Power law susceptibility function for the analysis of anomalous spectral response
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912062192484352 |
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| author | Allagui, Anis Balaguera, Enrique H. |
| author_facet | Allagui, Anis Balaguera, Enrique H. |
| contents | The extensions of the classical Debye model of susceptibility of dielectric materials to the well-known Cole-Cole, Davidson- Cole, or the Havriliak-Negami models is done by introducing non-integer power parameters to the frequency-domain function. This is very often necessary in order to account for anomalous deviations of the experimental data from the ideal case. The corresponding time-domain descriptions expressed in terms of the relaxation or response functions are in the form of first-order differential equations for the case of Debye model, but involves relatively complex integro-differential operators for the modified ones. In this work, we study the extension of the time-domain kinetic equation describing the Debye polarization function to include two extra degrees of freedom; one to transform the first-order time derivative of the polarization function to the Caputo fractional-order time derivative and another to change the linear term to a power term. From an electrical perspective, it results in a constant-phase element with two fractional parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_05219 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Power law susceptibility function for the analysis of anomalous spectral response Allagui, Anis Balaguera, Enrique H. Materials Science Applied Physics The extensions of the classical Debye model of susceptibility of dielectric materials to the well-known Cole-Cole, Davidson- Cole, or the Havriliak-Negami models is done by introducing non-integer power parameters to the frequency-domain function. This is very often necessary in order to account for anomalous deviations of the experimental data from the ideal case. The corresponding time-domain descriptions expressed in terms of the relaxation or response functions are in the form of first-order differential equations for the case of Debye model, but involves relatively complex integro-differential operators for the modified ones. In this work, we study the extension of the time-domain kinetic equation describing the Debye polarization function to include two extra degrees of freedom; one to transform the first-order time derivative of the polarization function to the Caputo fractional-order time derivative and another to change the linear term to a power term. From an electrical perspective, it results in a constant-phase element with two fractional parameters. |
| title | Power law susceptibility function for the analysis of anomalous spectral response |
| topic | Materials Science Applied Physics |
| url | https://arxiv.org/abs/2410.05219 |