 Nano Express
 Open Access
 Published:
Influence of Defect Number, Distribution Continuity and Orientation on Tensile Strengths of the CNTBased Networks: A Molecular Dynamics Study
Nanoscale Research Letters volume 17, Article number: 15 (2022)
Abstract
Networks based on carbon nanotube (CNT) have been widely utilized to fabricate flexible electronic devices, but defects inevitably exist in these structures. In this study, we investigate the influence of the CNTunit defects on the mechanical properties of a honeycomb CNTbased network, super carbon nanotube (SCNT), through molecular dynamics simulations. Results show that tensile strengths of the defective SCNTs are affected by the defect number, distribution continuity and orientation. Singledefect brings 0 ~ 25% reduction of the tensile strength with the dependency on defect position and the reduction is over 50% when the defect number increases to three. The distribution continuity induces up to 20% differences of tensile strengths for SCNTs with the same defect number. A smaller arranging angle of defects to the tensile direction leads to a higher tensile strength. Defective SCNTs possess various modes of stress concentration with different concentration degrees under the combined effect of defect number, arranging direction and continuity, for which the underlying mechanism can be explained by the effective crack length of the fracture mechanics. Fundamentally, the force transmission mode of the SCNT controls the influence of defects and the cases that breaking more force transmission paths cause larger decreases of tensile strengths. Defects are nonnegligible factors of the mechanical properties of CNTbased networks and understanding the influence of defects on CNTbased networks is valuable to achieve the proper design of CNTbased electronic devices with better performances.
Graphical Abstract
Introduction
Owing to the excellent mechanical and electronic properties [1,2,3,4,5], carbon nanotube (CNT) and graphene are promising candidates for the construction of the superstrong structure and carbonbased semiconductor devices. However, defects inevitably exist in CNT and graphene [6,7,8] and generally appear in the process of crystal growth and under the irradiation of particles and electrons [9, 10]. From the traditional view, defects in CNT and graphene may significantly deteriorate their properties. It is concluded that one or twoatom vacancy defects reduce the failure stresses of CNTs by as much as 26% and markedly reduce the failure strains [11]. The thermal conductivity of CNTs also remarkably decreases with the increase in defect concentration [12]. Nevertheless, defects are reported to bring benefits in tailoring the properties of CNT/graphene and obtaining new functionality in recent years. Defects can be controlled to modify the transport properties and catalytic activity of the grapheme [13, 14], optimize the electrical performance of the graphenebased nanodevices [15], and obtain graphene clusters with electrocatalytic capability for better efficiency of the fuel cells [16]. The defect engineering of CNT or graphene has been proposed to achieve the material design and obtain different functionalities via the control of defects [9, 17].
Assembling CNTs into macrostructures, such as fibers, films and foams, is one of the important ways to achieve the real application of CNTs [18,19,20]. For instance, the CNTbased flexible electronic devices [21,22,23,24] are produced by fabricating CNTs into fibers or films through the solution deposition methods and chemical vapor deposition growth. Moreover, to achieve stronger connections, CNTbased networks and structures are fabricated by introducing covalent bonding between CNT units [25, 26]. Up to now, various CNTbased covalent networks have been proposed in theoretical investigations and achieved in experiments [27,28,29,30,31,32]. However, the performances of the CNTbased covalent networks are not as superior as the theoretical prediction. One of the vital reasons is that some connections of CNTs are not effective and defects exist in those CNTbased structures in practice.
Excellent deformability and mechanical properties are fundamental requirements for the practical applications of CNTbased networks, so identifying the influence of defects in CNTbased networks has crucial theoretical and practical meanings for CNTbased macrostructures and devices. At present, lattice defects at the junction area of the CNT connection have been investigated for the CNTbased networks in theoretical investigations [33, 34]. However, defects could also appear in the region of the straight CNT units after a series of physical and chemical treatments. But CNT units are mostly regarded as defectfree in the previous studies and the influence of the CNTunit defect is not systematically investigated.
In this study, we investigate the influence of the CNTunit defects on a CNTbased honeycomb network, namely super carbon nanotube (SCNT). Molecular dynamics (MD) simulations are carried out to systematically investigate the defect number, distribution continuity and orientation on the tensile strength of the CNTbased honeycomb networks.
