Microscopic models for dielectric relaxation in disordered systems
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2004Citation:
Kalmykov, Y. P.Coffey, W. T.Crothers, D. S. F.Titov, S. V., 'Microscopic models for dielectric relaxation in disordered systems' in Physical Review E, 70, 4, (2004), pp 041103-1-041103-11Download Item:
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Abstract:
It is shown how the Debye rotational diffusion model of dielectric relaxation of polar molecules (which may
be described in microscopic fashion as the diffusion limit of a discrete time random walk on the surface of the
unit sphere) may be extended to yield the empirical Havriliak-Negami (HN) equation of anomalous dielectric
relaxation from a microscopic model based on a kinetic equation just as in the Debye model. This kinetic
equation is obtained by means of a generalization of the noninertial Fokker-Planck equation of conventional
Brownian motion (generally known as the Smoluchowski equation) to fractional kinetics governed by the HN
relaxation mechanism. For the simple case of noninteracting dipoles it may be solved by Fourier transform
techniques to yield the Green function and the complex dielectric susceptibility corresponding to the HN
anomalous relaxation mechanism.
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American Physical SocietyType of material:
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Physical Review E70
4
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