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Single wall carbon nanotubes polymerization under compression: An atomistic molecular dynamics study
Chemical Physics Letters 419 (2006) 394–399 www.elsevier.com/locate/cplett
Single wall carbon nanotubes polymerization under compression: An atomistic molecular dynamics study S.F. Braga *, D.S. Galva˜o Instituto de Fı´sica ‘Gleb Wataghin’, Universidade Estadual de Campinas, C.P. 6165, CEP 13083 970 Campinas, SP, Brazil Received 14 October 2005; in final form 28 November 2005 Available online 27 December 2005
Abstract Recently, it was reported experimental observations of crosslinking between carbon nanotubes (CNTs) under pressure. Similarly to CNT growth formation the details of these polymerization processes are still unclear. In this work, we report a molecular dynamics simulation of the polymerization of a bundle of single-wall carbon nanotubes under compression using Brenner reactive potentials. Our results show that for small tube diameters extensive crosslinking formation can occur. For larger tube diameter, we obtained the first theoretical evidences that scroll-like structures (recently experimentally obtained) can be formed from SWCNTs. Ó 2005 Elsevier B.V. All rights reserved.
1. Introduction The polymerization of carbon nanotubes (CNTs) is just one of the fascinating but difficult targets that nanoscience presents to us. The formation of chemical bonds between tubes opens the possibility for creating new superhard materials. New mechanical (high Young’s modulus [1–3]) and electronic properties [4] have been predicted to these condensed structures, as well as novel applications as potential porous gas storage materials and batteries [3]. The literature presents several investigations about nanotubes transformation under high pressure treatment [5–7]. Experimental results show evidences that a phase transition ˚ occurs when tubes with diameters around and above 13 A are compressed. The loss of the radial breathing mode (in Raman spectra) [5,6] and changes in diffraction patterns (for X-ray and neutron spectra) [7] of bundle of single wall CNTs are explained by models, where the tubes section evolve to an elliptical deformed geometry or assume a sixfold polygonal symmetry during compression. Several theoretical works have been carried out to address these experimental data but there are some *
Corresponding author. Fax: +55 19 37885343. E-mail address: scheila@ifi.unicamp.br (S.F. Braga).
0009-2614/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2005.11.115
disagreements about the geometric forms assumed by the radial section of the compressed tubes [5–10]. Oval [6,8– 10] and hexagonal [5,7,8] distortions of initial cylindrical ˚ . While Peters tubes are proposed for diameters above 10 A et al. [6] and James et al. [10] assume that the diameters determine the nature of tube distortions, Sluiter et al. [8] consider that the transformations are influenced by the commensurability of nanotubes with the threefold symmetry of hexagonal lattices. Yildrim et al. [11] observed the appearance of linkage between nanotubes in hexagonal lattices over high pressure, the same was observed by Reich et al. [12], Cheng et al. [13] observed spontaneous crosslinks between tubes, and Zhu et al. observed bonds between layers of compressed multiwalled carbon nanotubes [14]. Until now only three experimental works have reported crosslinked CNTs materials. Popov et al. [15] have obtained polymerized CNTs under pressure. They observed superhard phases with bulk modulus greater than that of diamond. Khabashesku et al. [16] present spectroscopic evidences that covalent interlinking of CNTs occur under high pressure and temperature. Applying electron irradiation technique some hard nanotube-based materials have been obtained by Kis and collaborators [17]. In this work, we report a molecular dynamics simulation (MDS) of the polymerization of CNTs under compression.
