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Cole–Cole equation
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Cole–Cole equation : ウィキペディア英語版
Cole–Cole equation
The Cole–Cole equation is a relaxation model that is often used to describe dielectric relaxation in polymers.

It is given by the equation
:
\varepsilon^
*(\omega) - \varepsilon_\infty = \frac{1+(i\omega\tau)^{1 - \alpha}}

where \varepsilon^
* is the complex dielectric constant, \varepsilon_s and \varepsilon_\infty are the "static" and "infinite frequency" dielectric constants, \omega is the angular frequency and \tau is a time constant.
The exponent parameter \alpha, which takes a value between 0 and 1, allows to describe different spectral shapes. When \alpha=0, the Cole-Cole model reduces to the Debye model. When \alpha>0, the relaxation is ''stretched'', i.e. it extends over a wider range on a logarithmic \omega scale than Debye relaxation.
Cole-Cole relaxation constitutes a special case of Havriliak-Negami relaxation when the symmetry parameter (β) is equal to 1 - that is, when the relaxation peaks are symmetric. Another special case of Havriliak-Negami relaxation (β<1, α=0) is known as Cole-Davidson relaxation, for an abridged and updated review of anomalous dielectric relaxation in dissored systems see Kalmykov.
== References ==


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