Abstract
Among various two-dimensional carbon allotropes, graphyne has received extensive research attention with outstanding physical features and excellent application prospects for energy storage systems, specifically lithium-ion batteries anode. The mechanical characteristic of the anode affects the performance and durability of the battery during charge/discharge cycles. Therefore, this research investigates the mechanical properties of \(\upalpha\)-, \(\upbeta \)-, and \(\upgamma \)-graphyne multilayer configurations using the molecular dynamics (MD) simulation approach. The results demonstrate that the mechanical properties of multilayer graphyne do not significantly depend on carbon layers; however, as the layer numbers increase, fracture stress and strain decrease approximately in both sheets with armchair and zigzag configurations, while armchair types are slightly more. In the fracture mechanism, brittle behavior is observed for both types, but the fracture occurs faster in the zigzag type because of the bond arrangement. Among multilayer graphyne-based structures, \({\upalpha}\)-graphyne owing to the maximum and \(\upgamma \)-graphyne due to the minimum percentages of acetylenic linkages, exhibit the lowest and the highest Young’s modulus, respectively. This behavior is also observed for fracture stresses. By increasing the layer numbers from one to four, Young’s modulus of multilayer configuration shows an increasing margin. After 5 layers, Young’s modulus is primarily independent of layer number because the two-dimensional structures evolve to three-dimensional configurations. The 10% strain is the allowable zone value for applying strain to multilayer structures to increase the ability to store the charge carriers. The multilayer anode configuration will yield and collapse for more than this value. The results of this paper introduce mechanical characteristics of multilayer graphyne-based sheets as promising candidates to design lithium-ion batteries anode.
Graphical abstract
![](http://media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjp%2Fs13360-022-02551-8/MediaObjects/13360_2022_2551_Figa_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1140%2Fepjp%2Fs13360-022-02551-8/MediaObjects/13360_2022_2551_Fig1_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1140%2Fepjp%2Fs13360-022-02551-8/MediaObjects/13360_2022_2551_Fig2_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1140%2Fepjp%2Fs13360-022-02551-8/MediaObjects/13360_2022_2551_Fig3_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1140%2Fepjp%2Fs13360-022-02551-8/MediaObjects/13360_2022_2551_Fig4_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1140%2Fepjp%2Fs13360-022-02551-8/MediaObjects/13360_2022_2551_Fig5_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1140%2Fepjp%2Fs13360-022-02551-8/MediaObjects/13360_2022_2551_Fig6_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1140%2Fepjp%2Fs13360-022-02551-8/MediaObjects/13360_2022_2551_Fig7_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1140%2Fepjp%2Fs13360-022-02551-8/MediaObjects/13360_2022_2551_Fig8_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1140%2Fepjp%2Fs13360-022-02551-8/MediaObjects/13360_2022_2551_Fig9_HTML.png)
Similar content being viewed by others
Data availability
This manuscript has associated data in a data repository. [Authors’ comment: The data that support the findings of this study are available from the corresponding author upon reasonable request.]
