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

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          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.

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          Most cited references11

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          Analysis of complex dielectric spectra. I. One-dimensional derivative techniques and three-dimensional modelling

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            Electrode polarization in dielectric measurements: a review

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              Analysis of the Dielectric Permittivity of Suspensions by Means of the Logarithmic Derivative of Its Real Part

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                Author and article information

                Contributors
                Journal
                Front Chem
                Front Chem
                Front. Chem.
                Frontiers in Chemistry
                Frontiers Media S.A.
                2296-2646
                11 May 2016
                2016
                : 4
                : 22
                Affiliations
                Department of Chemical Engineering, Sect. Organic Materials and Interfaces, Delft University of Technology Delft, Netherlands
                Author notes

                Edited by: Raúl A. Rica, ICFO - The Institute of Photonic Sciences, Spain

                Reviewed by: Hamit Yurtseven, Middle East Technical University, Turkey; Francisco José Arroyo, University of Jaen, Spain

                *Correspondence: J. van Turnhout j.vanturnhout@ 123456tudelft.nl

                This article was submitted to Physical Chemistry and Chemical Physics, a section of the journal Frontiers in Chemistry

                Article
                10.3389/fchem.2016.00022
                4862991
                27242997
                7d2aa94f-9dec-453f-8586-2a6687e60529
                Copyright © 2016 van Turnhout.

                This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

                History
                : 19 March 2016
                : 25 April 2016
                Page count
                Figures: 25, Tables: 1, Equations: 80, References: 36, Pages: 19, Words: 13141
                Categories
                Physics
                Original Research

                all-in-1modeling,electrode polarization,kk conversion frames,logarithmic derivatives and differences,matching debye kernels,multivariate apart-together fitting,spectral resolution,symbolic differential operators

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