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A highly efficient numerical method to investigate the conductivity of CNT/polymer composite

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Abstract

Compared to conventional electronic composites, polymer nanocomposites containing carbon nanotubes (CNT) have superior electrical properties. In the research, a highly efficient numerical method used to calculate the resistivity of the CNT/polymer composite is presented based on an integrated three-dimensional (3D) statistical resistor network model (RNM) which incorporates the tunneling effect between neighboring nanotubes. By this 3D RNM, the electrical properties of a composite brick in which a certain number of CNT are distributed randomly can be calculated. However, to guarantee the convergence of calculation, the number of CNTs must be larger than a threshold, and this may cause the calculation to be very time-consuming. In order to improve the computational efficiency, a modified calculation scheme using coarse-net model (CNM) is proposed. According to the scheme, a composite brick containing a large number of CNTs is divided into an array of cells, each of which has a limited volume and contains a small number of CNTs. These cells are assumed to be connected in a 3D network whereby each cell is considered as a resistor and its resistance can be calculated by the original integrated 3D model efficiently. Statistically, the effective resistance of such a resistor network that can be evaluated by Kirchhoff’s current law is the same as the resistance of the composite brick. The comparison between the conventional RNM and the CNM proves that the latter can improve the computational efficiency tremendously.

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Reference

  1. B. Arash, Q. Wang, V.K. Varadan, Carbon Nanotubes-Current Progress of Their Polymer Composites (IntechOpen, London, 2016), pp. 155–194

    Google Scholar 

  2. N. Hu, Z. Masuda, C. Yan, G. Yamamoto, H. Fukunaga, T. Hashida, The electrical properties of polymer nanocomposites with carbon nanotube fillers. Nanotechnology 19(21), 215701 (2008)

    Article  ADS  Google Scholar 

  3. Z. Zhou, X. Wang, S. Faraji, P.D. Bradford, Q. Li, Y. Zhu, Mechanical and electrical properties of aligned carbon nanotube/carbon matrix composites. Carbon 75, 307–313 (2014)

    Article  Google Scholar 

  4. J.Z. Kovacs, A review and analysis of electrical percolation in carbon nanotube polymer composites. Compos. Sci. Technol. 69(10), 1486–1498 (2009)

    Article  Google Scholar 

  5. M.H. Al-Saleh, U. Sundararaj, Review of the mechanical properties of carbon nanofiber/polymer composites. Compos. A 42(12), 2126–2142 (2011)

    Article  Google Scholar 

  6. A. Mora, P. Verma, S. Kumar, Electrical conductivity of CNT/polymer composites: 3D printing, measurements and modeling. Compos. B 183, 107600 (2020)

    Article  Google Scholar 

  7. F. Aviles, A.I. Oliva-Aviles, M. Cen-Puc, Piezoresistivity, strain, and damage self-sensing of polymer composites filled with carbon nanostructures. Adv. Eng. Mater. 20(7), 1701159 (2018)

    Article  Google Scholar 

  8. Z. Li, L. Wang, Y. Li, Y. Feng, W. Feng, Carbon-based functional nanomaterials: preparation, properties and applications. Compos. Sci. Technol. 179(28), 10–14 (2019)

    Google Scholar 

  9. X. Cao, X. Wei, G. Li, C. Hu, K. Dai, J. Guo, G. Zheng, C. Liu, C. Shen, Z. Guo, Strain sensing behaviors of epoxy nanocomposites with carbon nanotubes under cyclic deformation. Polymer 112, 1–9 (2017)

    Article  Google Scholar 

  10. Alamusi, N. Hu, Hisao Fukunaga, Satoshi Atobe, Yaolu Liu, J. Li, Piezoresistive strain sensors made from carbon nanotubes based polymer nanocomposites. Sensors 11(11), 10691–10723 (2011)

    Article  Google Scholar 

  11. A. Sanli, A. Benchirouf, C. Müller, O. Kanoun, Piezoresistive performance characterization of strain sensitive multi-walled carbon nanotube-epoxy nanocomposites. Sensors Actuat. A 254, 61–68 (2017)

    Article  Google Scholar 

  12. L. Vertuccio, V. Vittoria, L. Guadagno, F. De Santis, Strain and damage monitoring in carbon-nanotube-based composite under cyclic strain. Compos. A 71, 9–16 (2015)

    Article  Google Scholar 

  13. H. Kaiyan, Y. Weifeng, T. Shuying, L. Haidong, A fabrication process to make CNT/EP composite strain sensors. High Perform. Polym. 30(2), 224–229 (2018)

    Article  Google Scholar 

  14. Q. Cheng, J. Wang, K. Jiang, Q. Li, S. Fan, Fabrication and properties of aligned multiwalled carbon nanotube-reinforced epoxy composites. J. Mater. Res. 23(11), 2975–2983 (2008)

    Article  ADS  Google Scholar 

  15. C. Li, K. Friedrich, Y. Lin, P. Toro, Evaluation and visualization of the percolating networks in multi-wall carbon nanotube/epoxy composites. J. Mater. Sci. 44(15), 4003–4012 (2009)