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nite length) and X (periodic system) directions, and confined/compressed along the Y direction. As in our simulations the coordinates of the tubes are not commensurable with the dimensions of the box, for both models the compression of tubes are assured by moving artificial walls in a controlled way. A frozen graphene wall was chosen for computational efficiency. The walls are infinite (along Z for M-I, and along X and Z for M-II) and are separated from the first and last rows (columns) of tubes by ˚. 3.4 A We have considered these two different models as idealizations for CNTs compression processes. The maximum number of nanotubes is dictated by the computational limitations. In our models, we pay special attention to results obtained to tubes at the center of the models (region for polymerization analysis) since they experience the same environment of internal nanotubes in a real bundle. The simulations were carried out for three values of temperature: 300, 600 and 1000 K and two rates of compression ˚ /ps for each model: 0.0125 (VI-1) and 0.01875 (VI-2) A ˚ for M-I, and 0.025 (VII-1) and 0.0375 (VII-2) A/ps for M-II. Each graphene sheet was simultaneously moved by ˚ in M-I, and by 0.50 and 0.75 A ˚ in M-II. 0.25 and 0.375 A The system was allowed to relax for 40 ps. The compression velocity in M-I was selected as half of M-II considering that in the former the compression occurs simultaneously along the X and Y directions. For simplicity, all simulations were started from generic square CNT lattice configurations and the systems were allowed to relax and converge to their dynamical state. In all cases, after thermalization, the system spontaneously rearranged such that the internal CNTs formed a hexagonal configuration. The simulations have been divided in three main parts, generating a series of intermediate configurations (conf), following the basic steps: (i) velocity attribution – we start with a run of few steps in a Langevin dynamics, when the initial velocities are randomly attributed to the atoms (conf A), (ii) thermalization – then the system is thermalized in a running of 40 ps (conf B), (iii) compression – the tubes are compressed by moving
Hydrostatic-like and piston-displacement compression of CNTs have been simulated by two idealized models (Fig. 1: Model I (M-I) and Model II (M-II)). The polymerization of tubes (3, 3), (4, 4) and (10, 10) have been investigated for three different temperatures and two rates of compression. Our results indicate that tubes of small diam˚ ) polymerizes even at ambient temperature eter (around 5 A when compressed. 2. Methodology We performed molecular dynamics simulations with the reactive empirical bond-order potential (REBO) developed by Brenner [18,19]. REBO potential differs from traditional classical potentials by its capacity of describing atom rehybridizations and consequent bond breaking and formation during simulations. No predetermined hybridizations are assumed. REBO approach has been successfully used to study CNTs and fullerenes [20–23]. The interactions between non-bonded carbons are described via 6-12 Lennard-Jones potential considering the parameters proposed ˚ ¼ 27; 7 K). by Girifalco [24] and Stan [25] (r ¼ 3; 41 A; For the simulations we used a canonical-ensemble Nose´Hoover thermostat and a time step of 1 femtoseconds (fts) to the integration of dynamic equations. The models of compression considered as the building blocks of inputs are the tubes (3, 3), (4, 4) and (10, 10) with 60, 80 and 200 carbon atoms in the unit cell, respectively. The used initial configurations for simulations were tubes aligned along the axial direction with an intertube ˚ along radial direction inside a simulation distance of 2 A box (Fig. 1). This distance corresponds to the strong repulsive region of the Lennard-Jones potential, and was chosen in order to speed up the simulations. Test configurations ˚ were also starting from the equilibrium distance of 3.4 A considered. The M-I contains 36 infinite CNTs along axial direction, confined and hydrostatically-like compressed along X and Y directions. The M-II, idealized to nonhydrostatic compression, contains 16 CNTs with boundary conditions adjusted to be infinite along axial (tubes of infi-
M-II
Y X
M-I
Z
Fig. 1. Model I (M-I) and Model II (M-II) for the compression of nanotubes. View along the cross-section of the tubes and the movable walls. The dotted curves and lines indicate the repeated unit cell of the M-II model. The directions of compression are indicated by the arrows.
and fixing the position of the movable walls, and a running of 40 ps is carried out at constant temperature for relaxation (conf C). During all the simulation the system is maintained at constant temperature. For the small diameter tubes (3, 3) and (4, 4) the item (iii) was repeated 12 times (conf C to conf N) in M-I (M-II) for VI-1 (VII-1) and 10 times for VI-2 (VII-2), totalizing 520 ps and 440 ps for a complete run simulation. For the tubes (10, 10) these numbers have been increased by 17 and 13 times, respectively.
