Composites Research

The Korean Society for Composite Materials (한국복합재료학회)
권호 표지

A Study on the Simulation of Complex Permittivities of Carbon Black/Epoxy Composites at a High Frequency Band

고주파에서의 카본 블랙/에폭시 복합재료 복소유전율 모사에 대한 연구

  • 김태욱 (한국기계연구원 공정연구부 복합재료그룹) ;
  • 김천곤 (한국과학기술원 항공우주공학) ;
  • 김진봉 (한국기계연구원 공정연구부 복합재료그룹)
  • Published : 2005.06.01
Download PDF
⟨ Previous Next ⟩

Abstract

This paper presents a study on the permittivities of the carbon black/epoxy composite at microwave frequency. The measurements were performed at the frequency band of $1\;GHz\~18\;GHz$. The experimental data show that the complex permittivities of composites depend strongly on the natures and concentrations of the carbon black dispersion. The frequency characteristics of dielectric constants and ac conductivities of composites show the good conformity with descriptions of the percolation theory, satisfying the general scaling relation. The measuring frequency band is over the critical frequency, below that the ac conductivities of composites are constant to the frequency. The values of dielectric constants and ac conductivities have consistent relationships with the carbon black concentration. The A new scheme, that is a branch of Lichtenecker-Rother formula, is proposed to obtain a mixing law to describe the complex permittivities of the composites as function frequency and concentration of carbon black.

본 논문에서는 카본 블랙/에폭시 복합재료 적층판의 유전율에 대한 연구를 수행하였다. 유전율 측정은 $1\;GHz\~18\;GHz$의 주파수 영역에서 수행하였으며, 복합재료의 유전율은 카본 블랙 함유율의 주파수의 함수로 얻을 수 있었다. 유전율 및 전기 전도도의 주파수 특성은 Percolation 이론에서 제시된 경향을 만족하였다. 측정에 사용된 주파수 영역은 전기 전도도가 주파수의 함수관계를 가지는 최소 주파수인 임계주파수보다 크며, 복합재료의 유전율과 전기 전도도는 카본 블랙의 함유량과 일정한 관계를 가졌다. 본 연구에서는, 카본 블랙의 함유율에 따른 복합재료의 유전율을 모사하는 혼합법칙을 얻기 위하여 Lichteneker-Rother 방정식에 기초한 새로운 방법이 제시되었으며, 혼합법칙으로 계산된 복합재료 유전율 모사 결과는 실험적으로 얻은 유전율을 비교적 잘 모사하는 결과를 얻을 수 있었다.

Keywords

References

  1. J. Kubat, R. Kuzel, I. Krivka, P. Bengtsson, J. Prokes, 'New conductive polymeric systems,' Synthetic metal, Vol. 54, pp. 187-194, 1993 https://doi.org/10.1016/0379-6779(93)91059-B
  2. R. Wycist, R. Poniak, A. Pasternak, 'Conductive polymer materials with low filler content,' Journal of Electrostatics, Vol. 56, pp. 55-66, 2002 https://doi.org/10.1016/S0304-3886(01)00204-2
  3. R.B. Laibowitz, Y. Gefen, 'Dynamic scaling near the percolation threshold in thin Au films,' Physical Review Letters, Vol. 53, No.4, pp. 380-383, 1984 https://doi.org/10.1103/PhysRevLett.53.380
  4. Y. Song, T.W. Noh, S.I. Lee, J.R. Gaines, 'Experimental study of the three-dimensional ac conductivity and dielectric constant of a conductor-insulator composite near the percolation threshold,' Physical Review B, Vol. 33, No.2, pp. 904-908, 1986 https://doi.org/10.1103/PhysRevB.33.904
  5. S. Kirkpatrick, 'Percolation and conduction,' Reviews of Modern Physics, Vol. 45, No.4, pp. 574-588, 1973 https://doi.org/10.1103/RevModPhys.45.574
  6. D.J. Bergman and Y. Imry, 'Critical Behavior of the Complex Dielectric Constant near the Percolation Threshold of a Heterogeneous Material,' Physical Review Letters, Vol. 39, No. 19, pp. 1222-1225, 1977 https://doi.org/10.1103/PhysRevLett.39.1222
  7. James Baker-Javis et al, 'Transmission/Reflection and Short-Circuit Line Methods for Measuring Permittivity and Permeability,' NIST Technical Note 1341, 1355-R
  8. M.T. Cornor, S. Roy, T.A. Ezquerra, F.J.B Calleja, 'Broadband ac conductivity of conductor-polymer composites,' Physical Review B, Vol. 57, No.4, pp. 2286-2294, 1998 https://doi.org/10.1103/PhysRevB.57.2286
  9. T.A. Ezquerra, M.T. Connor, S. Roy, M. Kulescza, 'Alternating-current properties of graphite, carbon-black and carbon-fiber polymeric composites,' Composite Science and Technology, Vol. 61, pp. 903-909, 2001 https://doi.org/10.1016/S0266-3538(00)00176-7
  10. K. Benaboud, M.E. Achour, F. Carmona, L. Salome, 'Electrical Properties of carbon black-epoxy resin heterogeneous materials near the percolation threshold,' Ann. Chem. Sci. Mat, Vol. 23, pp. 315-318, 1998 https://doi.org/10.1016/S0151-9107(98)80082-2
  11. R. Schueler, J. Petermann, K. Schulte, H.P. Wentzel, 'Agglomeration and electrical percolation behavior of carbon black dispersed in epoxy resin,' Journal of applied polymer science, Vol. 63, No. 13, pp. 1741-1746, 1997 https://doi.org/10.1002/(SICI)1097-4628(19970328)63:13<1741::AID-APP5>3.0.CO;2-G
  12. K. Lichtenecker, K. Rother, 'Die Herleitung des logarithmischen Mischungsgesetz es aus allgemeinen Prinzipien der stationaren Stomung,' Physikalische. Zeitschrift. Vol. 32, pp. 255-260, 1931
  13. H. Ragossnig, A. Feltz, 'Characterization of dielectric powders by a new defined form factor,' Journal of the European Ceramic Society, Vol. 18, pp. 429-444, 1998 https://doi.org/10.1016/S0955-2219(97)00146-5
  14. Looyenga H., 'Dielectric Constants of Heterogeneous Mixture', Physica, Vol. 31, pp. 401-406, 1965 https://doi.org/10.1016/0031-8914(65)90045-5
  15. M.E. Achour, M. EI Malhi, J.L. Miane, F. Carmona, F. Lahjomri, 'Microwave Properties of Carbon Black-Epoxy Resin Composites and Their Simulation by Means of Mixture Laws', J. of Polymer Science, Vol. 73, pp. 969-973, 1999
  16. D. Pantea, H. Darmstadt, S. Kaliaguine, C. Roy, 'Electrical conductivity of conductive carbon blacks: influence of surface chemistry and topology,' Applied Surface Science, Vol. 217, pp. 181-193, 2003 https://doi.org/10.1016/S0169-4332(03)00550-6