Fractional Time Defect-Diffusion Model of Dielectric Relaxation
The defect-diffusion model has been used to explicate dielectric relaxation and other relaxation phenomena observed in some dielectric materials. In the model it was assumed that the defects move through the system by random-walk in one-dimension and the relaxation, which is instantaneous and independent of the state of other dipole sites, can only occur when a defect diffuses to a dipole. In this study, the defect-diffusion model is reconsidered by using the fractional calculus technique, and the model is extended to one- and three-dimensional fractional defect-diffusion model. A dipole correlation function derived from the fractional approach is identical with the Kohlrausch-Williams-Watts (KWW) non- exponential relaxation function, which is universal for describing the relaxation data of a wide variety of polar materials. Then, a new fractional complex susceptibility obtained from the defect diffusion model assisted fractional calculus is exposed, and it is shown that the results are compatible with empirical Cole-Cole and the Cole-Davidson type behavior, and Havriliak-Negami behavior is also obtained under the certain limits. The results obtained lead to a molecular interpretation of non-Debye type behavior. This suggests possible microscopic mechanisms for relaxation in polar materials having molecular chains.
ÇavuÅ MS, Bozdemir S