Advances in Condensed Matter Physics

Volume 2015, Article ID 735192, 5 pages

http://dx.doi.org/10.1155/2015/735192

## Influence of Size Effect on the Electronic and Elastic Properties of Graphane Nanoflakes: Quantum Chemical and Empirical Investigations

^{1}Department of Physics, Saratov State University, Saratov 410012, Russia^{2}Department of Physics, National Cheng Kung University, Tainan 701, Taiwan

Received 26 November 2014; Revised 23 April 2015; Accepted 23 April 2015

Academic Editor: Markus R. Wagner

Copyright © 2015 A. S. Kolesnikova et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

By application of empirical method it is found that graphene nanoflake (graphane) saturated by hydrogen is not elastic material. In this case, the modulus of the elastic compression of graphane depends on its size, allowing us to identify the linear parameters of graphane with maximum Young’s modulus for this material. The electronic structure of graphane nanoflakes was calculated by means of the semiempirical tight-binding method. It is found that graphane nanoflakes can be characterized as dielectric. The energy gap of these particles decreases with increasing of the length tending to a certain value. At the same time, the ionization potential of graphane also decreases. A comparative analysis of the calculated values with the same parameters of single-walled nanotubes is performed.

#### 1. Introduction

Graphane is a principal new and prospect material in nanoelectronics. Graphane was synthesized for the first time by the hydrogenation of graphene—a monolayer of graphite [1]. The crystal structure of graphane is two-dimensional and hexagonal. The hydrogen atoms are attached at opposite sides of the carbon atoms plane. It is necessary to distinguish the graphane nanoflakes and nanoribbons. The sizes of nanoflakes in the different directions differ no more than three times and do not exceed 100 nanometers.

The discovery of graphane has created prerequisites for the investigations of its properties and for the search of the probable application. For example, graphane has unique optical properties [2]. It is found that the dielectric functions of graphane nanoribbons spectra do not depend on the ribbon edge shapes and widths. Also, in the result of the graphane optical properties calculations, the presence of moderate anisotropy with respect to the type of light polarization is established. In [3], authors investigate thermal conduction in graphane nanoribbons by the nonequilibrium Green function method. It is demonstrated that thermal conduction can be effectively tuned by controlling the edge shape, width, and hydrogen vacancy concentration of graphane nanoribbons. Specifically, ballistic thermal conductance of graphane nanoribbons generally grows with the ribbon width. Big attention of researchers is devoted to investigation of the magnetic properties of graphane. In [4], it is shown that in the whole temperature range up to room temperature the hydrogenated graphene demonstrates a weak ferromagnetism. The origin of the magnetism is also determined to arise from the hydrogenated graphene itself.

Due to its unique properties, graphane has many applications. In particular, this material can find the application in the hydrogen energetics. It is established that the heating of graphane leads to release of the atomic hydrogen [5]. Therefore, graphane can be considered as one of the effective methods of hydrogen storage. Another significant application of graphane is its application in nanoelectronics as a base for the printed circuits with conducting and nonconducting sites [6]. One more possible field of graphane application is biosensing. In experimental work [7], the properties of graphane were considered for application in electrochemical oxidation of biomarkers. That can lead to finding of harmful ways for detection of biomarkers.

In present work [8], authors have studied theoretically the possibility of a superconducting state in two-dimensional hole-doped graphane. According to results of this work, the hole-doped graphane is a candidate for being a high temperature superconductor with a critical temperature as high as those of copper oxides.

One more perspective applied field of graphane is its use as thermoelectric materials for thermoelectric device. It is predicted that disordered armchair graphane nanoribbons with low thermal conductivity are promising candidates for constructing thermoelectric materials [9].

Although the properties of graphane nanoribbons have been studied extensively, the influence of size effect on the properties of graphane remained unexplored. At the same time, the variation of the geometrical dimensions of the objects could be an effective way to control the properties of graphane. The aim of this work is the theoretical investigation of the electronic and elastic properties of graphane nanoflakes by means of the quantum-chemical and empirical methods.

#### 2. Materials and Methods

##### 2.1. Empirical Method

To study the elastic properties and deformations of graphane nanoflakes we apply the empirical method based on the bond-order potential developed by Brenner [10]. The total energy is described by the sum of the binding energy , the torsional energy , and the van der Waals energy :

Each pair of covalently bonded atoms interacts via potential-energy:

This is the binding energy. Here is the repulsive pair term, is the attractive pair term, and is the distance between the chemically bonded atoms with numbers and . The function is a many-body term. This term was introduced to describe the specificity of the - interaction. So, the value of the binding energy depends on the position and chemical identity of atoms.

To describe nonbonded interaction between the atoms we have attended the torsional interaction energy to the total system energy. The torsional energy is given by the following formula:

The torsional potential is given as a function of dihedral angle . The torsion angle is defined in the usual way as the angle between the plane defined by the vectors and and that defined by and . Here atoms and are not chemically bonded.

Van der Waals energy defines the interaction between nonbonded atoms:

Van der Waals interaction energy is described by the Morse potential aswhere is the average bond energy, is the repulsion nucleus energy, and coefficients nm^{−1} and nm^{−1}. Calculated interatomic distance in graphite by described empirical method is equal to 0.1421 nm.

##### 2.2. Tight-Binding Method

Within this method the total energy is calculated by the following formula:where is the bond structure energy calculated as the sum of energies of the single-particle occupied states. is the interelectron and internuclear repulsion term.

The bond structure energy is determined by the following formula:

This expression is the sum of energies of the molecular orbitals obtained by diagonalizing the Hamiltonian, is the number of the occupied orbitals, and is the energy of the single-particle orbitals.

The phenomenon energy can be expressed as a sum of two-body potentials:where , are the number of the interaction atoms; , are the Cartesian coordinates.

The overlap matrix elements are calculated by the formulas which take into account four types of interaction, , , , and , and the pair repulsive potential:where and are the orbital moments of wave function and presents the bond type ( or ). The atomic terms , are the atomic orbital energies of carbon which are located on the main diagonal of the Hamiltonian. The values of the , atomic terms, the parameters (), and the equilibrium overlap integrals (, , , and ) are given in Table 1. The coefficients , , and are the power exponents, the coefficients and are determined by the overall shape and steepness of the function, and the parameter is a cutoff distance for the hopping matrix elements and repulsive interactions.