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We can monitor the temporal evolution of the total energy and polymerization patterns from the simulation results. The bonding among tubes can be monitored through the number of sp3 carbon atoms formed during compression. When no new bonds are formed during compression the total energy of the system is supposed to increase as a consequence of destabilization caused by tension on the tube walls [9]. The presence of discontinuities on the evolution of energy patterns are characteristics of phase transitions generally associated with changes in the radial section of the tubes [26]. Representative results for the total energy patterns are presented in Fig. 2 for simulations with M-I model. The tube response upon compression presents quite differentiated behaviors for small diameters [(3, 3) and (4, 4)] and large ones [(10, 10)]. For (3, 3) and (4, 4) the number of sp3 carbons increases during compression for all temperatures with energy stabilization. At 1000 K the number of sp3 carbon was about 10% and 14% of the total number of carbon for (4, 4) and (3, 3), respectively. For (3, 3) we clearly observed that the system became more stable with the formation of sp3 bonds. Comparing, in the insets of Fig. 2, the evolution on the number of sp3 for the two rates of compression investigated (solid and open symbols) we observed that the number of rehybridizations are very similar for different rates of compression. The maximum variation corresponds to 82 new sp3 carbons for 23% of compression of tubes (4, 4) at 1000 K and the rate of com˚ /ps (VI-1). pression of 0.0125 A In Fig. 3 (see supplementary material, videos 01, 02, 03 and 04 [27]) we present representative results of the new formed structures for (4, 4) in M-I. Considering the number of rehybridized carbons, M-I and M-II approaches showed very similar results. Model M-II allows greater compression of tubes and they evolve to graphitic structures. As we can see from the figures during different stages of compression oval and ‘peanut’ shapes, crosslink formations and tube coalescence can be observed. A detailed analysis of the morphology presented by crosslinked tubes revealed very remarkable structures (Fig. 4). We observed the formation of 4 and 6 carbon rings connectors during tube crosslink. These non-hexagonal rings have been observed for molecular dynamics investigations of CNTs junctions and CNTs surface reconstructions [28]. Interest-
Number of carbons with 4 bonds
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Percentage of area compression in MODEL I (%) Fig. 2. Mean total energy for tubes (10, 10), (4, 4) and (3, 3) for M-I. The results for temperatures of 300, 600 and 1000 K are represented by circles, triangles and squares, respectively. The solid line is used only to connect the symbols. Solid symbols represent the results obtained for (VI-1) and open symbols the results for (VI-2).
ingly, some of these structures were proposed [3,4] as possible condensed nanotube phases called tubulanes. The CNT polymerization is a complex problem and our results are the first theoretical evidence of their possible existence using a molecular dynamics approach coupled to a reactive potential. For (4, 4) and (3, 3) structures we have also observed the coalescence of adjacent tubes located near the movable
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Fig. 3. Dynamics of compression of (4, 4) tubes in M-I model. Snapshots at 300, 600 and 1000 K for (VI-1) and (VI-2) rates of compression. Intertube bonds and nanotubes deformations and coalescence can be observed.
Fig. 4. Details of some interlinked structures formed during dynamic compression in M-I model: (a,b) for tubes (3, 3), and (c–e) for tubes (4, 4). The new bonds are indicated in darker black.
walls. The phenomenon of coalescence for fullerenes [29] and carbon nanotubes [30,31] have been recently observed. A quite different pattern was observed for (10, 10) tubes. Using the M-I the compression procedure induced a transition to oval shape structures (Fig. 5 and Movie 05 [27])
but significant rehybridization and/or tube crosslink were not observed as energetically favorable. The number of carbon atoms converted to sp3 was very small (0.4%) for the investigated cases. Only few intertube connections are formed at 600 and 1000 K, mainly located at the most curvy regions of the ovally distorted tubes.
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Fig. 5. Dynamics of compression of (10, 10) tubes in M-I model. Snapshots at 300, 600 and 1000 K. Few intertube and intratube new bonds and nanotubes deformations can be observed.
Fig. 6. Details of some structures formed during dynamic compression in M-II model for tubes (10, 10). The new bonds are indicated in darker black.
Similar results were obtained using the M-II approach. Increasing the compression we observed, for (10, 10) tubes, collapsed structures that sometimes lead to the formation of nanoscroll-like structures (Fig. 6 and Movie 06 [27]). These scroll-like nanostructures have been recently proposed as possible multiwalled carbon nanotube precursors [23]. Carbon nanoscrolls have been recently synthesized and investigated [32,33]. Recent theoretical investigations show that nanoscroll can be converted to nanotubes by a zipper-like mechanism [34]. Our results are the first observations of their formation from carbon nanotubes. In summary, we have investigated using molecular dynamics reactive potentials the polymerization of carbon nanotubes upon compression. We have used two different approaches, hydrostatic-like and pistondisplacement type compression. Our results show that for the investigated cases extensive polymerization is pos-
sible only for small diameter tubes. We observed the formation of tubulane-like structures, which suggests that these small tubes are the best candidates for superhard materials. For structures of larger diameters, no significant polymerization was observed. After a critical compression limit we observed tube collapse that can sometimes lead to the formation of scroll-like nanostructures. These results support some recent models that proposed that nanoscrolls are intermediate/precursors of carbon nanotubes. Acknowledgements The authors acknowledge Dr. V.R. Colucci and Prof. R.H. Baughman for helpful discussions and the financial support from the Brazilian agencies CNPq, IMMP/MCT and FAPESP.
