Kavuran, G., Gurgenç, T. & Özkaynak, F. On the modeling of the multi-segment capacitance: a fractional-order model and Ag-doped SnO₂ electrode fabrication. J Mater Sci 57, 2775–2793 (2022). https://doi.org/10.1007/s10853-021-06670-y

DOI: https://doi.org/10.1007/s10853-021-06670-y

Abstract

This study proposes a methodology of electrochemical capacitor modeling via fractional-order impedance equation for porous electrodes fabricated with pure and Ag-doped SnO₂ nanoparticles. It was carried out to prove the assumption that fractional-order integrodifferential expressions better model the various real systems. Firstly, the pure and different amounts of silver (Ag)-doped tin oxide (SnO₂) nanoparticles were produced using the hydrothermal method. Tin (II) chloride dihydrate (SnCl₂·2H₂O) was used as an Sn source and (AgNO₃) as an Ag source. Hydrothermal synthesis was completed at 200 °C for 24 h. The synthesized particles were calcined at 600 °C for 2 h. All of the structural and morphological properties were investigated by FT-IR, XRD, FE-SEM, and EDX. It has been observed that the hydrothermal method successfully produced nano-SnO₂ particles without and with Ag dopant. As a result of the applied procedure, the structural properties of SnO₂ nanoparticles, such as physical shape, were changed from spherical-like to nano-sheet with the Ag doping. Next, the nanopowders were coated on AZ31 magnesium sheets. Electrochemical impedance spectroscopy measurements were examined to determine the capacitance of EC materials with Ag-doped SnO₂ nanoparticles. Finally, using the multi-objective cost function, the experimentally measured real and imaginary impedance parts are fitted to the proposed fractional-order model by the particle swarm optimization algorithm. It has been proven that fractional-order modeling enables finding the electrical parameters and properties of EC with higher accuracy. Furthermore, the Ag-doped SnO₂ electrode can significantly improve electrical performance because of the increase in conductivity. The total capacitance gets increased by 10.788% for 7% Ag-doped SnO₂ against pure SnO₂.