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 dynamic viscosity data for many systems of commercial linear backbone flexible polymers. We demonstrate that for disparate systems of polyethylenes, the three Cole-Cole model parameters have simple power law relationships to moments of the molecular weight distribution enabling direct molecular interpretation of the mechanical relaxation spectrum. A simple relationship between the Cole-Cole distribution and the Cross model for the non-linear flow curve can be deduced utilizing the empirical Cox-Merz rule. Accurately representing 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 three Cole-Cole parameters effectively replace single point material characterizations such as melt flow index. Development of higher resolution polymer characterization methods is imperative with the advent of metallocene catalyst technology, which enables the molecular weight and backbone architecture to be carefully controlled.