Cole Complex compliance

We will call this the HN function. They then proposed the use of a Cole-Cole plot, together with Eq. 5.61, to represent complex compliance data for polymeric liquids. Another generalization involving the introduction of an additional exponential parameter was proposed by Friedrich and Braun [136]. 

The complex modulus components E and E" (or G and G" or their compliance counterparts), are functions of the loading frequency or angular frequency co. To try to identify these functions, it is usual to determine E and E" experimentally in a wide interval of temperature and frequency and to build E" = f(E ) (Cole-Cole) plots. 

Marin and Graessley [137] used Cole-Cole plots, together with the original Cole-Cole function (Eq. 5.60) to interpret data for several polystyrenes prepared by anionic polymerization. They plotted the imaginary versus the real components of the complex retardational compliance, (fiS), defined as] (o)- l/(i (U t q). They found that for the sample with a molecular weight of about 37,000, which is near the critical molecular weight for viscosity, M, a plot of " co) versus J co) took the form of a circular arc and could thus be fitted to Eq. 5.62, by analogy with Eq. 5.60. 

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