Grain Growth in Graphene: Novel Aspects in Two Dimensions

该奖项支持三名研究人员之间的合作，对石墨烯和类似材料与其他片材或基材相互作用的行为进行建模，分析和模拟。 石墨烯片是以六边形晶格排列的碳原子的单原子厚的大分子。 石墨烯被誉为第一种真正的二维材料，自2004年首次分离出单个石墨烯片以来，石墨烯一直受到广泛研究，这是一项获得诺贝尔奖的成就。 这项研究的动机在很大程度上是石墨烯的特殊物理性质及其在工程和材料科学中的潜在应用。 实验工作证实，石墨烯的新电子特性以及其光学和热特性与变形、偏离完美结晶度以及存在褶皱和晶界等缺陷密切相关。 该项目将使用数学建模和科学计算来研究这些现象。 该研究将提供严格的洞察力和基本的科学理解，支持石墨烯片和相关碳大分子的应用，以开发新材料和新技术。该研究的特别重点是由二维碳原子大分子构建的各种二维或三维纳米结构中的图案形成和界面运动。 该项目解决了一系列与单层和双层石墨烯片，碳纳米管和其他碳纳米结构中的晶格注册效应相关的问题。 激发这项研究的现象包括图案形成和局部的石墨烯片和它的支撑衬底之间的晶格和取向失配驱动的波纹，在双层石墨烯的莫尔图案，在多晶石墨烯中的晶界运动，和多壁碳纳米管的波纹化和刻面。 几个变分问题被认为是这些问题的极小分析将产生洞察刚才提到的现象。 该项目的一部分是致力于研究传播的接口使用梯度流动力学。 大部分的研究活动取决于推导连续模型，保留晶格登记效应来描述碳纳米结构中的弱货车德瓦耳斯相互作用。 因此，本研究的一个重要组成部分是严格的理由，原子的连续程序，导致这样的连续模型。 理解和控制碳纳米结构和最近开发的货车德瓦尔斯异质结构中受晶格登记影响的现象对于在材料科学和纳米器件开发中成功使用这些结构是至关重要的。

This award supports a collaboration among three investigators on the modeling, analysis, and simulation of the behavior of sheets of graphene and similar materials interacting with other sheets or substrates. A graphene sheet is a single-atom-thick macromolecule of carbon atoms arranged in a hexagonal lattice. Hailed as the first truly two-dimensional material, graphene has been intensively studied since 2004 when individual graphene sheets were first isolated, a Nobel-prize-winning achievement. This research is motivated in large part by the exceptional physical properties of graphene and its potential applications in engineering and materials science. Experimental work confirms that the novel electronic properties of graphene, as well as its optical and thermal properties, are strongly coupled to deformation, deviations from perfect crystallinity, and the presence of defects such as wrinkles and grain boundaries. The project will use mathematical modeling and scientific computation to study these phenomena. It will provide rigorous insight and fundamental scientific understanding supporting applications of graphene sheets and related carbon macromolecules to develop new materials and technologies.The particular focus of this research is on pattern formation and interface motion in various two- or three-dimensional nanoscale structures built from two-dimensional macromolecules of carbon atoms. The project addresses a collection of problems related to lattice registry effects in single and bilayer graphene sheets, carbon nanotubes, and other carbon nanostructures. The phenomena motivating this study include pattern formation and localized wrinkling driven by lattice and orientation mismatches between a graphene sheet and its supporting substrate, moire patterns in bilayer graphene, motion of grain boundaries in polycrystalline graphene, and polygonization and faceting in multi-walled carbon nanotubes. Several variational problems are considered; analyzing the minimizers of these problems will yield insight into the phenomena just mentioned. A part of the project is devoted to studying propagation of interfaces using gradient flow dynamics. Much of the research activity hinges upon deriving continuum models that retain lattice registry effects to describe weak van der Waals interactions in carbon nanostructures. Hence, an important part of this study is the rigorous justification of the atomistic-to-continuum procedure that leads to such continuum models. Understanding and perhaps controlling phenomena influenced by lattice registry in carbon nanostructures and recently developed van der Waals heterostructures is essential for the successful use of these structures in materials science and nanoscale device development.