Application of fractional calculus to modelling of relaxation phenomena of organic dielectric materials

We have developed a model using fractional calculus for the isochronal description of the relative complex permittivity, taking into account three relaxation phenomena. The relaxation processes in organic dielectric materials (semi-crystalline polymers) are associated to molecular motions to a new structural equilibrium of less energy. Traditional calculus is limited to describe relaxation phenomena associated with the complex structure of semi-crystalline polymers, and fractional calculus becomes an alternative. The differential equations obtained for this model have derivatives of fractional order between 0 and 1, and the isochronal diagrams of the relative complex permittivity (epsilon(r)' and epsilon(r)") show clearly three dielectric relaxation phenomena. To test the validity of the model proposed we have used measurements of epsilon(r)* under isochronal conditions of a semi-crystalline polymer, Poly(ethylene-2,6-naphthalene dicarboxylate), or PEN, in a broad temperature range over several frequencies.