Elastic Properties Of Graphene Research Articles

Influence of temperature on the elastic properties of graphene and graphene-like nanosheets based on the asymptotic homogenization method

In this paper, the effective elastic properties of hexagonal monolayers such as graphene, boron nitride, silicon carbide, and aluminum nitride are evaluated using the asymptotic homogenization method taking into account temperature changes. The effective properties are determined analytically by considering temperature, force constants, bond lengths, and thickness, using atomic interactions within the context of the unit cell problem. The relationship between environmental temperature and the coefficient of thermal expansion is established by considering changes in the values ​​of bond stretching, bond angle bending, and torsion resistance constants at different temperatures from 0 to 1800 K. The results provided by the proposed homogeneous model are consistent with the valid findings of other researchers in the literature. It is found that these different hexagonal nanosheets exhibit isotropic temperature-dependent properties and their Young's and shear modulus decrease almost linearly as the temperature rises, considering a constant coefficient of thermal expansion. However, Poisson's ratio is found to be independent of temperature. Furthermore, the temperature-dependent elastic properties of these nanosheets become nonlinear when the variation of the coefficient of thermal expansion with temperature is taken into account. The Young and shear moduli of the nanosheets increase as the coefficient of thermal expansion decreases and vice versa. The highest elastic modulus values are obtained when the thermal expansion is close to its minimum threshold. However, it is recognized that the elastic modulus of graphene and boron nitride nanosheets is higher than that of silicon carbide and aluminum nitride at any temperature. As an alternative to lengthy computer modeling or rigorous testing, the homogeneous models provided can be used to simulate nanosheets.

2D Materials: Thickness‐Dependent Elastic Softening of Few‐Layer Free‐Standing MoSe2 (Adv. Mater. 23/2021)

Monolayer graphene is stronger than bulk graphite: the elastic properties of graphene are such that it could hypothetically withstand an elephant balancing on a pencil. A contactless optical technique, reported by Bartlomiej Graczykowski and co-workers in article number 2008614 now shows that this is not the case for MoSe2, an attractive semiconducting 2D material. This material becomes significantly softer by reducing its thickness from bulk to a few layers.

Ab Initio Study of Structural, Electronic, and Elastic Properties of Graphene

Since its discovery in 2004, graphene has attracted the intention of several researchers in the world because of its fascinating electronic and mechanical properties. Various theoretical and experimental works have been devoted to this material. In this paper, we used a full-potential linearized augmented plane-wave (FP-LAPW) method to investigate the structural, electronic, and mechanical properties of graphene in hexagonal structure within local density and generalized gradient approximations (LDA and GGA). Our results are found in good agreement with other theoretical and experimental contributions. Using a modified Becke–Johnsone GGA approximation, we have also confirmed that graphene is a zero-gap semiconductor with the presence of a Dirac cone. In our contribution, we have also calculated the elastic constants, the Young’s modulus and Poisson’s ratio of graphene that are found in good agreement with the results published in the literature.

Developing a nested micromechanical model to predict the relaxation moduli of graphene nanoplatelets/carbon fiber reinforced hybrid nanocomposites

A nested analytical method, a product of combining two micromechanical models is developed in this study. The proposed micromechanical method predicts the relaxation properties of polymer hybrid nanocomposites containing linearly visco-elastic matrix, transversely isotropic elastic carbon fibers, and graphene nanoplatelets. Calculations performed in this model are of two scales. The small scale, which is the domain of epoxy resin and graphene nanoplatelet interactions, and the large scale, which assumes the small scale as a homogenized isotropic matrix. In the large scale, the prescribed matrix is then reinforced by the unidirectional CFs. Each scale calculation gives the properties of the underlying material. Secant moduli and the field fluctuation techniques are adopted in this study. Resulting explicit formulae allows one to calculate the overall relaxation moduli of the graphene nanoplatelet/carbon fiber-reinforced polymer hybrid nanocomposites. By comparing the data obtained by experiments and the results extracted by the proposed micromechanical approach, the accuracy of the model becomes apparent. Addition of graphene nanoplatelets into the fibrous composites leads to an improvement in the relaxation properties of the hybrid nanocomposites. Also, the elastic properties of graphene nanoplatelet/carbon fiber-reinforced epoxy hybrid nanocomposites are reported. The role of graphene nanoplatelet agglomeration, frequently encountered in real engineering situations, in the mechanical response of unidirectional hybrid nanocomposites is examined. The effects of volume fraction of graphene nanoplatelets and CFs on the overall mechanical properties are investigated.

