| AVS 66th International Symposium & Exhibition | |
| 2D Materials | Monday Sessions |
| Session 2D+EM+MI+NS-MoM |
| Session: | Properties of 2D Materials including Electronic, Magnetic, Mechanical, Optical, and Thermal Properties I |
| Presenter: | Jaehyung Yu, University of Illinois at Urbana-Champaign |
| Authors: | J. Yu, University of Illinois at Urbana-Champaign E. Han, University of Illinois at Urbana-Champaign E. Annevelink, University of Illinois at Urbana-Champaign J. Son, University of Illinois at Urbana-Champaign E. Ertekin, University of Illinois at Urbana-Champaign P.Y. Huang, University of Illinois at Urbana-Champaign A.M. van der Zande, University of Illinois at Urbana-Champaign |
| Correspondent: | Click to Email |
A challenge and opportunity in nanotechnology is to understand and take advantage of the breakdown in continuum mechanics scaling laws as systems and devices approach atomic length scales. Such challenges are particularly evident in two-dimensional (2D) materials, which represent the ultimate limit of mechanical atomic membranes as well as molecular electronics. For example, after more than a decade of study, there is no consensus on the bending modulus of few layer graphene, with measured and predicted values ranging over two orders of magnitude, and with different scaling laws. However, comparing these studies is challenging because they probe very different and often fixed curvatures or magnitudes of deformation. To unravel the discrepancy, a systematic measurement of bending stiffness versus deformation is needed. The results have practical implications on predicting and designing the stiffness of many 2D mechanical systems like origami/kirigami nanomachines, stretchable electronics from 2D heterostructures, and resonant nanoelectromechanical systems.
In this study, we combine atomistic simulation and atomic scale imaging to theoretically and experimentally examine the bending behavior of few-layer graphene. First, we experimentally probe the nanoscale bending by laminating few-layer graphene over atomically sharp steps in boron nitride and imaging the cross-sectional profile using aberration-corrected STEM. Second, we use DFT simulations to examine the bending of few-layer graphene under compression. By measuring the nanoscale curvatures, we extract the simulated and experimental bending modulus while varying both the number of layers and the degree of nanoscale curvature.
We find remarkable agreement between the theory and experiment and observe an unexpected curvature dependent bending stiffness of few-layer graphene that deviates from continuum scale bending mechanisms. We find that the bending stiffness of few layer graphene versus curvature corresponds with a gradual change in scaling power with thickness from cubic to linear. We find that the transition in scaling behavior originates from a transition from shear, slip and the onset in superlubricity between the graphene layers at the van der Waals interface, verified by a simple Frenkel-Kontorova model. Our results provide a unified model for the bending of 2D materials and show that their multilayers can be orders of magnitude softer than previously thought, among the most flexible electronic materials currently known.