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Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.cplett.2005. 11.115. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
J.-P. Salvetat et al., Phys. Rev. Lett. 82 (1999) 944. J. Lu, Phys. Rev. Lett. 79 (1997) 1297. R.H. Baughman, D.S. Galvo, Chem. Phys. Lett. 211 (1993) 110. L. Chernozatonskii, E. Richter, M. Menon, Phys. Rev. B 65 (2002) 241404. U.D. Venkasteswaran et al., Phys. Rev. B 59 (1999) 10928. M.J. Peters, L.E. McNeil, J.P. Lu, D. Kahn, Phys. Rev. B 61 (2000) 5939. J. Tang et al., Phys. Rev. Lett. 85 (2000) 1887. M.H.F. Sluiter, V. Kumar, Y. Kawasoe, Phys. Rev. B 65 (2002) 161402. S.-P. Chan, W.-L. Yim, X.G. Gong, Z.F. Liu, Phys. Rev. B 68 (2003) 075404. J.A. Elliott, J.K.W. Sandler, A.H. Windle, R.J. Young, M.S.P. Shaffer, Phys. Rev. Lett. 92 (2004) 095501. T. Yildirim, O. Gulseren, C ¸ . kilic¸, S. Ciraci, Phys. Rev. B 62 (2000) 12648. S. Reich, C. Thomsen, P. Ordejon, Phys. Stat. Solidi B 235 (2003) 354. H. Cheng, G.P. Pez, A.C. Cooper, NanoLetters 3 (2003) 585.
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[14] C. Zhu, W. Guo, T.X. Yu, C.H. Woo, Nanotechnology 16 (2005) 1035. [15] M. Popov, M. Kyotani, R.J. Nemanich, Y. Koga, Phys. Rev. B 65 (2002) 033408. [16] V.N. Khabashesku et al., J. Phys. Chem. B 106 (2002) 11155. [17] A. Kis et al., Nat. Mater. 3 (2004) 153. [18] D.W. Brenner, Phys. Rev. B 42 (1990) 9458. [19] D.W. Brenner et al., J. Phys.: Condens. Mater. 14 (2002) 783. [20] D. Qian, W.K. Liu, R.S. Ruoff, J. Phys. Chem. B 105 (2001) 10753. [21] V.P. Sokhan, D. Nicholson, N. Quirke, J. Chem. Phys. 113 (2000) 2007. [22] Z.X. Zhang et al., Int. J. Mod. Phys. B 17 (2003) 4667. [23] P. Tangney, S.G. Louie, M.L. Cohen, Phys. Rev. Lett. 93 (2004) 65503. [24] L.A. Girifalco, M. Hodal, R.S. Lee, Phys. Rev. B 62 (2000) 13104. [25] G. Stan et al., Phys. Rev. B 62 (2000) 2173. [26] M.H.F. Sluiter, Y. Kawazoe, Phys. Rev. B 69 (2004) 224111. [27] Movies of simulations discussed in the Letter are presented as supplementary material. [28] M. Terrones, F. Banhart, N. Grobert, J.-C. Charlier, H. Terrones, P.M. Ajayan, Phys. Rev. Lett. 89 (2002) 75505. [29] E. Hernandez et al., NanoLetters 3 (2003) 1037. [30] M. Terrones et al., Science 288 (2003) 1226. [31] M. Endo et al., NanoLetters 4 (2004) 1451. [32] L.M. Viculis, J.J. Mack, R.B. Kaner, Science 299 (2003) 1361. [33] S.F. Braga et al., NanoLetters 4 (2004) 88. [34] S. Berber, D. Tomank, Phys. Rev. B 69 (2004) 233404.
