Combination of a standard viscoelastic model and fractional derivate calculus to the characterization of polymers

Polymeric materials are known to be more or less dispersive and absorptive. In the field of mechanical vibrations, dispersion has for 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 notion of complex Modulus of Elasticity, permits to establish the relation between the real and the imaginary components of the Modulus of Elasticity, i.e. respectively the dynamic and loss moduli. The loss factor is simply determined through taking the quote of these two components of the Modulus of Elasticity. The theoretical background for the interrelations between the dynamic modulus and the loss modulus is found in the Kramers-Kronig relations. However, and 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 behaviour of materials, but all fail in giving a full account of the phenomenon. Among these models, the standard viscoelastic model, or more known as the Zener model, is perhaps the most attractive one. To improve the performance of this model, the concept of fractional derivates has been incorporated into it, and 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 paper is to present the results of applying this model to rubber, both natural and filled, and to some other selected more general polymer.