Modeling cathode degradation in nickel-manganese-cobalt (NMC) lithium-ion batteries requires a comprehensive understanding of the underlying mechanisms that contribute to capacity fade and impedance rise over time. The primary degradation pathways include phase transitions, transition metal dissolution, and oxygen loss, each of which can be quantified through different modeling approaches. These models range from first-principles calculations to phenomenological descriptions, enabling researchers to predict long-term performance under various operating conditions.

Phase transitions in NMC cathodes occur due to structural rearrangements during lithium insertion and extraction. The layered structure of NMC materials undergoes reversible and irreversible changes as a function of state of charge. At high voltages, delithiation leads to a reduction in interlayer spacing, causing mechanical strain and potential particle cracking. These structural changes are often modeled using density functional theory (DFT) to predict the thermodynamic stability of different phases. DFT calculations can identify the formation of spinel-like or rock-salt phases at the surface, which are electrochemically inactive and contribute to capacity loss. Phase-field models are also employed to simulate the evolution of these secondary phases over multiple cycles, incorporating factors such as lithium diffusion kinetics and stress accumulation.

Transition metal dissolution is another critical degradation mechanism, particularly for manganese and nickel in NMC cathodes. The dissolution process is driven by acidic species in the electrolyte, often resulting from lithium salt decomposition or moisture contamination. Dissolved transition metals migrate to the anode, where they deposit and disrupt the solid electrolyte interphase (SEI), accelerating further degradation. First-principles models calculate the free energy of dissolution for different transition metals, revealing that manganese is more prone to dissolution than nickel or cobalt. Phenomenological models, such as those based on the Nernst-Planck equation, describe the transport of dissolved species through the electrolyte. These models are coupled with electrochemical impedance spectroscopy (EIS) data to quantify the impact of dissolution on cell resistance. Accelerated testing at elevated temperatures is often used to validate dissolution rates predicted by these models.

Oxygen loss from the NMC lattice is a significant concern at high voltages, particularly above 4.3 V versus lithium metal. Oxygen evolution leads to the formation of oxygen vacancies and surface reconstruction, which degrade electrochemical performance. Ab initio molecular dynamics (AIMD) simulations are used to study the thermodynamics of oxygen release, showing that nickel-rich compositions are more susceptible to oxygen loss due to their reduced oxygen binding energy. Kinetic Monte Carlo (kMC) models simulate the progression of oxygen vacancies and their impact on electronic conductivity. Experimental techniques such as differential electrochemical mass spectrometry (DEMS) provide quantitative data on oxygen gas evolution, which is incorporated into degradation models to improve their predictive accuracy.

Voltage windows and cycling conditions play a crucial role in accelerating cathode degradation. Operating at upper cutoff voltages above 4.3 V exacerbates phase transitions, transition metal dissolution, and oxygen loss. Models that incorporate voltage-dependent degradation rates use the concept of cumulative charge throughput to estimate capacity fade. For example, a linear or exponential relationship between capacity loss and the total charge passed can be established based on accelerated aging tests. Cycling at high rates introduces additional mechanical stress due to rapid lithium insertion and extraction, leading to particle fracture. Finite element models simulate the stress distribution within cathode particles, predicting crack initiation and propagation as a function of cycling rate and particle morphology.

First-principles approaches provide fundamental insights into degradation mechanisms but are often limited by computational cost when applied to long-term cycling. To bridge this gap, reduced-order models (ROMs) are developed, capturing the essential physics while remaining computationally efficient. ROMs for NMC degradation typically include empirical parameters derived from experimental data, such as the dependence of capacity fade on voltage and temperature. Machine learning techniques are increasingly used to identify patterns in degradation data, enabling the development of predictive models without explicit mechanistic descriptions. These data-driven models are particularly useful for optimizing cycling protocols to minimize degradation.

Phenomenological models often rely on coupled differential equations to describe the evolution of degradation processes. For example, a typical model might include equations for lithium inventory loss, active material loss, and impedance rise, each with their own rate constants. The parameters in these equations are fitted to experimental data from controlled aging studies. The resulting models can predict capacity fade under arbitrary cycling conditions, provided the operating conditions remain within the validated range. Sensitivity analysis is performed to identify the dominant degradation mechanisms under specific scenarios, guiding the design of more robust NMC cathodes.

Quantifying the interactions between different degradation mechanisms remains a challenge in modeling. Phase transitions, transition metal dissolution, and oxygen loss do not occur in isolation but influence each other through complex feedback loops. Multiscale modeling frameworks attempt to integrate these processes by coupling atomistic simulations with continuum-level descriptions. For instance, the formation of oxygen vacancies may increase the rate of transition metal dissolution, which in turn accelerates phase transitions at the particle surface. These coupled effects are captured through iterative simulations that update material properties based on the progression of each degradation mechanism.

Validation of degradation models requires extensive experimental data spanning a range of operating conditions. Cycle life testing under controlled voltages, temperatures, and cycling rates provides the necessary input for model calibration. Post-mortem analysis techniques, such as X-ray diffraction (XRD) and transmission electron microscopy (TEM), reveal the structural changes predicted by phase transition models. Inductively coupled plasma (ICP) spectroscopy quantifies transition metal dissolution, while gas chromatography (GC) measures oxygen evolution. The integration of these experimental results with modeling efforts ensures that predictions are grounded in observable phenomena.

The ultimate goal of degradation modeling is to enable predictive maintenance and optimize battery usage strategies. By understanding how voltage windows and cycling conditions influence degradation, battery management systems (BMS) can implement adaptive charging protocols to extend cell life. For example, limiting the upper cutoff voltage during fast charging reduces the rate of oxygen loss and transition metal dissolution. Models that accurately predict degradation under real-world conditions are essential for the development of next-generation NMC cathodes with improved longevity. Future advancements in computational power and experimental techniques will further refine these models, providing deeper insights into the complex interplay of degradation mechanisms.