Dipole loss average

The width of the dielectric loss peak given by equation (9.28b) can be shown to be 1.14 decades (see problem 9.3). Experimentally, loss peaks are often much wider than this. A simple test of how well the Debye model fits in a particular case is to make a so-called Cole-Cole plot, in which s" is plotted against e. It is easy to show from equations (9.28) that the Debye model predicts that the points should lie on a semi-circle with centre at [(fis + oo)/2, 0] and radius (e — Soo)/2- Figure 9.3 shows an example of such a plot. The experimental points lie within the semi-circle, corresponding to a lower maximum loss than predicted by the Debye model and also to a wider loss peak. A simple explanation for this would be that, in an amorphous polymer, the various dipoles are constrained in a wide range of different ways, each leading to a different relaxation time r, so that the observed values of s and e" would be the averages of the values for each value of r (see problem 9.4). 

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