References
J. Lu, Z. Chen, F. Pan, Y. Cui, K. Amine, High-performance anode materials for rechargeable lithium-ion batteries. Electrochem. Energy Rev. 1(1), 35–53 (2018). https://doi.org/10.1007/s41918-018-0001-4
M.V.F. Heinz, M.C. Bay, U.F. Vogt, C. Battaglia, Grain size effects on activation energy and conductivity: Na-β″-alumina ceramics and ion conductors with highly resistive grain boundary phases. Acta Mater. 213, 116940 (2021). https://doi.org/10.1016/j.actamat.2021.116940
D. Ma, Y. Li, M. Wu, L. Deng, X. Ren, P. Zhang, Enhanced cycling stability of Li-rich nanotube cathodes by 3D graphene hierarchical architectures for Li-ion batteries. Acta Mater. 112, 11–19 (2016). https://doi.org/10.1016/j.actamat.2016.04.010
N.S. Pavithra, G. Nagaraju, R. Viswanatha, Surfactant assisted sonochemical synthesis of zinc tungstate nanoparticles: Anode for Li-ion battery and photocatalytic activities. Eur. Phys. J. Plus 133(12), 1–9 (2018). https://doi.org/10.1140/epjp/i2018-12248-x
S. Goriparti, E. Miele, F. De Angelis, E. Di Fabrizio, R. Proietti Zaccaria, C. Capiglia, Review on recent progress of nanostructured anode materials for Li-ion batteries. J. Power Sour. 257, 421–443 (2014). https://doi.org/10.1016/j.jpowsour.2013.11.103
K. Persson et al., Lithium diffusion in graphitic carbon. J. Phys. Chem. Lett. 1(8), 1176–1180 (2010). https://doi.org/10.1021/jz100188d
N.A. Kaskhedikar, J. Maier, Lithium storage in carbon nanostructures. Adv. Mater. 21(25–26), 2664–2680 (2009). https://doi.org/10.1002/adma.200901079
M. Xu, T. Liang, M. Shi, H. Chen, Graphene-like two-dimensional materials. Chem. Rev. 113(5), 3766–3798 (2013). https://doi.org/10.1021/cr300263a
M.D. Stoller, S. Park, Z. Yanwu, J. An, R.S. Ruoff, Graphene-Based ultracapacitors. Nano Lett. 8(10), 3498–3502 (2008). https://doi.org/10.1021/nl802558y
R. Mukherjee, A.V. Thomas, A. Krishnamurthy, N. Koratkar, Photothermally reduced graphene as high-power anodes for lithium-ion Batteries. ACS Nano 6(9), 7867–7878 (2012). https://doi.org/10.1021/nn303145j
J. Pan et al., Layered-structure SbPO 4 /reduced graphene oxide: an advanced anode material for sodium ion batteries. ACS Nano 12(12), 12869–12878 (2018). https://doi.org/10.1021/acsnano.8b08065
S. Ullah, P.A. Denis, F. Sato, Beryllium doped graphene as an efficient anode material for lithium-ion batteries with significantly huge capacity: a DFT study. Appl. Mater. Today 9, 333–340 (2017). https://doi.org/10.1016/j.apmt.2017.08.013
P.R. Ilango, K. Prasanna, T. Subburaj, Y.N. Jo, C.W. Lee, Facile longitudinal unzip** of carbon nanotubes to graphene nanoribbons and their effects on LiMn2O4 cathodes in rechargeable lithium-ion batteries. Acta Mater. 100, 11–18 (2015). https://doi.org/10.1016/j.actamat.2015.08.021
X. Gao, H. Liu, D. Wang, J. Zhang, Graphdiyne: synthesis, properties, and applications. Chem. Soc. Rev. 48(3), 908–936 (2019). https://doi.org/10.1039/c8cs00773j
G. Abdi et al., Toward the synthesis, fluorination and application of N-graphyne. RSC Adv. 10(66), 40019–40029 (2020). https://doi.org/10.1039/d0ra08143d
L. **ao et al., Electronic-structure tuning of honeycomb layered oxide cathodes for superior performance. Acta Mater. 199, 34–41 (2020). https://doi.org/10.1016/j.actamat.2020.08.015
