Mechanical and dielectric relaxation phenomena of poly(ethylene‐2,6‐napthalene dicarboxylate) by fractional calculus approach

Abstract

Abstract The mechanical and dielectric relaxation phenomena in PEN‐films have been studied using fractional models. A mechanical fractional model for the description of dynamic modulus, E * = E ′ + iE ″, and a dielectric fractional model for the dynamic relative permittivity, ε = ε − i ε . These models takes into account three relaxation phenomena and the corresponding differential equations have derivatives of fractional order between 0 and 1. In applying the Fourier transform to fractional differential equations and in considering that each relaxation mode is associated to cooperative or noncooperative molecular movements, we calculated E *( i ω, T ) and ε ( i ω, T ). The isochronal diagrams of the real and imaginary parts of either E * and ϵ obtained from fractional models have been used to study the three relaxation phenomena (α, β*, and β) of poly(ethylene‐2,6‐napthalene dicarboxylate). An agreement between experiments and fractional models has been achieved for both mechanical and dielectric relaxation phenomena, and the effect of morphology samples on the fractional order parameters of the Fractional Models are related to molecular motions associated to α, β*, and β relaxations. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102:3354–3368, 2006