# Difference between revisions of "Dictionary:Cole-Cole relaxation model"

Matthallbot (talk | contribs) (Categorizing pages with HTML math) |
Chrisdinneen (talk | contribs) (Fixed Equations) |
||

Line 1: | Line 1: | ||

{{#category_index:C|Cole-Cole relaxation model}} | {{#category_index:C|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 | + | (kōl kōl) A model for induced polarization (IP) effects in which the effective impedance varies as a power of the frequency. The complex resistivity <math>\rho (\omega) </math> is given by |

− | <center> | + | <center><math>\rho (\omega) = R_0 \left\{ 1-m\left[ 1-\frac {1}{\left(1+i\omega\tau\right)^c}\right] \right\} </math>,</center> |

− | + | where ''R''<sub>''o''</sub> is the dc resistivity, <math> \tau </math> 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, <math>\tau </math> = 10<sup>-4</sup> to 10<sup>4</sup> depending on grain size, and ''c''=0.2 to 0.6 depending on the particle size distribution. Compare [[Dictionary:Warburg_impedance|''Warburg impedance'']], for which the value of ''c'' is 0.5. | |

− | |||

− | where ''R''<sub>''o''</sub> is the dc resistivity, | ||

− | |||

− |

## Revision as of 21:54, 23 February 2015

(kōl kōl) A model for induced polarization (IP) effects in which the effective impedance varies as a power of the frequency. The complex resistivity is given by

where *R*_{o} is the dc resistivity, 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, = 10^{-4} to 10^{4} 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.