A.R. Puigdollers, G. Alonso, P. Gamallo, First-principles study of structural, elastic and electronic properties of α-, β- and γ-graphyne. Carbon 96(4), 879–887 (2016). https://doi.org/10.1016/j.carbon.2015.10.043
Y. Mao, H. Soleymanabadi, Graphyne as an anode material for Mg-ion batteries: a computational study. J. Mol. Liq. 308, 113009 (2020). https://doi.org/10.1016/j.molliq.2020.113009
Q. Zhang, C. Tang, W. Zhu, C. Cheng, Strain-enhanced Li storage and diffusion on the graphyne as the anode material in the Li-ion battery. J. Phys. Chem. C 122(40), 22838–22848 (2018). https://doi.org/10.1021/acs.jpcc.8b05272
M. Makaremi, B. Mortazavi, C.V. Singh, Carbon ene-yne graphyne monolayer as an outstanding anode material for Li/Na ion batteries. Appl. Mater. Today 10, 115–121 (2018). https://doi.org/10.1016/j.apmt.2017.12.008
Y.Y. Zhang, Q.X. Pei, Y.W. Mai, Y.T. Gu, Temperature and strain-rate dependent fracture strength of graphynes. J. Phys. D. Appl. Phys. 47(42), 425301 (2014). https://doi.org/10.1088/0022-3727/47/42/425301
Y.Y. Zhang, Q.X. Pei, C.M. Wang, Mechanical properties of graphynes under tension: a molecular dynamics study. Appl. Phys. Lett. 101(8), 81909 (2012). https://doi.org/10.1063/1.4747719
J. Qu, H. Zhang, J. Li, S. Zhao, T. Chang, Structure-dependent mechanical properties of extended beta-graphyne. Carbon 120, 350–357 (2017). https://doi.org/10.1016/j.carbon.2017.05.051
Z. Xu, X. Lv, J. Li, J. Chen, Q. Liu, A promising anode material for sodium-ion battery with high capacity and high diffusion ability: graphyne and graphdiyne. RSC Adv. 6(30), 25594–25600 (2016). https://doi.org/10.1039/c6ra01870j
H.J. Hwang, J. Koo, M. Park, N. Park, Y. Kwon, H. Lee, Multilayer graphynes for lithium ion battery anode. J. Phys. Chem. C 117(14), 6919–6923 (2013). https://doi.org/10.1021/jp3105198
L. Wang, S. Yin, C. Zhang, Y. Huan, J. Xu, Mechanical characterization and modeling for anodes and cathodes in lithium-ion batteries. J. Power Sour. 392, 265–273 (2018). https://doi.org/10.1016/j.jpowsour.2018.05.007
S. Alavi, Molecular simulations: fundamentals and practice (Wiley, Canada, 2020)
H. Ghasemi, A. Rajabpour, A novel approach to calculate thermal expansion of graphene: molecular dynamics study. Eur. Phys. J. Plus 132(5), 1–5 (2017). https://doi.org/10.1140/epjp/i2017-11491-y
B. Azizi, S. Rezaee, M.J. Hadianfard, K.H. Dehnou, A comprehensive study on the mechanical properties and failure mechanisms of graphyne nanotubes (GNTs) in different phases. Comput. Mater. Sci. 182, 109794 (2020). https://doi.org/10.1016/j.commatsci.2020.109794
F. Mehralian, R.D. Firouz-Abadi, A. Vahid Moshtagh, Elastic properties of vertically aligned carbon nanotubes: a molecular dynamics study. Eur. Phys. J. Plus 134(10), 544 (2019). https://doi.org/10.1140/epjp/i2019-12903-8
R. Klessig, E. Polak, Efficient implementations of the Polak-Ribière conjugate gradient algorithm. SIAM J. Control 10(3), 524–549 (1972). https://doi.org/10.1137/0310040
J.M. Ducéré, C. Lepetit, R. Chauvin, Carbo -graphite: structural, mechanical, and electronic properties. J. Phys. Chem. C 117(42), 21671–21681 (2013). https://doi.org/10.1021/jp4067795
J. Yeo, G.S. Jung, F.J. Martín-Martínez, J. Beem, Z. Qin, M.J. Buehler, Multiscale design of graphyne-based materials for high-performance separation membranes. Adv. Mater. 31(42), 1805665 (2019). https://doi.org/10.1002/adma.201805665
