Linear viscoelastic behavior of branched polybutadiene: A fractional calculus approach

Abstract

A rheological constitutive equation for complex polymeric materials is derived starting from a special formulation of the Laplace transformed relaxance. Material functions such as the complex modulus Gym), the relaxation modulus G(t) and the relaxation time spectrum H(A) are derived. These material functions contain six material parameters, which divide these functions into three characteristic regions: the plateau region, which is in fact a power law region with a small slope, and, towards smaller frequencies, two additional power law regions with different slopes. The comparison of the measured dynamic moduli of modified polybutadienes with the predictions of the proposed phenomenological model shows good agreement. Due to the fact that the mentioned material functions can easily be used, this model represents a tool for the quantitative description and discrimination of certain materials showing intermediate power law regions.