Modeling of nonbonded interactions in graphene and carbon nanotubes

GolovatyDMS-1009849 石墨烯--一片键合的碳原子--的可能应用需要理解和控制机械变形与电子结构和输运性质之间的耦合。 这种耦合还没有被完全理解，部分原因是相互作用的石墨烯片的基本机械响应还没有被充分描述。 预测这种响应的重要因素是石墨烯层之间以及石墨烯和支撑衬底之间的非局部货车德瓦尔斯力。 该项目的目的是开发和研究石墨烯结构的连续模型，该模型以严格的方式结合货车德瓦尔斯力，解释原子的长程有序。 通过多尺度分析，连续体模型制定内的非线性杆和壳理论。 平衡配置的各种石墨烯结构-涉及多层和不同的基板-在外部负载下使用分叉理论的工具进行了分析。 同时，在考虑货车德瓦尔斯力影响的网络模型框架内，研究了纳米复合材料的热性能。 对由碳原子组成的大分子的兴趣刺激了材料科学和物理学的大量研究。 这项工作的大部分集中在碳纳米管上，最近又集中在纳米管的基本结构元素--石墨烯上。 石墨烯是一个单原子厚的碳原子层。 尽管经过了几十年的努力，但直到最近六年，科学家们才发现了生产孤立的单个石墨烯片的方法。 这一发现刺激了一系列关于石墨烯特殊的机械、热和电子特性的实验和理论工作。 利用这些特性可能会导致许多技术和产量的重大进步，例如更高效的太阳能电池，更快的微处理器，或更轻，更强的复合材料。 本项目的主要目标是利用数学模型来更好地理解碳纳米结构层之间原子尺度的力如何影响其机械和热特性。 项目研究人员正在开发和分析相互作用的石墨烯层的综合多尺度模型，利用现有理论的前沿思想以及引入新的数学工具。

GolovatyDMS-1009849 Possible applications of graphene -- a sheet of bondedcarbon atoms -- entail understanding and controlling the couplingbetween the mechanical deformation and electronic structure andtransport properties. This coupling is not fully understood, inpart because the basic mechanical response of interactinggraphene sheets is not yet adequately described. Important forpredicting this response are the nonlocal van der Waals forcesbetween layers of graphene and between graphene and a supportingsubstrate. The aim of the project is to develop and investigatecontinuum models of graphene structures that incorporate van derWaals forces in a rigorous way, accounting for long-rangeordering of atoms. Derived via a multiscale analysis, thecontinuum models are formulated within nonlinear rod and shelltheories. Equilibrium configurations of various graphenestructures -- involving multiple layers and different substrates-- under external loads are analyzed using the tools ofbifurcation theory. Also, the thermal properties of nanotubecomposites are investigated within the framework of a networkmodel taking into account the influence of van der Waals forces. Interest in macromolecules composed of carbon atoms hasstimulated a great deal of recent research in materials scienceand physics. Much of this work has focused on carbon nanotubesand, more recently, on the basic structural element of a nanotube-- graphene. Graphene is a single-atom-thick sheet of bondedcarbon atoms. Despite many decades of effort, only within thelast six years have scientists discovered methods for producingisolated individual graphene sheets. This discovery hasstimulated a flurry of experimental and theoretical work on theexceptional mechanical, thermal, and electronic properties ofgraphene. Exploiting these properties could lead to significantadvances in many technologies and yield, for example, moreefficient solar cells, faster microprocessors, or lighter,stronger composite materials. The principal goal of this projectis to employ mathematical modeling to gain a better fundamentalunderstanding of how atomic-scale forces between layers of acarbon nanostructure influence its mechanical and thermalcharacteristics. The project investigators are developing andanalyzing comprehensive multiscale models of interacting graphenelayers by utilizing ideas at the forefront of existing theoriesas well as by introducing new mathematical tools.