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.

References

References
1.
Hirsch
,
A.
,
2010
, “
The Era of Carbon Allotropes
,”
Nat. Mater.
,
9
(
11
), pp.
868
871
.10.1038/nmat2885
2.
Diederich
,
F.
, and
Kivala
,
M.
,
2010
, “
All-Carbon Scaffolds by Rational Design
,”
Adv. Mater.
,
22
(
7
), pp.
803
812
.10.1002/adma.200902623
3.
Enyashin
,
A. N.
, and
Ivanovskii
,
A. L.
,
2011
, “
Graphene Allotropes
,”
Phys. Status Solidi B
,
248
(
8
), pp.
1879
1883
.10.1002/pssb.201046583
4.
Baughman
,
R. H.
,
Eckhardt
,
H.
, and
Kertesz
,
M.
,
1987
, “
Structure-Property Predictions for New Planar Forms of Carbon: Layered Phases Containing sp2 and sp Atoms
,”
J. Chem. Phys.
,
87
(
11
), pp.
6687
6699
.10.1063/1.453405
5.
Brommer
,
D. B.
, and
Buehler
,
M. J.
,
2013
, “
Failure of Graphdiyne: Structurally Directed Delocalized Crack Propagation
,”
ASME J. Appl. Mech.
,
80
(
4
), p.
040908
.10.1115/1.4024176
6.
Cranford
,
S. W.
, and
Buehler
,
M. J.
,
2011
, “
Mechanical Properties of Graphyne
,”
Carbon
,
49
(
13
), pp.
4111
4121
.10.1016/j.carbon.2011.05.024
7.
Cranford
,
S. W.
,
Brommer
,
D. B.
, and
Buehler
,
M. J.
,
2012
, “
Extended Graphynes: Simple Scaling Laws for Stiffness, Strength and Fracture
,”
Nanoscale
,
4
(
24
), pp.
7797
7809
.10.1039/c2nr31644g
8.
Zhang
,
Y. Y.
,
Pei
,
Q. X.
, and
Wang
,
C. M.
,
2012
, “
Mechanical Properties of Graphynes Under Tension: A Molecular Dynamics Study
,”
Appl. Phys. Lett.
,
101
(
8
), p.
081909
.10.1063/1.4747719
9.
Zhao
,
J.
,
Wei
,
N.
,
Fan
,
Z.
,
Jiang
,
J.-W.
, and
Rabczuk
,
T.
,
2013
, “
The Mechanical Properties of Three Types of Carbon Allotropes
,”
Nanotechnology
,
24
(
9
), p.
095702
.10.1088/0957-4484/24/9/095702
10.
Yang
,
Y.
, and
Xu
,
X.
,
2012
, “
Mechanical Properties of Graphyne and Its Family—A Molecular Dynamics Investigation
,”
Comput. Mater. Sci.
,
61
, pp.
83
88
.10.1016/j.commatsci.2012.03.052
11.
Peng
,
Q.
,
Ji
,
W.
, and
De
,
S.
,
2012
, “
Mechanical Properties of Graphyne Monolayers: A First-Principles Study
,”
Phys. Chem. Chem. Phys.
,
14
(
38
), pp.
13385
13391
.10.1039/c2cp42387a
12.
Wang
,
G.
,
Si
,
M.
,
Kumar
,
A.
, and
Pandey
,
R.
,
2014
, “
Strain Engineering of Dirac Cones in Graphyne
,”
Appl. Phys. Lett.
,
104
(
21
), p.
213107
.10.1063/1.4880635
13.
Yue
,
Q.
,
Chang
,
S.
,
Kang
,
J.
,
Qin
,
S.
, and
Li
,
J.
,
2013
, “
Mechanical and Electronic Properties of Graphyne and Its Family Under Elastic Strain: Theoretical Predictions
,”
J. Phys. Chem. C
,
117
(
28
), pp.
14804
14811
.10.1021/jp4021189
14.
Ducéré
,
J.-M.
,
Lepetit
,
C.
, and
Chauvin
,
R.
,
2013
, “
Carbo-Graphite: Structural, Mechanical, and Electronic Properties
,”
J. Phys. Chem. C
,
117
(
42
), pp.
21671
21681
.10.1021/jp4067795
15.
Pan
,
L. D.
,
Zhang
,
L. Z.
,
Song
,
B. Q.
,
Du
,
S. X.
, and
Gao
,
H.-J.
,
2011
, “
Graphyne- and Graphdiyne-Based Nanoribbons: Density Functional Theory Calculations of Electronic Structures
,”
Appl. Phys. Lett.
,
98
(
17
), p.
173102
.10.1063/1.3583507
16.
Zhou
,
J.
,
Lv
,
K.
,
Wang
,
Q.
,
Chen
,
X. S.
,
Sun
,
Q.
, and
Jena
,
P.
,
2011
, “
Electronic Structures and Bonding of Graphyne Sheet and Its BN Analog
,”
J. Chem. Phys.
,
134
(
17
), p.
174701
.10.1063/1.3583476
17.
Malko
,
D.
,
Neiss
,
C.
,
Viñes
,
F.
, and
Görling
,
A.
