Magic auxeticity angle of graphene

doi:10.1016/j.carbon.2019.04.057

Carbon

Volume 149, August 2019, Pages 350-354

https://doi.org/10.1016/j.carbon.2019.04.057 Get rights and content

Abstract

Solids exhibit transverse shrinkage when they are stretched, except auxetics that abnormally demonstrate lateral expansion instead. Graphene possesses the unique normal-auxeticity (NA) transition when it is stretched along the armchair direction but not along the zigzag direction. Here we report on the anisotropic temperature-dependent NA transitions in strained graphene using molecular dynamics simulations. The critical strain where the NA transition occurs increases with respect to an increase in the tilt angle deviating from armchair direction upon uniaxial loading. The magic angle for the NA transition is 10.9°, beyond which the critical strain is close to fracture strain. In addition, the critical strain decreases with an increasing temperature when the tilt angle is smaller than the NA magic angle. Our results shed lights on the unprecedented nonlinear dimensional response of graphene to the large mechanical loading at various temperatures.

Graphical abstract

Introduction

Poisson's ratio is a mechanical parameter describing the transverse strain of materials in response to the axial deformation. Most solid materials shrink transversely when they are stretched in longitudinal direction, resulting in a positive Poisson's ratio (PPR) value. However, the abnormal ones, known as auxetics, will exhibit transverse expansion.

Graphene [1,2], a two-dimensional sheet consisting of a monolayer carbon atoms arranged in a hexagonal lattice, is widely regarded as the wonder material in the 21st century. In recent years, many researchers have reported the intrinsic negative Poisson's ratio (NPR) in various graphene derivative materials, including not only the specifically engineered structures such as graphene ribbons [3], kirigami graphene [4], rippled graphene [5], wrinkled graphene [6,7], porous graphene [8] and graphene-based carbon foams [9], but also the chemically altered materials such as oxidized graphene [10] and semi-fluorinated graphene [11]. Particularly, even the pristine graphene sheet could exhibit an intrinsic normal-auxeticity (NA) transition phenomenon from the normal behavior (PPR) to the auxetic behavior (NPR) under strain [3,12]. Once the NA transition occurs, the Poissons ratio changes sign from positive to negative. This is a mechanical phase transition, belonging to second-order phase transition, which is different from thermodynamic first-order phase transition. Such unique transition exclusively occurs when the graphene reaches an engineering strain of around 6% in the armchair direction in the tensile test, while is absent in the zigzag direction. A few efforts have been devoted to explain the underlying mechanisms of such behavior in graphene. In a molecular dynamics (MD) work [12], Jiang et al. reason out that such NA transition results from the competition between two deformation modes about the bond stretching and angle bending interaction. A recent first-principles study [13] done by Qin et al. argues that the decentralized electron localization function driven by strain leads to the electron localization function coupling between different types of bonds, resulting in an increase of the bond angle and thus the emergence of the NPR in graphene.

Considering that the graphene, a honeycomb like structure, has a rotational symmetry in the plane and there is only 30° apart between the armchair direction and the closest zigzag direction, we hypothesize that the anisotropy of the NA transition might imply a possible critical stretching direction between the armchair and the zigzag direction with respect to this NA transition phenomenon. To explore this issue, we have carried out extensive studies by taking advantage of our previous work [14], and shown that the NA transition disappears at a magic angle θ (shown in Fig. 1) of around 10.9° and this magic angle is weakly dependent on the temperature.

Section snippets

Simulation method

As well established, the method of MD simulations are widely used for various investigations [15]. Here all of our MD simulations were conducted on the platform of LAMMPS [16]. To describe the inter-atomic force among carbon atoms, we adopted the adaptive intermolecular reactive empirical bond order (AIREBO) potential [17], which has been widely utilized to investigate the mechanical properties of the carbon systems. A well known issue about the AIREBO potential is the artificial strengthening

Results and discussion

We have examined the collateral strain and Poisson's ratio as a function of the tensile strain in eight graphene samples. The engineering strain in the y direction is defined as $ε_{y} = (L_{y} - L_{y 0}) / L_{y 0}$ , where $L_{y 0}$ and $L_{y}$ are the lengths of sample in the y direction before and after the deformation. Similarly, the strain in the x direction is defined as $ε_{x} = (L_{x} - L_{x 0}) / L_{x 0}$ , where $L_{x 0}$ and $L_{x}$ are the lengths of sample in the x direction before and after the deformation. The collateral strain evolutions at the

Conclusion

In summary, we have investigated the anisotropic and temperature-dependent auxetic behaviors of the monolayer graphene using the molecular dynamics simulations. We have explicitly examined eight configurations with the tilt angle ranging from 0° to 19.1° with respect to the armchair direction. We have found the magic angle of 10.9°, and beyond which the NA mechanical transition disappears in the range of strain from 0 to 0.1. Further molecular dynamics studies have revealed that this NA magic

Disclosure statement

Authors have no conflict of interest to declare.

Acknowledgement

The authors would like to acknowledge the generous financial support from Battelle Energy Alliance, LLC under the DOE Idaho Operations Contract DE-AC07-05ID14517.

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Magic auxeticity angle of graphene

Abstract

Graphical abstract

Introduction

Section snippets

Simulation method

Results and discussion

Conclusion

Disclosure statement

Acknowledgement

J. Comput. Phys.

Carbon

Colloids Surf., B

Electric field effect in atomically thin carbon films

Science

Two-dimensional gas of massless Dirac fermions in graphene

Nature

Negative Poisson's ratio in single-layer graphene ribbons

Nano Lett.

Effects of size and surface on the auxetic behaviour of monolayer graphene kirigami

Sci. Rep.

Negative Poisson's ratio in rippled graphene

Nanoscale

Tailoring graphene to achieve negative Poisson's ratio properties

Adv. Mater.

Giant auxetic behaviour in engineered graphene

Ann. Phys.

Negative Poisson's ratio in periodic porous graphene structures

Phys. Status Solidi B

The negative Poisson's ratio in graphene-based carbon foams

Phys. Chem. Chem. Phys.

Negative Poisson's ratio in graphene oxide

Nanoscale

Sign-tunable Poisson's ratio in semi-fluorinated graphene

Nanoscale

Intrinsic negative Poisson's ratio for single-layer graphene

Nano Lett.

Origin of anisotropic negative Poisson's ratio in graphene

Nanoscale

The normal-auxeticity mechanical phase transition in graphene

2D Mater.