Single wall carbon nanotubes polymerization under compression: An atomistic molecular dynamics study S.F. Braga *, D.S. Galva˜o Instituto de Fı´sica ‘Gleb Wataghin’, Universidade Estadual de Campinas, C.P. 6165, CEP 13083 970 Campinas, SP, Brazil Received 14 October 2005; in final form 28 November 2005 Available online 27 December 2005
Abstract Recently, it was reported experimental observations of crosslinking between carbon nanotubes (CNTs) under pressure. Similarly to CNT growth formation the details of these polymerization processes are still unclear. In this work, we report a molecular dynamics simulation of the polymerization of a bundle of single-wall carbon nanotubes under compression using Brenner reactive potentials. Our results show that for small tube diameters extensive crosslinking formation can occur. For larger tube diameter, we obtained the first theoretical evidences that scroll-like structures (recently experimentally obtained) can be formed from SWCNTs. Ó 2005 Elsevier B.V. All rights reserved.
1. Introduction The polymerization of carbon nanotubes (CNTs) is just one of the fascinating but difficult targets that nanoscience presents to us. The formation of chemical bonds between tubes opens the possibility for creating new superhard materials. New mechanical (high Young’s modulus [1–3]) and electronic properties [4] have been predicted to these condensed structures, as well as novel applications as potential porous gas storage materials and batteries [3]. The literature presents several investigations about nanotubes transformation under high pressure treatment [5–7]. Experimental results show evidences that a phase transition ˚ occurs when tubes with diameters around and above 13 A are compressed. The loss of the radial breathing mode (in Raman spectra) [5,6] and changes in diffraction patterns (for X-ray and neutron spectra) [7] of bundle of single wall CNTs are explained by models, where the tubes section evolve to an elliptical deformed geometry or assume a sixfold polygonal symmetry during compression. Several theoretical works have been carried out to address these experimental data but there are some *
Corresponding author. Fax: +55 19 37885343. E-mail address: scheila@ifi.unicamp.br (S.F. Braga).
0009-2614/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2005.11.115
disagreements about the geometric forms assumed by the radial section of the compressed tubes [5–10]. Oval [6,8– 10] and hexagonal [5,7,8] distortions of initial cylindrical ˚ . While Peters tubes are proposed for diameters above 10 A et al. [6] and James et al. [10] assume that the diameters determine the nature of tube distortions, Sluiter et al. [8] consider that the transformations are influenced by the commensurability of nanotubes with the threefold symmetry of hexagonal lattices. Yildrim et al. [11] observed the appearance of linkage between nanotubes in hexagonal lattices over high pressure, the same was observed by Reich et al. [12], Cheng et al. [13] observed spontaneous crosslinks between tubes, and Zhu et al. observed bonds between layers of compressed multiwalled carbon nanotubes [14]. Until now only three experimental works have reported crosslinked CNTs materials. Popov et al. [15] have obtained polymerized CNTs under pressure. They observed superhard phases with bulk modulus greater than that of diamond. Khabashesku et al. [16] present spectroscopic evidences that covalent interlinking of CNTs occur under high pressure and temperature. Applying electron irradiation technique some hard nanotube-based materials have been obtained by Kis and collaborators [17]. In this work, we report a molecular dynamics simulation (MDS) of the polymerization of CNTs under compression.
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nite length) and X (periodic system) directions, and confined/compressed along the Y direction. As in our simulations the coordinates of the tubes are not commensurable with the dimensions of the box, for both models the compression of tubes are assured by moving artificial walls in a controlled way. A frozen graphene wall was chosen for computational efficiency. The walls are infinite (along Z for M-I, and along X and Z for M-II) and are separated from the first and last rows (columns) of tubes by ˚. 