Abstract
Epoxy composites filled with multiwall carbon nanotubes (MWCNTs) were prepared. Frequency dependencies (in the range 1–67 GHz) of complex dielectric permittivity of the composites were experimentally obtained and the effects of filler (0–0.023 vol. fr.) content on the dielectric properties of composites were investigated. Calculations of the concentration dependence of the dielectric permittivity under the Maxwell-Garnett model were carried out. The analysis showed that the calculations within the Maxwell-Garnett model, which take into account the dielectric characteristics of the components of composite and the aspect ratio of the nanotubes used as filler give coincidence with the experimental data only in the region φ < 0.006 vol. fr. The permittivity of composites was calculated within a power-law relation which considers an aspect ratio of the filler’s particles, value of an interface thickness and its dielectric characteristics. For the thickness of the interface of 40 nm in the investigated MWCNTs/epoxy composites, its permittivity was found to be 21.22 − i × 4.45. Considerations about fitting parameters and the most appropriate model to describe the concentration dependence of dielectric permittivity are given.
Similar content being viewed by others
References
Allaoui A, Bai S, Cheng HM, Bai JB (2002) Mechanical and electrical properties of a MWNT/epoxy composite. Compos Sci Technol 62:1993–1998
Daily CS, Sun W, Kessler MR, Tan X, Bowler N (2014) Modeling the interphase of a polymer-based nanodielectric. IEEE Trans Dielectr Electr Insul 21:488–496
Dang ZM, Lin YH, Nan CW (2003) Novel ferroelectric polymer composites with high dielectric constants. Adv Mater 15:1625–1629
Dang ZM, Wu JP, Xu HP, Yao SH, Jiang MJ, Bai J (2007) Dielectric properties of upright carbon fiber filled poly(vinylidene fluoride) composite with low percolation threshold and weak temperature dependence. Appl Phys Lett 91:072912
Dang ZM, Yuan JK, Yao SH, Liao RJ (2013a) Flexible nanodielectric materials with high permittivity for power energy storage. Adv Mater 25:6334–6365
Dang ZM, Yuan JK, Zha JW, Hu PH, Wang DR, Cheng ZY (2013b) High-permittivity polymer nanocomposites: influence of interface on dielectric properties. J Adv Dielectr 3:1330004–1330008
Garboczi EJ, Snyder KA, Douglas JF, Thorpe MF (1995) Geometrical percolation threshold of overlapping ellipsoids. Phys Rev E 52:819–828
Gershon D, Calame JP, Birnboim A (2001) Complex permittivity measurements and mixing laws of alumina composites. J Appl Phys 89:8110–8116
Guo N, DiBenedetto SA, Kwon DK, Wang L, Russell MT, Lanagan MT, Facchetti A, Marks TJ (2007) Supported metallocene catalysis for in situ synthesis of high energy density metal oxide nanocomposites. J Am Chem Soc 129:766–767
Jing X, Zhao W, Lan L (2000) The effect of particle size on electric conducting percolation threshold in polymer/conducting particle composites. J Mater Sci Lett 5:377–379
Karkkainen KK, Sihvola AH, Nikoskinen KI (2000) Effective permittivity of mixtures: numerical validation by the FDTD method. IEEE Trans Geosci Remote Sens 38:1303–1308
Keszei S, Matkó S, Bertalan G, Anna P, Marosi G, Tóth A (2005) Progress in interface modifications: from compatibilization to adaptive and smart interphases. Eur Polym J 41:697–705
Kim P, Doss NM, Tillotson JP, Hotchkiss PJ, Pan MJ, Marder SR, Li J, Calame JP, Perry JW (2009) High energy density nanocomposites based on surface-modified BaTiO3 and a ferroelectric polymer. ACS Nano 3:2581–2592
Koledintseva MY, DuBro RE, Schwartz RW (2009) Maxwell Garnett rule for dielectric mixtures with statistically distributed orientations of inclusions. Prog Electromagn Res 99:131–148
Kuzhir P, Paddubskaya A, Bychanok D, Nemilentsau A, Shuba M, Plusch A et al (2011) Microwave probing of nanocarbon based epoxy resin composite films: toward electromagnetic shielding. Thin Solid Films 519:4114–4118
Lewis TJ (2004) Interfaces are the dominant feature of dielectrics at the nanometric level. IEEE Trans Dielectr Electr Insul 11:739–753
Lewis TJ (2006) Nano-composite dielectrics: the dielectric nature of the nano-particle environment. IEEJ Trans Fundam Mater 126:1020–1030
Li J, Seok SI, Chu B, Dogan F, Zhang Q, Wang Q (2009) Nanocomposites of ferroelectric polymers with TiO2 nanoparticles exhibiting significantly enhanced electrical energy density. Adv Mater 21:217–221
