Phagraphene is a very attractive two-dimensional (2D) full carbon allotrope with very interesting mechanical, electronic, optical, and thermal properties. The objective of this study is to investigate the mechanical properties of this new graphene like 2D material. In this work, mechanical properties of phagraphene have been studied not only in the defect-free form, but also with the critical defect of line cracks, using the classical molecular dynamics simulations. Our study shows that the pristine phagraphene in zigzag direction experience a ductile behavior under uniaxial tensile loading and the nanosheet in this direction are less sensitive to temperature changes as compared to the armchair direction. We studied different crack lengths to explore the influence of defects on the mechanical properties of phagraphene. We also investigated the temperature effect on the mechanical properties of pristine and defective phagraphene. Our classical atomistic simulation results confirm that larger cracks can reduce the strength of the phagraphene. Moreover, it was shown the temperature has a considerable weakening effect on the tensile strength of phagraphene. The results of this study may be useful for the design of nano-devices using the phagraphene.
K SNovoselov, A KGeim, S VMorozov, DJiang, YZhang, S VDubonos, I VGrigorieva, A AFirsov. Electric field effect in atomically thin carbon films. Science, 2004, 306(5696): 666–669 https://doi.org/10.1126/science.1102896
SStankovich, D A Dikin, R D Piner, K A Kohlhaas, A Kleinhammes, YJia, YWu, S B T Nguyen, R S Ruoff. Synthesis of graphene-based nanosheets via chemical reduction of exfoliated graphite oxide. Carbon, 2007, 45(7): 1558–1565 https://doi.org/10.1016/j.carbon.2007.02.034
4
SStankovich, R D Piner, X Chen, NWu, S TNguyen, R SRuoff. Stable aqueous dispersions of graphitic nanoplatelets via the reduction of exfoliated graphite oxide in the presence of poly (sodium 4-styrenesulfonate). Journal of Materials Chemistry, 2006, 16(2): 155–158 https://doi.org/10.1039/B512799H
5
XWang, L Zhi, KMüllen. Transparent, conductive graphene electrodes for dye-sensitized solar cells. Nano Letters, 2008, 8(1): 323–327 https://doi.org/10.1021/nl072838r
6
SGhosh, I Calizo, DTeweldebrhan, E PPokatilov, D LNika, A ABalandin, WBao, F Miao, C NLau. Extremely high thermal conductivity of graphene: prospects for thermal management applications in nanoelectronic circuits. Applied Physics Letters, 2008, 92(15): 151911 https://doi.org/10.1063/1.2907977
7
A KGeim. Graphene: status and prospects. Science, 2009, 324(5934): 1530–1534
BMortazavi, L F C Pereira, J W Jiang, T Rabczuk. Modelling heat conduction in polycrystalline hexagonal boron-nitride films. Scientific Reports, 2015, 5(1): 13228 https://doi.org/10.1038/srep13228
11
SEigler. Graphene. An Introduction to the Fundamentals and Industrial Applications. Edited by Madhuri Sharon and Maheshwar Sharon. Angewandte Chemie International Editon. Wiley-Blackwell, 2016, doi: 10.1002/anie.201602067
12
TSainsbury, S Gnaniah, S JSpencer, SMignuzzi, N ABelsey, K RPaton, ASatti. Extreme mechanical reinforcement in graphene oxide based thin-film nanocomposites via covalently tailored nanofiller matrix compatibilization. Carbon, 2017, 114: 367–376 https://doi.org/10.1016/j.carbon.2016.11.061
13
YKim, J Lee, M SYeom, J WShin, HKim, Y Cui, J WKysar, JHone, Y Jung, SJeon, S MHan. Strengthening effect of single-atomic-layer graphene in metal–graphene nanolayered composites. Nature Communications, 2013, 4, doi: 10.1038/ncomms3114
