Departures from the Debye model

The dependence of e on s may be used to test how well the Debye model fits a real case. If we eliminate the parameter cot between Equations (3.25) and (3.26) we obtain 

This is the equation of a circle, centre [(es + e00)/2,0], radius (es- eoc)/2, so that a plot of e against e should give a semicircle, as shown in Fig. 3.3. Experimental results for many polar liquids give excellent agreement with this theoretical curve, their relaxation times being of the order of 10 11 s. 

Relaxations observed in polymers show broader dispersion curves and lower loss maxima than those predicted by the Debye model, and the (s s ) curve falls inside the semicircle. This led Cole and Cole (1941) to suggest the following semi-empirical equation for dielectric relaxations in polymers  

Equation (3.30) corresponds to a skewed distribution of relaxation times about r, but it again has no particular theoretical foundation apart from the improved agreement with experiment for certain materials. 

More recently, it has been suggested that a departure from the assumed exponential form of the approach to equilibrium may be responsible for the breadth of dipolar relaxation in polymers. A decay function that describes a wide range of slow relaxation processes is the so-called stretched exponential  

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