# Dictionary:Cole-Cole relaxation model

(kōl kōl) A model for induced polarization (IP) effects in which the effective impedance varies as a power of the frequency. The complex resistivity ${\displaystyle \rho (\omega )}$ is given by
${\displaystyle \rho (\omega )=R_{0}\left\{1-m\left[1-{\frac {1}{\left(1+i\omega \tau \right)^{c}}}\right]\right\}}$,
where Ro is the dc resistivity, ${\displaystyle \tau }$ is the time constant, and c is the frequency dependence. Typical ranges for parameters are m=0.1 to 1.0, depending on the mineral content, ${\displaystyle \tau }$ = 10-4 to 104 depending on grain size, and c=0.2 to 0.6 depending on the particle size distribution. Compare Warburg impedance, for which the value of c is 0.5.