Dielectric Relaxation as an Independent Examination of Relaxation Mechanisms in Entangled Polymers Using the Discrete Slip-Link Model

Dielectric spectroscopy is often used as a tool complementary to rheology for investigation of relaxation processes of a viscoelastic medium. In particular, dielectric relaxation of type-A polymers reveals the autocorrelation function of the end-to-end vector of a chain, whereas the relaxation modulus is the autocorrelation function for stress, which depends on more-local structural moments of the chain conformation. Here we examine published data for mono-disperse linear, bidisperse linear and star-branched polyisoprene using the discrete slip-link model (DSM). Although the DSM makes predictions very similar to tube theory for linear viscoelasticity, there are some noticeable differences in the predicted contributions of different processes. Also, the DSM uses a single mathematical object for blends and varying chain architectures, meaning that the two adjustable parameters should be independent of molecular weight, blending, architecture or flow field. Here we use one set of parameters (aside from the temperature dependence of friction) to predict both the rheology and dielectric relaxation for all these systems as a strong test of the theory. We find that all circumstances save one are well described. Namely, dilute long chains in a sea of short chains can be predicted rheologically, but dielectric relaxation data show a reduction in the relaxation time of long chains greater than that predicted by either the DSM or the expected Rouse motion. We find that a modified Liklitman-McLeish model makes nearly identical predictions. The dilute long-chain contribution to dielectric relaxation remains a challenge for all entanglement theories.