The Effects of Free Edge Interaction-Induced Knotting on the Buckling of Monolayer Graphene

TL;DR

This study reveals a novel knotting phenomenon caused by free edge interactions in graphene, significantly enhancing its post-buckling stability and stiffness, with potential implications for graphene-based mechanical applications.

Contribution

It introduces a new knotting mechanism induced by free edge interactions in graphene and analyzes its impact on buckling behavior and stability.

Findings

Knotting occurs from colliding buckling waves at warped edges.

Knotting increases graphene's mechanical stiffness fivefold.

Graphene exhibits a large, stable post-buckling strain regime of about 3%.

Abstract

Edge effects play an important role for many properties of graphene. While most works have focused on the effects from isolated free edges, we present a novel knotting phenomenon induced by the interactions between a pair of free edges in graphene, and investigate its effect on the buckling of monolayer graphene. Upon compression, the buckling of graphene starts gradually in the form of two buckling waves from the warped edges. The collision of these two buckling waves results in the creation of a knot structure in graphene. The knot structure enables the buckled graphene to exhibit two unique post-buckling characteristics. First, it induces a five-fold increase in graphene's mechanical stiffness during the buckling process. Second, the knotted structure enables graphene to exhibit a mechanically stable post-buckling regime over a large (3%) compressive strain regime, which is significantly larger than the critical buckling strain of about 0.5%. The combination of these two effects enables graphene to exhibit an unexpected post-buckling stability that has previously not been reported. We predict that numerical simulations or experiments should observe two distinct stress strain relations for the buckling of identical graphene samples, due to the characteristic randomness in the formation process of the knot structure.