A modified fractional model to describe the entire viscoelastic behavior of polybutadienes from flow to glassy regime

The dynamic mechanical behavior of a series of monodisperse polybutadienes has been investigated from the flow regime to the glassy state. Assuming a linear superposition of the entanglement and glass behavior a mathematical model of the spectrum of relaxation times is developed. It consists in a self-similar spectra for the entanglement contribution and a Fractional Maxwell Fluid (FMF) for the glassy contribution. The model closely represents the master curves of dynamic moduli over 15 logarithmic decades of frequency with three parameters for the flow regime (GN ⁰ _{N 0} and a cut-off parameter _max) and four parameters for the FMF. It is shown that one of the parameter of the FMF is similar to the power-law exponent of a self-similar spectra previously proposed in the literature to model the transition to glass.