Probing the acoustic phonon dispersion and sound velocity of graphene by Raman spectroscopy

The extraordinary thermal and elastic properties of graphene, mainly originating from its unique acoustic phonon branches near Γ point in Brillouin zone, have attracted great attention in its fundamental researches and practical applications. Here, we introduce an optical technique to accurately probe longitudinal acoustic (LA) and transverse acoustic (TA) phonon branches of graphene near Γ point by double resonant Raman scattering of the combination phonon modes in the range of 1650−2150 cm−1 along with the overtone 2D' mode at ∼3200 cm−1. The corresponding sound velocities (νTA=12.9km/s,νLA=19.9km/s) of graphene have been accessed, which are about 10% smaller than those of graphite. Based on νTA and νLA, the two-dimensional (2d) elastic stiffness (tension) coefficients c11 and c66, Young's modulus Y2d and Poisson's ratio σ2d can be estimated. The results demonstrate again that double resonant Raman spectroscopy is a powerful tool to probe the fundamental properties of graphene.

Deformation of Charged Graphene Membrane

Geometrical capacitors with memory (memcapacitors) are of interest because of potential applications in future computing machines. When employing a buckled membrane as one of the capacitor plates, two possible buckled positions serve as the states of low and high capacitance. Using the hybrid B3LYP/6-31G approximation, we investigate the snap-through transition of neutral and negatively charged buckled graphene membranes under the transverse load and external electrostatic field created by a point charge. Estimations show that the chosen calculation method reproduces the elastic properties of graphene within the limits of experimental error. The obtained results testify to the fact that the membrane charge and external electrostatic field affect notably the threshold snap-through switching force in nanosized membranes and, therefore, should be taken into account in the design and development of such nanodevices.

A modified molecular structure mechanics method for analysis of graphene

Based on molecular mechanics and the deformation characteristics of the atomic lattice structure of graphene, a modified molecular structure mechanics method was developed to improve the original one, that is, the semi-rigid connections were used to model the bond angle variations between the C-C bonds in graphene. The simulated results show that the equivalent space frame model with semi-rigid connections for graphene proposed in this article is a simple, efficient, and accurate model to evaluate the equivalent elastic properties of graphene. Though the present computational model of the semi-rigid connected space frame is only applied to characterize the mechanical behaviors of the space lattices of graphene, it has more potential applications in the static and dynamic analyses of graphene and other nanomaterials.

On the prediction of graphene’s elastic properties with reactive empirical bond order potentials

The elastic properties of graphene as described by the reactive empirical bond order potential are studied through uniaxial tensile tests calculations at both zero temperature, with a conjugate gradient approach, and room temperature, with molecular dynamics simulations. A perfect linear elastic behavior is observed at 0K up to ≈0.1% strain. The Young’s modulus and Poisson’s ratio obtained with this potential are of ≈730GPa and 0.39, respectively, with little chirality effects. These values differ significantly from former estimations, much closer to experimental values. We show that these former values have certainly been obtained by neglecting the effect of atomic relaxation, leading to a severe inaccuracy. At larger strains, an extended apparent linear domain is observed in the stress–strain curves, which is relevant to Young’s modulus calculations at finite temperature. Our molecular dynamics simulations at 300K have allowed obtaining the following, chirality dependent, apparent Young’s moduli, 860 and 761GPa, and Poisson’s ratios, 0.12 and 0.23, for armchair and zigzag loadings, respectively.

Effects of grafted carboxyl groups on structural stability and elastic properties of graphene

Molecular dynamics is employed to study the effect of grafted carboxyl groups on elasticity, high-temperature structural stability and compressive properties of armchair and zigzag graphene nanoribbons (AGNRs and ZGNRs). It is found that the Young's moduli decrease as the graft quantity increases from no graft to full grafts (–COOH). The fall for AGNR is larger than that for ZGNRs, which further increases the anisotropy of the elastic property. The structures after undergoing high temperature at 1500 K show that the AGNR exhibits less distortion than ZGNR and grafting carboxyl can obviously reduce structural deformation. Optimizing the GNRs with different in-plane compressive strains, it is evident that the buckling strain (∼11.1%) of ZGNR is larger than that (∼8.1%) of AGNRs, but the AGNR–COOH does not exhibit buckling until the strain is 9.7%, while ZGNR–COOH exhibits buckling at strain of 7.9%. The results indicate that grafting carboxyl reduces the elastic moduli of GNRs, but significantly improves structural stability at high temperature. Grafting carboxyl enhances resistance to compressive buckling of AGNR, but is bad for ZGNR.

