Title :
Application of fractional calculus to modelling of relaxation phenomena of organic dielectric materials
Author :
Reyes-Melo, M.E. ; Martinez-Vega, J.J. ; Guerrero-Salazar, C.A. ; Ortiz-Mendez, U.
Author_Institution :
Lab. de Genie Electrique, Paul Sabatier Univ., Toulouse, France
Abstract :
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.
Keywords :
dielectric materials; dielectric relaxation; differential equations; differentiation; permittivity; polymer structure; polymers; PEN; dielectric relaxation; differential equations; fractional calculus; isochronal diagrams; molecular motions; organic dielectric materials; poly(ethylene-2,6-naphthalene dicarboxylate); relative complex permittivity; semicrystalline polymer structure; structural equilibrium; Amorphous materials; Design for manufacture; Dielectric materials; Differential equations; Electric resistance; Fractals; Fractional calculus; Permittivity; Polymers; Temperature distribution;
Conference_Titel :
Solid Dielectrics, 2004. ICSD 2004. Proceedings of the 2004 IEEE International Conference on
Print_ISBN :
0-7803-8348-6
DOI :
10.1109/ICSD.2004.1350485