On the modeling of the multi-segment capacitance: a fractional-order model and Ag-doped SnO2 electrode fabrication

This study proposes a methodology of electrochemical capacitor modeling via fractional-order impedance equation for porous electrodes fabricated with pure and Ag-doped SnO 2 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 (SnO 2 ) nanoparticles were produced using the hydrothermal method. Tin (II) chloride dihydrate (SnCl 2 ·2H 2 O) was used as an Sn source and (AgNO 3 ) 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-SnO 2 particles without and with Ag dopant. As a result of the applied procedure, the structural properties of SnO 2 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 SnO 2 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 SnO 2 electrode can significantly improve electrical performance because of the increase in conductivity. The total capacitance gets increased by 10.788% for 7% Ag-doped SnO 2 against pure SnO 2 . Graphical abstract