Modulus Of Graphene Research Articles

Effect of structural defects and chemical functionalisation on the intrinsic mechanical properties of graphene

Due to its unique mechanical properties, graphene can be applied for reinforcement in nanocomposites. We analyse the Young's modulus of graphene at the semi-empirical PM6 level of theory. The internal forces are calculated and the Young's modulus is predicted for a finite graphene sheet when external strain is applied on the system. These results are in a good agreement with theoretical and experimental results from the literature giving values of about 1 TPa for the Young's modulus. Stress-strain curves are computed for elongation up to 20%. In addition, the influence of the presence of a single vacancy, as well as for oxygenation of a vacancy, on the mechanical properties of graphene has been analysed. Our results indicate that when applying the deformation locally onto the system, higher local stress can be induced, as confirmed by Finite Element Analysis. Also, the presence of structural defects in the system will stiffen the system upon low strain, but reduces the elastic limit from more than 20% strain for pristine graphene to less than 10% strain when defects are present.

Effect of Temperature on Young's Modulus of Graphene

The temperature dependence of the thermo-mechanical behavior of materials is of great importance in many engineering applications where the precise properties of materials over an extended temperature range are needed. The objective of this work is to present a density functional study to predict the temperature variation of Young's modulus of graphene. To this end, the energies of phonons as well as thermodynamic functions are calculated from phonon calculations via the quasi-harmonic approximation. It is observed that with the increase of strain the phonon energy decreases. Also, by increasing temperature up to a special value which is around 400 K, Young's modulus decreases appreciably. For the temperatures higher than 400 K, Young's modulus decreases with a lower rate and tends to be constant at high temperatures. The results obtained are in a good agreement with the experimental data previously reported in the literature.

Estimation of Young’s Modulus of Graphene by Raman Spectroscopy

The Young's modulus of graphene is estimated by measuring the strain applied by a pressure difference across graphene membranes using Raman spectroscopy. The strain induced on pressurized graphene balloons can be estimated directly from the peak shift of the Raman G band. By comparing the measured strain with numerical simulation, we obtained the Young's modulus of graphene. The estimated Young's modulus values of single- and bilayer graphene are 2.4 ± 0.4 and 2.0 ± 0.5 TPa, respectively.

Effect of Vacancy Defects on the Young's Modulus and Fracture Strength of Graphene: A Molecular Dynamics Study

AbstractThe Young's modulus of graphene with various rectangular and circular vacancy defects is investigated by molecular dynamics simulation. By comparing with the results calculated from an effective spring model, it is demonstrated that the Young's modulus of graphene is largely correlated to the size of vacancy defects perpendicular to the stretching direction. And a linear reduction of Young's modulus with the increasing concentration of mono‐atomic‐vacancy defects (i.e., the slope of −0.03) is also observed. The fracture behavior of graphene, including the fracture strength, crack initiation and propagation are then studied by the molecular dynamics simulation, the effective spring model, and the quantized fracture mechanics. The blunting effect of vacancy edges is demonstrated, and the characterized crack tip radius of 4.44 Å is observed.

Effect of hydrogen coverage on the Young's modulus of graphene

We blend together continuum elasticity and first-principles calculations to measure by a computer experiment the Young modulus of hydrogenated graphene. We provide evidence that hydrogenation generally leads to a much smaller longitudinal extension upon loading than in pristine graphene. Furthermore, the Young modulus is found to depend upon the loading direction for some specific conformers, characterized by an anisotropic linear elastic behavior.

Young's Modulus of Graphene Based on Finite Displacement Theory

Young’s modulus of monolayer graphene with carbon-circles is considered based on least-energy principle (LEP) and finite displacement theory (FDT). The relationships between the Young’s modulus and the numbers of carbon-circles of graphene are obtained. The results suggest that the Young’s modulus of graphene increases with the increasing number of carbon-circles in y-direction, but reduces with the increasing number in x-direction, and gradually comes to the constant .

Young's Modulus of Graphene Based on Variation Principle and Energy Conservation

Tensile strain in x-direction for monolayer graphene with carbon-circles is considered based on variation principle and energy conservation. The relations between the Young’s modulus in x-direction and the number of carbon-circles of graphene are obtained. The results show that the Young’s modulus of graphene in x-direction is independent of the number of carbon-circles in x-direction, but it increases with the increasing number of carbon-circles in y-direction and finally comes to the constant.

The Superior Dispersion of Easily Soluble Graphite

Graphene is a 2D one-atom-thick layer that has attracted enormous scientific attention on account of its extraordinary electronic and mechanical properties resulting from the hexagonally arrayed sp-hybridized carbon atom structure. Several efforts have been made to use graphene in devices and composites. The strong covalent bonds of carbon atoms provide high mechanical and thermal properties and chemical stability. The theoretical Young’s modulus of graphene is approximately 1060GPa. In addition, the high electrical conductivity (mobility: 20 000 cmV 1 s , velocity: c/300) through the p-electron cloud makes graphene a promising material in conducting composites and quantum electronics. As in other new materials (such as carbon nanotubes, various quantum dots, etc.), the development of mass productionmethods that can support the demand for graphene in a variety of large-scale applications is of high priority. Thus far, several methods for graphene production have been developed and can be summarized into three areas:mechanical exfoliation, graphene in solution, and epitaxial growth. Mechanical exfoliation produces the highest quality graphene, which is suitable for fundamental studies. Epitaxial growth provides the shortest path to graphene-based electronic circuits. Graphene in solution can offer lower costs and higher throughputs and may be used in a wide range of applications because of the significant practical utility of this material. However, the method is quite complicated and

Young’s modulus of graphene: A molecular dynamics study

The Young's modulus of graphene is investigated through the intrinsic thermal vibration in graphene which is ``observed'' by molecular dynamics and the results agree very well with the recent experiment [Lee et al., Science 321, 385 (2008)]. This method is further applied to show that the Young's modulus of graphene (1) increases with increasing size and saturates after a threshold value of the size; (2) increases from 0.95 to 1.1 TPa as temperature increases in the region [100, 500] K; (3) is insensitive to the isotopic disorder in the low disorder region $(l5%)$ and decreases gradually after further increasing the disorder percentage.

On the Flexural Characteristics of Multi-walled Carbon Nanotubes

ABSTRACTWe use an analytical solution for bending of coaxial orthotropic cylinders to model the flexural deformation of multi-walled nanotubes with any number of layers. The simulation results show that the bending stiffness of the MWNT increases with the number of nanotube layers. For fixed number of layers, MWNT with larger inner radius has greater bending stiffness. The bending stiffness also increases with out layer radius. For certain outer radius, smaller inner radius results in a larger stiffness. The effective elastic modulus of the MWNT also increases with the number of layers and the outer radius. For the same value of the outer radius, the MWNT with smaller inner radius has a larger effective elastic modulus. As the number of layers increases, the effective modulus approaches the in-plane elastic modulus of graphene. In this work we find that the interface conditions, i.e., perfect bonding or no friction, do not affect the bending stiffness and effective elastic modulus of the MWNT. Furthermore, the cross-section of MWNT does not show any warping under bending, which suggest the classic beam theory is applicable in determining the flexural response of MWNT.