Predictive modeling of the length of prepared CNT by CVD through ANN-MPSO and GEP

Document Type : Research Article


1 Department of Materials Engineering, Faculty of Engineering, University of Sistan and Baluchestan, Zahedan, Iran

2 Department of Materials Science and Engineering, Faculty of Engineering, Shahid Bahonar University of Kerman, Kerman, Iran


Floating catalyst chemical vapor deposition (FC-CVD) is considered as one of the most appropriate techniques for the preparation of carbon nanotubes (CNTs) on the industrial scale. This paper tried to model the length of CNTs prepared by FC-CVD using two approaches, i.e. gene expression programs and hybrid artificial neural networks. In this regard, the effect of various FC-CVD parameters, viz. temperature, time, preheat temperature, Ar gas flow, methane gas flow, ethylene gas flow, Al2O3 catalyst, and Fe catalyst, on the length of CNTs, were investigated. At first, a hybrid artificial neural network-modified particle swarm optimization strategy (ANN-MPSO) has been used to model the CNTs length as a function of practical variables. In the next step, the same modeling of the problem was done using gene expression programming (GEP) instead of ANN-MPSO. The accuracy of the developed hybrid ANN-MPSO and GEP models was compared with regard to the linear combination of mean absolute percentage error and correlation coefficient as criteria. The results confirmed that the ANN model upgraded by the meta-heuristics strategy could be effectively applied for an accurate predictive model in the estimation of the length of CNTs as a function of the most important practical FC-CVD parameters. Also, the sensitivity analysis confirmed that the precursor type of carbon (including CH4 and C2H4) and the preheat temperature have the highest and the least effect on the length of CNTs, respectively.

Graphical Abstract

Predictive modeling of the length of prepared CNT by CVD through ANN-MPSO and GEP


  • This paper tried to model the length of CNTs prepared by FC-CVD.
  • The modeling was performed by two methods: ANN-MPSO and GEP.
  • It was confirmed through performance criteria analysis that the ANN-MPSO strategy performed better in the prediction of CNTs length than the GEP models.