Methods
Structures of the SCNT Models
SCNT models are fabricated through the hierarchical assembly of CNTs and the detailed illustration can be seen from Additional file 1: Fig S1. According to the different assembly arrangements of CNTs, SCNT has two typical geometrical structures: zigzag structure and armchair structure, which are illustrated on the left side of Fig. 1a and b. The CNT unit with the chiral vector of (6,6) is adopted to fabricate armchair and zigzag SCNTs. Based on the hierarchical selfsimilar structure, SCNT is also represented by the chiral vector, with [10,0] for zigzag SCNT and [6,6] for armchair SCNT. The geometrical parameters for the SCNT models and CNT units are presented in Additional file 1: Table S1.
Settings of Defects and Constructions of Defective SCNT Models
Due to the different orientations, CNT units in the armchair and zigzag SCNT structures are divided into two types, i.e., (1) the diagonal CNT and the vertical CNT for zigzag SCNT, and (2) the diagonal CNT and the horizontal CNT for armchair SCNT. Accordingly, the singledefect of the armchair and zigzag SCNTs corresponds to the location of the CNT units, which are diagonal and vertical singledefects for zigzag SCNTs and diagonal and horizontal singledefects for armchair SCNTs. As for the multidefect cases, the defect number, distribution orientation and continuity are considered. In both zigzag and armchair SCNTs, there are three arranging orientations of the multidefects, which are parallel/diagonal/vertical to the loading direction. As presented on the right side of Fig. 1a and b, the defect orientation is illustrated by the angle θ, which is the angle between the loading direction and the arranging direction of defects. Defects are distributed continuously (green arrows) or discontinuously (blue arrows) along with the specific directions. The defect number is up to three. To provide more quantitative information, the defect concentration of each model is determined corresponding to the defect number and presented in Additional file 1: Table S2. In the following parts, however, we will still use the defect number for discussion since it is simpler and more intuitive for readers to understand.
The defective SCNT models can be obtained by deleting a group of atoms and disconnecting several CNT units in the defectfree SCNT models (Additional file 1: Fig. S2). To clearly illustrate the different cases of the defect distribution, the name of the defective model is expressed as ‘nD/V/H_degree_con/dis.’ ‘\(n\)’ is the number of the defects and ‘D/V/H’ indicates the location of the defect (D is diagonal, V is vertical, H is horizontal). The ‘degree’ represents the angle θ and ‘con/dis’ shows the continuity of the defect distribution. For example, the SCNT model with two diagonalCNT defects continuously distributed in parallel to the loading direction is named as ‘2D_0°_con’ and the model with the singledefect on the vertical CNT is named as ‘1V.’
Molecular Dynamics Simulations
Each resulting defective model experiences an energy minimization process to obtain the equilibrium configuration. After that, the axial tensile load is applied at one end of the SCNT model with the other end fixed (Fig. 2). The loading end moves at a constant rate of 0.1 Å/ps [28, 29, 35,36,37] and the radial direction of the SCNT model is free to shrink with the nonperiodic boundary. By summarizing the counterforce at the fixed end of the SCNT, the axial tensile force of each model is obtained, which is based on Newton’s third law. Nosé–Hoover extended ensemble [38] is adopted and the temperature of each system is kept stable at 0.5 K during the entire simulation process. Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potential [39] is applied to describe the interactions between carbon atoms, which is a popular and reliable force field for the simulations of carbonbased materials [40, 41]. All MD simulations in this study are carried out through the LAMMPS opensource code [42], a massively parallel simulator designed for largescale atomic systems.
Results and Discussions
Based on the results of MD simulations, the discussions about tensile strength and stress concentration of the defective SCNTs, as well as the underlying mechanisms of the influence of defect, are carried out and presented in the following three parts.
Dependency of SCNT Strengths on Defect Number, Distribution Continuity and Orientation
Tensile stress–strain curves of singledefect models are plotted in Fig. 3a and b, for armchair and zigzag SCNTs, respectively. Defectfree SCNT is set as a control group. It can be seen that most singledefects reduce the tensile strengths of SCNTs, while the defect on horizontal CNT brings almost no difference for the tensile curves of the armchair SCNT. Besides, the reductions of the strengths significantly rely on the defect location. For the zigzag SCNT, the singledefect on the diagonal CNT (model 1D) causes less strength reduction than the defect on the vertical CNT (model 1 V). In the armchair SCNT, the defect on the diagonal CNT (model 1D) is more influential than the one on the horizontal CNT (model 1H). Opposite to the great reduction of the ultimate strength, the shapes of the tensile curves are almost unchanged for all defective SCNTs, which means singledefects have a negligible effect on the tensile performances of the armchair and zigzag SCNT before fracture.
