Computational Paradigm for Simulating Free Boundary Diblock Copolymers

本计画结合模拟与数值方法来研究嵌段共聚物的自组装。特别是，该项目将导致开发高效和预测性的计算工具，预测呈现自由边界的嵌段共聚物的自组装。此外，这种形式主义将被用来开发一种方法，用于解决逆问题，找到一个掩模组件的几何形状，这将直接对目标设计的共聚物的自组装。共聚物在科学和工程中无处不在，它们提供了现代工业过程所依赖的独特特性，以跟上摩尔定律，并构成了自组装科学研究的优秀模型系统。因此，该研究在其他物理和生物科学中出现的更一般的自组装过程的多尺度建模和计算中具有更广泛的影响。该项目的具体目标是：1）开发一个创新的、有效的计算框架，用于预测自由表面情况下嵌段共聚物在二维和三维空间中的自组装; 2）使用该框架来理解自组装和自由表面几何形状上的热力学、动力学和表面张力之间的耦合; 3）将该框架应用于预测模板的几何形状，其将引导自组装朝向目标设计。二嵌段共聚物是由分子链制成的熔体，所述分子链具有沿其主链沿着的两种化学上不同的物质，所述分子链自组装成用于高密度硬盘驱动器、药物递送系统、磁点、纳米孔、纳米线、具有定制的纳米级孔隙度的膜、电池燃料电池和硅电容器中的有序结构。由于熔体表面在自组装中起着至关重要的作用，本研究将开发一种计算范式，使自由边界二嵌段共聚物的自组装模拟。这种模式结合了动态界面的水平集方法与描述平衡状态下二嵌段共聚物自组装的自洽场理论。这些研究将由PI进行，PI在跨学科环境中与二嵌段共聚物领域的专家密切合作，带来建模和计算思想的协同作用。这项工作的更广泛的影响还包括：1）在跨学科的国际团队中培训计算学生，2）来自代表性不足的群体的本科生的整合，以及3）潜在的工业相关性。

This project combines modeling with numerical methods for the investigation of the self-assembly of block copolymers. In particular, this project will result in the development of efficient and predictive computational tools that predict the self-assembly of block copolymers that present a free boundary. In addition, this formalism will be used to develop a methodology for solving the inverse problem of finding the geometry of a mask component that will direct the self-assembly of copolymer towards a target design. Copolymers are ubiquitous in science and engineering, they provide unique characteristics that modern industrial processes depend on to keep up with Moore's law and constitute an excellent model system for scientific studies of self-assembly. Therefore, the research has a broader impact in the multiscale modeling and computation of more general self-assembly processes that arise in other physical and biological sciences. The specific objectives of the project are: 1) to develop an innovative, effective computational framework for predicting the self-assembly of block copolymer in both two and three spatial dimensions in the case of free surfaces; 2) to use this framework to understand the coupling between thermodynamic, kinetic and surface tension forces on the self-assembly and on the geometry of the free surface; 3) to apply this framework to the prediction of a template's geometry that will direct the self-assembly towards a target design. Diblock copolymers are melts made of molecular chains with two chemically different species along their backbone that self-assemble into ordered structures used in high density hard drives, drug delivery systems, magnetic dots, nano-pores, nano-wires, membranes with tailored nano-scales porosity, in battery fuel cells and silicon capacitors. Since the surface of the melt plays a crucial role in the self-assembly, this research will develop a computational paradigm that enables the simulation of the self-assembly of free boundary diblock copolymers. This paradigm combines the level-set methodology for dynamic interfaces with the self-consistent field theory describing the self-assembly of diblock copolymers at equilibrium. These studies will be carried out by the PI who works in an interdisciplinary environment with close collaborations with experts in the field of diblock copolymers that bring forth a synergy of modeling and computational ideas. The broader impacts of the work also include 1) the training of computational students in an interdisciplinary, international team, 2) the integration of undergraduate from underrepresented groups, and 3) potential industrial relevance.