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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

Another illustration that Δε′ and Δε″cf increase the resolution of dielectric spectroscopy. We simulated the different spectra of 2 nearby HN relaxations, which fuse together into a single ε″h peak. By contrast, the new differences do hint, even for these very close by relaxations, to the presence of 2 relaxations. This is in part due to the absence of the conduction loss in Δε′ and Δε″cf.
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Figure 18: Another illustration that Δε′ and Δε″cf increase the resolution of dielectric spectroscopy. We simulated the different spectra of 2 nearby HN relaxations, which fuse together into a single ε″h peak. By contrast, the new differences do hint, even for these very close by relaxations, to the presence of 2 relaxations. This is in part due to the absence of the conduction loss in Δε′ and Δε″cf.

Mentions: An enhanced resolution becomes of course more acute if the relaxation processes tend to overlap as often occurs in colloidal systems. Such a merger is also the case for the 2 HN relaxations considered in Figure 15. In Figure 18 we compare the ensuing spectra of Δε′ and Δε″cf of these associated HN relaxations with the traditionally used spectrum of ε″h, which at low frequencies also contains the additional conduction loss. The 2 underlying HN relaxations can in particularly be conceived in the Δε″cf spectrum. The distinction in the Δε′ spectrum is less, but better than in the ε″-curve, which merely shows one united peak.


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)

Another illustration that Δε′ and Δε″cf increase the resolution of dielectric spectroscopy. We simulated the different spectra of 2 nearby HN relaxations, which fuse together into a single ε″h peak. By contrast, the new differences do hint, even for these very close by relaxations, to the presence of 2 relaxations. This is in part due to the absence of the conduction loss in Δε′ and Δε″cf.
© Copyright Policy
Related In: Results  -  Collection

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

Figure 18: Another illustration that Δε′ and Δε″cf increase the resolution of dielectric spectroscopy. We simulated the different spectra of 2 nearby HN relaxations, which fuse together into a single ε″h peak. By contrast, the new differences do hint, even for these very close by relaxations, to the presence of 2 relaxations. This is in part due to the absence of the conduction loss in Δε′ and Δε″cf.
Mentions: An enhanced resolution becomes of course more acute if the relaxation processes tend to overlap as often occurs in colloidal systems. Such a merger is also the case for the 2 HN relaxations considered in Figure 15. In Figure 18 we compare the ensuing spectra of Δε′ and Δε″cf of these associated HN relaxations with the traditionally used spectrum of ε″h, which at low frequencies also contains the additional conduction loss. The 2 underlying HN relaxations can in particularly be conceived in the Δε″cf spectrum. The distinction in the Δε′ spectrum is less, but better than in the ε″-curve, which merely shows one united peak.

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