Characterization of polymers by means of a standard viscoelastic model and fractional derivate calculus

Polymeric materials are known to be more or less dispersive and absorptive. Dispersion has a consequence that the dynamic modulus is frequency dependent, and absorption is exhibited by the fact that these materials have the ability to absorb energy under vibratory motion. The phenomenon of dispersion in conjunction with the powerful notion of complex Modulus of Elasticity (MOE), permits to establish the relation between the real and the imaginary components of the MOE, that is, respectively the Storage and loss moduli. The loss factor is simply determined through taking the Ratio of these two MOE components. The theoretical background for the interrelations between the Storage modulus and the loss modulus is found in the Kramers-Kronig relations. However, due to the mathematical difficulties encountered in using the exact expressions of these relations, approximations are necessary for applications in practical situations. On the other hand, several simple models have been proposed to explain the viscoelastic behavior of materials, but all fail in giving a full account of the phenomenon. Among these models, the standard viscoelastic model, better known as the Zener model, is perhaps the most attractive. To improve the performance of this model, the concept of fractional derivates has been incorporated into it, which results in a four-parameter model. Applications have also shown the superiority of this model when theoretical predictions are compared to experimental data of different polymeric materials. The aim of this article is to present the results of applying this model to rubber, both natural and filled, and to some other selected more general polymer.