Grain Growth in Graphene: Novel Aspects in Two Dimensions

University Of Akron, Akron OH

Investigators

Abstract

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.