Memory Effect and Fractional Differential Dynamics in Planar Microsupercapacitors Based on Multiwalled Carbon Nanotube Arrays

The development of portable electronic devices has greatly stimulated the need for miniaturized power sources. Planar supercapacitors are micro-scale electrochemical energy storage devices that can be integrated with other microelectronic devices on a chip. In this paper, we study the behavior of microsupercapacitors with in-plane interdigital electrodes of carbon nanotube array under sinusoidal excitation, step voltage input and sawlike voltage input. Considering the anomalous diffusion of ions in the array and interelectrode space, we propose a fractional-order equivalent circuit model that successfully describes the measured impedance spectra. We demonstrate that the response of the investigated micro-supercapacitors is linear and the system is time-invariant. The numerical inversion of the Laplace transforms for electric current response in an equivalent circuit with a given impedance leads to results consistent with potentiostatic measurements and cyclic voltammograms. The use of electrodes based on an ordered array of nanotubes reduces the role of nonlinear effects in the behavior of a supercapacitor. The effect of the disordering of nanotubes with increasing array height on supercapacitor impedance is considered in the framework of a distributed-order subdiffusion model

Fractional Differential Generalization of the Single Particle Model of a Lithium-Ion Cell

The effect of anomalous diffusion of lithium on the discharge curves and impedance spectra of lithium-ion batteries (LIB) is studied within the fractional differential generalization of the single-particle model. The distribution of lithium ions in electrolyte and electrode particles is expressed through the Mittag–Leffler function and the Lévy stable density. Using the new model, we generalize the equivalent circuit of LIB. The slope of the low-frequency rectilinear part of the Nyquist diagram does not always unambiguously determine the subdiffusion index and can be either larger or smaller than the slope corresponding to normal diffusion. The new aspect of capacity degradation related to a change in the type of ion diffusion in LIB components is discussed

Influence of the Surface Roughness of a Silicon Disk Resonator on Its Q-Factor

This article presents a silicon disk resonator of the whispering-gallery-mode (WGM) type. The calculated Q-factor of the silicon WGM resonator was 107. Two methods of studying the surface roughness of a silicon WGM resonator with a nonlinear profile by means of Helios 650 scanning electron microscope and Bruker atomic force microscope (AFM) are presented. The results obtained by the two methods agreed well with each other. A comparison of the surface roughness values of WGM resonators manufactured using different technological approaches is presented. Based on the obtained data, a preliminary estimated Q-factor calculation of the resonators was performed, which was refined by numerical calculation using the finite-difference time-domain (FDTD) method. The effect of the surface roughness of the resonator on its Q-factor was found. Reducing the surface roughness of the resonator from 30 nm to 1–2 nm led to an increase in its Q-factor from 104 to 107