8th Liquid Matter Conference September 6-10, 2011 Wien, Austria ...

P7.28Thu 811:10-14:00Effects of anomalous diffusion of mobile charges andimpedance spectroscopy for finite-length situations insoft matterLuiz Roberto Evangelista, 1 Ervin Kaminski Lenzi, 1 Giovanni Barbero, 2 and JamesRoss Macdonald 31 Universidade Estadual de Maringá, Departamento de Física, Avenida Colombo, 5790,87010340, Maringá, Brazil2 Dipartimento di Fisica del Politecnico di Torino, Torino, Italy3 University of North Carolina, Department of Physics and Astronomy, Chapel Hill,North Carolina, United States of AmericaThe redistribution of ions in confined soft matter samples can be described in the framework ofthe Poisson-Nernst-Plank (PNP) models. A normal-diffusion treatment of this and more generalsituations appeared in 1953 [1]. Recently, two finite length fractional anomalous diffusion solvingPoisson’s equation (PNPA) models have been proposed and their responses explored [2, 3]. Inthis work, we first discuss the responses and the physical appropriateness and usefulness of thesetwo empirical, but plausible, independent generalization of PNP model incorporating anomalousdiffusion of PNPA type with power-law frequency-response elements involving fractionalexponent [4]. The first model [3] involves the common separation of the expression for ordinaryPNP impedance into an interface diffusion part and a high-frequency limiting conductance andcapacitance, followed by the replacement of all normal diffusion elements in the former byanomalous ones. The second model [2], alternatively generalizes the normal time derivatives inthe continuity equation by replacing them with fractional ones and leads to no plateau, except inthe PNP limit, but instead predicts an immediate power-law increase as the frequency decreasesbelow the Debye relaxation one. Fitting of experimental frequency response data sets leads tomuch poorer fits for the second model than for the first one. Other possibilities of generalizationare discussed, including a model that combines fractional derivatives with ordinary ones andnonlocal memory effects.[1] J. R. Macdonald, Phys. Rev. 92, 4 (1953).[2] E. K. Lenzi, L. R. Evangelista, and G. Barbero, J. Phys. Chem. B 113, 11371 (2009).[3] J. R. Macdonald, J. Phys. : Condensed Matter 22, 495101 (2010).[4] J. R. Macdonald, L. R. Evangelista, E. K. Lenzi, and G. Barbero, J. Phys. Chem. C (2011), toappear.28