Electrochemical modeling of lithium plating and stripping is a critical tool for understanding and mitigating one of the most challenging failure mechanisms in lithium-ion batteries. This phenomenon occurs when lithium ions, instead of intercalating into the graphite anode, deposit as metallic lithium on the anode surface during charging. Under certain conditions, such as fast charging or low temperatures, the thermodynamic and kinetic limitations of intercalation favor plating, leading to capacity loss, accelerated degradation, and safety risks.

The fundamental mechanism of lithium plating arises from the competition between intercalation and plating kinetics. When the local overpotential at the anode-electrolyte interface exceeds the thermodynamic potential for lithium deposition, metallic lithium forms. The governing equations for this process stem from Butler-Volmer kinetics, mass transport, and nucleation theory. The Butler-Volmer equation describes the current density for lithium intercalation and plating:

\[ j = j_0 \left[ \exp\left(\frac{\alpha_a F \eta}{RT}\right) - \exp\left(-\frac{\alpha_c F \eta}{RT}\right) \right] \]

Here, \( j \) is the current density, \( j_0 \) is the exchange current density, \( \alpha_a \) and \( \alpha_c \) are the anodic and cathodic transfer coefficients, \( F \) is Faraday’s constant, \( \eta \) is the overpotential, \( R \) is the gas constant, and \( T \) is temperature. When \( \eta \) becomes sufficiently negative (i.e., the anode potential drops below 0 V vs. Li/Li+), lithium plating dominates.

Mass transport limitations further exacerbate plating. The diffusion of lithium ions in the electrolyte is governed by Fick’s law:

\[ \frac{\partial c}{\partial t} = D \nabla^2 c \]

where \( c \) is the lithium-ion concentration and \( D \) is the diffusion coefficient. At high currents or low temperatures, concentration gradients develop, reducing ion availability at the anode surface and increasing the likelihood of plating.

Nucleation theory explains how lithium deposits initiate and grow. The classical nucleation model describes the energy barrier for forming a critical nucleus:

\[ \Delta G^* = \frac{16 \pi \gamma^3}{3 (\Delta \mu)^2} \]

where \( \Delta G^* \) is the critical nucleation energy, \( \gamma \) is the surface energy, and \( \Delta \mu \) is the chemical potential difference driving deposition. Smaller nuclei dissolve due to high surface energy, but once a critical size is reached, growth becomes favorable. Stochastic models incorporate nucleation site density and growth rates to predict plating morphology, which ranges from dendritic (high surface area) to mossy (dense).

Electrochemical models simulate plating thresholds by coupling these equations with battery operation conditions. Key parameters include:

- Current density: Higher currents increase overpotential, pushing the anode potential below 0 V vs. Li/Li+.
- Temperature: Lower temperatures reduce ion mobility and reaction kinetics, favoring plating.
- State of charge (SOC): At high SOC, graphite intercalation slows, increasing plating risk.
- Electrode porosity and tortuosity: Poor electrolyte access raises concentration overpotential.

Models predict plating onset using dimensionless numbers like the Sand’s time criterion, which estimates when concentration polarization leads to zero ion concentration at the electrode:

\[ \tau = \frac{\pi D}{4} \left( \frac{zF c_0}{j} \right)^2 \]

Beyond this point, plating becomes inevitable. Simulations also incorporate phase-field models to track lithium deposition morphology, revealing how dendrites penetrate separators and cause short circuits.

The implications of lithium plating for battery safety and lifespan are severe. Plated lithium reacts irreversibly with the electrolyte, forming solid-electrolyte interphase (SEI) and consuming active lithium. This reduces capacity and increases impedance. Dendritic growth poses a direct short-circuit risk, potentially triggering thermal runaway. Models show that even partial plating accelerates degradation, as dead lithium fragments detach from the anode, creating electrically isolated regions.

Under fast charging, simulations reveal that plating initiates at the anode-separator interface due to local current hotspots. Pulse charging protocols can mitigate this by allowing ion concentration gradients to relax. At low temperatures, models highlight the need for preheating strategies, as ion transport limitations dominate plating behavior.

Electrochemical modeling thus provides a predictive framework for identifying unsafe operating conditions and optimizing battery designs. By quantifying the interplay between thermodynamics, kinetics, and transport, these models guide the development of charging protocols, electrolyte formulations, and anode materials that suppress plating. Future advancements will integrate multi-scale approaches, linking atomistic nucleation events to macroscopic battery performance, further refining predictions of lithium plating and its consequences.

In summary, electrochemical modeling of lithium plating and stripping is indispensable for advancing battery technology. By elucidating the governing mechanisms and predicting failure thresholds, these models enable safer, longer-lasting energy storage systems. The insights gained from simulations inform material selection, operational limits, and design improvements, ensuring that lithium-ion batteries meet the demands of fast charging and extreme environments without compromising reliability.