Theoretical Studies of Inhomogeneous Polymers

我们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。这项研究将建立在PI和同事对场理论计算机模拟(FTS)方法的最新发展的基础上，使聚合物和复杂流体的场理论模型的数值研究成为可能，而不需要任何简化的假设，如平均场近似。这项研究将包括以下部分：(1)FTS方法的基础：这将包括开发用于求解该方法核心的复杂扩散方程的改进算法，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方案。实空间重整化群理论也将被应用于隔离晶格截止效应，并使聚合物溶液模型的系统粗粒化成为可能。(2)共聚物合金中的胶束相：FTS方法将被用于研究嵌段共聚物-均聚物共混物在中间相分离转变附近的胶束形成，其中平均场理论预计将失败。(3)含化学无序的嵌段和接枝共聚物体系：建立了星形嵌段和接枝嵌段共聚物的简化模型，可以准确地计算出退火态和猝灭态的无序度平均值。这些模型将被数值和解析研究，以研究具有两种无序的系统之间自组装行为的差异，涨落效应的作用，以及成分玻璃化转变的存在。总体目标是对商业共聚材料中不可避免的化学无序如何影响结构和热力学有一个基本的了解。(4)共聚物薄膜中的缺陷控制：在具有特殊周长边界条件的嵌段共聚薄膜的FTS模拟中，将考察平移和键取向有序性。研究结果将用于评估梯度外延技术在制造无缺陷共聚物薄膜方面的有效性，这些薄膜可用于先进电子、光学和磁性设备的超高密度图案化。这项研究将与加州大学伯克利分校E.J.克莱默的实验室实验紧密结合。这项研究将涉及研究生和博士后研究人员的培训。通过这个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，该联盟是一个行业-国家实验室-学术合作伙伴关系，将致力于工业聚合物和复杂流体配方的计算设计。%将对非均质聚合物的平衡性质进行全面的理论和计算研究。这项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，该联盟是一个行业-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.***