Velocities of sound and the densities of phonon states in a uniformly strained flat graphene sheet

Abstract

The effect of elastic strain on the mechanical and physical properties of graphene has been inten sively studied in recent years. Using the molecular dynamics method, a surface has been built in the three dimensional space of components of the plane strain tensor bounds the region of the structural stability of a flat graphene sheet without considering thermal vibrations and the influence of boundary conditions. The velocities of sound and the densities of phonon states in graphene subjected to an elastic strain within the region of the structural stability have been calculated. It has been shown that one of the velocities of sound becomes zero near the stability boundary of a flat graphene sheet. During biaxial tension of graphene, there is no gap in its phonon spectrum; however, it forms under uniaxial tension along the zigzag or armchair direc tions and also under combined tensile and compressive strains.

Graphene nanoribbon winding around carbon nanotube

“…Graphene is an elastically isotropic material whose longitudinal and bending rigidities, for small strain, do not depend on the direction of the applied stress [88]. For definiteness, let us consider the nanoribbon with zigzag edges shown in Fig.…”

“…These structures exist due to the balance between energy reduction with increasing area between graphene sheets interacting via van der Waals forces and increase of energy due to the sheet bending. Bending stiffness of graphene is very small that is why it tends to wrinkle under stress [19][20][21].…”

Energy transfer in strained graphene assisted by discrete breathers excited by external ac driving

“…The equilibrium positions of atoms in uniformly strained graphene are found by minimizing the potential energy of the crystal. For the chosen strain components the equilibrium flat configuration of graphene is stable 73 . It should be pointed out that the maximal level of strain used in our simulations is very high and it is at the stability border of graphene reported in the literature.…”

Scroll configurations of carbon nanoribbons

“…A detailed discussion of the choice of the interatomic potential parameters can be found in [37]. The same set of potentials has been successfully used to simulate the heat transfer along the carbon nanotubes and nanoribbons [39,40] for the analysis of spatially localized oscillations [41][42][43][44][45][46] and also for the investigation of theoretical strength and post-critical behavior of deformed graphene [47][48][49][50].…”