Last time we talked about open-circuit potentials (OCPs), and we explained how they drive the direction of lithium intercalation reactions. But how are these reactions characterized? This is where reaction kinetics come into play. Reaction kinetics dictate how quickly lithium ions can intercalate or deintercalate into an electrode’s active material and are a fundamental part of understanding battery performance and designing better models.

Reaction kinetics, in the context of batteries, describe the rates of the electrochemical reactions that occur at the interface between the electrodes and the electrolyte. These reactions involve the transfer of lithium ions across the interface and the simultaneous transfer of electrons through the external circuit. As a result, they are strongly influenced by the concentrations and potentials in both the electrodes and the electrolyte. The rate at which these reactions occur directly impacts a battery's power output, efficiency, and charge/discharge behavior.

When the battery is operating, the electrodes are no longer at their OCPs, and there is a driving force for the reactions. This driving force is defined as the overpotential, which is the difference between the electrode potential (minus the electrolyte potential) and the OCP. Reaction kinetics provide the mathematical framework for linking this overpotential to the actual rate of the interfacial reactions.

The most commonly used equation to describe reaction kinetics in batteries is the Butler-Volmer equation. It provides a detailed, non-linear relationship between the overpotential and the current density (reaction rate) at the electrode surface.

The Butler-Volmer equation is expressed as,

where

• i is the net current density.

• i₀​ is the exchange current density, which represents the reaction rate at equilibrium.

• η is the overpotential.

• αₐ and α꜀​ are the anodic and cathodic charge transfer coefficients, respectively.

• F is the Faraday constant, R is the universal gas constant, and T is the temperature.

Note that, if αₐ = α꜀ = 0.5, the two exponentials can be combined into a hyperbolic sine function, which is commonly found in battery models. At small overpotentials, both terms in the equation contribute, leading to a symmetrical response around equilibrium and representing a reversible reaction. However, at higher overpotentials, one term dominates (depending on whether the reaction is anodic or cathodic), and the equation simplifies to the Tafel equation:

The Tafel equation is commonly used to describe irreversible reactions, as the current becomes exponentially small when the overpotential is negative.

In physics-based models, reaction kinetics play a critical role in describing the interfacial behavior between the electrodes and the electrolyte. These kinetics strongly couple the equations for the concentrations and potentials in the electrodes and the electrolyte.

The Butler-Volmer equation is used to describe the reversible reaction of lithium intercalation into active material particles. The Tafel equation, on the other hand, is typically applied to irreversible degradation reactions, such as the growth of the solid-electrolyte interphase (SEI).

Reaction kinetics are the bridge between the thermodynamics of equilibrium (OCPs) and the dynamic behavior of a battery under use. They are a key factor in the trade-off between current and capacity. In our next post, we’ll discuss battery capacity—how it is measured and which factors influence it.