溶液模型。(2)共聚物合金中的胶束相：FTS方法将应用于研究嵌段共聚物-均聚物共混物在中间相非结合转变附近的胶束形成，在此平均场理论预计将失败。(3)具有化学无序性的嵌段和接枝共聚物体系：将构建多分散星形嵌段和接枝嵌段共聚物的简化模型，在该模型中，退火和淬火无序性都可以精确地进行平均。这些模型将通过数值和分析研究两种无序系统的自组装行为差异、涨落效应的作用以及组成玻璃化转变的存在。总体目标是获得一个基本的理解如何化学无序，不可避免的在商业共聚物材料，影响结构和热力学。(4)共聚物薄膜中的缺陷控制：平移和键取向顺序将在具有特殊周界条件的嵌段共聚物薄膜的FTS模拟中进行研究。该结果将用于评估石墨外延在制造无缺陷共聚物薄膜方面的功效，该共聚物薄膜可用于先进电子、光学和磁性器件的超高密度图像化。该研究将与加州大学圣巴巴拉分校E.J. Kramer实验室的实验紧密结合。该研究将涉及研究生和博士后研究人员的培训。通过该项目获得的基本理解将通过UCSB的一个新的复杂流体设计联盟来利用，这是一个工业-国家实验室-学术合作伙伴关系，将解决工业聚合物和复杂流体配方的计算设计问题。将对非均相聚合物的平衡性质进行全面的理论和计算研究。该研究将涉及研究生和博士后研究人员的培训。通过该项目获得的基本理解将通过UCSB的一个新的复杂流体设计联盟来利用，这是一个工业-国家实验室-学术合作伙伴关系，将解决工业聚合物和复杂流体配方的计算设计问题

A comprehensive theoretical and computational investigation of the equilibrium properties on inhomogeneous polymers will be carried out. The research will build on the recent developments by the PI and co-workers on the field-theoretic computer simulation (FTS) method, enabling numerical investigations of field theory models of polymers and complex fluids without any simplifying assumptions such as the mean-field approximation. The research will have the following components: (1) Foundations of the FTS method: This will include development of improved algorithms for solving the complex diffusion equation central to the method and development of efficient numerical schemes for time integration of the complex Langevin equations used to implement chemical potential field updates. Real-space renormalization group theory will also be applied to isolate lattice cutoff effects and to enable systematic coarse-graining of polymer solution models. (2) Micelle phases in copolymer alloys: The FTS method will be applied to investigate micelle formation in block copolymers-homopolymer blends near mesophase unbinding transitions, where mean-field theory is expected to fail. (3) Block and graft copolymer systems with chemical disorder: Simplified models of poydisperse star-block and graft-block copolymers will be constructed in which both annealed and quenched disorder averages can be exactly carried out. The models will be numerically and analytically investigated to study the differences in self-assembly behavior between systems with the two types of disorder, the role of fluctuation effects, and the existence of compositional glass transitions. The overall objective is to gain a fundamental understanding of how chemical disorder, unavoidable in commercial copolymer materials, influences structure and thermodynamics. (4) Defect control in thin copolymer films: Translational and bond-orientational order will be examined in FTS simulations of block copolymer films with special perimeter boundary conditions. The results will be used to assess the efficacy of graphoepitaxy for creating defect-free copolymer films that can be used in ultra-high density patterning of advanced electronic, optical, and magnetic devices. The research will be closely coupled with experiments in the laboratory of E.J. Kramer at UCSB. The research will involve training of graduate students and post-doctoral researchers. The fundamental understanding gained through this project will be leveraged through a new Complex Fluids Design Consortium at UCSB, an industry-national lab-academic partnership that will address computational design of industrial polymer and complex fluid formulations.%%%A comprehensive theoretical and computational investigation of the equilibrium properties on inhomogeneous polymers will be carried out. The research will involve training of graduate students and post-doctoral researchers. The fundamental understanding gained through this project will be leveraged through a new Complex Fluids Design Consortium at UCSB, an industry-national lab-academic partnership that will address computational design of industrial polymer and complex fluid formulations.***