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# Havriliak-Negami relaxation

Havriliak-Negami relaxation is an empirical modification of the Debye relaxation model, accounting for the asymmetry and broadness of the dielectric dispersion curve. The model was first used to describe the dielectric relaxation of some polymers1, by adding two exponential parameters to the Debye equation:

$\hat{\varepsilon}(\omega) = \varepsilon_{\infty} + \frac{\Delta\varepsilon}{(1+(i\omega\tau)^{\alpha})^{\beta}},$

where $\varepsilon_{\infty}$ is the permittivity at the high frequency limit, $\Delta\varepsilon = \varepsilon_{s}-\varepsilon_{\infty}$ where $\varepsilon_{s}$ is the static, low frequency permittivity, and τ is the characteristic relaxation time of the medium. The exponents α and β describe the asymmetry and broadness of the corresponding spectra.