3.4 A We have considered these two different models as idealizations for CNTs compression processes. The maximum number of nanotubes is dictated by the computational limitations. In our models, we pay special attention to results obtained to tubes at the center of the models (region for polymerization analysis) since they experience the same environment of internal nanotubes in a real bundle. The simulations were carried out for three values of temperature: 300, 600 and 1000 K and two rates of compression ˚ /ps for each model: 0.0125 (VI-1) and 0.01875 (VI-2) A ˚ for M-I, and 0.025 (VII-1) and 0.0375 (VII-2) A/ps for M-II. Each graphene sheet was simultaneously moved by ˚ in M-I, and by 0.50 and 0.75 A ˚ in M-II. 0.25 and 0.375 A The system was allowed to relax for 40 ps. The compression velocity in M-I was selected as half of M-II considering that in the former the compression occurs simultaneously along the X and Y directions. For simplicity, all simulations were started from generic square CNT lattice configurations and the systems were allowed to relax and converge to their dynamical state. In all cases, after thermalization, the system spontaneously rearranged such that the internal CNTs formed a hexagonal configuration. The simulations have been divided in three main parts, generating a series of intermediate configurations (conf), following the basic steps: (i) velocity attribution – we start with a run of few steps in a Langevin dynamics, when the initial velocities are randomly attributed to the atoms (conf A), (ii) thermalization – then the system is thermalized in a running of 40 ps (conf B), (iii) compression – the tubes are compressed by moving
Hydrostatic-like and piston-displacement compression of CNTs have been simulated by two idealized models (Fig. 1: Model I (M-I) and Model II (M-II)). The polymerization of tubes (3, 3), (4, 4) and (10, 10) have been investigated for three different temperatures and two rates of compression. Our results indicate that tubes of small diam˚ ) polymerizes even at ambient temperature eter (around 5 A when compressed. 2. Methodology We performed molecular dynamics simulations with the reactive empirical bond-order potential (REBO) developed by Brenner [18,19]. REBO potential differs from traditional classical potentials by its capacity of describing atom rehybridizations and consequent bond breaking and formation during simulations. No predetermined hybridizations are assumed. REBO approach has been successfully used to study CNTs and fullerenes [20–23]. The interactions between non-bonded carbons are described via 6-12 Lennard-Jones potential considering the parameters proposed ˚ ¼ 27; 7 K). by Girifalco [24] and Stan [25] (r ¼ 3; 41 A; For the simulations we used a canonical-ensemble Nose´Hoover thermostat and a time step of 1 femtoseconds (fts) to the integration of dynamic equations. The models of compression considered as the building blocks of inputs are the tubes (3, 3), (4, 4) and (10, 10) with 60, 80 and 200 carbon atoms in the unit cell, respectively. The used initial configurations for simulations were tubes aligned along the axial direction with an intertube ˚ along radial direction inside a simulation distance of 2 A box (Fig. 1). This distance corresponds to the strong repulsive region of the Lennard-Jones potential, and was chosen in order to speed up the simulations. Test configurations ˚ were also starting from the equilibrium distance of 3.4 A considered. The M-I contains 36 infinite CNTs along axial direction, confined and hydrostatically-like compressed along X and Y directions. The M-II, idealized to nonhydrostatic compression, contains 16 CNTs with boundary conditions adjusted to be infinite along axial (tubes of infi-
M-II
Y X
M-I
Z
Fig. 1. Model I (M-I) and Model II (M-II) for the compression of nanotubes. View along the cross-section of the tubes and the movable walls. The dotted curves and lines indicate the repeated unit cell of the M-II model. The directions of compression are indicated by the arrows.
and fixing the position of the movable walls, and a running of 40 ps is carried out at constant temperature for relaxation (conf C). During all the simulation the system is maintained at constant temperature. For the small diameter tubes (3, 3) and (4, 4) the item (iii) was repeated 12 times (conf C to conf N) in M-I (M-II) for VI-1 (VII-1) and 10 times for VI-2 (VII-2), totalizing 520 ps and 440 ps for a complete run simulation. For the tubes (10, 10) these numbers have been increased by 17 and 13 times, respectively.
