# An analytic investigation for the edge effect on mechanical properties of graphene nanoribbons

## TL;DR

This paper analytically investigates how warped free edges due to compressive edge stress affect the mechanical properties of graphene nanoribbons, revealing width-dependent reductions in Young's modulus and Poisson's ratio, including negative values in ultra-narrow ribbons.

## Contribution

It provides explicit analytical formulas for the mechanical properties of graphene nanoribbons considering edge warping effects, advancing understanding of nanoscale edge influences.

## Key findings

- Young's modulus decreases with edge warping and width reduction
- Poisson's ratio is reduced and can become negative in ultra-narrow ribbons
- Results align with previous theoretical studies

## Abstract

We derive analytical expressions for the Young's modulus and the Poisson's ratio of the graphene nanoribbon, in which free edges are warped by the compressive edge stress. Our analytical formulas explicitly illustrate the reduction of the Young's modulus by the warped free edges, leading to the obvious width dependence for the Young's modulus of the graphene nanoribbon. The Poisson's ratio is also reduced by the warped free edges, and negative Poisson's ratio can be achieved in the graphene nanoribbon with an ultra-narrow width. These results are comparable with previous theoretical works.

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Source: https://tomesphere.com/paper/1812.07794