Among the many potential two-dimensional carbon allotropes inspired by graphene, graphynes have received exceptional attention recently. Graphynes exhibit remarkable mechanical properties depending on their structure. The similar structure and two-dimensional nature of these materials yield many properties that are similar to those of graphene, but the presence of heterogeneous bond types is expected to lead to distinct properties. The main subject of this work is graphdiyne, one of the few graphynes that has been fabricated in large quantities. In this paper, we perform fracture analysis on graphdiyne and find a delocalized failure mechanism in which a crack propagates along a diagonal with respect its original direction. The covalence of the material allows for this simple but intriguing phenomenon to be investigated. Graphene is also tested to compare the behavior. This mechanism has implications for the toughness and robustness of this material, which is topical for many device applications recently proposed in the literature. Further, connections of such delocalized failure mechanisms are made to that of hidden length and sacrificial bonding in some biological systems such as proteins, bone, and nacre.
Issue Section:
Research Papers
References
1.
Geim
, A. K.
, and Novoselov
, K. S.
, 2007
, “The Rise of Graphene
,” Nature Mater.
, 6
(3
), pp. 183
–191
.10.1038/nmat18492.
Saito
, R.
, Fujita
, M.
, Dresselhaus
, G.
, and Dresselhaus
, M. S.
, 1992
, “Electronic-Structure of Graphene Tubules Based on C-60
,” Phys. Rev. B
, 46
(3
), pp. 1804
–1811
.10.1103/PhysRevB.46.18043.
Saito
, R.
, Fujita
, M.
, Dresselhaus
, G.
, and Dresselhaus
, M. S.
, 1992
, “Electronic-Structure of Chiral Graphene Tubules
,” Appl. Phys. Lett.
, 60
(18
), pp. 2204
–2206
.10.1063/1.1070804.
Novoselov
, K. S.
, Geim
, A. K.
, Morozov
, S. V.
, Jiang
, D.
, Zhang
, Y.
, Dubonos
, S. V.
, Grigorieva
, I. V.
, and Firsov
, A. A.
, 2004
, “Electric Field Effect in Atomically Thin Carbon Films,” Science
, 306
(5696
), pp. 666
–669
.10.1126/science.11028965.
Kim
, K. S.
, Zhao
, Y.
, Jang
, H.
, Lee
, S. Y.
, Kim
, J. M.
, Kim
, K. S.
, Ahn
, J. H.
, Kim
, P.
, Choi
, J. Y.
, and Hong
, B. H.
, 2009
, “Large-Scale Pattern Growth of Graphene Films for Stretchable Transparent Electrodes
,” Nature
, 457
(7230
), pp. 706
–710
.10.1038/nature077196.
Hirsch
, A.
, 2010
, “The Era of Carbon Allotropes
,” Nature Mater.
, 9
(11
), pp. 868
–871
.10.1038/nmat28857.
Enyashin
, A. N.
, and Ivanovskii
, A. L.
, 2011
, “Graphene Allotropes
,” Phys. Status Solidi B
, 248
(8
), pp. 1879
–1883
.10.1002/pssb.2010465838.
Haley
, M. M.
, Brand
, S. C.
, and Pak
, J. J.
, 1997
, “Carbon Networks Based on Dehydrobenzoannulenes: Synthesis of Graphdiyne Substructures
,” Angew. Chem., Int., Ed.
, 36
(8
), pp. 836
–838
.10.1002/anie.1997083619.
Haley
, M. M.
, 2008
, “Synthesis and Properties of Annulenic Subunits of Graphyne and Graphdiyne Nanoarchitectures
,” Pure Appl. Chem.
, 80
(3
), pp. 519
–532
.10.1351/pac20088003051910.
Li
, G. X.
, Li
, Y. L.
, Liu
, H. B.
, Guo
, Y. B.
, Li
, Y. J.
, and Zhu
, D. B.
, 2010
, “Architecture of Graphdiyne Nanoscale Films
,” Chem. Commun. (Cambridge)
, 46
(19
), pp. 3256
–3258
.10.1039/b922733d11.
Ivanovskii
, A. L.
, 2013
, “Graphynes and Graphdyines
,” Prog. Solid State Chem.
, 41
(1–2
), pp. 1
–19
.10.1016/j.progsolidstchem.2012.12.00112.
Malko
, D.
, Neiss
, C.
, Vines
, F.
, and Gorling
, A.
, 2012
, “Competition for Graphene: Graphynes With Direction-Dependent Dirac Cones
,” Phys. Rev. Lett.
, 108
(8
), p. 086804.10.1103/PhysRevLett.108.08680413.
Long
, M. Q.
, Tang
, L.
, Wang
, D.
, Li
, Y. L.
