Rheological and molecular characterization of linear backbone flexible polymers with the Cole-Cole model relaxation spectrum

The empirical Cole-Cole distribution is an analytical three parameter model of the relaxation spectra that provides accurate fits to experimental dyna mic viscosity data for many systems of commercial linear backbone flexible polymers. We demonstrate that for disparate systems of polyethylenes, the t hree Cole-Cole model parameters have simple power law relationships to mome nts of the molecular weight distribution enabling direct molecular interpre tation of the mechanical relaxation spectrum. A simple relationship between the Cole-Cole distribution and the Cross model for the non-linear flow cur ve can be deduced utilizing the empirical Cox-Merz rule. Accurately represe nting the linear viscoelastic material functions with empirical analytical relaxation spectra containing relatively few fitting parameters that can be readily interpreted is a major advance in polymer characterization. The th ree Cole-Cole parameters effectively replace single point material characte rizations such as melt flow index. Development of higher resolution polymer characterization methods is imperative with the advent of metallocene cata lyst technology, which enables the molecular weight and backbone architectu re to be carefully controlled.