Calculation of molecular weight distribution using extended Cole-Cole model and quadratic mixing rule

We suggest a numerical method to calculate molecular weight distribution from linear viscoelastic data. The calculation method consists of three components: (1) a viscoelastic model of a monodisperse polymer as a function of molecular weight; (2) the mixing rule connecting viscoelastic data of monodisperse and polydisperse polymers through molecular weight distribution; (3) an algorithm which calculates the molecular weight distribution from the chosen mixing rule. Since we cannot measure the relaxation modulus of all monodisperse samples, we need an accurate monodisperse model for any molecular weight. It is known that a dynamic test is more reliable than a relaxation test, while the mixing rule needs relaxation modulus. Hence, we should have a smart numerical method that can convert dynamic data to relaxation modulus with the minimum conversion error. If we use the numerical method, then we have to generate numerical data from the model. Then it takes quite a long time. On the other hand, if we have a monodisperse model with the analytical relaxation spectrum, then calculation time can be reduced dramatically. Since the conversion from relaxation modulus to dynamic modulus suffers from smaller errors than the reverse conversion because of ill-posedness of the interconversion, the analytical conversion can be implemented more quickly at an acceptable level of errors. This paper proposes a new method satisfying the requirements.