Negative Poisson's Ratio in Single-Layer Graphene Ribbons

TL;DR

This paper reports the discovery of negative Poisson's ratio in single-layer graphene ribbons caused by edge stress-induced warping, with a predictive analytical model explaining the phenomenon based on geometry and edge effects.

Contribution

It presents the first observation of intrinsic NPR in graphene ribbons and introduces an analytical inclined plate model to predict Poisson's ratio based on size and edge warping.

Findings

NPR observed in graphene ribbons narrower than 10 nm

NPR values reach as low as -1.51

Analytical model accurately predicts Poisson's ratio based on geometry

Abstract

The Poisson's ratio characterizes the resultant strain in the lateral direction for a material under longitudinal deformation. Though negative Poisson's ratios (NPR) are theoretically possible within continuum elasticity, they are most frequently observed in engineered materials and structures, as they are not intrinsic to many materials. In this work, we report NPR in single-layer graphene ribbons, which results from the compressive edge stress induced warping of the edges. The effect is robust, as the NPR is observed for graphene ribbons with widths smaller than about 10 nm, and for tensile strains smaller than about 0.5%, with NPR values reaching as large as -1.51. The NPR is explained analytically using an inclined plate model, which is able to predict the Poisson's ratio for graphene sheets of arbitrary size. The inclined plate model demonstrates that the NPR is governed by the interplay between the width (a bulk property), and the warping amplitude of the edge (an edge property), which eventually yields a phase diagram determining the sign of the Poisson's ratio as a function of the graphene geometry.