Frontiers in Chemistry (May 2016)
Better resolved low frequency dispersions by the apt use of Kramers-Kronig relations, differential operators and all-in-1 modelling
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 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. The development of all-in-1 modelling 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 modelling of a suspension with the complex dipolar coefficient. It guarantees a secure correction for the electrode polarization, so that the modelling with the help of the differences and can zoom in on the genuine colloidal relaxations.
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