Mode-coupling theory and polynomial fitting functions: A complex-plane representation of dielectric data on polymers

Recently, it has been shown that the higher-order $A_3$ and $A_4$ scenarios of the mode-coupling theory (MCT) are in many cases capable of providing a good description of the complicated dielectric spectra often encountered in polymeric systems. In this paper, more data from dielectric measurements on poly(ethylene terephthalate), poly(vinylidene fluoride), Nylon-66, poly(chlorotrifluoroethylene) (PCTFE), and the polymer gel system poly(acrylonitrile)–ethylene carbonate–propylene carbonate are evaluated within the $A_4$ scenario of the MCT. For all these systems, very good agreement is found between the theoretical and experimental spectra. The data analysis is demonstrated to be facilitated considerably by plotting the data in the complex plane whereby the elliptic functions derived from the theory for the frequency-dependent dielectric function can be replaced by polynomials. For PCTFE, the scaling behavior predicted by the MCT could be verified and the temperature dependences of the extracted scaling parameters were found to be consistent with theory.