In-plane force fields and elastic properties of graphene

Bond stretching and angle bending force fields, appropriate to describe in-plane properties of graphene sheets, are derived using first principles' methods. The obtained force fields are fitted by analytical anharmonic potential energy functions, providing efficient means of calculations in molecular mechanics simulations. Using both molecular dynamics simulations and first principles' methods, numerical results regarding the mechanical behavior of graphene monolayers under various loads, like uniaxial tension in different directions or hydrostatic tension, are presented and compared. Graphene's response in shear stress is also investigated using molecular dynamics, where a noticeable asymmetric mechanical behavior is found. Stress-strain curves and elastic constants, such as, Young modulus, Poisson's ratio, bulk modulus, and shear modulus, are calculated. Our results are compared with available experimental estimates, as well as, with corresponding theoretical calculations. Finally, the effects of the anharmonicity of the extracted bond stretching and angle bending potentials on the mechanical properties of graphene are discussed.

DFT investigation of the influence of ordered vacancies on elastic and magnetic properties of graphene and graphene‐like SiC and BN structures

AbstractInfluence of ordered monovacancies on elastic properties of graphene is theoretically investigated by density functional theory (DFT) calculations. Inverse linear dependence of the graphene Young's modulus on the concentration of vacancies has been revealed and migration rate of the vacancies has been calculated as a function of applied strain. It is shown that the migration rate can be controlled by applying various strains or temperatures. The influence of ordered monovacancies on magnetic properties of graphene as well as graphene‐like hexagonal carbon silicide (2D‐SiC) and the boron nitride (h‐BN) structures is investigated. It is established that the presence of vacancies in all systems yields the appearance of local magnetic moment. However, in 2D‐SiC structure the magnetic moment occurs only in the case of a Si vacancy. Influence of the distance between vacancies on the ferromagnetic or anti‐ferromagnetic ordering for all structures is established.

Analytical methods for the mechanics of graphene bubbles

When placing a graphene membrane on a substrate, gas molecules may be trapped underneath to form bubbles. The size of a graphene bubble (e.g., diameter and height) depends on the number of gas molecules that are trapped, the elastic properties of graphene, and the interfacial adhesion between graphene and the substrate. A mechanics analysis of such graphene bubbles is conducted via membrane and nonlinear plate theories, so that the interfacial adhesion can be determined directly from measurements of the bubble size. A comparison of the results from these two models establishes that the membrane analysis is sufficient for relatively large bubbles. The adhesion energy of mechanically exfoliated graphene on silicon oxide is extracted from two reported data sets using the simple membrane theory, and the values range from 0.097 to 0.43 J/m2. Moreover, the strain distribution of the graphene bubbles and transport of gas molecules among the bubbles are discussed.

Elastic properties of graphene: The Keating model

The elastic properties of graphene have been described in terms of the Keating model. It has been shown that the two-dimensional structure of graphene is described by two independent elastic constants, like an isotropic solid. The Young’s modulus and the Poisson’s ratio have been determined. The results are compared with the experimental data obtained for graphite.

Thickness of graphene and single-wall carbon nanotubes

Young's modulus and the thickness of single wall carbon nanotubes (CNTs) obtained from prior atomistic studies are largely scattered. In this paper we establish an analytic approach to bypass atomistic simulations and determine the tension and bending rigidities of graphene and CNTs directly from the interatomic potential. The thickness and elastic properties of graphene and CNTs can also be obtained from the interatomic potential. But the thickness, and therefore elastic moduli, also depend on type of loading (e.g., uniaxial tension, uniaxial stretching, equibiaxial stretching), as well as the nanotube radius $R$ and chirality when $Rl1\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. This explains why the thickness obtained from prior atomistic simulations is scattered. This analytic approach is particularly useful in the study of multiwall CNTs since their stress state may be complex even under simple loading (e.g., uniaxial tension) due to the van der Waals interactions between nanotube walls. The present analysis also provides an explanation of Yakobson's paradox that the very high Young's modulus reported from the atomistic simulations together with the shell model may be due to the not-well-defined CNT thickness.