X. Deng, M. Si, J. Dai, Communication: oscillated band gaps of B/N-codoped α-graphyne. J. Chem. Phys. 137(20), 201101 (2012). https://doi.org/10.1063/1.4769354
T. Ohta, A. Bostwick, T. Seyller, K. Horn, E. Rotenberg, Controlling the electronic structure of bilayer grapheme. Science 313(5789), 951–954 (2006). https://doi.org/10.1126/science.1130681
J. Yun et al., Tunable band gap of graphyne-based homo- and hetero-structures by stacking sequences, strain and electric field. Phys. Chem. Chem. Phys. 20(42), 26934–26946 (2018). https://doi.org/10.1039/c8cp03533d
A. León, M. Pacheco, Electronic properties of β-graphyne bilayers. Chem. Phys. Lett. 620, 67–72 (2015). https://doi.org/10.1016/j.cplett.2014.12.038
Y. Hang, W.Z. Wu, J. Yu, W.L. Guo, Tuning the energy gap of bilayer α-graphyne by applying strain and electric field. Chin. Phys. B 25(2), 23102 (2015). https://doi.org/10.1088/1674-1056/25/2/023102
J.L. Zhang, G.C. Shan, Stacking control in graphene-based materials: a promising method for fascinating physical properties. Front. Phys. 14(2), 23301 (2019). https://doi.org/10.1007/s11467-018-0871-2
B. Bhattacharya, U. Sarkar, N. Seriani, Electronic properties of homo- and heterobilayer graphyne: the idea of a nanocapacitor. J. Phys. Chem. C 120(47), 26579–26587 (2016). https://doi.org/10.1021/acs.jpcc.6b07092
R. Majidi, A. Karami, Electronic properties of bilayer and trilayer graphyne in the presence of electric field. Struct. Chem. 25(3), 853–858 (2014). https://doi.org/10.1007/s11224-013-0350-x
H. Shin, J. Kim, H. Lee, O. Heinonen, A. Benali, Y. Kwon, Nature of interlayer binding and stacking of sp-sp2 hybridized carbon layers: a quantum monte carlo study. J. Chem. Theory Comput. 13(11), 5639–5646 (2017). https://doi.org/10.1021/acs.jctc.7b00747
T.C. O’Connor, J. Andzelm, M.O. Robbins, AIREBO-M: a reactive model for hydrocarbons at extreme pressures. J. Chem. Phys. 142(2), 24903 (2015). https://doi.org/10.1063/1.4905549
G. Lei, Y. Zhang, H. Liu, F. Song, Mechanical properties of hollow and water-filled graphyne nanotube and carbon nanotube hybrid structure. Nanotechnology 29(19), 195702 (2018). https://doi.org/10.1088/1361-6528/aab075
M. Li, Y. Zhang, Y. Jiang, Y. Zhang, Y. Wang, H. Zhou, Mechanical properties of γ-graphyne nanotubes. RSC Adv. 8(28), 15659–15666 (2018). https://doi.org/10.1039/c8ra01970c
B. Faria, N. Silvestre, J.N.C. Lopes, Strength and fracture of graphyne and graphdiyne nanotubes. Comput. Mater. Sci. 171, 109233 (2020). https://doi.org/10.1016/j.commatsci.2019.109233
M. Kohestanian, Z. Sohbatzadeh, S. Rezaee, Mechanical properties of continuous fiber composites of cubic silicon carbide (3C-SiC) / different types of carbon nanotubes (SWCNTs, RSWCNTs, and MWCNTs): a molecular dynamics simulation. Mater. Today Commun. 23, 100922 (2020). https://doi.org/10.1016/j.mtcomm.2020.100922
S. Plimpton, Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117(1), 1–19 (1995). https://doi.org/10.1006/jcph.1995.1039
H. Rafii-Tabar, Modelling the nano-scale phenomena in condensed matter physics via computer-based numerical simulations. Phys. Rep. 325(6), 239–310 (2000). https://doi.org/10.1016/S0370-1573(99)00087-3
