Teng Zhang: Mechanical and Aerospace Engineering, Syracuse University |

Title: Mathematical Models for Topological Defects in Graphene |

Abstract:Topological defects such as disclination, dislocation and grain boundary are ubiquitous in large-scale fabricated graphene. Due to its atomic scale thickness, the deformation energy in a free standing graphene sheet can be easily released through out-of- plane wrinkles which, if controllable, may be used to tune the electrical and mechanical properties of graphene. In this talk, I will first demonstrate that a generalized von Karman equation for a flexible solid membrane can be used to describe graphene wrinkling in the presence of topological defects. In this framework, a given distribution of topological defects in a graphene sheet is represented as an eigenstrain field which is determined from a Poisson equation and can be conveniently implemented in finite element (FEM) simulations. Comparison with atomistic simulations indicates that the proposed continuum model is capable of accurately predicting the atomic scale wrinkles near disclination/dislocation cores while also capturing the large scale graphene configurations under specific defect distributions such as those leading to a sinusoidal surface ruga or a catenoid funnel. A great challenge in designing arbitrarily curved graphene with topological defects is that the defect distribution for a specific 3D shape of graphene membrane is usually unknown, which is actually an inverse problem involving highly nonlinear deformation. In the second part of my talk, I will show how to apply the phase field crystal (PFC) method to search for a triangular lattice pattern with the lowest energy on a given curved surface, which then serves as a good approximation of the graphene lattice structure conforming to that surface. |