Skip to main content
SpringerLink
Log in

Predicting Percolation Threshold Value of EMI SE for Conducting Polymer Composite Systems Through Different Sigmoidal Models

  • Original Research Article
  • Published:
Journal of Electronic Materials Aims and scope Submit manuscript

Abstract

Like electrical conductivity, the electromagnetic interference shielding effectiveness (EMI SE) of carbon-containing polymeric composites also goes through a transition phase known as the percolation threshold (PT). In this study, the applicability of various sigmoidal models such as sigmoidal–Boltzmann (SB), sigmoidal–dose response (SD), sigmoidal–Hill (SH), sigmoidal–logistic (SL), and sigmoidal–logistic-1 (SL-1) to determine the PT of EMI SE has been tested for composites of ethylene vinyl acetate (EVA) copolymer and acrylonitrile butadiene rubber (NBR) matrix reinforced with various particulate and fibrous carbon fillers. It is observed that the SB and SD models predicted similar PT. On the other hand, other models reported different values when validated for any particular composite system. The difference in results of PT has been discussed in detail from a viewpoint of the benefits and vice versa of these models. Also, the classical percolation theory has been applied to determine the PT of EMI SE for comparison with the values obtained through the sigmoidal models. In order to judge the universal acceptability of these models, the EMI SE results have been tested for various polymeric composites taken from some published literature. The results indicate that all the models except the SL-1 model can be successfully applied for predicting the PT of EMI SE for polymer composites.

Graphical Abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6.
Fig. 7 
Fig. 8. 

Similar content being viewed by others

References

  1. R.J. Chandra, B. Shivamurthy, S.D. Kulkarni, and M.S. Kumar, Mater. Res. Express 6, 082008 (2019).

    Article  CAS  Google Scholar 

  2. T. Williams, in EMC Prod. Des. (Newnes, 1992), pp. 171–210.

  3. M.-S. Cao, W.-L. Song, Z.-L. Hou, B. Wen, and J. Yuan, Carbon 48, 788 (2010).

    Article  CAS  Google Scholar 

  4. X. Luo, and D.D.L. Chung, Compos. Part B Eng. 30, 227 (1999).

    Article  Google Scholar 

  5. K. Balasubramanian, M. Tirumali, Y. Badhe, and Y. R. Mahajan, in Aerosp. Mater. Mater. Technol. (Springer, 2017), pp. 439–453.

  6. Z. Fan, D. Wang, Y. Yuan, Y. Wang, Z. Cheng, Y. Liu, and Z. Xie, Chem. Eng. J. 381, 122696 (2020).

    Article  CAS  Google Scholar 

  7. V.T. Rathod, J.S. Kumar, and A. Jain, Appl. Nanosci. 7, 519 (2017).

    Article  CAS  Google Scholar 

  8. P. Los, A. Lukomska, and R. Jeziorska, Polimery 61, (2016).

  9. B. Moazzenchi, and M. Montazer, Colloids Surf. Physicochem. Eng. Asp. 571, 110 (2019).

    Article  CAS  Google Scholar 

  10. K. Raagulan, J.S. Ghim, R. Braveenth, M.J. Jung, S.B. Lee, K.Y. Chai, B. Mi Kim, and J. Lee, Nanomaterials 10, 2086 (2020).

    Article  CAS  Google Scholar 

  11. L.-C. Jia, D.-X. Yan, Y. Yang, D. Zhou, C.-H. Cui, E. Bianco, J. Lou, R. Vajtai, B. Li, and P.M. Ajayan, Adv. Mater. Technol. 2, 1700078 (2017).

    Article  Google Scholar 

  12. Y. Xu, Y. Yang, D.-X. Yan, H. Duan, G. Zhao, and Y. Liu, Chem. Eng. J. 360, 1427 (2019).

    Article  CAS  Google Scholar 

  13. J. Han, J. Lee, J. Lee, and J. Yeo, Adv. Mater. 30, 1704626 (2018).

    Article  Google Scholar 

  14. R. Kumar, A. Sharma, A. Pandey, A. Chaudhary, N. Dwivedi, D.P. Mondal, and A.K. Srivastava, Sci. Rep. 10, 1 (2020).

    Article  Google Scholar 

  15. A. Sharma, R. Kumar, V.K. Patle, R. Dhawan, A. Abhash, N. Dwivedi, D.P. Mondal, and A.K. Srivastava, Compos. Commun. 22, 100433 (2020).

    Article  Google Scholar 

  16. J. Varghese, N. Joseph, H. Jantunen, S. K. Behera, H. T. Kim, M. T. Sebastian, Handb. Adv. Ceram. Compos. Def. Secur. Aerosp. Energy Appl. 165 (2020).

  17. Z. Liu, G. Bai, Y. Huang, F. Li, Y. Ma, T. Guo, X. He, X. Lin, H. Gao, and Y. Chen, J. Phys. Chem. C 111, 13696 (2007).

