中国物理B ›› 2006, Vol. 15 ›› Issue (1): 182-189.doi: 10.1088/1009-1963/15/1/029

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Dielectric responses of graded composites having generalized gradation profiles

余建华1, 魏恩泊2, 顾国庆3   

  1. (1)Department of Physics, The Chinese University of Hong Kong, Hong Kong, China; (2)Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China; (3)School of Information Science and Technology, East China Normal University, Shanghai 200062, China
  • 收稿日期:2005-01-27 修回日期:2005-04-26 出版日期:2006-01-20 发布日期:2006-01-20
  • 基金资助:
    Project supported by National Natural Science Foundation of China (Grant Nos 40476062 and 10374026). Yu Kin-Wah acknowledges the support from RGC Earmarked Grant of the Hong Kong SAR Government.

Dielectric responses of graded composites having generalized gradation profiles

Wei En-Bo (魏恩泊)a, Gu Guo-Qing (顾国庆)b, Yu Kin-Wah (余建华)c    

  1. a Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China; b School of Information Science and Technology, East China Normal University, Shanghai 200062, China; c Department of Physics, The Chinese University of Hong Kong, Hong Kong, China
  • Received:2005-01-27 Revised:2005-04-26 Online:2006-01-20 Published:2006-01-20
  • Supported by:
    Project supported by National Natural Science Foundation of China (Grant Nos 40476062 and 10374026). Yu Kin-Wah acknowledges the support from RGC Earmarked Grant of the Hong Kong SAR Government.

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摘要： Under an external uniform electric field, the dielectric response of graded cylindrical composites having generalized dielectric profile inclusions is investigated. The generalized dielectric profile of graded cylindrical inclusion is expressed in the form, $\varepsilon _i (r)=c(b+ r)^k\e^{\beta r}$ where $r$ is the radial variable of the cylindrical inclusions and $c$, $b$, $k$ and $\beta $ are parameters. The local potential solution of generalized dielectric profile graded composites is derived by means of the power series method and the effective dielectric response is predicted in the dilute limit. Moreover, from the result of generalized profile, the analytical solutions of local potentials and the effective responses of graded composites having three cases of dielectric profiles, i.e., the exponential profile $\varepsilon_\i (r)=c\e^{\beta r}$, the general power law profile $\varepsilon_\i (r)=c(b+r)^k$ and the profile $\varepsilon_\i (r)=cr^k\e^{\beta r}$, are sorted out, respectively. In the dilute limit, our exact results are used to test the validity of differential effective dipole approximation (DEDA) for estimating the effective response of graded cylindrical composites, and it is shown that the DEDA is in excellent agreement with the exact result.

关键词: generalized profiles, graded composite, effective response

Abstract: Under an external uniform electric field, the dielectric response of graded cylindrical composites having generalized dielectric profile inclusions is investigated. The generalized dielectric profile of graded cylindrical inclusion is expressed in the form, $\varepsilon _i (r)=c(b+ r)^k{\rm e}^{\beta r}$ where $r$ is the radial variable of the cylindrical inclusions and $c$, $b$, $k$ and $\beta $ are parameters. The local potential solution of generalized dielectric profile graded composites is derived by means of the power series method and the effective dielectric response is predicted in the dilute limit. Moreover, from the result of generalized profile, the analytical solutions of local potentials and the effective responses of graded composites having three cases of dielectric profiles, i.e., the exponential profile $\varepsilon(r)_{\rm i}=c{\rm e}^{\beta r}$, the general power law profile $\varepsilon_{\rm i}(r)=c(b+r)^k$ and the profile $\varepsilon_{\rm i}(r)=cr^k{\rm e}^{\beta r}$, are sorted out, respectively. In the dilute limit, our exact results are used to test the validity of differential effective dipole approximation (DEDA) for estimating the effective response of graded cylindrical composites, and it is shown that the DEDA is in excellent agreement with the exact result.

Key words: generalized profiles, graded composite, effective response

中图分类号:  (Permittivity (dielectric function))

  • 77.22.Ch