Abstract
The dielectric spectra of colloidal systems and other dielectric media often contain a typical low frequency dispersion, which usually remains unnoticed, because of the presence of strong conduction losses. The KK relations offer a means for converting ' into " data. This allows us to calculate conduction free " spectra in which the l.f. dispersion will show up undisturbed. This interconversion can be done on line with a moving frame of logarithmically spaced ' data. The coefficients of the conversion frames were obtained by kernel matching and by using symbolic differential operators. Logarithmic derivatives and differences of ' and " provide another option for conduction free data analysis. These difference-based functions actually derived from approximations to the distribution function, have the additional advantage of improving the resolution power of dielectric studies. A high resolution is important because of the rich relaxation structure of colloidal suspensions and most other dielectric media. The development of all-in-1 modeling facilitates the conduction free and high resolution data analysis. This mathematical tool allows the apart-together fitting of multiple data and multiple model functions. It proved also useful to go around the KK conversion altogether. This was achieved by the combined approximating ' and " data with a complex rational fractional power function. The all-in-1 minimization turned out to be also highly useful for the dielectric modeling of a suspension with the complex dipolar coefficient. It guarantees a secure correction for the electrode polarization, so that the modeling with the help of the differences ' and " can zoom in on the genuine colloidal relaxations.
Original language | English |
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Title of host publication | Current Topics on Chemistry and Biochemistry |
Editors | Charbell Miguel Haddad Kury |
Publisher | B P International |
Chapter | 3 |
Pages | 40-82 |
Volume | 5 |
ISBN (Electronic) | 978-93-5547-856-6 |
ISBN (Print) | 978-93-5547-855-9 |
DOIs | |
Publication status | Published - 2022 |
Bibliographical note
Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-careOtherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.
Keywords
- All-in-1modeling
- electrode polarization
- KK conversion frames
- logarithmic derivatives and differences
- matching Debye kernels
- multivariate apart-together fitting
- spectral resolution
- symbolic differential operators