,
2012
, “
Competition for Graphene: Graphynes With Direction-Dependent Dirac Cones
,”
Phys. Rev. Lett.
,
108
(
8
), p.
086804
.10.1103/PhysRevLett.108.086804
18.
Kim
,
B. G.
, and
Choi
,
H. J.
,
2012
, “
Graphyne: Hexagonal Network of Carbon With Versatile Dirac Cones
,”
Phys. Rev. B
,
86
(
11
), p.
115435
.10.1103/PhysRevB.86.115435
19.
Sevinçli
,
H.
, and
Sevik
,
C.
,
2014
, “
Electronic, Phononic, and Thermoelectric Properties of Graphyne Sheets
,”
Appl. Phys. Lett.
,
105
(
22
), p.
223108
.10.1063/1.4902920
20.
Li
,
Y.
,
Xu
,
L.
,
Liu
,
H.
, and
Li
,
Y.
,
2014
, “
Graphdiyne and Graphyne: From Theoretical Predictions to Practical Construction
,”
Chem. Soc. Rev.
,
43
(
8
), pp.
2572
2586
.10.1039/c3cs60388a
21.
Sun
,
C.
,
Liu
,
Y.
,
Xu
,
J.
,
Chi
,
B.
,
Bai
,
C.
,
Liu
,
Y.
,
Li
,
S.
,
Zhao
,
X.
, and
Li
,
X.
,
2015
, “
Density Functional Study of α-Graphyne Derivatives: Energetic Stability, Atomic and Electronic Structure
,”
Phys. E
,
70
, pp.
190
197
.10.1016/j.physe.2015.03.006
22.
Xue
,
M.
,
Qiu
,
H.
, and
Guo
,
W.
,
2013
, “
Exceptionally Fast Water Desalination at Complete Salt Rejection by Pristine Graphyne Monolayers
,”
Nanotechnology
,
24
(
50
), p.
505720
.10.1088/0957-4484/24/50/505720
23.
Jang
,
B.
,
Koo
,
J.
,
Park
,
M.
,
Lee
,
H.
,
Nam
,
J.
,
Kwon
,
Y.
, and
Lee
,
H.
,
2013
, “
Graphdiyne as a High-Capacity Lithium Ion Battery Anode Material
,”
Appl. Phys. Lett.
,
103
(
26
), p.
263904
.10.1063/1.4850236
24.
Chang
,
T.
, and
Gao
,
H.
,
2003
, “
Size-Dependent Elastic Properties of a Single-Walled Carbon Nanotube Via a Molecular Mechanics Model
,”
J. Mech. Phys. Solids
,
51
(
6
), pp.
1059
1074
.10.1016/S0022-5096(03)00006-1
25.
Chang
,
T.
,
Geng
,
J.
, and
Guo
,
X.
,
2005
, “
Chirality- and Size-Dependent Elastic Properties of Single-Walled Carbon Nanotubes
,”
Appl. Phys. Lett.
,
87
(
25
), p.
251929
.10.1063/1.2149216
26.
Geng
,
J.
, and
Chang
,
T.
,
2006
, “
Nonlinear Stick-Spiral Model for Predicting Mechanical Behavior of Single-Walled Carbon Nanotubes
,”
Phys. Rev. B
,
74
(
24
), p.
245428
.10.1103/PhysRevB.74.245428
27.
Chang
,
T.
,
2010
, “
A Molecular Based Anisotropic Shell Model for Single-Walled Carbon Nanotubes
,”
J. Mech. Phys. Solids
,
58
(
9
), pp.
1422
1433
.10.1016/j.jmps.2010.05.004
28.
Ma
,
T.
,
Li
,
B.
, and
Chang
,
T.
,
2011
, “
Chirality- and Curvature-Dependent Bending Stiffness of Single Layer Graphene
,”
Appl. Phys. Lett.
,
99
(
20
), p.
201901
.10.1063/1.3660739
29.
Nair
,
A. K.
,
Cranford
,
S. W.
, and
Buehler
,
M. J.
,
2011
, “
The Minimal Nanowire: Mechanical Properties of Carbyne
,”
Europhys. Lett.
,
95
(
1
), p.
16002
.10.1209/0295-5075/95/16002
30.
Liu
,
M.
,
Artyukhov
,
V. I.
,
Lee
,
H.
,
Xu
,
F.
, and
Yakobson
,
B. I.
,
2013
, “
Carbyne From First Principles: Chain of C Atoms, a Nanorod or a Nanorope
,”
ACS Nano
,
7
(
11
), pp.
10075
10082
.10.1021/nn404177r
31.
Ashley
,
J. K.
,
Neta Aditya Reddy
,
Y.
, and
Steven
,
W. C.
,
2014
, “
Confinement and Controlling the Effective Compressive Stiffness of Carbyne
,”
Nanotechnology
,
25
(
33
), p.
335709
.10.1088/0957-4484/25/33/335709
32.
Yuan
,
Q.
, and
Ding
,
F.
,
2014
, “
Formation of Carbyne and Graphyne on Transition Metal Surfaces
,”
Nanoscale
,
6
(
21
), pp.
12727
12731
.10.1039/C4NR03757J
You do not currently have access to this content.