Molecular Mass Distribution of Polydisperse Linear Polymers from Rheological Data

It is widely known that the molecular mass distribution (MMD) of an industrial polymer has an influence on its flow properties. Various propositions have been made (e.g. by Malkin et al. [MaBl+1974]) on how to account for the effect of the different weight fractions of such a polydisperse system. The solutions to this problem are considerations of polymer dynamics, as e.g. carried out in the book by Doi and Edwards [DoEd1986]. These suggest a unique relation between the linear viscoelastic properties of the polymer and its MMD. Anyway, one encounters numerous difficulties when trying to solve the inverse problem by using such models. A different approach uses the flow curve for finding the MMD of a polymer [MaTe1987]. Although this problem is known to be ill-posed, solutions can be found. An investigation of both types of problems is made and the possibilities for obtaining a solution are discussed, and compared on the basis of the underlying mathematics and physics. From this comparison, a new method is developed which is capable of MMD calculation from different rheological data with an emphasis on simplicity, short calculation time and versatility. The method is tested on five different (uni- and bimodal) polymers and the results are compared to earlier methods.