When the defect number increases, the strength reductions of defective zigzag SCNTs are generally more explicit than defective armchair SCNTs. The relative tensile strength is calculated for each model as the ratio of the strength of the defective model \({\sigma }_{d}\) to that of the defectfree model \({\sigma }_{0}\). Specific values of the tensile strength and relative tensile strength of both zigzag and armchair SCNTs are listed in Table 1. It can be seen that the largest drop of tensile strength is 51.5% for zigzag SCNTs, but the corresponding value is only 38.9% for armchair SCNTs.
The distribution orientation and continuity of defects have a combined effect on the tensile strengths of defective SCNTs. In both zigzag and armchair SCNTs, the greatest drop of the tensile strength happens to the model with three continuously distributed defects. But the defects are vertically arranged in zigzag SCNT (3V_90° _con), while in armchair SCNTs it happens to both the vertical (3D_90°_con) and the diagonal direction (3D_60°_con). As for the smallest reduction of the tensile strength, model 3D_0°_dis of zigzag SCNT has only 6.8% reduction and all Hdefect cases of armchair SCNTs bring almost no reduction for the tensile strength.
The relative tensile strength of each model is plotted versus the defect number in Figs. 4 and 5 for zigzag and armchair SCNTs, respectively. The defect number of 0 indicates the defectfree model. In Fig. 4a, tensile strengths of the defective zigzag SCNTs are compared between different defect orientations, for both continuous and discontinuous cases. It can be seen that the model with a larger angle to the loading direction has a larger reduction of tensile strength. As the increase in the defect number, the reductions induced by parallel distributed defects (0°) are all less than 10%, while the values for vertical orientations (90°) are almost triple for the same defect number. Moreover, the effect of orientation is more remarkable when defects are continuously distributed. The differences between parallel (0°) and diagonal distribution (30°) of defects are less than 5% when defects are discontinuously distributed, but the values turn to be 10 ~ 20% for continuous cases.
The differences induced by the defect continuity can be easily known from Fig. 4b. For each arranging orientation, the gap of each case is getting larger with the increase in defect number but the orientationdependent characteristics are obvious. Significant strength differences can be observed for the diagonal distributed defects (30°), while the strength variations are insensitive to the distribution continuity of vertically (90°) and parallel (0°) distributed defects.
For armchair SCNTs, the combined influences of defect number, distribution continuity and orientation are distinct from the zigzag SCNT (Fig. 5). Diagonal and vertical distributions of defects possess approximating decreasing trends of tensile strengths as the defect number increases, while the parallel distributed defects bring no change of tensile strengths. For vertical and diagonal cases, the differences induced by the continuity turn to be obvious when the defects are more than one, but the vertically distributed defects have larger gaps than the diagonal cases.
Different Stress Concentration Degrees and Modes Induced by Defects
The decreased strengths of defective SCNTs mainly result from the stress concentration around the defective positions. In Fig. 6, the local atomic stress distributions of the defective armchair and zigzag SCNTs are presented. It can be seen that under the same strain state the stressconcentration region expands dramatically for both armchair and zigzag SCNTs, meaning that more atoms are under highstress states as the increase in defect number. To quantitatively evaluate the stress concentration degree induced by different defects, the stress level of the stressconcentrated area is identified for each model. The average stress of the stressconcentrated area is calculated and compared with that of the farfield area, then the ratio of these two average stresses is defined as the stressconcentration factor \({K}_{s}\). The detailed processes of the calculation are illustrated in Additional file 1: Fig. S3.
Specific values of \({K}_{s}\) are summarized in Table 2 for all models. To illustrate the relationship of stress and tensile strength in a more legible way, \({K}_{s}\) is plotted with the relative tensile strength in Fig. 7a and b, for zigzag and armchair SCNTs, respectively. It can be seen that the \({K}_{s}\) is inversely correlated with the trend of relative tensile strength for both armchair and zigzag SCNTs. Therefore, it can be concluded that, for defective SCNTs, higher values of stress concentration factor correspond to the smaller tensile strengths, which is consistent with the general rules of stress concentration.
