Semi-empirical physics-based simulation of time-domain current responses in electrochemical impedance spectroscopy and their conversion to frequency-domain spectra

Electrochemical impedance spectroscopy (EIS) is a widely used technique for probing the dynamic processes that govern the performance of advanced energy storage and conversion systems. However, conventional frequency-domain EIS models often struggle to accurately capture the complex interplay between charge transfer, double-layer capacitance, and mass transport in systems with non-planar geometries or heterogeneous interfaces. In this study, we present a time-domain-dependent EIS model that integrates an equivalent circuit framework with mass transport equations to simultaneously account for Faradaic and non-Faradaic processes at cylindrical graphite electrodes in Fe²⁺/Fe³⁺ redox electrolytes. Unlike traditional approaches, our model bridges time- and frequency-domain analyses by predicting both cyclic voltammetry Lissajous patterns and frequency-domain impedance spectra, including Nyquist and Bode plots. The model was validated against experimental data and systematically applied to investigate the influence of key parameters—including reaction rate constant, active surface area, CPE characteristics, and electrode radius—on impedance behavior. The results reveal how these variables shape charge transfer kinetics, capacitive contributions, and mass transport limitations, offering mechanistic insights that are difficult to obtain using conventional frequency-domain models alone. This work establishes a robust platform for interpreting EIS data in complex electrochemical systems and provides a valuable tool for the design and optimization of next-generation energy storage technologies, including redox flow batteries, supercapacitors, and electrocatalytic devices. The model's flexibility and predictive power offer new opportunities for advancing the understanding of interfacial processes critical to high-performance electrochemical energy systems.