Defect-assisted fractional stochastic Ising model of dielectric relaxation

In this study, a fractional dielectric relaxation model giving better results than the existing dielectric relaxation models is developed. During the development of the model, Glauber?s stochastic Ising model and Glarum?s defect diffusion model are re-analyzed by using the fractional calculus technique. The results obtained are compared both with the results of the classical defect diffusion and stochastic Ising models, and a superiority of the fractional solutions according to these models is shown. Then, a new cooperative relaxation model, namely ?Defect Assisted Fractional Stochastic Ising Model?, is developed by combining the defect diffusion and stochastic Ising approaches, which are solved by using the fractional calculus technique. The results of this model are compared with the dielectric relaxation data represented by some empirical functions. It is shown that frequency dependent plots of the Fourier transform of correlation function obtained from the cooperative model are fully compatible with the empirical KWW, Cole-Cole, Cole-Davidson and Havriliak-Negami functions. The results obtained leads to a new molecular interpretation of the universal non-Debye type behaviors mentioned above.