[1] R. Zhang, Q. Wen, W. Qian, D.S. Su, Q. Zhang, F. Wei, Superstrong ultralong carbon nanotubes for mechanical energy storage, Adv. Mater. 23 (2011) 3387-3391.
[2] B.C. Edwards, Design and deployment of a space elevator, Acta Astronaut. 47 (2000) 735-744.
[3] N. Sano, H. Wang, M. Chhowalla, I. Alexandrou, G.A. Amaratunga, Nanotechnology: Synthesis of carbon ‘onions’ in water, Nature, 414 (2001) 506-507.
[4] H. Zhu, X.S. Li, B. Jiang, C.L. Xu, Y.F. Zhu, D.H. Wua, X.H. Chen, Formation of carbon nanotubes in water by the electric-arc technique, Chem. Phys. Lett. 366 (2002) 664-669.
[5] H. Lange, M. Sioda, A. Huczko, Y.Q. Zhu, H.W. Kroto, D.R.M.Walton, Nanocarbon production by arc discharge in water, Carbon, 41 (2003) 1617-1623.
[6] M.V. Antisari, R. Marazzi, R. Krsmanovic, Synthesis of multiwall carbon nanotubes by electric arc discharge in liquid environments, Carbon, 41 (2003) 2393-2401.
[7] A. Thess, R. Lee, P. Nikolaev, H. Dai, P. Petit, J. Robert et al., Crystalline ropes of metallic carbon nanotubes, Science, 273 (1996) 483-487.
[8] W. Liu, S.-P. Chai, A.R. Mohamed, U. Hashim, Synthesis and characterization of graphene and carbon nanotubes: A review on the past and recent developments, J. Ind. Eng. Chem. 20 (2014) 1171-1185.
[9] R. Saito, G. Dresselhaus, M.S. Dresselhaus, Physical Properties of Carbon Nanotubes, Imperial College Press, London, 1998.
[10] P. Harris, Carbon Nanotubes and Related Structures, Cambridge University Press, Cambridge, 1999.
[11] S. Iijima, Helical microtubules of graphitic carbon, Nature, 354 (1991) 56-58.
[12] P.P. Wulan, T.P.J. Silaen, Synthesis of ACNT on quartz substrate with catalytic decomposition reaction from Cinnamomum camphora by using FC-CVD method, AIP Conf. Proc. 1840, (2017) 080003-1–080003-8.
[13] Y. Li, G. Xu, H. Zhang, T. Li, Y. Yao,Q. Li, Z. Dai, Alcohol-assisted rapid growth of vertically aligned carbon nanotube arrays, Carbon, 91 (2015) 45-55.
[14] Q. Wen, R. Zhang, W. Qian, Y. Wang, P. Tan, J. Nie, F. Wei, Growing 20 cm long DWNTs/TWNTs at a rapid growth rate of 80-90 μm/s, Chem. Mater. 22 (2010) 1294-1296.
[15] G.-Y. Xiong, D. Wang, Z. Ren, Aligned millimeter-long carbon nanotube arrays grown on single crystal magnesia, Carbon, 44 (2006) 969-973.
[16] W. Zhou, Z. Han, J. Wang, Y. Zhang, Z. Jin, X. Sun, Y. Zhang, C. Yan, Y. Li, Copper catalyzing growth of single-walled carbon nanotubes on substrates, Nano lett. 6 (2006) 2987-2990.
[17] Q. Li, X.F. Zhang, R.F. DePaula, L.X. Zheng, Y.H. Zhao, L. Stan et al., Sustained growth of ultralong carbon nanotube arrays for fiber spinning, Adv. Mater. 18 (2006) 3160-3163.
[18] E. Einarsson, Y. Murakami, M. Kadowaki, S. Maruyama, Growth dynamics of vertically aligned single-walled carbon nanotubes from in situ measurements, Carbon, 46 (2008) 923-930.
[19] E.R. Meshot, D.L. Plata, S. Tawfick, Y. Zhang, E.A. Verploegen, A.J. Hart, Engineering vertically aligned carbon nanotube growth by decoupled thermal treatment of precursor and catalyst, ACS Nano, 3 (2009) 2477-2486.
[20] B.H. Choi, H. Yoo, Y.B. Kim, J.H. Lee, Effects of Al buffer layer on growth of highly vertically aligned carbon nanotube forests for in situ yarning, Microelectron. Eng. 87 (2010) 1500-1505.
[21] G.D. Nessim, A. Al-Obeidi, H. Grisaru, E.S. Polsen, C.R. Oliver, T. Zimrin et al., Synthesis of tall carpets of vertically aligned carbon nanotubes by in situ generation of water vapor through preheating of added oxygen, Carbon, 50 (2012) 4002-4009.
[22] M.Z. Naghadehi, M. Samaei, M. Ranjbarnia, V. Nourani, State-of-the-art predictive modeling of TBM performance in changing geological conditions through gene expression programming. 126 (2018) 46-57.
[23] A.H. Gandomi, A.H. Alavi, S. Kazemi, M. Gandomi, Formulation of shear strength of slender RC beams using gene expression programming, part I: Without shear reinforcement, Automat. Constr. 42 (2014) 112-121.
[24] E. Momeni, R. Nazir, D.J. Armaghani, H. Maizir, Prediction of pile bearing capacity using a hybrid genetic algorithm-based ANN, Measurement, 57 (2014) 122-131.
[25] A. Shafaei, G.R. Khayati, A predictive model on size of silver nanoparticles prepared by green synthesis method using hybrid artificial neural network-particle swarm optimization algorithm, Measurement, 150 (2020) 107199.
