Nanocomposites and nanomaterials

Temperature behavior of fractional power dispersive systems with medium dispersion
Fliunt O. Ye.
Faculty of Electronics and Computer Technologies, Ivan Franko National University of Lviv, Dragomanov Str., 50, Lviv-79005, Ukraine 
E-mail: ofliunt@gmail.com

Slow compared to the rate of change of the applied external field processes in condensed matters show both temporal and frequency dependencies which often obey power fractional law. Fractional power dispersive systems show interesting unexpected behavior on frequency, temperature and other physical parameters. Power frequency or temporal dispersions are often explained as caused by disordering of some type and may be used for studying of material disordering nature and level. It’s shown, that character of behavior of fractional power dispersive systems depends on the range of value of exponent 0 < n < 1. Systems or materials with very small values of n are named as flat losses systems, showing almost frequency independent losses in the wide frequency range. In contrary, materials with n close to 1 show strong unlimited in wide frequency range increasing of both real and imaginary components of the spectra towards low frequencies. They are often characterized by thermally activated Arrhenius law. In this work temperature behavior of power dispersive system with 0.6 < n < 0.9, often connected with charge carrier hopping transport, has been analyzed and the model of temperature behavior has been proposed. 
The novel approach for describing the behavior of dielectric spectra ω−(1−n) where n ≈ 0.7-0.9 characteristic for charge carrier hopping systems has been proposed. The physical model of dielectric response of hopping charge carrier systems is based on the assumption of thermally activated properties of effective dipoles distributed via relaxation time. The effective dipoles reflect characteristic values of complex formations on the base of elementary hopping processes interacting between themselves. The model gives fractional power fractional law response without any additional assumption. Temperature increase of real and imaginary components of complex dielectric constant is explained according to an inverse Arrhenius law exp(T/T0) with frequency dependent T0. Often experimentally observed a linear temperature decrease of n with temperature is expected according to the model. The proposed model explain a universality of behavior of dispersive systems characteristic for hopping charge carrier medias, confirmed by many experimental results.