Rheology of polydisperse star polymer melts: Extension of the parameter-free tube model of Milner and McLeish to arbitrary arm-length polydispersity

This paper considers the extension of the parameter-free tube model of Milner and McLeish for stress relaxation in melts of monodisperse star polymers to star polymers whose arms have a continuous molecular weight distribution such as the Flory distribution in the case of star-nylons and star-polyesters. Exact expressions are derived for the relaxation spectrum and the relaxation modulus for star polymers having an arbitrary continuous arm-length distribution. For a Flory distribution a comparison is made with results of dynamic measurements on a melt of 8-arm poly(e-caprolactone) (PCL) stars. An excellent quantitative agreement over a large frequency range is found, however, only if one treats, in contrast with the original parameter-free tube model approach, the entanglement molecular weight that determines the relaxation spectrum as a fitting parameter independent of the entanglement molecular weight of the linear PCL. This discrepancy is not in anyway related to the polydispersity in arm-length, but a consequence of the thermorheological complexity of the PCL stars. A similar discrepancy has been observed for hydrogenated polybutadiene stars, as described by Levine and Milner.