, and Shuai
, Z. G.
, 2011
, “Electronic Structure and Carrier Mobility in Graphdiyne Sheet and Nanoribbons: Theoretical Predictions
,” ACS Nano
, 5
(4
), pp. 2593
–2600
.10.1021/nn102472s14.
Cranford
, S. W.
, and Buehler
, M. J.
, 2012
, “Selective Hydrogen Purification Through Graphdiyne Under Ambient Temperature and Pressure
,” Nanoscale
, 4
(15
), pp. 4587
–4593
.10.1039/c2nr30921a15.
Sun
, C.
, and Searles
, D. J.
, 2012
, “Lithium Storage on Graphdiyne Predicted by DFT Calculations
,” J. Phys. Chem. C
, 116
(50
), pp. 26222
–26226
.10.1021/jp309638z16.
Robertson
, A. W.
, Allen
, C. S.
, Wu
, Y. A.
, He
, K.
, Olivier
, J.
, Neethling
, J.
, Kirkland
, A. I.
, and Warner
, J. H.
, 2012
, “Spatial Control of Defect Creation in Graphene at the Nanoscale
,” Nat Commun.
, 3
, p. 1144
.10.1038/ncomms214117.
Cranford
, S. W.
, and Buehler
, M. J.
, 2011
, “Mechanical Properties of Graphyne
,” Carbon
, 49
(13
), pp. 4111
–4121
.10.1016/j.carbon.2011.05.02418.
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/c2nr31644g19.
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/c2cp42387a20.
Kang
, J.
, Li, J. B., Wu, F. M., Li, S. S., and Xia, J. B., 2011
, “Elastic, Electronic, and Optical Properties of Two-Dimensional Graphyne Sheet
,” J. Phys. Chem. C
, 115
(42
), pp. 20466
–20470
.10.1021/jp206751m21.
Pei
, Y.
, 2012
, “Mechanical Properties of Graphdiyne Sheet
,” Physica B
, 407
(22
), pp. 4436
–4439
.10.1016/j.physb.2012.07.02622.
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. 081909.10.1063/1.474771923.
Yang
, Y. L.
, and Xu
, X. M.
, 2012
, “Mechanical Properties of Graphyne and Its Family—A Molecular Dynamics Investigation
,” Comput. Mater. Sci.
, 61
, p. 83
–88
.10.1016/j.commatsci.2012.03.05224.
Lee
, C.
, Wei, X. D., Kysar, J. W., and Hone, J., 2008
, “Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene
,” Science
, 321
(5887
), pp. 385
–388
.10.1126/science.115799625.
Liu
, F.
, Ming
, P. M.
, and Li
, J.
, 2007
, “Ab Initio Calculation of Ideal Strength and Phonon Instability of Graphene Under Tension
,” Phys. Rev. B
, 76
(6
), p. 064120.10.1103/PhysRevB.76.06412026.
Zhang
, J. F.
, Zhao
, J. J.
, and Lu
, J. P.
, 2012
, “Intrinsic Strength and Failure Behaviors of Graphene Grain Boundaries
,” ACS Nano
, 6
(3
), pp. 2704
–2711
.10.1021/nn300135627.
Kim
, K.
, Artyukhov, V. I., Regan, W., Liu, Y. Y., Crommie, M. F., Yakobson, B. I., and Zettl, A., 2012
, “Ripping Graphene: Preferred Directions
,” Nano Lett.
, 12
(1
), pp. 293
–297
.10.1021/nl203547z28.
Plimpton
, S.
, 1995
, “Fast Parallel Algorithms for Short-Range Molecular-Dynamics
,” J. Comput. Phys.
, 117
(1
), pp. 1
–19
.10.1006/jcph.1995.103929.
van Duin
, A. C. T.
, Dasgupta
, S.
, Lorant
, F.
, and Goddard
, W. A.
, 2011
, “ReaxFF: A Reactive Force Field for Hydrocarbons
,” J. Phys. Chem. A
, 105
(41
), pp. 9396
–9409
.10.1021/jp004368u30.
Flores
, M. Z. S.
, Autreto
, P. A. S.
, Legoas
, S. B.
, and Galvao
, D. S.
, 2009
, “Graphene to Graphane: A Theoretical Study
,” Nanotechnology
, 20
(46
), p. 465704.10.1088/0957-4484/20/46/46570431.
Sen
, D.
, Novoselov
, K. S.
, Reis
, P. M.
, and Buehler
, M. J.
, 2010
, “Tearing Graphene Sheets From Adhesive Substrates Produces Tapered Nanoribbons
,” Small
, 6
(10
), pp. 1108
–1116
.10.1002/smll.20100009732.
Tsai
, D. H.
