Modeling degradation mechanisms in batteries is a critical aspect of improving their performance, longevity, and safety. Two of the most studied degradation phenomena are solid-electrolyte interphase (SEI) growth and particle cracking, which significantly impact the capacity and power fade of lithium-ion batteries. Accurate modeling of these mechanisms enables better battery design, management, and optimization. Approaches to modeling these phenomena can be broadly categorized into empirical and physics-based methods, each with distinct advantages and limitations. Validation of these models against experimental data ensures their reliability and applicability.

SEI growth is a primary degradation mechanism in lithium-ion batteries, occurring at the anode-electrolyte interface. The SEI layer forms due to electrochemical reactions between the anode material and the electrolyte, consuming active lithium ions and increasing cell impedance. Over time, SEI growth leads to capacity loss and reduced efficiency. Particle cracking, on the other hand, occurs in electrode materials, particularly in high-capacity anodes like silicon or nickel-rich cathodes, due to mechanical stresses induced by repeated lithiation and delithiation. This cracking results in loss of electrical contact, increased resistance, and accelerated degradation.

Empirical models rely on experimental data to describe degradation trends without delving into the underlying physical or chemical processes. These models often use mathematical functions, such as exponential or polynomial fits, to correlate degradation with factors like cycle number, state of charge, temperature, and current rate. For SEI growth, empirical models may describe the increase in SEI thickness or impedance as a function of time or cycles. Similarly, particle cracking can be modeled by tracking capacity fade or resistance increase without explicitly considering stress or fracture mechanics. Empirical models are computationally efficient and useful for real-time applications like battery management systems (BMS), where simplicity and speed are prioritized. However, their lack of mechanistic insight limits their predictive capability under conditions outside the training data.

Physics-based models, in contrast, incorporate fundamental principles of electrochemistry, mechanics, and thermodynamics to describe degradation processes. For SEI growth, these models account for reaction kinetics, diffusion of species, and electron tunneling through the SEI layer. A common approach involves solving coupled partial differential equations for lithium-ion concentration, electrolyte potential, and SEI formation rate. Particle cracking models integrate mechanical stress calculations with electrochemical reactions, simulating how volumetric changes during cycling lead to fracture. These models often employ finite element analysis (FEA) or other numerical methods to resolve stress distributions and crack propagation. Physics-based models provide deeper insights into degradation mechanisms and can predict behavior under novel operating conditions. However, their complexity and computational cost make them less suitable for real-time applications.

Validation of degradation models is essential to ensure their accuracy and reliability. Empirical models are typically validated by comparing their predictions with experimental data from aging tests under controlled conditions. Metrics such as root mean square error (RMSE) or coefficient of determination (R²) quantify the agreement between model and data. Physics-based models require more extensive validation, often involving multiple types of experiments. For SEI growth, techniques like electrochemical impedance spectroscopy (EIS) or X-ray photoelectron spectroscopy (XPS) provide data on SEI thickness and composition. Particle cracking validation may involve post-mortem analysis using scanning electron microscopy (SEM) or in-situ stress measurements. Cross-validation with independent datasets further strengthens confidence in the model.

A hybrid approach combining empirical and physics-based methods can leverage the strengths of both. Reduced-order models (ROMs) simplify physics-based equations to reduce computational cost while retaining mechanistic insights. Machine learning techniques can also enhance degradation modeling by identifying patterns in large datasets and improving predictive accuracy. For example, neural networks trained on both experimental and simulated data can predict SEI growth or particle cracking under varying conditions.

The choice between empirical and physics-based modeling depends on the application. Empirical models are well-suited for BMS and operational forecasting, where rapid predictions are needed. Physics-based models are more appropriate for research and development, where understanding degradation mechanisms is crucial for material and cell design. Hybrid approaches offer a middle ground, balancing accuracy and computational efficiency.

Several challenges remain in modeling degradation mechanisms. SEI growth is influenced by complex interfacial reactions that are not fully understood, and particle cracking depends on material properties that can vary significantly. Multiscale modeling, integrating atomistic, mesoscale, and continuum approaches, is a promising direction to address these complexities. Additionally, coupling degradation models with other aspects of battery behavior, such as thermal effects or cell-level performance, remains an active area of research.

In summary, modeling SEI growth and particle cracking involves a trade-off between empirical simplicity and physics-based rigor. Empirical models provide fast predictions but lack generality, while physics-based models offer deeper insights at higher computational cost. Validation against experimental data is critical for both approaches. Advances in hybrid modeling and machine learning are bridging the gap between these methods, enabling more accurate and versatile degradation predictions. As battery technology evolves, continued refinement of these models will play a key role in enhancing performance and durability.