Moreover, the stress concentration level induced by defects is related to the stress concentration mode, which varies as the defect location, distribution continuity and orientation. According to the snapshots of MD simulations, the stress concentration modes of the defective armchair and zigzag SCNTs are illustrated in Fig. 8a and b. The disconnected CNTs are colored as black and the stressconcentrated CNTs are redcolored. It can be seen that the stressconcentration modes of both zigzag and armchair SCNTs change as the defect arrangements. For zigzag SCNTs, model 1 V has a symmetrical layout of the two stressconcentrated CNTs, while the stressconcentrated CNTs in model 1D are staggered. As for armchair SCNTs, explicit stress concentration can be observed for the 1D model, while there is no stressconcentrated area in the 1H model. That is why the disconnection of the horizontal CNTs does not affect the tensile strengths of armchair SCNTs.
The stress concentration modes of multidefect SCNTs are also obtained based on the atomic stress distributions (Fig. 8c, d). As the increase in the defect number, stress concentration modes of the defective SCNTs are affected by both the distribution orientation and continuity of defects. For both armchair and zigzag SCNTs, the stress concentration regions extend with the increase in the defect number, and the extension generally follows the orientations of defect arrangement. However, the number of concentrated CNTs is not always proportional to the defect number but depends on the arranging continuity. For most discontinuous cases, the numbers of stressconcentrated CNTs proportionally increase as the defect number increases. Yet for continuously distributed cases, the number of concentrated CNTs keeps unchanging when the defect number increases. Besides, there are no stressconcentration phenomena for all horizontal defects of defective armchair SCNT models, no matter the settings of defect number and the distribution continuity. Thus, the stressconcentration modes of the armchair SCNTs with two or three horizontal defects are not presented in Fig. 8d.
The stressconcentration levels of the defective SCNTs are significantly related to their stressconcentration modes. The modes with more stressconcentrated CNTs lead to lower stressconcentration degrees because such SCNT models could bear the stress concentration more uniformly. Hence, when the defect number is fixed, the model with discontinuously distributed defects generally possesses lower stressconcentration degrees than one with continuously distributed defects, since the former one owns more stressconcentrated CNTs. However, some models with discontinuous defects have superpositions of the stress concentration at the same CNT unit, such as the zigzag SCNT models 2V_90°_dis and 3V_90°_dis in Fig. 8c. As a result, the stress concentration degrees of these models are much higher and the corresponding tensile strengths are much lower.
Underlying Mechanisms of the Influence of Defect
Effective Crack Length
In the research of the macrolevel honeycomb structure, the influence of defects has been systematically investigated and the defects are generally regarded as ellipse cracks [43, 44]. As a CNTbased honeycomb structure, the defects in this study can also be approximatively treated as ellipse cracks. According to the theory of fracture mechanics, it is known that the length of the ellipse crack primarily determines the stressconcentration level at the tip of the crack. Similarly, in this study, the influence of defects can be concluded from the comparisons of the crack lengths.
For qualitative comparisons, the crack length of each defect is roughly set as the longest distance of the damaged ranges, which is l in Fig. 9a. However, in the fracture mechanics, only the stress component that is perpendicular to the defect length effectively results in the stress concentration at the crack tip, which is the opening mode (Mode I) of the crack propagation. Therefore, the length that essentially determines the stressconcentration degree of the SCNT is the effective crack length, which is the projected length of the ellipse crack perpendicular to the loading direction (l_{E} in Fig. 9). In the study of the defective graphene [45], a similar approach of effective defect length is adopted for the discussion of stress concentration induced by defects.
By comparing the effective crack lengths of different defects (Fig. 9b), the reason for different stressconcentration degrees of defective SCNTs can be explained. In zigzag SCNT, the defect along with the vertical orientation (90°) always has the longest effective lengths when the crack length is fixed. Thus, the stressconcertation degrees of the models with vertically distributed defects are larger than those of the other cases, so the tensile strengths are much lower. For armchair SCNT, it should be noticed that the effective lengths of the vertical defects are approximate to that of the diagonal orientated defects for the same crack length. That is why these two cases often have approximate tensile strengths. Besides, when the defect orientation is parallel to the loading direction, the effective lengths of the cracks keep unchanged for both zigzag and armchair SCNTs, which is consistent with the invariable tendency of the stressconcentration degrees and tensile strengths of the most parallel distributed defects.
