Better Resolved Low Frequency Dispersions by the Apt Use of Kramers-Kronig Relations, Differential Operators, and All-In-1 Modeling

van Turnhout, J.

doi:10.3389/fchem.2016.00022

Better Resolved Low Frequency Dispersions by the Apt Use of Kramers-Kronig Relations, Differential Operators, and All-In-1 Modeling

Title

Better Resolved Low Frequency Dispersions by the Apt Use of Kramers-Kronig Relations, Differential Operators, and All-In-1 Modeling

Author

van Turnhout, J. (TU Delft OLD ChemE/Organic Materials and Interfaces)

Date

2016-05-11

Abstract

The dielectric spectra of colloidal systems 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 ε′ into ε″ data. This allows us to calculate conduction free ε″ 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 ε′ data. The coefficients of the conversion frames were obtained by kernel matching and by using symbolic differential operators. Logarithmic derivatives and differences of ε′ and ε″ 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. 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 ε′ and ε″ 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 ε′ and ε″ can zoom in on the genuine colloidal relaxations.

Subject

all-in-1modeling,
electrode polarization
KK conversion frames
logarithmic derivatives and differences
matching Debye kernels
multivariate apart-together fitting
spectral resolution
tting,spectralresolution,symbolic differential operators
OA-Fund TU Delft

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http://resolver.tudelft.nl/uuid:3f8f7ed2-9822-4875-99c4-4ff4247a4b92

DOI

https://doi.org/10.3389/fchem.2016.00022

ISSN

2296-2646

Source

Frontiers in Chemistry, 4

Part of collection

Institutional Repository