We investigate the influence of the ohmic character of the electrodes on the impedance spectroscopy of a cell of a dielectric liquid containing ions. According to our calculations, the finite conductivity of the electrodes is responsible for an increasing of the real part of the electrical impedance in the low frequency range. It follows that the anomalous increasing of the resistance of the cell, experimentally observed by several groups, could be related also to the exchange of charge at the electrodes. Our analysis is based on a generalization of the Butler-Wolmer equation, for small values of the external voltage.
The Nd–Nd and Nd–Yb energy transfer processes are studied in lead fluoroindogallate glasses with the following molar composition: 30PbF2–20GaF3–15InF3–15ZnF2–(20–X)CaF2–XNdF3 (with X=0.1, 0.5, 1, 2, 4, and 5), 30PbF2–20GaF3–15InF3–15ZnF2–(20–X)CaF2–XYbF3 (with X=0.1, 0.5, 1, 2, 3, and 5), and 30PbF2–20GaF3–15InF3–15ZnF2–(19–X)CaF2–XYbF3–1NdF3 (with X=0.1, 0.5, 1, 2, 3, and 5.5). The Dexter, Yokota–Tanimoto, and Holstein formalisms were used to treat the experimental data. The following microparameters of energy transfer were obtained: CDD(Nd–Nd)≈7×10−40, CDA(Nd–Nd)=2.5×10−40, and CDA(Nd–Yb)≈3×10−40 cm6/s. It was also shown that the energy migration between Nd ions depends on the third power of temperature (T3) up to a saturation value of about 80 K. This behavior was attributed to the site to site energy migration. The Yb doped samples presented no nonradiative losses for the Yb3+ emission at 969 nm.
The analysis of Macdonald for electrolytes is generalized to the case in which two groups of ions are present. We assume that the electrolyte can be considered as a dispersion of ions in a dielectric liquid, and that the ionic recombination can be neglected. We present the differential equations governing the ionic redistribution when the liquid is subjected to an external electric field, describing the simultaneous diffusion of the two groups of ions in the presence of their own space charge fields. We investigate the influence of the ions on the impedance spectroscopy of an electrolytic cell. In the analysis, we assume that each group of ions have equal mobility, the electrodes perfectly block and that the adsorption phenomena can be neglected. In this framework, it is shown that the real part of the electrical impedance of the cell has a frequency dependence presenting two plateaux, related to a type of ambipolar and free diffusion coefficients. The importance of the considered problem on the ionic characterization performed by means of the impedance spectroscopy technique was discussed.
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