| Standard analytical techniques like chromatography and spectrometry are not sensitive enough to resolve architectural details in branched polymer melts such as metallocene-catalyzed polyethylene to industrially acceptable levels. This has led to the belief that linear rheology, which is highly responsive to subtle differences in branching structure, can be employed as an analytical technique. A major difficulty hindering the application of rheology as an analytical tool has been the inability of the current analytical theory for branched polymers, which is based on the idea of "dynamic dilution", to describe the physics of branch point motion. We examine shortcomings of this theory, including the problem of branch point motion, using three case studies. We use a simulation model called the dual slip link model in which entanglements between chains are modeled as slip links that couple the dynamics of pairs of chains.; First, in the late-time relaxation of symmetric stars we investigate the breakdown of the molecular picture implied by the "dynamic dilution" theory, by monitoring the dielectric and stress relaxation functions. We present a terminal relaxation model using the slip link model that offers a better description of the late-time dynamics.; Next, we address the failure of the analytical theory to predict the anomalously slow viscoelastic response of asymmetric stars. We need to distinguish between the first-passage time and complete retraction time of the asymmetric arm in order to correctly set the timescale for the diffusion of the branch point. Although the slip link model fails for long arms, where it over-predicts the relaxation time, it points out that the timescale which sets the frequency of the branch point motion should be larger than the first-passage time of an arm.; Finally, we study the effects of polydispersity on stars and H-polymers and find that the viscoelasticity of star polymers is insensitive to moderate amounts of poly-dispersity. However, H-polymers are extremely sensitive, especially to polydispersity in the arms. We submit that the relaxation of H-polymers is greatly accelerated if any one of the four arms is short. We suggest the experimental synthesis of asymmetric H-polymers in order to test this hypothesis. |
