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
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.
Received: 27 January 2005
Revised: 26 April 2005
Accepted manuscript online:
PACS:
77.22.Ch
(Permittivity (dielectric function))
Fund: 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.
Cite this article:
Wei En-Bo (魏恩泊), Gu Guo-Qing (顾国庆), Yu Kin-Wah (余建华) Dielectric responses of graded composites having generalized gradation profiles 2006 Chinese Physics 15 182
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