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

van Turnhout J - Front Chem (2016)

Bottom Line: It proved also useful to go around the KK conversion altogether.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.

View Article: PubMed Central - PubMed

Affiliation: Department of Chemical Engineering, Sect. Organic Materials and Interfaces, Delft University of Technology Delft, Netherlands.

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.

No MeSH data available.


Related in: MedlinePlus

Illustration of the different conversions covered. The resulting ε″kk and dε′∕dlnω will improve the l.f. spectral resolution, both with respect to ohmic conduction and to EP.
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Figure 6: Illustration of the different conversions covered. The resulting ε″kk and dε′∕dlnω will improve the l.f. spectral resolution, both with respect to ohmic conduction and to EP.

Mentions: Figure 6 shows the various conversions we will discuss below. For each we will give the coefficients of the appropriate conversion frames. The main focus will be on getting one liners for the conversion of ε′ to ε″kk and ε″ to dε′∕dlnω. Although, as just said, we will also shortly touch upon the conversion of θ to lnεa or for that matter of ε″ to ε′.


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

van Turnhout J - Front Chem (2016)

Illustration of the different conversions covered. The resulting ε″kk and dε′∕dlnω will improve the l.f. spectral resolution, both with respect to ohmic conduction and to EP.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4862991&req=5

Figure 6: Illustration of the different conversions covered. The resulting ε″kk and dε′∕dlnω will improve the l.f. spectral resolution, both with respect to ohmic conduction and to EP.
Mentions: Figure 6 shows the various conversions we will discuss below. For each we will give the coefficients of the appropriate conversion frames. The main focus will be on getting one liners for the conversion of ε′ to ε″kk and ε″ to dε′∕dlnω. Although, as just said, we will also shortly touch upon the conversion of θ to lnεa or for that matter of ε″ to ε′.

Bottom Line: It proved also useful to go around the KK conversion altogether.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.

View Article: PubMed Central - PubMed

Affiliation: Department of Chemical Engineering, Sect. Organic Materials and Interfaces, Delft University of Technology Delft, Netherlands.

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.

No MeSH data available.


Related in: MedlinePlus