Force Transmission Modes of SCNTs
The essential reason determining the influence of defects is the force transmission mode of the SCNTs. Based on the static force analysis, the force transmission modes of the armchair and zigzag SCNT are identified and illustrated in Fig. 10b. A detailed analysis of the freebody diagrams is presented in Fig. 10a. It can be seen that the mode of the zigzag SCNT is just the zigzaglike path that separates at the diagonal CNTs but merges at the longitudinal CNTs. Differently, the armchair SCNT has the CNTbundle mode, in which the parallel chains comprised by diagonal CNTs are relatively independent for force transmission and the transverse CNT only plays a connection role.
Because of the different force transmission modes, the influence of defects is distinct for armchair and zigzag SCNTs. In zigzag SCNTs, the defect on vertical CNT cuts two force transmission paths simultaneously, whereas the defect on diagonal CNT only interdicts one path. Accordingly, more forces are released when the defects are located at the vertical CNTs, causing more decreases in the tensile strengths. In armchair SCNTs, only the defect on diagonal CNTs cut the real force transmission path, while the disconnection of transverse CNT has a neglectable effect on the force transmission network. That is why the defect on horizontal CNT brings no change for tensile strengths. Therefore, a defect at a more crucial position of the force transmission network causes a greater reduction of the tensile strength.
As for the multidefect cases, the affected range of the force transmission path varies as the change of both defect number and orientation (illustrated as the black arrows in Fig. 10b). For zigzag SCNTs, the longitudinal distributed defects always induce the same width of the loadtransfer path whatever the defect number is. Differently, the defects along with the diagonal and vertical directions proportionally widen the affected ranges of the force transmission network when the defect number increases. For armchair SCNTs, due to the ‘CNTbundle’ force transmission mode, the defects along diagonal and vertical directions interdict the same width of the force transmission paths along loading direction, so the tensile strengths of these two directions are approximately the same in most cases. Defects along with the parallel direction do not cut any force transmission path, so they always do not affect the tensile strengths of armchair SCNTs.
Conclusions
In this study, the influence of CNTunit defects is investigated for the tensile strengths of the SCNTs via MD simulations. According to the above discussions, conclusions are obtained as follows.

(1)
The influence of defects is nonnegligible for the performances of CNTbased networks and involves various factors including defect number, distribution continuity and orientation.

(2)
As the increase of the defect number, the tensile strengths of SCNTs generally keep decreasing and the decreasing rate significantly depends on the defect orientation and continuity.

(3)
Various stressconcentration modes are found for different arrangements of defects, which is notably correlated to the concentration degree and the tensile strength.

(4)
The influence of defects can be explained by the fracture mechanics. The cases with longer crack lengths along the loading direction lead to higher stressconcentration degrees and lower tensile strengths.

(5)
The force transmission mode of SCNTs is the essential mechanism determining the influence of the defect. Armchair and zigzag SCNTs have different force transmission modes, so the influence of defect is distinct for these two structures.

(6)
The existence of the defect breaks the force transmission network of SCNTs and larger affected ranges result in greater reductions of the tensile strength, which depends on defect arrangements.
The obtained conclusions provide a further view to the comprehensive understanding of the defect on CNTbased networks, which are valuable for the design of the CNTbased networks. With the proper optimization, CNTbased networks are believed to possess more favorable performances and better applications.
Availability of data and materials
The datasets generated and/or analyzed during the current study are not publicly available since the data also forms part of an ongoing study, but are available from the corresponding author on reasonable request.
