MODELING THE DYNAMIC PROPERTIES OF MONODISPERSE LINEAR POLYMER MELTS WITH WEDGE SPECTRA

A mathematical model of the spectrum of relaxation times for molten li near monodisperse homopolymers has been developed which is the sum of two variations of the well-known wedge spectrum. Adjusting the six par ameters of the model allows fitting the storage and loss moduli within experimental error over a range of 10-12 logarithmic decades of frequ ency which encompass the flow, plateau, transition, and glassy zones o f 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 los s moduli cross can all be easily calculated from the model parameters. The limiting low- and high-frequency behaviors of the storage and los s moduli predicted by the model are consistent with experiment and wit h linear viscoelastic theory. For the transition zone, the model can c losely mimic the dynamic behavior predicted by normal-coordinate molec ular theories. The model is applied to experimental data for five narr ow-distribution polystyrenes having molecular weights in the range of 60 000-540 000.