Frequency dependence ionic conductivity

The dramatic slowing down of molecular motions is seen explicitly in a vast area of different probes of liquid local structures. Slow motion is evident in viscosity, dielectric relaxation, frequency-dependent ionic conductance, and in the speed of crystallization itself. In all cases, the temperature dependence of the generic relaxation time obeys to a reasonable, but not perfect, approximation the empirical Vogel-Fulcher law ... 

In contrast to a-Agl, structurally disordered ionic materials usually exhibit strongly frequency-dependent ionic conductivities. Examples... 

Fig. 2. Frequency dependent ionic conductivity was measured at 25°. C. R= IL/gelatin...

The concentration dependence of ionic mobility at high ion concentrations and also in the melt is still an unsolved problem. A mode coupling theory of ionic mobility has recently been derived which is applicable only to low concentrations [18]. In this latter theory, the solvent was replaced by a dielectric continuum and only the ions were explicitly considered. It was shown that one can describe ion atmosphere relaxation in terms of charge density relaxation and the elctrophoretic effect in terms of charge current density relaxation. This theory could explain not only the concentration dependence of ionic conductivity but also the frequency dependence of conductivity, such as the well-known Debye-Falkenhagen effect [18]. However, because the theory does not treat the solvent molecules explicitly, the detailed coupling between the ion and solvent molecules have not been taken into account. The limitation of this approach is most evident in the calculation of the viscosity. The MCT theory is found to be valid only to very low values of the concentration. 

Kahnt H (1991) Ionic transport in oxide glasses and frequency dependence of conductivity. Ber Bunsenges Phys Chem 95 1021... 

Let us summarize by modeling the velocity autocorrelation function using Debye-Huckel type interactions between charged point defects in ionic crystals, one can evaluate the frequency-dependent conductivity and give an interpretation of the universal dielectric response. 

Using the theory presented in Sections II and VII, we find in analytic form the frequency dependence of the ionic complex conductivity. The features of this dependence are as follows. 

Conventional two-electrode dc measurements on ceramics only yield conductivities that are averaged over contributions of bulk, grain boundaries and electrodes. Experimental techniques are therefore required to split the total sample resistance Rtot into its individual contributions. Four-point dc measurements using different electrodes for current supply and voltage measurement can, for example, be applied to avoid the influence of electrode resistances. In 1969 Bauerle [197] showed that impedance spectroscopy (i.e. frequency-dependent ac resistance measurements) facilitates a differentiation between bulk, grain boundary and electrode resistances in doped ZrC>2 samples. Since that time, this technique has become common in the field of solid state ionics and today it is probably the most important tool for investigating electrical transport in and electrochemical properties of ionic solids. Impedance spectroscopy is also widely used in liquid electrochemistry and reviews on this technique be found in Refs. [198 201], In this section, just some basic aspects of impedance spectroscopic studies in solid state ionics are discussed. 

A pair of 1 cm2 area plates spaced apart by 0.25 mm and filled with a resin having a permittivity of 10 (a typical value early in cure) has a capacitance of about 35 pF. The HP4192A has a tan 5X accuracy of 0.002 when measuring 35 pF at 1000 Hz 18), which is satisfactory for most resin studies at that frequency. However, the tan 5X accuracy of the HP4192A degrades to about 0.05 at 5 Hz, which limits the smallest conductivity that can be measured. In the final stages of typical cures, e approaches a value of 4-5, while e" approaches a value that depends on frequency. At low frequencies, the e" value is usually dominated by ionic conductivity, denoted by ct (see Sect. 3.1.1). In this case, the resistance Rx is L/ctA, which when combined with Eq. (2-16) yields... 

The conducting properties of a liquid in a porous medium can provide information on the pore geometry and the pore surface area [17]. Indeed, both the motion of free carriers and the polarization of the pore interfaces contribute to the total conductivity. Polymer foams are three-dimensional solids with an ultramacropore network, through which ionic species can migrate depending on the network structure. Based on previous works on water-saturated rocks and glasses, we have extracted information about the three-dimensional structure of the freeze-dried foams from the dielectric response. Let be d and the dielectric constant and the conductivity, respectively. Dielectric properties are usually expressed by the frequency-dependent real and imaginary components of the complex dielectric permittivity ... 

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