MOLECULAR-WEIGHT DISTRIBUTIONS FROM LINEAR VISCOELASTIC MEASUREMENTS

A method is presented whereby the molecular weight distribution of a m olten polymer can be determined from measured values of the storage an d loss moduli (the response of the system to small amplitude oscillato ry shear flow). The Curtiss-Bird theory for the constitutive behavior of polymer melts is used. This results in an integral equation relatin g 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 applica bility of the scheme by considering concocted ''data'' for given molec ular weight distributions. The scheme is also used to predict the mole cular weight distributions of polystyrene from complex viscosity data that have been presented in the literature. Variations between the pre dicted and measured molecular weight distributions can be attributed t o the inadequacy of the underlying molecular theory at large frequenci es. The predicted average molecular weights obtained using the truncat ed dynamic data are in reasonable agreement with the experimental valu es.