Generalized Electrodiffusion Equation with Fractality of Space-Time: Experiment and Theory

J Phys Chem A. 2018 Apr 26;122(16):4099-4110. doi: 10.1021/acs.jpca.8b00188. Epub 2018 Apr 12.

Abstract

Physical and technological principles of formation of clathrate structures for supramolecular electronics are given in this paper. It has been established that supramolecular nature of the "host-guest" conjunction, in general, and hierarchical architecture of the corresponding clathrates, in particular, provide realization of such an extraordinary effect as an optically or a magnetically controlled phenomenon of colossal "negative capacity" with a predicted frequency interval of manifestation, magnitude, and multiplicity. For the first time, the experimental confirmation of the behavior of the electretized fractal clathrate GaSe⟨β-CD⟨FeSO4⟩⟩ as a dissipative element, which accumulates inductive energy, is demonstrated. A general approach for obtaining the generalized transport equations with fractional derivatives by using the Liouville equation with fractional derivatives for a system of classical particles and the Zubarev nonequilibrium statistical operator method within Renyi statistics is presented. New non-Markovian electrodiffusion equations for ions in a spatially heterogeneous medium with the fractal structure and a generalized Cattaneo-type diffusion equation taking into account the fractality of space-time are obtained. The model of subdiffusion impedance based on the Cattaneo equation with fractional derivatives is applied to multilayer nanostructures. Nyquist diagrams for different valuses of the parameter τ (delay time of a flow relative to a concentration gradient) and the subdiffusion coefficient Dα are calculated.