Collaborative Research: Modeling and Simulation of the Growth of Graphene Multilayers and Heterostructures

该奖项支持二维材料数学和计算建模的研究和教育活动。受最近在不同二维材料（如石墨烯和六方氮化硼）的分离和转移方面的技术进步的启发，研究人员将专注于两种类型的问题：异质结构，其中两种材料在同一平面上聚集在一起，以及石墨烯的堆叠二维层。与均匀单层相比，异质结构和堆叠层包含更多的自由度，可以用来制造具有专门设计的电子，微机械和光学特性的材料。这些新型材料在许多领域都有应用，这些领域被认为对美国的战略利益至关重要，如纳米技术、信息技术和能源技术。迄今为止，这方面的努力主要是试验性的，采用试错法。这里开发的多尺度数学和计算模型将通过提供合理的框架来优化生产过程，从而为该领域做出实质性贡献。此外，该框架可以扩展到研究其他材料，如半导体量子点阵列，磁性簇，或金属有机表面网络，这些材料是能量转换，热传输和其他器件应用的有希望的候选者。两名研究生将接受跨学科培训，并将在会议上介绍他们的研究结果，这将加强他们的专业培训。推广工作包括在加州大学欧文分校的加州数学和科学暑期学校（COSMOS）中教授高中生。这些努力将有助于培养未来的科学家。该项目将研究控制石墨烯多层膜和异质结构的生长和形态的机制的非线性动力学，并通过（1）开发和应用最先进的自适应数值方法进行大规模计算和（2）进行重要组成过程的分析，数值和建模研究来制定控制其生长的策略。该研究将为此类材料的合理设计提供一个新的框架。一个重大的挑战是，异质结构和堆叠层的结构和形态是由原子尺度的现象，并通过扩散的多个物种和弹性相互作用超过数百纳米的长度尺度。因此，没有单一的模型能够描述石墨烯异质结构形成中涉及的所有过程。研究人员将采用多尺度方法，其中将开发原子和介观算法来确定材料特性，并预测应变在异质结构和垂直堆叠片材中的作用以及原子结构和缺陷。原子模拟将提供新的连续相场模型，描述在更大的尺度上的多组分平面内和垂直堆叠的片材的生长的材料参数和力。这些问题的高度非线性性质使得快速，准确和强大的数值方法对他们的研究至关重要。

This award supports research and educational activities in mathematical and computational modeling of two-dimensional materials. Motivated by recent technological advancements in the isolation and transfer of different two-dimensional materials, such as grapheme and hexagonal boron nitride, the investigators will focus on two types of problems: heterostructures, where two materials are brought together in the same plane, and stacked two-dimensional layers of graphene. Compared to homogeneous monolayers, heterostructures and stacked layers contain many more degrees of freedom that can be exploited to fabricate materials with specifically designed electronic, micromechanical and optical properties. These novel materials have applications in many areas identified as critical to US strategic interests such as nanotechnology, information technology, and energy technology. Thus far, efforts in this area have been mainly experimental, using trial-and-error approaches. The multiscale mathematical and computational models developed here will make a substantial contribution to the field by providing a rational framework to optimize the production process. Further, this framework can be extended to examine other materials such as arrays of semiconductor quantum dots, and magnetic clusters, or metal-organic surface networks that are promising candidates for energy conversion, thermal transport, and other device applications. Two graduate students will receive interdisciplinary training and will present their findings at conferences, which will enhance their professional training. Outreach efforts include teaching high school students as part of the California State Summer School for Mathematics and Science (COSMOS) at UC Irvine. These efforts will help develop future generations of scientists. This project will investigate the nonlinear dynamics of the mechanisms that govern the growth and morphology of graphene multilayers and heterostructures and to develop strategies to control its growth by (1) developing and applying state-of-the-art adaptive numerical methods to large-scale computation and (2) performing analytical, numerical, and modeling studies of important constituent processes. The research will provide a novel framework for the rational design of such materials. A significant challenge is that the structure and morphology of heterostructures and stacked layers is determined both by atomic-scale phenomena and by the diffusion of multiple species and elastic interactions over length scales of hundreds of nanometers. Consequently, no single model is able to describe all the processes involved in the formation of graphene heterostructures. The investigators will adopt a multiple-scale approach in which atomistic and mesoscale algorithms will be developed to determine material properties and to predict the role of strain in heterostructures and vertically-stacked sheets as well as the atomic structures and defects. The atomistic simulations will provide material parameters and forces to new continuum phase field models that describe the growth of multicomponent in-plane and vertically-stacked sheets at larger scales. The highly nonlinear nature of these problems makes fast, accurate, and robust numerical methods essential to their study.