UC Berkeley

Graphene is the strongest material ever discovered and has an extremely high Young's modulus (~ 1 GPa). Although stretching the sp2 covalent bonds between carbon atoms is very difficult, significant deflections do develop in graphene membranes. In fact, thermal rippling naturally emerges in graphene at any finite temperature. Moreover, the topological defects mediating plastic deformation often cause out-of-plane crumpling, an effective way to reduce the total elastic energy of the topological defect. It is even possible to design specific stress states to produce periodic wrinkles in graphene with adjustable wave lengths.

This work aims to understand how buckling influences the elastic and plastic behavior of graphene-based nanostructures. While the elastic moduli may be straightforwardly computed using structure optimization techniques with applied test stresses, it is a nontrivial task to obtain elastic properties at any specific temperature. Further, linear elastic theories are not able to describe large buckling because the second order nonlinear terms in the definition of the Lagrangian finite strain tensor cannot be neglected. In addition, the existence of topological defects and constraints need to be properly treated. Finally, buckling and defects of a curved surface such as a nanotube is even more complicated and poses other intriguing challenges.

To proceed, we employ Monte Carlo techniques to obtain fundamental elastic properties of graphene at desired temperatures, which supplies useful inputs for a nonlinear continuum model for graphene. This model not only takes into account, in a suitable manner, both large out-of-plane buckling and interactions among edge dislocations with periodic boundary conditions, but also serves as a handy tool for simulating nanoindentation experiments and the controlled wrinkling of graphene. At last, we focus on the Stone-Wales defect mediated plasticity of CNTs. Specifically, a kinetic Monte Carlo framework is designed to model the defect dynamics over a long time scale. We find that in large nanotubes, a chain of closely packed dislocations (called a "dislocation worm") may have less buckling and lower formation energy than the conventional dislocation glide under high tensile stresses.