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 (ε\´_r and ε"_r) show clearly three dielectric relaxation phenomena. To test the validity of the model proposed we have used measurements of ε*_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.