Anomalous diffusion, cole-cole relaxation and the space in which they occur: Puzzles and problems

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.