Mechanical properties of carbyne: experiment and simulations
 Sergiy Kotrechko^{1}Email author,
 Igor Mikhailovskij^{2},
 Tatjana Mazilova^{2},
 Evgenij Sadanov^{2},
 Andrei Timoshevskii^{1},
 Nataliya Stetsenko^{1} and
 Yurij Matviychuk^{1}
https://doi.org/10.1186/s1167101507612
© Kotrechko et al.; licensee Springer. 2015
 Received: 16 October 2014
 Accepted: 18 January 2015
 Published: 31 January 2015
Abstract
The results of the highfield technique for obtaining and testing the carbyne strength in situ are presented. By using molecular dynamics simulation and ab initio calculations, a comprehensive analysis of the results is executed. Highfield technique for experimental measurement of the carbyne strength in situ is briefly described. It is shown that the technique used gives a lower estimation for strength of carbyne, which equals 251 GPa at T = 77 K. This value is close to the strength 7.85 nN (250 GPa) of contact atomic bond between carbyne and graphene sheet, from which the monatomic chain is pulled. The strength of carbyne itself is determined by strength of an edge atomic bond and it is ≈ 12.35 nN (393 GPa) at T = 0 K. For carbynes containing more than 10 to 12 atoms, the coefficient of elasticity (k _{ Y } = 145.40 nN) and the elastic modulus (Y = 4631 GPa) are ascertain.
Keywords
 Carbyne
 Carbon monatomic chains
 Strength
 Ab initio simulation
 Highfield method
 Field emission microscope
Background
Carbonbased materials are among the most promising objects of modern nanotechnology. Carbyne is the linear allotrope of carbon. To date, carbyne, as an object of research, leaves behind graphene by the number of works, due to its unique physical, mechanical, and chemical properties [14], as well as due to promising applications [510]. The possibility of realization of these unusual functional properties is significantly depending on the strength and elasticity of carbyne. Moreover, obtaining of carbyne by unraveling of nanotubes or graphene sheets is governed by its mechanical properties [5,6,10,11]. Therefore, recently, quite a lot of works on the problem of the strength and stability of monatomic carbon chains appeared [1217]. However, until now, the strength of carbyne was evaluated by the results of ab initio modeling of tension of monatomic carbon chains. Only recently, the first experimental data on in situ determination of the tensile strength of carbyne by highfield method have been published [18,19]. An ultrahigh ultimate level of strength of these chains, which at T = 5 K exceeds 270 GPa, was ascertained [19]. This is more than twice higher than the experimental strength of graphene which is equal to 130 GPa [20]. Despite the considerable interest in the carbyne, information about its mechanical properties is scattered in specific works that does not allow obtaining complete representation about these properties. This work is addressed to a brief description of the experimental data obtained by measuring of strength of carbyne, as well as to the results of the molecular dynamics and ab initio modeling of tension of monatomic carbon chains of finite length.
Methods
where ξ is a dimensionless constant equal to 1.145 ± 0.033 which is independent of the carbyne length and the tips’ radius.
Along with the experimental determination of the strength of carbyne, the work presents molecular dynamics (MD) simulation of the formation of monatomic carbon chains by pulling it out of the graphene sheet. Model of monolayers of carbon atoms included 44 of the interacting atoms and 30 boundary (edge) atoms. Boundary (edge) atoms are held in position of the lattice nodes. Such a model is a stable relatively homogeneous deformation and artifactual phase transformations. In the calculations, we used the fact that the electric forces which create axial tension are localized on top of the carbon chain. In mesoscopic electric field, induced charge is really localized at the top of a linear chain. Consequently, the mechanical strength of the electric field is localized at the top of nanowires. In our calculations, the axial mechanical load varied in the range 7 to 9 nN.
For the analysis of atomism of deformation and break of a monatomic chain, ab initio calculations were employed. The number of atoms in the carbyne was varied from 2 to 13. Full energies of chains were calculated by the pseudopotential method (software QuantumESPRESSO (QE) [25]). This method was applied for modeling the mechanical properties of the chains. Pseudopotentials for carbon were generated according to the scheme Vanderbilt ultrasoft using the package Vanderbilt code version 7.3.4 [26]. To determine the accuracy of the calculation of the total energies of carbon chains, test calculations for infinite chains with the polyyne and cumulene were performed. Interatomic distances and total energies, consistent with the results of the work [27], were obtained. The value of the cutoff energy is E _{cut} = 450 eV.
Results and discussion
Observation of such chains indicates that they survived and not destroyed at the maximum value of electric field strength, which according to Equation 4, corresponds to mechanical stress of 251 GPa. This strength value was measured at 77 K and it is 7% lower than the strength of 270 GPa previously obtained at a lower temperature 5 K [19]. Influence of local force fluctuation due to the thermal vibration of atoms in carbyne chains is one of the reasons for such difference. The distribution of carbyne chain lengths was determined by the fieldelectron technique using the values of compression factor and the radius r _{0} of the carbon tips. As the statistical analysis showed, the distribution of the carbyne chain length directly calculated from Equation 3 has a mean value of 3.5 nm, with a variance of 1.8 nm.
where E is the total electron energy and a is the current distances between the first and second atoms in a chain (length of edge bond).
where l _{0} and l are the initial and current chain lengths.
where S is the effective crosssectional area of the chain, through which the force interaction between the atoms in the chain is transmitted. In this work, as well as in [23], the effective value of the diameter of the chain was assumed to be equal 0.2 nm.
As it was noted above, the average length of monatomic chains produced at the surface of the carbon specimen is equal to 3.5 nm. A chain of such length should contain about 28 atoms. In accordance with the results of ab initio calculations, the strength of such a chain should be ≈ 12.35 nN (393 GPa), which is 1.46 to 1.56 times higher than experimentally measured strengths of 270 (5 K) and 251 (77 K) of the contact atomic bond between the chain and the graphene.
Conclusions
 1.
Carbyne is the strongest material in the world. Experimental estimation of its strength gives the values 270 GPа (at 5 K) and 251 GPa (at 77 K). This is more than two times higher than the strength of graphene (130 GPа).
 2.
For carbyne of length approximately 1,36 nm, ab initiocalculated value equals 393 GPа (at 0 K). Such a significant difference (from 1.46 to 1.56 times) between the experimental and ab initio values of strength is due to the fact that in the experiment, the strength of contact bond between the chain and the graphene sheet is measured, and ab initio calculations gives the strength of atomic bonds in the chain itself. It means that these experimental values should be considered as a lower bound for the strength of carbyne.
 3.Mechanical properties of carbyne containing more than 4 and less than 12 atoms are governed by the scale and ‘evenodd’ effects:

‘Evenodd’ effect manifests itself in the fact that carbynes with an odd number of atoms have the greater values of the strength.

Scale effect lies in growth of modulus of elasticity of chain growth. The strength of ‘even’ carbynes increases monotonically, and the strength of ‘odd’ ones varies nonmonotonically. Carbynes containing five atoms have the highest strength which equals 13.09 nN (417 GPa).

 4.
When the number of atoms in the carbyne exceeds 12, its mechanical properties become independent of the number of atoms and its parity. Strength of such carbyne is ≈ 12.35 nN (393 GPa) (at 0 K), the coefficient of elasticity  k _{ Y } = 145.40 nN, and elastic modulus  Y = 4631 GPa.
Declarations
Acknowledgements
The authors gratefully acknowledge the financial support from Project # 15/14Н Program ‘Nanosystems, Nanomaterials and Nanotechnologies’ of NAS of Ukraine.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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