S.W. Cranford, M.J. Buehler, Mechanical properties of graphyne. Carbon 49(13), 4111–4121 (2011). https://doi.org/10.1016/j.carbon.2011.05.024
D.H. Tsai, The virial theorem and stress calculation in molecular dynamics. J. Chem. Phys. 70(3), 1375–1382 (1979). https://doi.org/10.1063/1.437577
J.A. Zimmerman, E.B. Webb, J.J. Hoyt, R.E. Jones, P.A. Klein, D.J. Bammann, Calculation of stress in atomistic simulation. Model. Simul. Mater. Sci. Eng. 12(4), S319–S332 (2004). https://doi.org/10.1088/0965-0393/12/4/S03
Y.Y. Zhang, Y.T. Gu, Mechanical properties of graphene: effects of layer number, temperature and isotope. Comput. Mater. Sci. 71, 197–200 (2013). https://doi.org/10.1016/j.commatsci.2013.01.032
X. Zhang, Z. Zhang, S. Yao, A. Chen, X. Zhao, Z. Zhou, An effective method to screen sodium-based layered materials for sodium ion batteries. npj Comput. Mater. 4(1), 1–6 (2018). https://doi.org/10.1038/s41524-018-0070-2
P. Roy, S.K. Srivastava, Nanostructured anode materials for lithium ion batteries. J. Mater. Chem. A 3(6), 2454–2484 (2015). https://doi.org/10.1039/c4ta04980b
W. Zhou, Effects of external mechanical loading on stress generation during lithiation in Li-ion battery electrodes. Electrochim. Acta 185, 28–33 (2015). https://doi.org/10.1016/j.electacta.2015.10.097
J.C. Barbosa, R. Gonçalves, C.M. Costa, S. Lanceros-Mendez, Recent advances on materials for lithium-ion batteries. Energies 14(11), 3145 (2021). https://doi.org/10.3390/en14113145
C. Zhang, J. Xu, L. Cao, Z. Wu, S. Santhanagopalan, Constitutive behavior and progressive mechanical failure of electrodes in lithium-ion batteries. J. Power Sour. 357, 126–137 (2017). https://doi.org/10.1016/j.jpowsour.2017.04.103
K. Liu, J. Wu, Mechanical properties of two-dimensional materials and heterostructures. J. Mater. Res. 31(7), 832–844 (2016). https://doi.org/10.1557/jmr.2015.324
O.L. Blakslee, D.G. Proctor, E.J. Seldin, G.B. Spence, T. Weng, Elastic constants of compression-annealed pyrolytic graphite. J. Appl. Phys. 41(8), 3373–3382 (1970). https://doi.org/10.1063/1.1659428
J.L. Tsai, J.F. Tu, Characterizing mechanical properties of graphite using molecular dynamics simulation. ICCM Int. Conf. Compos. Mater. 31(1), 194–199 (2009)
Y. Qi, H. Guo, L.G. Hector, A. Timmons, Threefold increase in the Young’s modulus of graphite negative electrode during lithium intercalation. J. Electrochem. Soc. 157(5), A558 (2010). https://doi.org/10.1149/1.3327913
L.G.B. Manhani, L.C. Pardini, F.L. Neto, Assessement of tensile strength of graphites by the Iosipescu coupon test. Mater. Res. 10(3), 233–239 (2007). https://doi.org/10.1590/S1516-14392007000300003
Funding
This work was financially supported by the National Key Research and Development Program of China (2019YFC1907805).
Author information
Authors and Affiliations
Corresponding authors
Ethics declarations
Conflict of interest
The authors declare no conflict of interest.
Rights and permissions
About this article
Cite this article
Momen, R., Rezaee, R., Azizi, B. et al. Evaluation of mechanical properties of multilayer graphyne-based structures as anode materials for lithium-ions batteries. Eur. Phys. J. Plus 137, 360 (2022). https://doi.org/10.1140/epjp/s13360-022-02551-8
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/s13360-022-02551-8