A General Equivalent Electrical Circuit Model for the Characterization of MXene/Graphene Oxide Hybrid-Fiber Supercapacitors By Electrochemical Impedance Spectroscopy
Authors: Mainka Julia , Gao Wei , He Nanfei , Dillet Jérôme , Lottin Olivier 
Published: July 2022

Main text :
Performance engineering of electrochemical energy-storage devices such as Supercapacitors (SCs) requires updated modelling capable of characterizing their electrical output in unique device geometries. In this work, an Equivalent Electrical Circuit (EEC) is developed to fit the impedance data of MXene/reduced Graphene Oxide (rGO) hybrid fiber-shaped supercapacitors (FSCs) fabricated by wet-spinning [1]. The model is applied for the interpretation of impedance data measured on FSCs using different active materials - rGO and MXene in the case of pseudo-capacitors (Figure - upper right side) and pure carbon in the case of Electrical Double-Layer Capacitors (EDLCs) - and polyvinylalcohol (PVA) gel infiltrated with sulfuric acid as the electrolyte and separator.
The FSC charge storage behavior is modelled using a Transmission Line Model (TLM) including a finite Warburg impedance for pseudo-capacitance [2], and a Constant-Phase Element (CPE) for the electrostatic contribution (Figure – upper left side). The high frequency part of the Nyquist plots is characterized by a 45° straight line and the use of a TLM clearly improves the fit quality compared to a Randles circuit usually used for pseudo-capacitor modeling [1,2]. The 45° high frequency line and the difference between the two circuits becomes more visible as the length of the SC yarns increases (Figure – lower left side), which is consistent with the observed increase in internal resistance with fiber length evidenced with the TLM. Finally, the low frequency part of the spectra is correctly modeled by a CPE without any leakage resistance, showing that self-discharge is not a significant issue for the electrostatic contribution, at least in the frequency range tested.
The fitting results on all tested devices indicate that the internal resistance of the TLM predominantly corresponds to the electrical resistance of the fiber (Figure – lower right side), i.e. the electron conductive phase of the electrode, instead of the electrolyte ionic resistance in usual SCs [2-4].
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Figure caption:
(Left) Experimental impedance spectra measured on rGO/MXene fibers-shaped supercapacitors (FSCs) of different length and fitting curves obtained with the herein developed equivalent electrical circuit (EEC). (Right) Internal resistance of the EEC identified by fitting the spectra on the left side per unit length of the FSCs and electric resistance of the rGO/MXene fibers of the electrodes.

Figure 1