14
BMortazavi, F Hassouna, ALaachachi, ARajabpour, SAhzi, D Chapron, VToniazzo, DRuch. Experimental and multiscale modeling of thermal conductivity and elastic properties of PLA/expanded graphite polymer nanocomposites. Thermochimica Acta, 2013, 552: 106–113 https://doi.org/10.1016/j.tca.2012.11.017
HMalekpour, K H Chang, J C Chen, C Y Lu, D L Nika, K S Novoselov, A A Balandin. Thermal conductivity of graphene laminate. Nano Letters, 2014, 14(9): 5155–5161 https://doi.org/10.1021/nl501996v
17
BMortazavi, H Yang, FMohebbi, GCuniberti, TRabczuk. Graphene or h-BN paraffin composite structures for the thermal management of Li-ion batteries: a multiscale investigation. Applied Energy, 2017, 202: 323–334 https://doi.org/10.1016/j.apenergy.2017.05.175
18
M AMsekh, M Silani, MJamshidian, PAreias, XZhuang, GZi, P He, TRabczuk. Predictions of J integral and tensile strength of clay/epoxy nanocomposites material using phase field model. Composites. Part B, Engineering, 2016, 93: 97–114 https://doi.org/10.1016/j.compositesb.2016.02.022
19
AAlmasi, M Silani, HTalebi, TRabczuk. Stochastic analysis of the interphase effects on the mechanical properties of clay/epoxy nanocomposites. Composite Structures, 2015, 133: 1302–1312 https://doi.org/10.1016/j.compstruct.2015.07.061
20
NVu-Bac, M Silani, TLahmer, XZhuang, TRabczuk. A unified framework for stochastic predictions of mechanical properties of polymeric nanocomposites. Computational Materials Science, 2015, 96: 520–535 https://doi.org/10.1016/j.commatsci.2014.04.066
21
MSilani, H Talebi, SZiaei-Rad, PKerfriden, S P ABordas, TRabczuk. Stochastic modelling of clay/epoxy nanocomposites. Composite Structures, 2014, 118: 241–249 https://doi.org/10.1016/j.compstruct.2014.07.009
22
K MHamdia, M A Msekh, M Silani, NVu-Bac, XZhuang, TNguyen-Thoi, TRabczuk. Uncertainty quantification of the fracture properties of polymeric nanocomposites based on phase field modeling. Composite Structures, 2015, 133: 1177–1190 https://doi.org/10.1016/j.compstruct.2015.08.051
23
BMortazavi, A Dianat, GCuniberti, TRabczuk, . Application of silicene, germanene and stanene for Na or Li ion storage: a theoretical investigation. Electrochimica Acta, 2016, 213: 865–870 https://doi.org/10.1016/j.electacta.2016.08.027
24
A H NShirazi R, Abadi, M, Izadifar N, Alajlan T., Rabczuk Mechanical responses of pristine and defective C3N nanosheets studied by molecular dynamics simulations. Computational Materials Science, 2018, 147, 316–321 https://doi.org/10.1016/j.commatsci.2018.01.058
25
JMahmood, E K Lee, M Jung, DShin, H JChoi, J MSeo, S MJung, DKim, F Li, M SLah, NPark, H J Shin, J H Oh, J B Baek. Two-dimensional polyaniline (C3N) from carbonized organic single crystals in solid state. Proceedings of the National Academy of Sciences of the United States of America, 2016, 113(27): 7414–7419 https://doi.org/10.1073/pnas.1605318113
BMortazavi, O Rahaman, TRabczuk, L F CPereira. Thermal conductivity and mechanical properties of nitrogenated holey graphene. Carbon, 2016, 106: 1–8 https://doi.org/10.1016/j.carbon.2016.05.009
28
BMortazavi, Y Rémond, SAhzi, VToniazzo. Thickness and chirality effects on tensile behavior of few-layer graphene by molecular dynamics simulations. Computational Materials Science, 2012, 53(1): 298–302 https://doi.org/10.1016/j.commatsci.2011.08.018
29
BMortazavi, O Rahaman, ADianat, TRabczuk. Mechanical responses of borophene sheets: a first-principles study. Physical Chemistry Chemical Physics, 2016, 18(39): 27405–27413 https://doi.org/10.1039/C6CP03828J