, 1979
, “Virial Theorem and Stress Calculation in Molecular-Dynamics
,” J. Chem. Phys.
, 70
(3
), pp. 1375
–1382
.10.1063/1.43757733.
Zimmerman
, J. A.
, Webb
, E. B.
, Hoyt
, J. J.
, Jones
, R. E.
, Klein
, P. A.
, and Bammann
, D. J.
, 2004
, “Calculation of Stress in Atomistic Simulation Modelling and Simulation
,” Mater. Sci. Eng.
, 12
(4
), pp. S319
–S332
.10.1088/0965-0393/12/4/S0334.
Zhao
, H.
, and Aluru
, N. R.
, 2010
, “Temperature and Strain-Rate Dependent Fracture Strength of Graphene
,” J. Appl. Phys.
, 108
(6
), p. 064321.10.1063/1.348862035.
Ni
, Z. H.
, Bu, H., Zou, M., Yi, H., Bi, K. D., and Chen, Y. F., 2010
, “Anisotropic Mechanical Properties of Graphene Sheets From Molecular Dynamics
,” Physica B
, 405
(5
), pp. 1301
–1306
.10.1016/j.physb.2009.11.07136.
Chuvilin
, A. M. J. C.
, Algara-Siller
, G.
, Kaiser
, U.
, 2009
, “From Graphene Constrictions to Single Carbon Chains
,” New J. Phys.
, 11
(8
), p. 083019.10.1088/1367-2630/11/8/08301937.
Moras
, G.
, Pastewka, L., Walter, M., Schnagl, J., Gumbsch, P., and Moseler, M., 2011
, “Progressive Shortening of sp-Hybridized Carbon Chains Through Oxygen-Induced Cleavage
,” J. Phys. Chem. C
, 115
(50
), pp. 24653
–24661
.10.1021/jp209198g38.
Tykwinski
, R. R.
, Chalifoux, W., Eisler, S., Lucotti, A., Tommasini, M., Fazzi, D., Del Zoppo, M., and Zerbi, G., 2010
, “Toward Carbyne: Synthesis and Stability of Really Long Polyynes
,” Pure Appl. Chem.
, 82
(4
), pp. 891
–904
.10.1351/PAC-CON-09-09-0439.
Fantner
, G. E.
, Hassenkam, T., Kindt, J. H., Weaver, J. C., Birkedal, H., Pechenik, L., Cutroni, J. A., Cidade, G. A. G., Stucky, G. D., Morse, D. E., and Hansma, P. K., 2005
, “Sacrificial Bonds and Hidden Length Dissipate Energy as Mineralized Fibrils Separate During Bone Fracture
,” Nature Mater.
, 4
(8
), pp. 612
–616
.10.1038/nmat142840.
Fantner
, G. E.
, Oroudjev, E., Schitter, G., Golde, L. S., Thurner, P., Finch, M. M., Turner, P., Gutsmann, T., Morse, D. E., Hansma, H., and Hansma, P. K., 2006
“Sacrificial Bonds and Hidden Length: Unraveling Molecular Mesostructures in Tough Materials
,” Biophys. J.
, 90
(4
), pp. 1411
–1418
.10.1529/biophysj.105.06934441.
Espinosa
, H. D.
, Rim, J. E., Barthelat, F., and Buehler, M. J., 2009
, “Merger of Structure and Material in Nacre and Bone—Perspectives on de Novo Biomimetic Materials
,” Prog. Mater. Sci.
, 54
(8
), pp. 1059
–1100
.10.1016/j.pmatsci.2009.05.00142.
Nalla
, R. K.
, Kinney
, J. H.
, and Ritchie
, R. O.
, 2003
, “Mechanistic Fracture Criteria for the Failure of Human Cortical Bone
,” Nature Mater.
, 2
(3
), pp. 164
–168
.10.1038/nmat83243.
Dimas
, L. S.
, and Buehler
, M. J.
, 2012
, “Influence of Geometry on Mechanical Properties of Bio-Inspired Silica-Based Hierarchical Materials
,” Bioinspir. Biomim.
, 7
(3
), p. 036024
.10.1088/1748-3182/7/3/03602444.
Qin
, Z.
, and Buehler
, M. J.
, 2010
“Cooperative Deformation of Hydrogen Bonds in Beta-Strands and Beta-Sheet Nanocrystals
,” Phys. Rev. E
, 82
(6
), p. 061906.10.1103/PhysRevE.82.06190645.
Diao
, J. K.
, Gall
, K.
, and Dunn
, M. L.
, 2004
, “Yield Strength Asymmetry in Metal Nanowires
,” Nano Lett.
, 4
(10
), pp. 1863
–1867
.10.1021/nl0489992Copyright © 2013 by ASME
You do not currently have access to this content.
