Molecular mechanics of single layer graphene sheets

Получены наборы материальных и геометрических параметров силового поля DREIDING и балочного элемента, точно воспроизводящие механические модули графена в рамках стандартного метода ММ и метода МСМ. Эти методы реализованы в компьютерных кодах Pioner и MSC.Marc соответственно. Компьютерное моделирование частот и форм собственных колебаний однослойного графенового листа показало, что как частоты, так и соответствующие им формы собственных колебаний, полученные обоими методами, близки между собой, а также близки к частотам и формам колебаний почти квадратной сплошной пластинки, моделирующей ОГЛ. Sets of material and geometric parameters of the DREIDING force field and beam element, which accurately reproduce the mechanical modules of graphene in the framework of the standard MM method and the MSM method, are obtained. These methods are implemented in computer codes Pioner and MSC.Marc, respectively. Computer simulation of the frequencies and modes of natural vibrations of a single-layer graphene sheet showed that both the frequencies and the corresponding modes of natural vibrations obtained by both methods are close to each other, as well as close to the frequencies and modes of vibration of an almost square continuous plate simulating a single-layer graphene sheet.

Download Full-text

Free Vibration of Single Layer Graphene Sheets: Lattice Structure Versus Continuum Plate Theories

Journal of Nanotechnology in Engineering and Medicine ◽

10.1115/1.4004323 ◽

2011 ◽

Vol 2 (3) ◽

Cited By ~ 11

Author(s):

S. Arghavan ◽

A. V. Singh

Keyword(s):

Graphene Sheet ◽

Lattice Structure ◽

Plate Theory ◽

Single Layer ◽

Torsional Stiffness ◽

Single Layer Graphene ◽

Mode Shapes ◽

Graphene Sheets ◽

Layer Graphene ◽

Young’S Moduli

Prospect of applications of graphene sheets in composites and other advanced materials have drawn attention from a broad spectrum of research fields. This paper deals with the methods to find mechanical properties of such nanoscale structures. First, the lattice structure method with the Poisson’s ratio of 0.16 and the thickness of 3.4 Å is used to obtain the Young’s moduli for the in-plane and out-of-plane deformation states. This method has the accuracy of molecular dynamics simulations and efficiency of the finite element method. The graphene sheet is modeled as a plane grid of carbon atoms taken as the nodal points, each of which carries the mass of the carbon atom and is assigned as a six degrees of freedom. The covalent bond between two adjacent carbon atoms is treated as an extremely stiff frame element with all three axial, bending, and torsional stiffness components. Subsequently, the computed Young’s moduli, approximately 0.11 TPa for bending and 1.04 TPa for the in-plane condition, are used for studying the vibrational behaviors of graphene sheets by the continuum plate theory. The natural frequencies and corresponding mode shapes of various shaped single layer graphene sheet ), such as rectangular, skewed, and circular, are computed by the two methods which are found to yield very close results. Results of the well-established continuum plate theory are very consistent with the lattice structure method, which is based on accurate interatomic forces.

Download Full-text