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DIELECTRIC LOSS AND RELAXATION - II T he description of dielectric loss and relaxation with emphasis on materials in the condensed phase is continued in this chapter. We begin with Jonscher's universal law which is claimed to apply to all dielectric materials. Distinction is made here between dielectrics that show negligible conduction currents and those through which appreciable current flows by carrier transport. Formulas for relaxation are given by Jonscher for each case. Again, this is an empirical approach with no fundamental theory to backup the observed frequency dependence of s* according to a power law. The relatively recent theory of Hill and Dissado, which attempts to overcome this restriction, is described in considerable detail. A dielectric may be visualized as a network of passive elements as far as the external circuit is concerned and the relaxation phenomenon analyzed by using the approach of equivalent circuits is explained. This method, also, does not provide further insight into the physical processes within the dielectric, though by a suitable choice of circuit parameters we can reasonably reproduce the shape of the loss curve. Finally, an analysis of absorption in the optical frequency range is presented both with and without electron damping effects. 4.1 JONSCHER'S UNIVERSAL LAW On the basis of experimentally observed similarity of the co-s" curves for a large number of polymers, Johnscher 1 has proposed an empirical "Universal Law" which is supposed to apply to all dielectrics in the condensed phase. Let us denote the exponents at low frequency and high frequency as m and n respectively. Here low and high frequency have a different connotation than that used in the previous chapter. Both low and high frequency refer to the post-peak frequency. The loss factor in terms of the susceptibility function is expressed as
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X ® 2 m \ where 1/CQi and 1/ccb are well defined, thermally activated frequency parameters. The empirical exponents m and n are both less than one and m is always greater than \-n by a factor between 2 and 6 depending on the polymer and the temperature, resulting in a pronounced asymmetry in the loss curve. Both m and n decrease with decreasing temperature making the loss curve broader at low temperatures when compared with the loss curve at higher temperatures. In support of his equation Jonscher points out that the low temperature p-relaxation peak in many polymers is much broader and less symmetrical than the high temperature a-relaxation peak. In addition to polymers the dielectric loss in inorganic materials is associated with hopping of charge carriers, to some extent, and the loss in a wide range of materials is thought to follow relaxation laws of the type: For co » co p fiT (4.2) For CD « co p YYITT -z']Ka>>» (4.3) where the exponents fall within the range 0< m< 1 0<n The physical picture associated with hopping charges between two localized sites is explained with the aid of fig. 3-5 of the previous chapter. This picture is an improvement over the
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