Abstract
Density functional theory (B3LYP, B3LYP-D2 and wB97XD functionals) was used in finite models of zigzag carbon nanotubes (CNT), (n,0)×k with n = 6–9 and k = 2–4, to systematically investigate the effects of size on their structural and electronic properties. We found that the ratio between the length (L t) and the diameter (d t) of the pristine CNT has to be larger than 2, i.e., L t/d t > 2, in order to provide the observed experimental trends of C=C bond distances, as well as to maintain the atomic charges nearly constant and zero around the center of the tube. Therefore, the concepts of useful length and volume were developed and tested for the encapsulation process of HCN and C2H2 into CNTs. The energies involved in these processes, as well as the changes in molecular structure and electronic properties of the dopants and the CNTs are discussed and rationalized by the amount of charge transferred between dopant and CNT.
![](http://media.springernature.com/lw685/springer-static/image/art%3A10.1007%2Fs00894-017-3319-7/MediaObjects/894_2017_3319_Figa_HTML.gif)
Illustration of zigzag CNT length and diameter ratio in order to represent C=C bond experimental trend
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00894-017-3319-7/MediaObjects/894_2017_3319_Fig1_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00894-017-3319-7/MediaObjects/894_2017_3319_Fig2_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00894-017-3319-7/MediaObjects/894_2017_3319_Fig3_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00894-017-3319-7/MediaObjects/894_2017_3319_Fig4_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00894-017-3319-7/MediaObjects/894_2017_3319_Fig5_HTML.gif)
Similar content being viewed by others
References
Iijima S (1991) Helical microtubules of graphitic carbon. Nature 354:56–58. doi:10.1038/354056a0
Konsta-Gdoutos MS, Metaxa ZS, Shah SP (2010) Highly dispersed carbon nanotube reinforced cement based materials. Cem Concr Res 40:1052–1059. doi:10.1016/j.cemconres.2010.02.015
Aliev AE, Oh J, Kozlov ME, Kuznetsov AA, Fang S, Fonseca AF, Ovalle R, Lima MD, Haque MH, Gartstein YN, Zhang M, Zakhidov AA, Baughman RH (2009) Giant-stroke, superelastic carbon nanotube aerogel muscles. Science 323:1575–1578. doi:10.1126/science.1168312
Shi H, Ok JG, Won Baac H, Jay Guo L (2011) Low density carbon nanotube forest as an index-matched and near perfect absorption coating. Appl Phys Lett 99:211103. doi:10.1063/1.3663873
Wang Y, Yeow JTW (2009) A review of carbon nanotubes-based Gas sensors. J Sens 2009:1–24. doi:10.1155/2009/493904
Villalpando-Páez F, Romero AH, Muñoz-Sandoval E, Martínez LM, Terrones H, Terrones M (2004) Fabrication of vapor and gas sensors using films of aligned CNx nanotubes. Chem Phys Lett 386:137–143. doi:10.1016/j.cplett.2004.01.052
Okotrub AV, Bulusheva LG, Tomanek D (1998) X-ray spectroscopic and quantum–chemical study of carbon tubes produced in arc-discharge. Chem Phys Lett 289:341–349. doi:10.1016/S0009-2614(98)00405-9
Rochefort A, Salahub DR, Avouris P (1999) Effects of finite length on the electronic structure of carbon nanotubes. J Phys Chem B 103:641–646. doi:10.1021/jp983725m
Bandow S, Hiraoka T, Yumura T, Hirahara K, Shinohara H, Iijima S (2004) Raman scattering study on fullerene derived intermediates formed within single-wall carbon nanotube: from peapod to double-wall carbon nanotube. Chem Phys Lett 384:320–325. doi:10.1016/j.cplett.2003.12.032
