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Technical Brief

An Analytical Molecular Mechanics Model for Elastic Properties of Graphyne-n

[+] Author and Article Information
Juan Hou, Zhengnan Yin

Shanghai Key Laboratory of Mechanics
in Energy Engineering,
Shanghai Institute of Applied Mathematics and Mechanics,
Shanghai University,
Shanghai 200072, China

Yingyan Zhang

School of Computing, Engineering and Mathematics,
University of Western Sydney, Penrith South DC,
New South Wales 2751, Australia

Tienchong Chang

Shanghai Key Laboratory of Mechanics
in Energy Engineering,
Shanghai Institute of Applied Mathematics and Mechanics,
Shanghai University,
Shanghai 200072, China
State Key Laboratory of Ocean Engineering,
School of Naval Architecture,
Ocean and Civil Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: tchang@staff.shu.edu.cn

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received March 9, 2015; final manuscript received April 26, 2015; published online June 16, 2015. Editor: Yonggang Huang.

J. Appl. Mech 82(9), 094501 (Sep 01, 2015) (5 pages) Paper No: JAM-15-1126; doi: 10.1115/1.4030502 History: Received March 09, 2015; Revised April 26, 2015; Online June 16, 2015

Graphynes, a new family of carbon allotropes, exhibit superior mechanical properties depending on their atomic structures and have been proposed as a promising building materials for nanodevices. Accurate modeling and clearer understanding of their mechanical properties are essential to the future applications of graphynes. In this paper, an analytical molecular mechanics model is proposed for relating the elastic properties of graphynes to their atomic structures directly. The closed-form expressions for the in-plane stiffness and Poisson's ratio of graphyne-n are obtained for small strains. It is shown that the in-plane stiffness is a decreasing function whereas Poisson's ratio is an increasing function of the number of acetylenic linkages between two adjacent hexagons in graphyne-n. The present analytical results enable direct linkages between mechanical properties and lattice structures of graphynes; thereby, providing useful guidelines in designing graphyne configurations to suit their potential applications. Based on an effective bond density analysis, a scaling law is also established for the in-plane stiffness of graphyne-n which may have implications for their other mechanical properties.

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Figures

Grahic Jump Location
Fig. 1

Schematic illustration of geometric structure (a) and bond types (b) of graphyne-n. Benzene rings with aromatic bonds (labeled a) are connected by acetylenic linkages (/) with repeating single (b) and triple (c) bonds.

Grahic Jump Location
Fig. 2

(a) Graphene-n (n = 2) subject to tension. The dashed-dotted box indicates the unit cell (with lengths of ua and uz), while the dashed box marks are the representative local structures used in the present analytical model. (b) Force equilibrium of local structures.

Grahic Jump Location
Fig. 3

(a) In-plane stiffness, (b) shear stiffness, and (c) Poisson's ratio of graphene-n as functions of the number of acetylenic linkages

Grahic Jump Location
Fig. 4

Dependence of the normalized in-plane stiffness, real bond density, and effective bond density on the number of acetylenic linkages

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