    Article  ADS  Google Scholar 

  16. I. Balberg, N. Binenbaum, Cluster structure and conductivity of three-dimensional continuum systems. Phys. Rev. A 31(2), 1222–1225 (1985)

    Article  ADS  Google Scholar 

  17. M. Haghgoo, R. Ansari, M.K. Hassanzadeh-Aghdam, Prediction of electrical conductivity of carbon fiber-carbon nanotube-reinforced polymer hybrid composites. Compos. B 167, 728–735 (2019)

    Article  Google Scholar 

  18. H. Zheng, Zhu, Shen, Gong, On the mechanism of piezoresistivity of carbon nanotube polymer composites. Polym. Int. J. Sci. Technol. Polym. 55(16), 4136–4149 (2014)

    Google Scholar 

  19. Z. Liu, W. Peng, Y. Zare, D. Hui, K.Y. Rhee, Predicting the electrical conductivity in polymer carbon nanotube nanocomposites based on the volume fractions and resistances of the nanoparticle, interphase, and tunneling regions in conductive networks. RSC Adv. 8(34), 19001–19010 (2018)

    Article  ADS  Google Scholar 

  20. R. Atif, F. Inam, Modeling and simulation of graphene based polymer nanocomposites: advances in the last decade. Graphene 05(2), 96–142 (2016)

    Article  Google Scholar 

  21. Y. Chen, S. Wang, F. Pan, J. Zhang, A numerical study on electrical percolation of polymer-matrix composites with hybrid fillers of carbon nanotubes and carbon black. J. Nanomater. 2014, 614794 (2014)

    Google Scholar 

  22. B.M. Lee, K.J. Loh, A 2D percolation-based model for characterizing the piezoresistivity of carbon nanotube-based films. J. Mater. Sci. 50(7), 2973–2983 (2015)

    Article  ADS  Google Scholar 

  23. Y.L. Alamusi, N. Liu, Hu, Numerical simulations on piezoresistivity of cnt/polymer based nanocomposites. Comput. Mater. Continua 20(2), 101–117 (2010)

    Google Scholar 

  24. B. Hu, N. Hu, Y. Li, K. Akagi, W. Yuan, T. Watanabe, Y. Cai, Multi-scale numerical simulations on piezoresistivity of CNT/polymer nanocomposites. Nanoscale Res. Lett. 7(1), 402 (2012)

    Article  ADS  Google Scholar 

  25. J.G. Simmons, Generalized Formula for the Electric Tunnel Effect between Similar Electrodes Separated by a thin insulating film. J. Appl. Phys. 34(6), 1793 (1963)

    Article  ADS  Google Scholar 

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Acknowledgments

This work was supported by the Chinese National Natural Science Fund (Grant Nos.: 11472232, 11632004, U1864208), the Key Project of Natural Science Foundation of CQ CSTC (No. cstc2017jcyjBX0063), the Key Program for International Science and Technology Cooperation Projects of the Ministry of Science and Technology of China (No. 2016YFE0125900), National Science and Technology Major Project (2017-VII-0011-0106), Science and Technology Planning Project of Tianjin (20ZYJDJC00030), the Key Program of Research and Development of Hebei Province (202030507040009), the Fund for Innovative Research Groups of Natural Science Foundation of Hebei Province (A2020202002) and the Key Project of Natural Science Foundation of Tianjin (S20ZDF077).

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Authors and Affiliations

  1. School of Manufacturing Science and Engineering, Key Laboratory of Testing for Manufacturing Process, Ministry of Education; Shock and Vibration of Engineering Materials and Structures Key Laboratory of Sichuan Province, Southwest University of Science and Technology, Mianyang, 621010, China

    Ying Qin, Huang Kaiyan & Yuan Weifeng

  2. The College of Nuclear Technology and Automation Engineering, Chengdu University of Technology, Chengdu, 610059, China

    Fan Shuai

  3. College of Aerospace Engineering, Chongqing University, Chongqing, 400044, China

    Huang Kaiyan

  4. State Key Laboratory of Reliability and Intelligence Electrical Equipment, School of Mechanical Engineering, and National Engineering Research Center for Technological Innovation Method and Tool, Hebei University of Technology, Tianjin, 300130, China

    Hu Ning

Authors
  1. Ying Qin
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  2. Fan Shuai
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  3. Huang Kaiyan
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  4. Hu Ning
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  5. Yuan Weifeng
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Contributions

K. Huang and W. Yuan were responsible for conceptualization and resources; methodology was performed by Q. Ying; software was performed by S. Fan; data curation was performed by Q. Ying and S. Fan; Q. Ying and K. Huang were responsible for writing—original draft preparation; W. Yuan and N. Hu were responsible for writing—review and editing and funding acquisition. All authors have read and agreed to the published version of the manuscript.

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Correspondence to Huang Kaiyan or Yuan Weifeng.

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Qin, Y., Shuai, F., Kaiyan, H. et al. A highly efficient numerical method to investigate the conductivity of CNT/polymer composite. Appl. Phys. A 127, 200 (2021). https://doi.org/10.1007/s00339-021-04317-y

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  • DOI: https://doi.org/10.1007/s00339-021-04317-y

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