The Dynamics of Entangled Polymer Molecules.

Available from UMI in association with The British Library. Requires signed TDF. Functional integrals for the motion of polymer molecules are developed from the Langevin equations describing the motion of an unentangled molecule. The applicability of Gauss winding number as a dynamic constraint is considered. This constraint is included in the functional integrals and a model for the dynamics of one molecule entangled with many others developed, using an average over all the other molecules. The model is applied to rigid ring and rod molecules and gives a reptation like t^ {1/2} behavior. This calculation illustrates the importance of the number of constraints used and a method of calculating this number developed. The model is applied to a motion of a single polymer molecule and physical properties are calculated. The results for centre of mass diffusion Dalpha1/N ^2 and longest relaxation time gamma, alphaN^{35} are in agreement with experimental results, but the predictions for some other physical properties are poor, for example eta(0)alphaN ^{25}. Calculation of the diffusion of a point on the molecule gives a reptation like of behaviour of t^{1/2} at small t, changing first to t^{1/4 } and then to t as t increases.