TY - CHAP

T1 - Anomalous diffusion, cole-cole relaxation and the space in which they occur

T2 - Puzzles and problems

AU - Ishai, Paul Ben

AU - Lerner, Shimon

AU - Puzenko, Alexander A.

AU - Feldman, Yuri

PY - 2013

Y1 - 2013

N2 - The origin of the Cole-Cole dielectric spectral equation is investigated by considering its attendant susceptibility as originating in the Laplace transform of the fractional Fokker-Planck equation. The eigenvalues of the solution point to the interaction of the dipole with its local molecular conditions, as dictated by the local fields involved, as the origin of the spectral broadening (described by the parameter α). This view is compared to ideas in the literature pointing to a dipole-matrix interaction as the cause of spectral broadening. The question is posed concerning what information exists in the as yet unexplored element of the CC function, namely the dielectric strength, Δε. In this context a new derivation of Fröhlich's B(T) function is proposed, that relies on fully accessible experimental values only and is capable of unifying all parameters of the Cole-Cole function via the calculated correlation between dipoles. This function is demonstrated via an electron hopping process, exhibiting Cole-Cole dielectric behavior, observed in a ferroelectric KTN crystal.

AB - The origin of the Cole-Cole dielectric spectral equation is investigated by considering its attendant susceptibility as originating in the Laplace transform of the fractional Fokker-Planck equation. The eigenvalues of the solution point to the interaction of the dipole with its local molecular conditions, as dictated by the local fields involved, as the origin of the spectral broadening (described by the parameter α). This view is compared to ideas in the literature pointing to a dipole-matrix interaction as the cause of spectral broadening. The question is posed concerning what information exists in the as yet unexplored element of the CC function, namely the dielectric strength, Δε. In this context a new derivation of Fröhlich's B(T) function is proposed, that relies on fully accessible experimental values only and is capable of unifying all parameters of the Cole-Cole function via the calculated correlation between dipoles. This function is demonstrated via an electron hopping process, exhibiting Cole-Cole dielectric behavior, observed in a ferroelectric KTN crystal.

UR - http://www.scopus.com/inward/record.url?scp=84870502452&partnerID=8YFLogxK

U2 - 10.1007/978-94-007-5012-8_3

DO - 10.1007/978-94-007-5012-8_3

M3 - Chapter

AN - SCOPUS:84870502452

SN - 9789400750111

T3 - NATO Science for Peace and Security Series B: Physics and Biophysics

SP - 37

EP - 48

BT - Recent Advances in Broadband Dielectric Spectroscopy

A2 - Kalmykov, Yuri

ER -