Anisotropy and Stress-Assisted Thermal Activation Kinetics of Graphene Fracture

We have experimentally determined the fracture toughness anisotropy of graphene, showing that the zigzag (ZZ) direction has slightly lower fracture energy than the armchair (AC) direction. This provides an experimental benchmark for widely scattered theoretical predictions, and provides constraints for future models of graphene fracture. We then demonstrate that fracture initiation of graphene is a stress-assisted thermal activation process, and determine the activation energy and activation volume for the process by using Eyring kinetics. These precise measurements are facilitated by exploiting the mechanical exfoliation process used to fabricate graphene, which naturally produces an enormous number of single- and few-atomic height steps on the parent graphite sample’s surface. These steps are a vestige of fracture events occurring in single- and few-layered graphene planes during exfoliation, and as such provide a previously untapped, convenient, and versatile platform for quantitatively determining graphene’s fracture behavior. The measurements are performed using atomic force microscopy (AFM) to image or manipulate these step edges. For investigating facture anisotropy, AFM was used to image the geometry and orientations of the steps with lattice resolution. Two distinct categories of steps were observed depending on the exfoliation direction and local lattice orientation: parallel groups of straight steps well-aligned with local ZZ directions, and steps comprising nanoscale ZZ and AC segments. A fracture mechanics analysis of the microscale morphology and statistics of directions of these steps yielded an experimental measurement of the anisotropy ratio of graphene’s fracture toughness <i>G</i> such that <i>G</i>_ZZ/<i>G</i>_AC=0.971, i.e., ZZ direction has a slightly lower fracture toughness than AC direction. To study the kinetics of fracture initiation, AFM was then used to cut single- and few-layered graphene at those step edges as a function of applied stress and temperature. The results support the hypothesis that fracture initiation is a stress-assisted thermal activation process, offering new physical insights into this phenomenon. In addition to these scientific insights, the AFM-based methodology itself is new. It permits high spatial resolution (sub-nanometer) measurements with facile sample preparation, high throughput due to the typically high areal density of steps, and quantitative measurements applicable to fracture mechanics models. Thus, it is a powerful tool for investigating the nanoscale fracture of graphene and other 2D materials.