25 - Frequency dependent conductivity, microwave dielectric relaxation and proton dynamics

Summary

Definitions

Electrical properties can be determined at various frequencies. The interaction between an electromagnetic wave and condensed matter can be described using permittivity and conductivity concepts. Fig. 25.1 shows the permittivity, a, versus frequency, v (or more usually ω= 2πν). In the high frequency region, there are various resonances arising from ionic (molecular) and electronic motions. The latter are usually described in terms of optical spectroscopy. In the low frequency region, on the other hand, dipolar and space charge relaxations, usually called dielectric relaxation, are expected. The space charge region, often observed in usual a.c. conductivity measurements, may be described in terms of a (complex) impedance formalism (see Chapters 26 & 27). These relaxations are directly related to the bulk conductivity and to electrode/electrolyte interfacial phenomena. They depend strongly on the microstructure on a 0.1–100 urn scale (porosity, surface topology) and on chemical reactions at the interface (polarization, diffusion). This low frequency domain corresponds to ‘free charges’, which can move in association with an alternative electric field, while the vibrational region at higher frequencies corresponds to ‘atom bonded fixed charges’ (‘dipoles’).

How are ions able to move in a solid? The standard answer to this question states that two different kinds of ionic motions can be discerned, namely oscillatory motion and jump diffusion (see Chapter 30). In fact, the motion is not only limited to oscillations and to statistical hopping from site to site.