30
BMortazavi, A Dianat, ORahaman, GCuniberti, TRabczuk. Borophene as an anode material for Ca, Mg, Na or Li ion storage: a first-principle study. Journal of Power Sources, 2016, 329: 456–461 https://doi.org/10.1016/j.jpowsour.2016.08.109
31
YLiu, X Peng. Recent advances of supercapacitors based on two-dimensional materials. Applied Material Today, 2017, 8: 104–115 https://doi.org/10.1016/j.apmt.2017.05.002
32
BMortazavi, M Shahrokhi, TRabczuk, L F CPereira. Electronic, optical and thermal properties of highly stretchable 2D carbon Ene-yne graphyne. Carbon, 2017, 123: 344–353 https://doi.org/10.1016/j.carbon.2017.07.066
33
W RLiu. Graphene-based energy devices. In: Rashid bin Mohd Yusoff, ed. Graphene-Based Energy Devices. Wiley-VCH, 2015, 85–122 https://doi.org/10.1002/9783527690312.ch3
34
FXia, D B Farmer, Y M Lin, P Avouris. Graphene field-effect transistors with high on/off current ratio and large transport band gap at room temperature. Nano Letters, 2010, 10(2): 715–718 https://doi.org/10.1021/nl9039636
35
L SPanchakarla, K SSubrahmanyam, S KSaha, AGovindaraj, H RKrishnamurthy, U VWaghmare, C N RRao. Synthesis, structure, and properties of boron- and nitrogen-doped graphene. Advanced Materials, 2009, 21: 4726–4730 https://doi.org/10.1002/adma.200901285
36
ALherbier, X Blase, Y MNiquet, FTriozon, SRoche. Charge transport in chemically doped 2D graphene. Physical Review Letters, 2008, 101(3): 036808 https://doi.org/10.1103/PhysRevLett.101.036808
37
ZLiu, L Ma, GShi, WZhou, Y Gong, SLei, XYang, J Zhang, JYu, K PHackenberg, ABabakhani, J CIdrobo, RVajtai, JLou, P M Ajayan. In-plane heterostructures of graphene and hexagonal boron nitride with controlled domain sizes. Nature Nanotechnology, 2013, 8(2): 119–124 https://doi.org/10.1038/nnano.2012.256
38
DVan Tuan, J Kotakoski, TLouvet, FOrtmann, J CMeyer, SRoche. Scaling properties of charge transport in polycrystalline graphene. Nano Letters, 2013, 13(4): 1730–1735 https://doi.org/10.1021/nl400321r
39
BMortazavi, O Rahaman, MMakaremi, ADianat, G Cuniberti, TRabczuk. First-principles investigation of mechanical properties of silicene, germanene and stanene. Physica E: Low-Dimensional Systems and Nanostructures, 2017, 87: 228–232. https://doi.org/10.1016/j.physe.2016.10
40
ACresti, N Nemec, BBiel, GNiebler, FTriozon, GCuniberti, SRoche. Charge transport in disordered graphene-based low dimensional materials. Nano Research, 2008, 1(5): 361–394 https://doi.org/10.1007/s12274-008-8043-2
41
BMortazavi, A Lherbier, ZFan, AHarju, TRabczuk, J CCharlier. Thermal and electronic transport characteristics of highly stretchable graphene kirigami. Nanoscale, 2017, 9(42): 16329–16341 https://doi.org/10.1039/C7NR05231F
42
ZWang, X F Zhou, X Zhang, QZhu, HDong, M Zhao, A ROganov. Phagraphene: a low-energy graphene allotrope composed of 5-6-7 carbon rings with distorted dirac cones. Nano Letters, 2015, 15(9): 6182–6186 https://doi.org/10.1021/acs.nanolett.5b02512
43
YLiu, Z Chen, SHu, GYu, Y Peng. The influence of silicon atom doping phagraphene nanoribbons on the electronic and magnetic properties. Materials Science and Engineering B, 2017, 220: 30–36 https://doi.org/10.1016/j.mseb.2017.03.002
44
A YLuo, R Hu, Z QFan, H LZhang, J HYuan, C HYang, Z HZhang. Electronic structure, carrier mobility and device properties for mixed-edge phagraphene nanoribbon by hetero-atom doping. Organic Electronics, 2017, 51: 277–286 https://doi.org/10.1016/j.orgel.2017.09.025
45
