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

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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.