Grain Growth in Graphene: Novel Aspects in Two Dimensions

该奖项支持三名研究人员合作，对石墨烯片材和类似材料与其他片材或衬底相互作用的行为进行建模、分析和模拟。石墨烯是一种单原子厚度的大分子碳原子，排列在六角形晶格中。自2004年首次分离出单个石墨烯薄片以来，石墨烯一直被誉为第一个真正的二维材料，这是一项获得诺贝尔奖的成就。这项研究在很大程度上是由于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，石墨烯的新的电子性质以及它的光学和热性质与变形、偏离完美结晶度以及存在褶皱和晶界等缺陷有很强的耦合。该项目将使用数学建模和科学计算来研究这些现象。它将为石墨烯及其相关碳大分子的应用提供严谨的洞察力和基础性的科学理解，以开发新的材料和技术。本研究的重点是由碳原子的二维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薄片、碳纳米管和其他碳纳米结构中的晶格注册效应有关的问题。这些现象包括石墨烯的晶格和取向失配、双层石墨烯中的莫尔图案、多晶石墨烯中晶界的运动以及多壁碳纳米管中的多边形化和小面化。我们考虑了几个变分问题；分析这些问题的极小化将使我们对刚才提到的现象有更深入的了解。该项目的一部分致力于利用梯度流动力学研究界面的传播。许多研究活动依赖于推导出连续统模型，该模型保留了晶格注册效应来描述碳纳米结构中弱的范德华相互作用。因此，这项研究的一个重要部分是对导致这种连续体模型的原子到连续体过程的严格证明。了解和控制碳纳米结构和最近发展起来的范德华异质结构中晶格注册所影响的现象，对于这些结构在材料科学和纳米器件开发中的成功应用是至关重要的。

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.