    Article  CAS  Google Scholar 

  18. D.D.L. Chung, Carbon 39, 279 (2001).

    Article  CAS  Google Scholar 

  19. S. Sankaran, K. Deshmukh, M.B. Ahamed, and S.K. Pasha, Compos. Part Appl. Sci. Manuf. 114, 49 (2018).

    Article  CAS  Google Scholar 

  20. A. J. Epstein, in Conduct. Polym. Plast. (Elsevier, 1999), pp. 1–9.

  21. M.H. Al-Saleh, and U. Sundararaj, Carbon 47, 1738 (2009).

    Article  CAS  Google Scholar 

  22. J. Liang, Y. Wang, Y. Huang, Y. Ma, Z. Liu, J. Cai, C. Zhang, H. Gao, and Y. Chen, Carbon 47, 922 (2009).

    Article  CAS  Google Scholar 

  23. N. Li, Y. Huang, F. Du, X. He, X. Lin, H. Gao, Y. Ma, F. Li, Y. Chen, and P.C. Eklund, Nano Lett. 6, 1141 (2006).

    Article  CAS  Google Scholar 

  24. Y. Yang, M.C. Gupta, K.L. Dudley, and R.W. Lawrence, J. Nanosci. Nanotechnol. 5, 927 (2005).

    Article  CAS  Google Scholar 

  25. R. Jan, A. Habib, M.A. Akram, I. Ahmad, A. Shah, M. Sadiq, and A. Hussain, Mater. Res. Express 4, 035605 (2017).

    Article  Google Scholar 

  26. S.H. Lee, S. Yu, F. Shahzad, W.N. Kim, C. Park, S.M. Hong, and C.M. Koo, Nanoscale 9, 13432 (2017).

    Article  CAS  Google Scholar 

  27. S.S. Pradhan, L. Unnikrishnan, S. Mohanty, and S.K. Nayak, J. Electron. Mater. 49, 1749 (2020).

    Article  CAS  Google Scholar 

  28. M. Mishra, A.P. Singh, V. Gupta, A. Chandra, and S.K. Dhawan, J. Alloys Compd. 688, 399 (2016).

    Article  CAS  Google Scholar 

  29. D. Wanasinghe, F. Aslani, G. Ma, and D. Habibi, Nanomaterials 10, 541 (2020).

    Article  CAS  Google Scholar 

  30. M. Rahaman, A. Aldalbahi, P. Govindasami, N. Khanam, S. Bhandari, P. Feng, and T. Altalhi, Polymers 9, 527 (2017).

    Article  Google Scholar 

  31. M. Rahaman, T.K. Chaki, and D. Khastgir, Adv. Sci. Lett. 10, 115 (2012).

    Article  CAS  Google Scholar 

  32. A.L. Navarro-Verdugo, F.M. Goycoolea, G. Romero-Meléndez, I. Higuera-Ciapara, and W. Argüelles-Monal, Soft Matter 7, 5847 (2011).

    Article  CAS  Google Scholar 

  33. J. Reséndiz-Muñoz, M.A. Corona-Rivera, J.L. Fernández-Muñoz, M. Zapata-Torres, A. Márquez-Herrera, and V.M. Ovando-Medina, Bull. Mater. Sci. 40, 1043 (2017).

    Article  Google Scholar 

  34. E.A. Hernández-Caraballo, O. Rodríguez-Rodríguez, and V. Rodríguez-Pérez, Environ. Exp. Bot. 64, 225 (2008).

    Article  Google Scholar 

  35. M. Rahaman, T.K. Chaki, and D. Khastgir, Polym. Compos. 32, 1790 (2011).

    Article  CAS  Google Scholar 

  36. N.J.S. Sohi, S. Bhadra, and D. Khastgir, Carbon 49, 1349 (2011).

    Article  CAS  Google Scholar 

  37. M. Rahaman, T.K. Chaki, and D. Khastgir, J. Mater. Sci. 46, 3989 (2011).

    Article  CAS  Google Scholar 

  38. L. Haanstra, P. Doelman, and J.O. Voshaar, Plant Soil 84, 293 (1985).

    Article  CAS  Google Scholar 

  39. A. DeLean, P.J. Munson, and D. Rodbard, Am. J. Physiol.-Endocrinol. Metab. 235, E97 (1978).

    Article  CAS  Google Scholar 

  40. C. Ritz and J. Strebig, J. Stat. Softw. 12, (2005).

  41. M.B. Hinojosa, J.A. Carreira, J.M. Rodríguez-Maroto, and R. García-Ruíz, Sci. Total Environ. 396, 89 (2008).

    Article  CAS  Google Scholar 

  42. R.L. Buchanan, J.L. Smith, and W. Long, Int. J. Food Microbiol. 58, 159 (2000).

    Article  CAS  Google Scholar 

  43. N. Bairagi, and D. Adak, Chaos Solitons Fractals 103, 52 (2017).

    Article  Google Scholar 

  44. S. Blatt, D.A. Joseph, G.C. Cutler, A.R. Olson, and S. White, Can. Entomol. 152, 374 (2020).

    Article  Google Scholar 

  45. B. Anandaraj, S. Eswaramoorthi, T.P. Rajesh, J. Aravind, and P.S. Babu, Int. J. Environ. Sci. Technol. 15, 2595 (2018).

