Anomalous Diffusion Model for Description of Lithium-Ion Cell Impedance

Recently, in the components of the lithium-ion accumulators (LIA) an anomalously diffusion behavior of ion transport has been discovered. Currently, the microscopic models LIA, consecutively taking into account sub- or superdiffusion and percolation of lithium ions into LIA, are unavailable. The semi-empirical LIA models, using the fractional-order impedances, based on the impedances of fractional order, which are substantiated by the anomalous diffusion of ions in a percolative disordered medium are becoming popular. In the work an assessment of the influence of anomalous diffusion on the impedance spectra within the framework of sub-diffusion generalization of the electrochemical model has been carried out. Using the subdivision equations with the time derivatives of fractional order, the LIA electrochemical model has been modified. Within the framework of this model, using the Fourier transform of fractional differential operators, an equivalent circuit, generalizing popular LIA circuit models has been derived. It has been shown that the slope of a rectilinear low-frequency part of the Nyquist diagram does not always unambiguously determine the subdivision coefficient α and can be both larger and smaller than the slope corresponding to normal diffusion. It has been stipulated that the degradations of the battery properties is associated with a change of the diffusion type in the LIA components.
Renat T. Sibatov
Ulyanovsk State University, Ulyanovsk, Russia
Ekaterina V. Morozova
Ulyanovsk State University, Ulyanovsk, Russia
Boris M. Kostishko
Ulyanovsk State University, Ulyanovsk, Russia
Vyacheslav V. Svetukhin
SMC «Technological Center», Moscow, Russia
Evgeny P. Kitsyuk
SMC «Technological Centre», Moscow, Russia
Alexander A. Pavlov
Institute of Nanotechnology of Microelectronics of the Russian Academy of Sciences, Moscow, Russia