First-order approximation, relaxation spectra

Partial master curves of 10 g.dL"l solutions of a,o)-alkaline earth dicarboxylato PBD in xylene at 297 K are reported in Figure 10, and result from a good frequency-temperature superposition of the experimental data.l7 Only the G" master curve of the solution of Be-based HTP is ill-defined due to the poor accuracy in the determination of the very small values of G". The shift factors support an apparent Arrhenius-type of dependence (Figure 11), from which the activation energy of the observed secondary ionic relaxation process was calculated and found to decrease as the radius of the alkaline earth cations increases (Figure 12). One also observes that the relaxation spectrum calculated by the first order approximation of Ninomiya and Ferry S is displaced along the time scale in relation with the cation size (Figure 13). The dynamic behavior of the 10 g.dL solution is obviously... 

Actually, relaxation processes do not follow a first-order kinetics. In a glass there is a relatively wide variety of situations leading to the existence of a spectrum of relaxation times. A static relaxation kinetics can be approximated by... 

Derive an expression for the first-, second-, and third-order approximation of the relaxation spectrum for a Maxwell element in shear. 

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