Limitations of kramers-kronig transform for calculation of the DC conductance magnitude from dielectric measurements

The Kramers-Kronig (K-K) transform relates the real and imaginary parts of the complex susceptibility as a consequence of the principle of causality. It is a special case of the Hilbert transform and it is often used for estimation of the DC conductance from dielectric measurements. In this work, the practical limitations of a numerical implementation of the Kramers-Kronig transform was investigated in the case of materials that exhibit both DC conductance and quasi-DC (QDC) charge transport processes such as epoxy resins. The characteristic feature of a QDC process is that the real and imaginary parts of susceptibility (permittivity) follow fractional power law dependences with frequency with the low frequency exponent approaching -1. Dipolar relaxation in solids on the other hand has a lower frequency exponent <;1. The computational procedure proposed by Jonscher for calculation of the K-K transform involves extrapolation and truncation of the data to low frequencies so that convergence of the integrals is ensured. The validity of the analysis is demonstrated by performing K-K transformation on real experimental data and on theoretical data generated using the Dissado-Hill function. It has been found that the algorithm works well for dielectric relaxation responses but it is apparent that it does not work in the case of a low frequency power law in which the low frequency exponent approaches -1, i.e. in the case of QDC responses. In this case convergence can only be guaranteed by extrapolating the low frequency power law over many decades towards zero frequency.