    Article  CAS  Google Scholar 

  46. A.W. El-Kareh, and T.W. Secomb, Neoplasia 7, 705 (2005).

    Article  CAS  Google Scholar 

  47. S. M. Swinton and C. P. Lyford, J. Agric. Biol. Environ. Stat. 97 (1996).

  48. E.A. Christou, M. Grossman, and L.G. Carlton, J. Mot. Behav. 34, 67 (2002).

    Article  Google Scholar 

  49. S.K. Pankaj, N.N. Misra, and P.J. Cullen, Innov. Food Sci. Emerg. Technol. 19, 153 (2013).

    Article  CAS  Google Scholar 

  50. J. Weiner, S. Kinsman, and S. Williams, Am. J. Bot. 85, 1638 (1998).

    Article  CAS  Google Scholar 

  51. S. Kawakita, N. Ishikawa, H. Takahashi, R. Okuno, and T. Takahashi, J. Agric. Meteorol. 76, 81 (2020).

    Article  Google Scholar 

  52. M.A. Martín, R. Fernández, M.C. Gutiérrez, and J.A. Siles, Process Saf. Environ. Prot. 117, 245 (2018).

    Article  Google Scholar 

  53. H. Bazyar, L. Xu, H. J. de Vries, S. Porada, and R. Lammertink, Environ. Sci. Water Res. Technol. (2020).

  54. A. Ware, and N. Power, Renew. Energy 104, 50 (2017).

    Article  CAS  Google Scholar 

  55. S. Yahuza, B.I. Dan-Iya, and I.A. Sabo, J. Biochem. Microbiol. Biotechnol. 8, 42 (2020).

    Article  Google Scholar 

  56. A. Farazmand and M. Amir-Maafi, Persian J. Acarol. 7, (2018).

  57. M. Abdulrasheed, I.I. Hussein, I. Ahmad, M.M. Namadina, F. Muhammad, and S. Ibrahim, Bioremed. Sci. Technol. Res. 8, 27 (2020).

    Article  Google Scholar 

  58. V.K. Shante, and S. Kirkpatrick, Adv. Phys. 20, 325 (1971).

    Article  Google Scholar 

  59. S.M. Mishra, and B.D. Rohera, Pharm. Dev. Technol. 24, 954 (2019).

    Article  CAS  Google Scholar 

  60. N. Jarvis, M. Larsbo, and J. Koestel, Geoderma 287, 71 (2017).

    Article  Google Scholar 

  61. B. Tavagh-Mohammadi, M. Masihi, and M. Ganjeh-Ghazvini, Phys. Stat. Mech. Its Appl. 460, 304 (2016).

    Article  CAS  Google Scholar 

  62. D. Amaro, J. Bennett, D. Vodola, and M. Müller, Phys. Rev. A 101, 032317 (2020).

  63. M. Rahaman, I. A. Al Ghufais, G. Periyasami, and A. Aldalbahi, Int. J. Polym. Sci. 2020, (2020).

  64. N. Joseph, and M.T. Sebastian, Mater. Lett. 90, 64 (2013).

    Article  CAS  Google Scholar 

  65. R. Ravindren, S. Mondal, P. Bhawal, S.M.N. Ali, and N.C. Das, Polym. Compos. 40, 1404 (2019).

    Article  CAS  Google Scholar 

  66. S. Mondal, S. Ganguly, M. Rahaman, A. Aldalbahi, T.K. Chaki, D. Khastgir, and N.C. Das, Phys. Chem. Chem. Phys. 18, 24591 (2016).

    Article  CAS  Google Scholar 

Download references

Acknowledgments

We acknowledge King Saud University, Riyadh, Saudi Arabia, for funding this work through Researchers Supporting Project Number (RSP-2021/30).

Funding

This study was funded by Researchers Supporting Project Number from King Saud University, Riyadh, Saudi Arabia (RSP-2021/30).

Author information

Authors and Affiliations

  1. Department of Chemistry, College of Science, King Saud University, Riyadh, 11451, Saudi Arabia

    Mostafizur Rahaman & Ali Aldalbahi

  2. Department of Plastic and Polymer Engineering, Maharashtra Institute of Technology, Aurangabad, Maharashtra, 431010, India

    Prashant Gupta

  3. Zienkiewicz Centre for Computational Engineering, College of Engineering, Swansea University, Swansea, SA1 8EN, United Kingdom

    Mokarram Hossain

Authors
  1. Mostafizur Rahaman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Prashant Gupta
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mokarram Hossain
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ali Aldalbahi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Mostafizur Rahaman or Ali Aldalbahi.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary file1 (PDF 321 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rahaman, M., Gupta, P., Hossain, M. et al. Predicting Percolation Threshold Value of EMI SE for Conducting Polymer Composite Systems Through Different Sigmoidal Models. J. Electron. Mater. 51, 1788–1803 (2022). https://doi.org/10.1007/s11664-022-09444-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11664-022-09444-7

Keywords

Search

Navigation