References
Ruoff RS, Lorents DC (1995) Mechanical and thermal properties of carbon nanotubes. Carbon 33:925–930
Charlier JC, Blase X, Roche S (2007) Electronic and transport properties of nanotubes. Rev Mod Phys 79:677–732
Castro Neto AH, Guinea F, Peres NMR, Novoselov KS, Geim AK (2009) The electronic properties of grapheme. Rev Mod Phys 81:109–162
Galashev AE, Rakhmanova OR (2014) Mechanical and thermal stability of graphene and graphenebased materials. Phys Usp 57:970–989
Cao L, Li X, Jia C, Liu G, Liu Z, Zhou G (2018) Spincharge transport properties for graphene/graphyne zigzagedged nanoribbon heterojunctions: a firstprinciples study. Carbon 127:519–526
Meyer JC, Kisielowski C, Erni R, Rossell MD, Crommie MF, Zettl A (2008) Direct imaging of lattice atoms and topological defects in graphene membranes. Nano Lett 8:3582–3586
Hashimoto A, Suenaga K, Gloter A, Urita K, Iijima S (2004) Direct evidence for atomic defects in graphene layers. Nature 430:870–873
Tian W, Li W, Yu W, Liu X (2017) A review on lattice defects in graphene: types generation, effects and regulation. Micromachines 8:163
Banhart F, Kotakoski J, Krasheninnikov AV (2011) Structural defects in graphene. ACS Nano 5:26–41
RodriguezManzo JA, Banhart F (2009) Creation of individual vacancies in carbon nanotubes by using an electron beam of 1 Å diameter. Nano Lett 9:2285–2289
Mielke SL, Troya D, Zhang S, Li JL, Xiao S, Car R et al (2004) The role of vacancy defects and holes in the fracture of carbon nanotubes. Chem Phys Lett 390:413–420
Hao F, Fang D, Xu Z (2011) Mechanical and thermal transport properties of graphene with defects. Appl Phys Lett 99:41901
Sahalianov IY, Radchenko TM, Tatarenko VA, Cuniberti G (2020) Sensitivity to strains and defects for manipulating the conductivity of graphene. EPL (Europhys Lett) 132:48002
Szroeder P, Sahalianov I, Radchenko T, Tatarenko V, Prylutskyy Y (2019) The strain and impuritydependent electron states and catalytic activity of graphene in a static magnetic field. Opt Mater 96:109284
Vicarelli L, Heerema SJ, Dekker C, Zandbergen HW (2015) Controlling defects in graphene for optimizing the electrical properties of graphene nanodevices. ACS Nano 9:3428–3435
Zhang L, Xu Q, Niu J, Xia Z (2015) Role of lattice defects in catalytic activities of graphene clusters for fuel cells. Phys Chem Chem Phys 17:16733–16743
Chu K, Wang J, Liu Y, Geng Z (2018) Graphene defect engineering for optimizing the interface and mechanical properties of graphene/copper composites. Carbon 140:112–123
Foroughi J, Spinks GM, Wallace GG, Oh J, Kozlov ME, Fang S et al (2011) Torsional carbon nanotube artificial muscles. Science 334:494–497
Kim SH, Haines CS, Li N, Kim KJ, Mun TJ, Choi C et al (2017) Harvesting electrical energy from carbon nanotube yarn twist. Science 357:773–778
DeGraff J, Liang R, Le MQ, Capsal JF, Ganet F, Cottinet PJ (2017) Printable lowcost and flexible carbon nanotube buckypaper motion sensors. Mater Des 133:47–53
Sun D, Timmermans MY, Tian Y, Nasibulin AG, Kauppinen EI, Kishimoto S et al (2011) Flexible highperformance carbon nanotube integrated circuits. Nat Nanotechnol 6:156–161
Yamada T, Hayamizu Y, Yamamoto Y, Yomogida Y, IzadiNajafabadi A, Futaba DN et al (2011) A stretchable carbon nanotube strain sensor for humanmotion detection. Nat Nanotechnol 6:296–301
Park S, Vosguerichian M, Bao Z (2013) A review of fabrication and applications of carbon nanotube filmbased flexible electronics. Nanoscale 5:1727–1752
Zhang X, Lu W, Zhou G, Li Q (2020) Understanding the Mechanical and conductive properties of carbon nanotube fibers for smart electronics. Adv Mater 32:1–21
Terrones M, Banhart F, Grobert N, Charlier JC, Terrones H, Ajayan PM (2002) Molecular junctions by joining singlewalled carbon nanotubes. Phys Rev Lett. 89: 075505
Fu Y, Carlberg B, Lindahl N, Lindvall N, Bielecki J, Matic A et al (2012) Templated growth of covalently bonded threedimensional carbon nanotube networks originated from graphene. Adv Mater 24:1576–1581
Wang M, Qiu X, Zhang X (2007) Mechanical properties of super honeycomb structures based on carbon nanotubes. Nanotechnology 18:075711
Coluci VR, Pugno NM, Dantas SO, Galvao DS, Jorio A (2007) Atomistic simulations of the mechanical properties of “Super” carbon nanotubes. Nanotechnology 18:16
