Electrochemical impedance spectroscopy (EIS) is a powerful technique for analyzing battery systems, providing insights into kinetic and transport processes, interfacial phenomena, and degradation mechanisms. Modeling EIS responses is critical for interpreting complex spectra and linking them to physical processes within batteries. Two primary approaches dominate this field: equivalent circuit modeling (ECM) and physics-based modeling. Each has distinct advantages, limitations, and diagnostic applications in battery research and development.

Equivalent circuit modeling simplifies the electrochemical system into a network of electrical components such as resistors, capacitors, and inductors. These components represent physical processes like charge transfer, double-layer capacitance, and mass transport. A common ECM for lithium-ion batteries includes elements like the ohmic resistance (Rs), charge transfer resistance (Rct), double-layer capacitance (Cdl), and Warburg impedance (Zw) for diffusion. The strength of ECM lies in its simplicity and ease of fitting experimental data. Engineers and researchers can quickly extract parameters like Rct to assess electrode kinetics or Zw to evaluate diffusion limitations. ECM is particularly useful for comparative studies, such as tracking changes in interfacial resistance during cycling or diagnosing state of health (SOH) by monitoring the evolution of circuit parameters over time. However, ECM has limitations. The lack of direct physical meaning in some circuit elements can lead to ambiguous interpretations, especially when multiple processes contribute to the same frequency response. Additionally, ECM parameters are often valid only under specific conditions, limiting their generalizability across different operating states or battery chemistries.

Physics-based modeling, in contrast, employs electrochemical theory to derive impedance responses from first principles. These models incorporate governing equations such as the Butler-Volmer equation for charge transfer, Fick’s laws for diffusion, and Poisson’s equation for double-layer effects. Physics-based approaches can explicitly account for spatial variations in concentration and potential, enabling a more rigorous analysis of impedance spectra. For instance, the porous electrode theory combined with concentrated solution theory provides a framework for modeling impedance in composite electrodes, capturing the distributed nature of reactions and transport in real battery systems. Physics-based models are particularly valuable for probing mechanisms that ECM cannot resolve, such as the interplay between solid-state diffusion and electrolyte transport or the effects of electrode microstructure on impedance. These models also enable predictive capabilities, allowing researchers to simulate impedance responses under untested conditions or design optimized electrode architectures. However, physics-based modeling demands detailed knowledge of material properties and system geometry, which are not always available. The computational cost is also higher compared to ECM, making it less practical for rapid diagnostics or real-time applications.

The choice between ECM and physics-based modeling depends on the diagnostic objectives. For routine performance evaluation or quality control, ECM offers a fast and interpretable solution. For example, tracking the increase in Rct over cycles can indicate electrolyte decomposition or passivation layer growth, while changes in Zw may signal electrode pore blockage or lithium plating. In contrast, physics-based modeling is indispensable for fundamental research, such as investigating the impact of novel electrode materials or electrolyte formulations on impedance characteristics. Hybrid approaches are increasingly common, where ECM provides initial parameter estimates that inform physics-based models, or where simplified physical models are used to guide the selection of ECM components.

Diagnostic applications of EIS modeling span multiple aspects of battery development and operation. In manufacturing, EIS helps identify process variations by detecting anomalies in electrode coatings or electrolyte wetting. In aging studies, models decompose impedance contributions from different degradation modes, such as solid-electrolyte interphase (SEI) growth, active material loss, or contact resistance increase. For safety assessment, EIS can reveal early signs of lithium plating or internal shorts by detecting deviations in the low-frequency impedance response. Advanced applications include state estimation, where ECM parameters are integrated into battery management systems (BMS) for real-time monitoring of state of charge (SOC) and state of health (SOH).

The integration of machine learning with EIS modeling is an emerging trend. Data-driven techniques can automate the extraction of ECM parameters or enhance physics-based models by identifying hidden patterns in large impedance datasets. However, these methods require careful validation to ensure physical plausibility and avoid overfitting.

Despite the progress, challenges remain in EIS modeling. The interpretation of intermediate-frequency arcs, often attributed to a combination of processes, remains ambiguous in many systems. Temperature effects complicate impedance analysis, as both kinetic and transport parameters exhibit strong thermal dependencies. Furthermore, the application of EIS to next-generation batteries, such as solid-state or lithium-sulfur systems, demands new modeling frameworks to address unique interfacial and morphological characteristics.

In summary, modeling EIS responses is a multifaceted task that balances simplicity and physical fidelity. Equivalent circuit models excel in practicality and speed, while physics-based models offer deeper mechanistic insights. The diagnostic power of EIS modeling lies in its ability to disentangle complex electrochemical processes, enabling better design, monitoring, and optimization of battery systems. Future advancements will likely focus on hybrid methodologies, enhanced computational tools, and expanded applications to emerging battery technologies.