Li ST, Yin GL, Chen G, Li JY, Bai SN, Zhong LS et al (2010) Short-term breakdown and long-term failure in nanodielectrics: a review. IEEE Trans Dielectr Electr Insul 17:1523–1535
Liu L, Kong LB, Yin WY, Chen Y, Matitsine S (2010) Microwave dielectric properties of carbon nanotube composites. In: Marulanda JM (ed) Carbon nanotubes. InTech, Rijeka, pp 93–108
Murugaraj P, Mainwaring D, Mora-Huertas N (2005) Dielectric enhancement in polymer-nanoparticle composites through interphase polarizability. J Appl Phys 98:054304
Nan CW, Shen Y, Ma J (2010) Physical properties of composites near percolation. Annu Rev Mater Res 40:131–151
Perets YuS, Matzui LYu, Vovchenko LL, Prylutskyy YuI, Scharff P, Ritter U (2014) The effect of boron nitride on electrical conductivity of nanocarbon-polymer composites. J Mater Sci 49:2098–2105
Pitsa D, Danikas MG (2011) Interfaces features in polymer nanocomposites: a review of proposed models. Nano 6:497–508
Pradeep L, Nelson A, Preetha P (2018) Effect of interphase permittivity on the electric field distribution of epoxy nanocomposites. In: AIP conference proceedings. https://doi.org/10.1063/1.5038685
Qiao M, Lei X, Ma Y, Tian L, He X, Su K, Zhang Q (2017) Application of yolk–shell Fe3O4@N-doped carbon nanochains as highly effective microwave-absorption material. Nano Res 11:1500–1519
Rahmat M, Hubert P (2011) Carbon nanotube–polymer interactions in nanocomposites: a review. Composites Sci Technol 72:72–84
Seiler J, Kindersberger J (2014) Insight into the interphase in polymer nanocomposites. IEEE Trans Dielectr Electr Insul 21:537–547
Steeman PAM, Maurer FHJ (1992) An interlayer model for the complex dielectric constant of composites. Colloid Polym Sci 270:1069–1079
Tanaka T, Kozako M, Fuse N, Ohki Y (2005) Proposal of a multi-core model for polymer nanocomposite dielectrics. IEEE Trans Dielectr Electr Insul 12:669–681
Thomas P, Varughese KT, Dwarakanath K, Varma KBR (2010) Dielectric properties of Poly(vinylidene fluoride)/CaCu3Ti4O12 composites. Compos Sci Technol 70:539–545
Todd MG, Shi FG (2003) Molecular basis of the interphase dielectric properties of microelectronic and optoelectronic packaging materials. IEEE Trans Compon Pack 26:667–672
Todd M, Shi F (2004) Dielectric characteristics of complex composite systems containing interphase regions. In: IEEE Xplore. https://doi.org/10.1109/ISAPM.2004.1288000
Todd MG, Shi FG (2005) Complex permittivity of composite systems: a comprehensive interphase approach. IEEE Trans Dielectr Electr Insul 12:601–611
Tuncer E, Serdyuk YV, Gubanski SM (2002) Dielectric mixtures: electrical properties and modeling. IEEE Trans Dielectr Electr Insul 9:809–828
Usanov DA, Skripal AV, Romanov AV (2011) Complex permittivity of composites based on dielectric matrices with carbon nanotubes. Tech Phys 56:102–106
Velasco-Santos C, Martinez-Hernandez AL, Castano VM (2005) Carbon nanotube-polymer nanocomposites: the role of interfaces. Compos Interface 11:567–586
Wang J, Wang J, Qi S, Sun Y, Tian G, Wu D (2017) Investigation of percolation theory and permittivity model with one-dimensional fillers. EPL 117:17001
Webman I, Jortner J, Cohen MH (1977) Numerical simulations of the Hall effect in inhomogeneous materials. Phys Rev B 15:1936–1940
Yuan JK, Dang ZM, Yao SH, Zha JW, Zhou T, Li ST, Bai J (2010) Fabrication and dielectric properties of advanced high permittivity polyaniline/poly(vinylidene fluoride) nanohybrid films with high energy storage density. J Mater Chem 20:2441–2447
Zhang L, Cheng ZY (2011) Development of polymer-based 0–3 composites with high dielectric constant. J Adv Dielectr 4:389–406
Author information
Authors and Affiliations
Contributions
LM and LV designed and directed the research. OY and OLoz carried out experiments. OY, LM, LV, OLaz and YP analyzed and interpreted the data. OY and LM wrote the manuscript.
Corresponding author
Ethics declarations
Conflict of interest
The authors declare no competing interests including financial one.
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Yakovenko, O.S., Matzui, L.Y., Vovchenko, L.L. et al. Complex permittivity of polymer-based composites with carbon nanotubes in microwave band. Appl Nanosci 10, 2691–2697 (2020). https://doi.org/10.1007/s13204-019-01083-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13204-019-01083-5