Celebi AT, Kirca M, Baykasoglu C, Mugan A, To AC (2014) Tensile behavior of heat welded CNT network structures. Comput Mater Sci 88:14–21
Wang Y, Zhu Y, Wang F, Liu X, Wu H (2017) Superelasticity and deformation mechanism of threedimensional pillared graphene network structures. Carbon 118:588–596
Dasgupta A, Rajukumar LP, Rotella C, Lei Y, Terrones M (2017) Covalent threedimensional networks of graphene and carbon nanotubes: synthesis and environmental applications. Nano Today 12:116–135
Liu F, Zou R, Hu N, Ning H, Yan C, Liu Y et al (2018) Understanding the mechanical properties and deformation behavior of 3D graphenecarbon nanotube structures. Mater Des 160:377–383
Zhou R, Liu R, Li L, Wu X, Zeng XC (2011) Carbon Nanotube superarchitectures: an ab initio study. J Phys Chem C 115:18174–18185
Xu L, Wei N, Zheng Y, Fan Z, Wang HQ, Zheng JC (2012) Graphenenanotube 3D networks: intriguing thermal and mechanical properties. J Mater Chem 22:1435–1444
Yakobson BI, Campbell MP, Brabec CJ, Bernholc J (1997) High strain rate fracture and Cchain unraveling in carbon nanotubes. Comput Mater Sci 8:341–348
Jensen BD, Wise KE, Odegard GM (2015) The effect of time step, thermostat, and strain rate on ReaxFF simulations of mechanical failure in diamond, graphene, and carbon nanotube. J Comput Chem 36:1587–1596
Zhao J, Jiang JW, Jia Y, Guo W, Rabczuk T (2013) A theoretical analysis of cohesive energy between carbon nanotubes, graphene and substrates. Carbon 57:108–119
Nosé S (2002) A molecular dynamics method for simulations in the canonical ensemble. Mol Phys 100:191–198
Stuart SJ, Tutein AB, Harrison JA (2000) A reactive potential for hydrocarbons with intermolecular interactions. J Chem Phys 112:6472–6486
Faria B, Silvestre N, Canongia Lopes JN (2013) Tensiontwisting dependent kinematics of chiral CNTs. Compos Sci Technol 74:211–220
Zhang T, Li X, Gao H (2014) Defects controlled wrinkling and topological design in graphene. J Mech Phys Solids 67:2–13
Plimpton S (1995) Fast parallel algorithms for shortrange molecular dynamics. J Comput Phys 117:1–19
Ouyang S, Deng Z, Hou X (2018) Stress concentration in octagonal honeycombs due to defects. Compos Struct 204:814–821
Chen DH, Ozaki S (2009) Stress concentration due to defects in a honeycomb structure. Compos Struct 89:52–59
Qin X, Yan W, Guo X, Gao T (2018) Effects of area, aspect ratio and orientation of rectangular nanohole on the tensile strength of defective graphenea molecular dynamics study. RSC Adv 8:17034–17043
Acknowledgements
Not applicable.
Funding
The National Natural Science Foundation of China (52108237) and the Suzhou University of Science and Technology Research Project for the introducing talents (332011102), are gratefully acknowledged for the significant financial support in writing and modifying the manuscript. The Science and Technology Innovation Commission of Shenzhen Municipality (JCYJ20190808175607486) gave financial support for the design of the study and collection, analysis, and interpretation of data in this study.
Author information
Authors and Affiliations
Contributions
XS proposed the idea of this study, conducted simulations and analysis, wrote original draft, and did the editing. XH did the project administration and supervision, provided resources and funding acquisition, as well as reviewing. LS and XL helped conducting simulations and provided crucial advice for the revision of the draft. All authors read and approved the final manuscript.
Corresponding authors
Ethics declarations
Competing interests
The authors declare that they have no competing interests.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary Information
Additional file 1.
Supplementary materials.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Shi, X., He, X., Sun, L. et al. Influence of Defect Number, Distribution Continuity and Orientation on Tensile Strengths of the CNTBased Networks: A Molecular Dynamics Study. Nanoscale Res Lett 17, 15 (2022). https://doi.org/10.1186/s1167102203656w
Received:
Accepted:
Published:
DOI: https://doi.org/10.1186/s1167102203656w
Keywords
 CNTbased network
 Molecular dynamics simulation
 Influence of defect
 Mechanical performance