Prediction of Polymer Molecular Weight Distribution from Rheology: Polydimethylsiloxane Blends

We apply a model that connects rheological properties of linear polymer blends with their molecular weight distributions (MWDs). The model is based on the assumption that the relaxation time, ti, of a chain depends on an average molecular weight, M, which determines the effect of the environment where the molecule reptates, and its own molecular weight according to ti = (kE / 0 N G )·M 3.4 - b·Mi b where kE is the constant of proportionality between zero shear viscosity, ho, and weight average molecular weight, Mw, in unimodal polydisperse systems and 0 N G is the plateau modulus. We deduce that the MWD is related to the relaxation spectrum as H(t) = ( 0 N G /b)·M·W(M). Therefore, the MWD is obtained from the relaxation spectrum, which is deduced from the dynamic moduli, G’(w) and G’’(w), constrained by the plateau modulus, the zero shear viscosity and the steady state compliance, 0 e J . The maximum entropy method has been used to solve the integral equation that provides the relaxation spectra from experimental dynamic moduli. The model has been tested in polydimethylsiloxane blends with weight average molecular weight ranging from 94 to 630 kDa and polydispersity from 1.5 to 3.3. Good agreement is found between experimental and calculated MWDs.