[26] M.M. Jafari, G.R. Khayati, M. Hosseini, H. Danesh-Manesh, Modeling and optimization of roll-bonding parameters for bond strength of Ti/Cu/Ti clad composites by artificial neural networks and genetic algorithm, Int. J. Eng. Trans. C, 30 (2017) 1885-1893.
[27] K. Patra, A.K. Jha, T. Szalay, J. Ranjan, L. Monostori, Artificial neural network based tool condition monitoring in micro mechanical peck drilling using thrust force signals, Precis. Eng. 48 (2017) 279-291.
[28] V. Rajamohan, R. Sedaghati, S. Rakheja, Optimum design of a multilayer beam partially treated with magnetorheological fluid, Smart Mater. Struct. 19 (2010) 065002.
[29] M. Zeraati, G.R. Khayati, N. Materials, Optimization of micro hardness of nanostructure Cu-Cr-Zr alloys prepared by the mechanical alloying using artificial neural networks and genetic algorithm, Journal of Ultrafine Grained and Nanostructured Materials, 51 (2018) 183-192.
[30] P. Zhu, S. Zhou, J. Zhen, Y. Li, Application of artificial neural network in composite research. In: Tan Y., Shi Y., Tan K.C. (eds), Advances in Swarm Intelligence, ICSI 2010, Lecture Notes in Computer Science, 6146 (2010) 558-563.
[31] J. Kennedy, R. Eberhart, Particle swarm Optimization, in Proceedings of IEEE International Conference on Neural Networks IV, 1995.
[32] R.R. Karri, J. Sahu, Modeling and optimization by particle swarm embedded neural network for adsorption of zinc (II) by palm kernel shell based activated carbon from aqueous environment, Journal of environmental management. 206 (2018) 178-191.
[33] S. Du, W. Li, K. Cao, A learning algorithm of artificial neural network based on GA-PSO, 2006 6th World Congress on Intelligent Control and Automation, Dalian, 2006, pp. 3633-3637.
[34] X.H. Shi, Y.H. Lu, C.G. Zhou, H.P. Lee, W.Z. Lin Y.C. Liang, Hybrid evolutionary algorithms based on PSO and GA, The 2003 Congress on Evolutionary Computation (CEC '03), Canberra, ACT, Australia, Vol.4 (2003) pp. 2393-2399.
[35] G.-G. Wang, A.H. Gandomi , X.-S. Yang, A.H. Alavi, A novel improved accelerated particle swarm optimization algorithm for global numerical optimization, Eng. Computation. 31 (2014) 1198-1220.
[36] J.R. Koza, Genetic Programming II, Automatic Discovery of Reusable Subprograms, MIT Press, Cambridge, MA, 1194.
[37] İ. Karahan, R. Özdemir, A new modeling of electrical resistivity properties of ZnFe alloys using genetic programming, Optoelectron. Adv. Mat. 4 (2010) 812-815.
[38] A.H. Gandomi, D.A. Roke, Assessment of artificial neural network and genetic programming as predictive tools, Adv. Eng. Softw. 88 (2015) 63-72.
[39] S.N. Sivanandam, S.N. Deepa, Genetic algorithm optimization problems, in Introduction to Genetic Algorithms, Springer, 2008, pp. 165-209.
[40] M.İ. Coşkun, İ.H. Karahan, Modeling corrosion performance of the hydroxyapatite coated CoCrMo biomaterial alloys, J. Alloy. Compd. 745 (2018) 840-848.
[41] Y. Benjamini, Opening the box of a boxplot, Am. Stat. 42 (1988) 257-262.
[42] B. Tiryaki, Predicting intact rock strength for mechanical excavation using multivariate statistics, artificial neural networks, and regression trees, Eng. Geol. 99 (2008) 51-60.
[43] A.R. Sayadi, M.R. Khalesi, M.K. Borji, A parametric cost model for mineral grinding mills, Miner. Eng. 55 (2014) 96-102.
[44] A.R. Sayadi, A. Lashgari, J.J. Paraszczak, Hard-rock LHD cost estimation using single and multiple regressions based on principal component analysis, Tunn. Undergr. sp. Tech. 27 (2012) 133-141.
[45] H.F. Kaiser, An index of factorial simplicity, Psychometrika, 39 (1974) 31-36.
[46] R.S. Faradonbeh, M. Monjezi, Prediction and minimization of blast-induced ground vibration using two robust meta-heuristic algorithms, Eng. Comput. 33 (2017) 835-851.
[47] O. Nerushev, S. Dittmar, R.-E. Morjan, F. Rohmund, E.E.B. Campbell, Particle size dependence and model for iron-catalyzed growth of carbon nanotubes by thermal chemical vapor deposition, J. Appl. Phys. 93 (2003) 4185-4190.
[48] R. Morjan, O.A. Nerushev, M. Sveningsson, F. Rohmund, L.K.L. Falk, E.E.B. Campbell, Growth of carbon nanotubes from C60, Appl. Phys.78 (2004) 253-261.
[49] M. Kumar, Y. Ando, Chemical vapor deposition of carbon nanotubes: a review on growth mechanism and mass production, J. Nanosci. Nanotechnol. 10 (2010) 3739-3758.
[50] F. Ding, P. Larsson, J.A. Larsson, R. Ahuja, H. Duan, A. Rosén, K. Bolton, The importance of strong carbon-metal adhesion for catalytic nucleation of single-walled carbon nanotubes, Nano Lett. 8 (2008) 463-468.