Computational Paradigm for Simulating Free Boundary Diblock Copolymers

本项目将建模与数值方法相结合，研究嵌段共聚物的自组装过程。特别是，该项目将导致高效和预测计算工具的发展，预测具有自由边界的嵌段共聚物的自组装。此外，这种形式将用于开发一种方法，用于解决寻找掩膜组件几何形状的反问题，这将指导共聚物的自组装朝向目标设计。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，该研究对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具有更广泛的影响。该项目的具体目标是：1)开发一种创新的、有效的计算框架，用于在自由表面的情况下预测嵌段共聚物在二维和三维空间中的自组装；2)利用这一框架来理解热力学、动力学和表面张力对自组装和自由表面几何形状的耦合作用；3)将此框架应用于模板几何形状的预测，从而将自组装导向目标设计。双嵌段共聚物是由分子链组成的熔体，分子链的主干上有两种化学性质不同的共聚物，它们自组装成有序的结构，用于高密度硬盘驱动器、药物输送系统、磁点、纳米孔、纳米线、具有定制纳米级孔隙度的膜、电池燃料电池和硅电容器。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成为可能。这种范式结合了动态界面的水平集方法和描述平衡状态下双嵌段共聚物自组装的自一致场理论。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，从而产生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)在一个跨学科的国际团队中训练计算机专业的学生；2)整合来自代表性不足群体的本科生；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.