Application of Fractional Viscoelastic Models to Amorphous Polymers

Abstract

Fractional calculus is a useful mathematical tool to describe viscoelastic materials showing power-law relaxation behavior, characteristic of inhomogeneous systems. In this study, we applied the 3-elements fractional Maxwell model containing a power law element in addition to viscous and elastic elements to the viscoelastic properties of amorphous polymers. In the case of reorientation mode, which is the main relaxation process of the rubbery polymers, the 3-elements fractional Maxwell provides a relatively broad terminal relaxation than the Rouse-Zimm model, which has already been well-established for the viscoelastic response of linear polymers. This result could be attributed to the polymeric systems being well coarse-grained over a long-time scale. On the other hand, the model well described the frequency dependence of the complex modulus of the glassy component of amorphous polymers.