Scaling behavior and strain dependence of in-plane elastic properties of graphene

TL;DR

This study uses atomistic simulations to analyze how the in-plane elastic properties of graphene depend on system size and strain, confirming theoretical predictions and explaining experimental observations.

Contribution

It provides detailed simulation results on size and strain effects on graphene's elastic moduli, aligning with membrane theory and addressing experimental discrepancies.

Findings

Elastic moduli vanish with system size as a power law with exponent ~0.325.

Elastic moduli increase with tensile strain, explaining experimental observations.

Poisson ratio scaling disagrees with self-consistent screening approximation predictions.

Abstract

We show by atomistic simulations that, in the thermodynamic limit, the in-plane elastic moduli of graphene at finite temperature vanish with system size $ L $ as a power law $ ~ L^{-\eta_u} $ with $ \eta_u \simeq 0.325 $, in agreement with the membrane theory. Our simulations clearly reveal the size and strain dependence of graphene's elastic moduli, allowing comparison to experimental data. Although the recently measured difference of a factor 2 between the asymptotic value of the Young modulus for tensilely strained systems and the value from {\it ab initio} calculations remains unsolved, our results do explain the experimentally observed increase of more than a factor 2 for a tensile strain of only a few permille. We also discuss the scaling of the Poisson ratio, for which our simulations disagree with the predictions of the self-consistent screening approximation.