Temperature-Dependent Fractional Dynamics in Pseudo-Capacitors with Carbon Nanotube Array/Polyaniline Electrodes.

Igor O Yavtushenko,Evgeny P Kitsyuk,Marat Yu Makhmud-Akhunov,Renat T Sibatov,Vyacheslav V Svetukhin

doi:10.3390/nano12050739

Abstract

Pseudo-capacitors with electrodes based on polyaniline and vertically aligned multiwalled carbon nanotubes (PANI/VA-MWCNT) composite are studied. Fractional differential models of supercapacitors are briefly discussed. The appropriate fractional circuit model for PANI/MWCNT pseudo-capacitors is found to be a linearized version of the recently proposed phase-field diffusion model based on the fractional Cahn–Hilliard equation. The temperature dependencies of the model parameters are determined by means of impedance spectroscopy. The fractional-order is weakly sensitive to temperature, and the fractional dynamic behavior is related to the pore morphology rather than to thermally activated ion-hopping in PANI/MWCNT composite.

Highlights

Conductive polymers such as polythiophene, polyaniline (PANI), polyacetylene, etc.have redox properties and can be used as electrode materials for electrochemical power sources
The proposed model is a linearized version of the nonlinear model based on the fractional Cahn–Hilliard equation of phase-field diffusion and suitable for the analysis of temperature-dependent fractional dynamics
Pseudo-capacitors with electrodes based on PANI/VA-MWCNT composites have been manufactured and investigated

Summary

Introduction

Conductive polymers such as polythiophene, polyaniline (PANI), polyacetylene, etc. have redox properties and can be used as electrode materials for electrochemical power sources. The complex morphology of the entangled nanotube agglomerates leads to a slowdown in the transport of charge carriers [5], including subdiffusive anomalous transport [6] To eliminate this disadvantageous feature, electrodes based on an array of vertically aligned (oriented) multiwalled carbon nanotubes (VA-MWCNTs) are used [5,7]. This geometry contributes to an increase in the electronic and ionic conductivity in the composite, and the specific active surface area can be larger than in the case of an entangled. We determine the temperature dependencies of the fractional model parameters for PANI/VA-MWCNT pseudo-capacitors

Materials and Experimental Methods

Fractional Differential Models of Supercapacitors

Havriliak–Negami Response

Phase-Field Model

Linearized Model

Conclusions