Modeling the dynamic properties of monodisperse linear polymer melts with wedge spectra

Abstract

A mathematical model of the spectrum of relaxation times for molten linear monodisperse homopolymers has been developed which is the sum of two variations of the well-known wedge spectrum. Adjusting the six parameters of the model allows fitting the storage and loss moduli within experimental error over a range of 10–12 logarithmic decades of frequency which encompass the flow, plateau, transition, and glassy zones of viscoelastic behavior. Model parameters are easily determined with a desktop microcomputer using standard nonlinear least-squares fitting procedures. All six model parameters correspond directly to prominent features of experimental data. The plateau modulus, viscosity, steady-state shear compliance, and the frequency at which the storage and loss moduli cross can all be easily calculated from the model parameters. The limiting low- and high-frequency behaviors of the storage and loss moduli predicted by the model are consistent with experiment and with linear viscoelastic theory. For the transition zone, the model can closely mimic the dynamic behavior predicted by normal-coordinate molecular theories. The model is applied to experimental data for five narrow-distribution polystyrenes having molecular weights in the range of 60 000–540 000.