Molecular weight distributions from linear viscoelastic measurements

A method is presented whereby the molecular weight distribution of a molten polymer can be determined from measured values of the storage and loss moduli (the response of the system to small amplitude oscillatory shear flow). The Curtiss-Bird theory for the constitutive behavior of polymer melts is used. This results in an integral equation relating the moduli to the molecular weight distribution. The method that we describe here uses a regularization scheme with quadratic programming to extract the MWD from the components of the moduli (or, equivalently, from the components of the complex viscosity). We verify the applicability of the scheme by considering concocted data for given molecular weight distributions. The scheme is also used to predict the molecular weight distributions of polystyrene from complex viscosity data that have been presented in the literature. Variations between the predicted and measured molecular weight distributions can be attributed to the inadequacy of the underlying molecular theory at large frequencies. The predicted average molecular weights obtained using the truncated dynamic data are in reasonable agreement with the experimental values.