P FYuan, Z Q Fan, Z H Zhang. Magneto-electronic properties and carrier mobility in phagraphene nanoribbons: a theoretical prediction. Carbon, 2017, 124: 228–237 https://doi.org/10.1016/j.carbon.2017.08.068
46
L F CPereira, BMortazavi, MMakaremi, TRabczuk. Anisotropic thermal conductivity and mechanical properties of phagraphene: a molecular dynamics study. RSC Advances, 2016, 6(63): 57773–57779 https://doi.org/10.1039/C6RA05082D
47
RAbadi, R P Uma, M Izadifar, TRabczuk. The effect of temperature and topological defects on fracture strength of grain boundaries in single-layer polycrystalline boron-nitride nanosheet. Computational Materials Science, 2016, 123: 277–286 https://doi.org/10.1016/j.commatsci.2016.06.028
48
BMortazavi, G Cuniberti. Mechanical properties of polycrystalline boron-nitride nanosheets. RSC Advances, 2014, 4(37): 19137–19143 https://doi.org/10.1039/C4RA01103A
49
RAbadi, R P Uma, M Izadifar, TRabczuk. Investigation of crack propagation and existing notch on the mechanical response of polycrystalline hexagonal boron-nitride nanosheets. Computational Materials Science, 2017, 131: 86–99 https://doi.org/10.1016/j.commatsci.2016.12.046
50
HTalebi, M Silani, S PBordas, PKerfriden, TRabczuk. Molecular dynamics/XFEM coupling by a three-dimensional extended bridging domain with applications to dynamic brittle fracture. International Journal for Multiscale Computational Engineering, 2013, 11(6): 527–541 https://doi.org/10.1615/IntJMultCompEng.2013005838
51
HTalebi, M Silani, TRabczuk. Concurrent multiscale modeling of three dimensional crack and dislocation propagation. Advances in Engineering Software, 2015, 80: 82–92 https://doi.org/10.1016/j.advengsoft.2014.09.016
52
MSilani, H Talebi, A MHamouda, TRabczuk. Nonlocal damage modelling in clay/epoxy nanocomposites using a multiscale approach. Journal of Computational Science, 2016, 15: 18–23 https://doi.org/10.1016/j.jocs.2015.11.007
53
HTalebi, M Silani, S P ABordas, PKerfriden, TRabczuk. A computational library for multiscale modeling of material failure. Computational Mechanics, 2014, 53(5): 1047–1071 https://doi.org/10.1007/s00466-013-0948-2
54
P RBudarapu, R Gracie, S P ABordas, TRabczuk. An adaptive multiscale method for quasi-static crack growth. Computational Mechanics, 2014, 53(6): 1129–1148 https://doi.org/10.1007/s00466-013-0952-6
55
BMortazavi, G Cuniberti, TRabczuk. Mechanical properties and thermal conductivity of graphitic carbon nitride: a molecular dynamics study. Computational Materials Science, 2015, 99: 285–289 https://doi.org/10.1016/j.tafmec.2013.12.004
56
K MHamdia, M Silani, XZhuang, PHe, T Rabczuk. Stochastic analysis of the fracture toughness of polymeric nanoparticle composites using polynomial chaos expansions. International Journal of Fracture, 2017, 206(2): 215–227 https://doi.org/10.1007/s10704-017-0210-6
57
SPlimpton. Fast parallel algorithms for short-range molecular dynamics. Journal of Computational Physics, 1995, 117(1): 1–19 https://doi.org/10.1006/jcph.1995.1039
58
AStukowski. Visualization and analysis of atomistic simulation data with OVITO–the Open Visualization Tool. Modelling and Simulation in Materials Science and Engineering, 2010, 18(1): 015012 https://doi.org/10.1088/0965-0393/18/1/015012
59
D HTsai. The virial theorem and stress calculation in molecular dynamics. Journal of Chemical Physics, 1979, 70(3): 1375–1382 https://doi.org/10.1063/1.437577
60
CLee, X Wei, J WKysar, JHone. Measurement of the elastic properties and intrinsic strength of monolayer grapheme. Science, 2008, 321(5887): 385–388 https://doi.org/10.1126/science.1157996