Lee RKF, Cox BJ, Hill JM (2010) The geometric structure of single-walled nanotubes. Nanoscale 2:859–72. doi:10.1039/b9nr00433e
Jindal V, Imtani A (2008) Bond lengths of armchair single-waled carbon nanotubes and their pressure dependence. Comput Mater Sci 44:156–162. doi:10.1016/j.commatsci.2008.01.020
Zhang J, Zuo JM (2009) Structure and diameter-dependent bond lengths of a multi-walled carbon nanotube revealed by electron diffraction. Carbon N Y 47:3515–3528. doi:10.1016/j.carbon.2009.08.024
Kanamitsu K, Saito S (2002) Geometries, electronic properties, and energetics of isolated single walled carbon nanotubes. J Phys Soc Jpn 71:483–486. doi:10.1143/JPSJ.71.483
Budyka MF, Zyubina TS, Ryabenko AG, Lin SH, Mebel AM (2005) Bond lengths and diameters of armchair single wall carbon nanotubes. Chem Phys Lett 407:266–271. doi:10.1016/j.cplett.2005.03.088
Green MJ, Behabtu N, Pasquali M, Adams WW (2009) Nanotubes as polymers. Polymer (Guildf) 50:4979–4997. doi:10.1016/j.polymer.2009.07.044
Harigaya K, Fujita M (1993) Dimerization structures of metallic and semiconducting fullerene tubules. Phys Rev B 47:16563–16569. doi:10.1103/PhysRevB.47.16563
Ramachandran CN, De Fazio D, Sathyamurthy N, Aquilanti V (2009) Guest species trapped inside carbon nanotubes. Chem Phys Lett 473:146–150. doi:10.1016/j.cplett.2009.03.068
Wang W, Wang D, Zhang Y, Ji B, Tian A (2011) Hydrogen bond and halogen bond inside the carbon nanotube. J Chem Phys 134:1–7. doi:10.1063/1.3549572
Chehel AM, Tang T, Cuervo J (2013) Quantum mechanical treatment of binding energy between DNA nucleobases and carbon nanotube: a DFT analysis. Phys E Low Dimens Syst Nanostruct 54:65–71. doi:10.1016/j.physe.2013.05.024
Soleymanabadi H, Kakemam J (2013) A DFT study of H2 adsorption on functionalized carbon nanotubes. Phys E Low Dimens Syst Nanostruct 54:115–117. doi:10.1016/j.physe.2013.06.015
Petrushenko IK, Ivanov NA (2013) Ionization potentials and structural properties of finite-length single-walled carbon nanotubes: DFT study. Phys E Low Dimens Syst Nanostruct 54:262–266. doi:10.1016/j.physe.2013.07.004
Jankowska M, Kupka T, Stobiński L, Kaminský J (2015) DFT studies on armchair (5, 5) SWCNT functionalization. Modification of selected structural and spectroscopic parameters upon two-atom molecule attachment. J Mol Graph Model 55:105–114. doi:10.1016/j.jmgm.2014.11.006
Kupka T, Chełmecka E, Pasterny K, Stachów M, Stobiński L (2012) DFT calculations of structures, 13C-NMR chemical shifts, and Raman RBM mode of simple models of small-diameter zigzag (4,0) carboxylated single-walled carbon nanotubes. Magn Reson Chem 50:142–151. doi:10.1002/mrc.2874
dos Santos MVP, Aguiar EC, da Silva JBP, Longo RL (2013) PICVib: an accurate, fast, and simple procedure to investigate selected vibrational modes at high theoretical levels. J Comput Chem 34:611–21. doi:10.1002/jcc.23166
Frey JT, Doren DJ (2011) TubeGen online. http://turin.nss.udel.edu/research/tubegenonline.html. Accessed 8 August 2012
Becke AD (1988) Density-functional exchange-energy approximation with correct asymptotic behavior. Phys Rev A 38:3098–3100. doi:10.1103/PhysRevA.38.3098
Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Scalmani G, Barone V, Mennucci B, Petersson GA, Nakatsuji H, Caricato M, Li X, Hratchian HP, Izmaylov AF, Bloino J, Zheng G, Sonnenberg JL, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Montgomery Jr. JA, Peralta JE, Ogliaro F, Bearpark M, Heyd JJ, Brothers E, Kudin KN, Staroverov VN, Kobayashi R, Normand J, Raghavachari K, Rendell A, Burant JC, Iyengar SS, Tomasi J, Cossi M, Rega N, Millam JM, Klene M, Knox JE, Cross JB, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Martin RL, Morokuma K, Zakrzewski VG, Voth GA, Salvador P, Dannenberg JJ, Dapprich S, Daniels AD, Farkas O, Foresman JB, Ortiz JV, Cioslowski J, Fox DJ (2009) Gaussian 09 rev. A.02
Boys SF, Bernardi F (1970) The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors. Mol Phys 19:553–566. doi:10.1080/00268977000101561
Glendening ED, Badenhoop JK, Reed AE, Carpenter JE, Ohmann JA, Morales CM, Weinhold F (2004) NBO 5.0
Grimme S (2004) Accurate description of van der Waals complexes by density functional theory including empirical corrections. J Comput Chem 25:1463–1473. doi:10.1002/jcc.20078
Grimme S (2006) Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J Comput Chem 27:1787–1799. doi:10.1002/jcc.20495
Liu LV, Tian WQ, Chen YK, Zhang YA, Wang YA (2010) Theoretical studies on structures, 13C NMR chemical shifts, aromaticity, and chemical reactivity of finite-length open-ended armchair single-walled carbon nanotubes. Nanoscale 2:254–61. doi:10.1039/b9nr00159j
Matsuo Y, Tahara K, Nakamura E (2003) Theoretical studies on structures and aromaticity of finite-length armchair carbon nanotubes. Org Lett. doi:10.1021/ol0349514
Kupka T, Stachów M, Stobiński L, Kaminský J (2016) DFT study of zigzag (n, 0) single-walled carbon nanotubes: 13C NMR chemical shifts. J Mol Graph Model 67:14–19. doi:10.1016/j.jmgm.2016.04.008
Petrushenko IK, Ivanov NA (2013) Structural and electronic properties of finite-length single-walled carbon and silicon carbide nanotubes: DFT study. Mod Phys Lett B 27:1350210. doi:10.1142/S0217984913502102
Galano A (2006) On the influence of diameter and length on the properties of armchair single-walled carbon nanotubes: a theoretical chemistry approach. Chem Phys 327:159–170. doi:10.1016/j.chemphys.2006.04.019
Cai J, Li G, Wang C, Xie Z (2010) Structure of graphene, and mechanical and bonding characteristics of single wall carbon nanotube by linear scaling quantum mechanical method. J Mater Sci Technol 26:614–618. doi:10.1016/S1005-0302(10)60094-1
Kupka T, Stachów M, Stobiński L, Kaminský J (2016) Calculation of Raman parameters of real-size zigzag (n, 0) single-walled carbon nanotubes using finite-size models. Phys Chem Chem Phys 18:25058–25069. doi:10.1039/C6CP04100K
Liu H, Murad S, Jameson CJ (2006) Ion permeation dynamics in carbon nanotubes. J Chem Phys 125:84713. doi:10.1063/1.2337289
Ge M, Sattler K (1993) Vapor-condensation generation and STM analysis of fullerene tubes. Science 260:515–8. doi:10.1126/science.260.5107.515
Okazaki T, Iizumi Y, Okubo S, Kataura H, Liu Z, Suenaga K, Tahara Y, Yudasaka M, Okada S, Iijima S (2011) Coaxially stacked coronene columns inside single-walled carbon nanotubes. Angew Chem Int Ed 50:4853–4857. doi:10.1002/anie.201007832
Pascal TA, Goddard WA, Jung Y (2011) Entropy and the driving force for the filling of carbon nanotubes with water. Proc Natl Acad Sci USA 108:11794–8. doi:10.1073/pnas.1108073108
Vijay D, Sakurai H, Sastry GN (2011) The impact of basis set superposition error on the structure of π-π dimers. Int J Quantum Chem 111:1893–1901. doi:10.1002/qua.22486
Chai JD, Head-Gordon M (2008) Systematic optimization of long-range corrected hybrid density functionals. J Chem Phys 128:84106. doi:10.1063/1.2834918
