Research Papers

Failure of Graphdiyne: Structurally Directed Delocalized Crack Propagation

[+] Author and Article Information
Dieter B. Brommer

Laboratory for Atomistic and Molecular Mechanics (LAMM),
Department of Civil and Environmental Engineering,
Massachusetts Institute of Technology,
77 Massachusetts Avenue,
Room 1-235 A&B,
Cambridge, MA 02139;
Department of Mechanical Engineering,
Massachusetts Institute of Technology,
77 Massachusetts Avenue,
Cambridge, MA 02139

Markus J. Buehler

Laboratory for Atomistic and Molecular Mechanics (LAMM),
Department of Civil and Environmental Engineering,
Massachusetts Institute of Technology,
77 Massachusetts Avenue,
Room 1-235 A&B,
Cambridge, MA 02139;
Center for Computational Engineering,
Massachusetts Institute of Technology,
77 Massachusetts Avenue,
Cambridge, MA 02139; and
Department of Civil Engineering,
Massachusetts Institute of Technology,
77 Massachusetts Avenue,
Cambridge, MA 02139
e-mail: mbuehler@MIT.EDU

1Corresponding author.

Manuscript received January 17, 2013; final manuscript received March 27, 2013; accepted manuscript posted May 31, 2013; published online May 31, 2013. Editor: Yonggang Huang.

J. Appl. Mech 80(4), 040908 (May 31, 2013) (6 pages) Paper No: JAM-13-1031; doi: 10.1115/1.4024176 History: Received January 17, 2013; Revised March 27, 2013; Accepted April 10, 2013

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.

Copyright © 2013 by ASME
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Geim, A. K., and Novoselov, K. S., 2007, “The Rise of Graphene,” Nature Mater., 6(3), pp. 183–191. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
Hirsch, A., 2010, “The Era of Carbon Allotropes,” Nature Mater., 9(11), pp. 868–871. [CrossRef]
Enyashin, A. N., and Ivanovskii, A. L., 2011, “Graphene Allotropes,” Phys. Status Solidi B, 248(8), pp. 1879–1883. [CrossRef]
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. [CrossRef]
Haley, M. M., 2008, “Synthesis and Properties of Annulenic Subunits of Graphyne and Graphdiyne Nanoarchitectures,” Pure Appl. Chem., 80(3), pp. 519–532. [CrossRef]
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. [CrossRef]
Ivanovskii, A. L., 2013, “Graphynes and Graphdyines,” Prog. Solid State Chem., 41(1–2), pp. 1–19. [CrossRef]
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. [CrossRef]
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. [CrossRef] [PubMed]
Cranford, S. W., and Buehler, M. J., 2012, “Selective Hydrogen Purification Through Graphdiyne Under Ambient Temperature and Pressure,” Nanoscale, 4(15), pp. 4587–4593. [CrossRef] [PubMed]
Sun, C., and Searles, D. J., 2012, “Lithium Storage on Graphdiyne Predicted by DFT Calculations,” J. Phys. Chem. C, 116(50), pp. 26222–26226. [CrossRef]
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. [CrossRef] [PubMed]
Cranford, S. W., and Buehler, M. J., 2011, “Mechanical Properties of Graphyne,” Carbon, 49(13), pp. 4111–4121. [CrossRef]
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. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
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. [CrossRef]
Pei, Y., 2012, “Mechanical Properties of Graphdiyne Sheet,” Physica B, 407(22), pp. 4436–4439. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef] [PubMed]
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. [CrossRef]
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. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
Plimpton, S., 1995, “Fast Parallel Algorithms for Short-Range Molecular-Dynamics,” J. Comput. Phys., 117(1), pp. 1–19. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef] [PubMed]
Tsai, D. H., 1979, “Virial Theorem and Stress Calculation in Molecular-Dynamics,” J. Chem. Phys., 70(3), pp. 1375–1382. [CrossRef]
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. [CrossRef]
Zhao, H., and Aluru, N. R., 2010, “Temperature and Strain-Rate Dependent Fracture Strength of Graphene,” J. Appl. Phys., 108(6), p. 064321. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef] [PubMed]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef] [PubMed]
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. [CrossRef]
Diao, J. K., Gall, K., and Dunn, M. L., 2004, “Yield Strength Asymmetry in Metal Nanowires,” Nano Lett., 4(10), pp. 1863–1867. [CrossRef]


Grahic Jump Location
Fig. 1

Structure of graphdiyne, geometry of model, and application of boundary conditions. (a) and (b) Chemical structure of graphdiyne and simulation setup. The structure of graphdiyne contains aromatics of the sp2 motif linked by sp1 acetylene that consist of alternating triple and single bonds, where there are two triple and three single bonds. This is a distinct departure from the structure of graphene. (c) Geometry of the test specimen with relevant dimensions to complement description in Sec. 2. The sample is loaded in the x-direction in mode I.

Grahic Jump Location
Fig. 2

Stress-strain plot and connection with geometry: (a) stress-strain curves for loading in the x-direction comparing graphene and graphdiyne. A “saw-tooth” behavior can be seen for graphdiyne. Our data shows the implications of the bond breaking mechanisms on the overall stress-strain response of this material. (b) and (d) and (c) and (e) show principal stress distributions for graphene and graphdiyne, respectively. These materials are at a point near the first cracking event.

Grahic Jump Location
Fig. 3

Mechanism of failure in graphdiyne, visualized using principal stress distributions. The field plots are presented at different deformation states to show the propagation of the crack and to expose the delocalized failure mechanism. The respective strains are (a) = 3.9%, (b) = 4.2%, (c) = 4.4%, (d) = 4.5%, (e) = 5.5%, and (f) = 6.5%. We notice that the crack begins to propagate along the y-axis but almost immediately progresses along a diagonal. This causes a reorganization of stress concentration that deviates from the failure behavior of graphene that is directed along the axis of the initial crack (see also Fig. 5).

Grahic Jump Location
Fig. 4

Detailed view of the molecular mechanism of failure of graphdiyne, clearly reveal the two-tiered fracture process. The horizontal propagation occurs at a faster rate than that of the diagonal bonds causing the region of partial failure to grow as the system is loaded. We present here a closer view of the samples above at strains of (a) = 3.9%, (b) = 4.2%, (c) = 4.4%, (d) = 4.5%, (e) = 5.5%, and (f) = 6.5%, respectively. This figure presents the crack from the formation of a small group of delocalized voids to (e) and (f) in which several bonds are broken in isolation from the continuous crack.

Grahic Jump Location
Fig. 5

Comparison of crack propagation for graphene and graphdiyne. Graphene (panels (a) and (c)) is shown at a strain of 17.2% while graphdiyne (panels (b) and (d)) is shown at a strain of 6.5%. The difference in direction in crack propagating is that graphene follows a path that is straight in the y-direction and graphdiyne's propagates along a path that is diagonal to the vertical. Graphene experiences symmetric stress distributions about the crack and graphdiyne's crack turns and re-centers itself along the diagonal.



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