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We can monitor the temporal evolution of the total energy and polymerization patterns from the simulation results. The bonding among tubes can be monitored through the number of sp3 carbon atoms formed during compression. When no new bonds are formed during compression the total energy of the system is supposed to increase as a consequence of destabilization caused by tension on the tube walls [9]. The presence of discontinuities on the evolution of energy patterns are characteristics of phase transitions generally associated with changes in the radial section of the tubes [26]. Representative results for the total energy patterns are presented in Fig. 2 for simulations with M-I model. The tube response upon compression presents quite differentiated behaviors for small diameters [(3, 3) and (4, 4)] and large ones [(10, 10)]. For (3, 3) and (4, 4) the number of sp3 carbons increases during compression for all temperatures with energy stabilization. At 1000 K the number of sp3 carbon was about 10% and 14% of the total number of carbon for (4, 4) and (3, 3), respectively. For (3, 3) we clearly observed that the system became more stable with the formation of sp3 bonds. Comparing, in the insets of Fig. 2, the evolution on the number of sp3 for the two rates of compression investigated (solid and open symbols) we observed that the number of rehybridizations are very similar for different rates of compression. The maximum variation corresponds to 82 new sp3 carbons for 23% of compression of tubes (4, 4) at 1000 K and the rate of com˚ /ps (VI-1). pression of 0.0125 A In Fig. 3 (see supplementary material, videos 01, 02, 03 and 04 [27]) we present representative results of the new formed structures for (4, 4) in M-I. Considering the number of rehybridized carbons, M-I and M-II approaches showed very similar results. Model M-II allows greater compression of tubes and they evolve to graphitic structures. As we can see from the figures during different stages of compression oval and ‘peanut’ shapes, crosslink formations and tube coalescence can be observed. A detailed analysis of the morphology presented by crosslinked tubes revealed very remarkable structures (Fig. 4). We observed the formation of 4 and 6 carbon rings connectors during tube crosslink. These non-hexagonal rings have been observed for molecular dynamics investigations of CNTs junctions and CNTs surface reconstructions [28]. Interest-
Number of carbons with 4 bonds
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Percentage of area compression in MODEL I (%) Fig. 2. Mean total energy for tubes (10, 10), (4, 4) and (3, 3) for M-I. The results for temperatures of 300, 600 and 1000 K are represented by circles, triangles and squares, respectively. The solid line is used only to connect the symbols. Solid symbols represent the results obtained for (VI-1) and open symbols the results for (VI-2).
ingly, some of these structures were proposed [3,4] as possible condensed nanotube phases called tubulanes. The CNT polymerization is a complex problem and our results are the first theoretical evidence of their possible existence using a molecular dynamics approach coupled to a reactive potential. For (4, 4) and (3, 3) structures we have also observed the coalescence of adjacent tubes located near the movable
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Fig. 3. Dynamics of compression of (4, 4) tubes in M-I model. Snapshots at 300, 600 and 1000 K for (VI-1) and (VI-2) rates of compression. Intertube bonds and nanotubes deformations and coalescence can be observed.
Fig. 4. Details of some interlinked structures formed during dynamic compression in M-I model: (a,b) for tubes (3, 3), and (c–e) for tubes (4, 4). The new bonds are indicated in darker black.
walls. The phenomenon of coalescence for fullerenes [29] and carbon nanotubes [30,31] have been recently observed. A quite different pattern was observed for (10, 10) tubes. Using the M-I the compression procedure induced a transition to oval shape structures (Fig. 5 and Movie 05 [27])
but significant rehybridization and/or tube crosslink were not observed as energetically favorable. The number of carbon atoms converted to sp3 was very small (0.4%) for the investigated cases. Only few intertube connections are formed at 600 and 1000 K, mainly located at the most curvy regions of the ovally distorted tubes.
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Fig. 5. Dynamics of compression of (10, 10) tubes in M-I model. Snapshots at 300, 600 and 1000 K. Few intertube and intratube new bonds and nanotubes deformations can be observed.
Fig. 6. Details of some structures formed during dynamic compression in M-II model for tubes (10, 10). The new bonds are indicated in darker black.
Similar results were obtained using the M-II approach. Increasing the compression we observed, for (10, 10) tubes, collapsed structures that sometimes lead to the formation of nanoscroll-like structures (Fig. 6 and Movie 06 [27]). These scroll-like nanostructures have been recently proposed as possible multiwalled carbon nanotube precursors [23]. Carbon nanoscrolls have been recently synthesized and investigated [32,33]. Recent theoretical investigations show that nanoscroll can be converted to nanotubes by a zipper-like mechanism [34]. Our results are the first observations of their formation from carbon nanotubes. In summary, we have investigated using molecular dynamics reactive potentials the polymerization of carbon nanotubes upon compression. We have used two different approaches, hydrostatic-like and pistondisplacement type compression. Our results show that for the investigated cases extensive polymerization is pos-
sible only for small diameter tubes. We observed the formation of tubulane-like structures, which suggests that these small tubes are the best candidates for superhard materials. For structures of larger diameters, no significant polymerization was observed. After a critical compression limit we observed tube collapse that can sometimes lead to the formation of scroll-like nanostructures. These results support some recent models that proposed that nanoscrolls are intermediate/precursors of carbon nanotubes. Acknowledgements The authors acknowledge Dr. V.R. Colucci and Prof. R.H. Baughman for helpful discussions and the financial support from the Brazilian agencies CNPq, IMMP/MCT and FAPESP.
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