Moura LG, Malard LM, Carneiro MA, Venezuela P, Capaz RB, Nishide D, Achiba Y, Shinohara H, Pimenta MA (2009) Charge transfer and screening effects in polyynes encapsulated inside single-wall carbon nanotubes. Phys Rev B Condens Matter Mater Phys 80:10–13. doi:10.1103/PhysRevB.80.161401
Rao AM, Eklund PC, Bandow S, Thess A, Smalley RE (1997) Evidence for charge transfer in doped carbon nanotube bundles from Raman scattering. Nature 388:257–259
Voggu R, Rao KV, George SJ, Rao CNR (2010) A simple method of separating metallic and semiconducting single-walled carbon nanotubes based on molecular charge transfer. J Am Chem Soc 132:5560–1. doi:10.1021/ja100190p
Voggu R, Rout CS, Franklin AD, Fisher TS, Rao CNR (2008) Extraordinary sensitivity of the electronic structure and properties of single-walled carbon nanotubes to molecular charge-transfer. J Phys Chem C 112:13053–13056. doi:10.1021/jp805136e
Dresselhaus MS, Dresselhaus G, Saito R, Jorio A (2005) Raman spectroscopy of carbon nanotubes. Phys Rep 409:47–99. doi:10.1016/j.physrep.2004.10.006
Araújo RCM, da Silva JBP, Ramos MN (1995) An ab initio study of hydrogen complexes of the X-H∙∙∙π type between acetylene and HF or HCl. Spectrochim Acta A Mol Biomol Spectrosc 51:821–830. doi:10.1016/0584-8539(94)00194-G
Ramos MN, Lopes KC, Silva WLV, Tavares AM, Castriani FA, do Monte SA, Ventura E, Araújo RCMU (2006) An ab initio study of the C2H2–HF, C2H(CH3)–HF and C2(CH3)2–HF hydrogen-bonded complexes. Spectrochim Acta A Mol Biomol Spectrosc 63:383–390. doi:10.1016/j.saa.2005.05.024
Boncel S, Zając P, Koziol KKK (2013) Liberation of drugs from multi-wall carbon nanotube carriers. J Control Release 169:126–140. doi:10.1016/j.jconrel.2013.04.009
Prakash S, Malhotra M, Shao W, Tomaro-Duchesneau C, Abbasi S (2011) Polymeric nanohybrids and functionalized carbon nanotubes as drug delivery carriers for cancer therapy. Adv Drug Deliv Rev 63:1340–1351. doi:10.1016/j.addr.2011.06.013
Acknowledgments
The authors are thankful to the Brazilian funding agencies Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Fundação de Amparo à Ciência e Tecnologia do Estado de Pernambuco (FACEPE) and Instituto Nacional de Ciência e Tecnologia: Nanotecnologia para Marcadores Integrados (inct-INAMI) for supporting the Computational and Theoretical Chemistry Laboratory of Departamento de Química Fundamental-Universidade Federal de Pernambuco (dQF-UFPE) and the Centro Nacional de Processamento de Alto Desempenho de Pernambuco (CENAPAD-PE) where this work was developed. Some calculations were performed on the High Performance Computing Center (HPCC) at the University of Florida, which is gratefully acknowledged. E.C. de Aguiar thanks CAPES and FACEPE for the scholarships, and R.L.L. thanks CNPq for the PQ-fellowship (Proc. no. 308823/2014-1).
Author information
Authors and Affiliations
Corresponding author
Additional information
This paper belongs to Topical Collection Brazilian Symposium of Theoretical Chemistry (SBQT 2015)
Electronic supplementary material
Below is the link to the electronic supplementary material.
ESM 1
(DOCX 503 kb)
Rights and permissions
About this article
Cite this article
Aguiar, E.C., Longo, R.L. & da Silva, J.B.P. Modeling zigzag CNT: dependence of structural and electronic properties on length, and application to encapsulation of HCN and C2H2 . J Mol Model 23, 144 (2017). https://doi.org/10.1007/s00894-017-3319-7
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00894-017-3319-7