Comparison of Classical and Fractional Viscoelastic Models for Describing Entangled Polymer Solutions

Fractional viscoelastic models provide an excellent description of rheological data for polymer systems with power-law behavior. However, the physical interpretation of their model parameters, which carry fractional units of time, remains elusive. We show that for poly(ethylene oxide) (PEO) solutions, the fractional Maxwell model (FMM) requires fewer model elements than classical spring-dashpot models for a reasonable description of the data and that it can be applied consistently to solutions with varying degrees of viscoelasticity. The fractional parameters exhibit scaling laws similar to classical parameters as a function of polymer concentration. To attach physical meaning to the fractional parameters, we derive an analytical expression for the relaxation time spectrum associated with the FMM and find it to be equivalent to the empirical dual asymptote model.