Addressing limitations of the endpoint slippage analysis

Some rate of oxidation and reduction side-reactions will inevitably coexist in most rechargeable batteries, contributing to reversible and irreversible self-discharge. While parasitic reduction traps electrons, parasitic oxidation donates electrons to the cells inventory and can lead to temporary capacity gain. This causes direct capacity measurements to be an unreliable source of information about the total extent of side-reactions happening in the cell. The most widely used method to determine the rate of these two types of parasitic processes involves analyzing the slippage of endpoints, which consists in tracking the termination of cell charge and discharge when data is represented along a cumulative capacity axis. Here, we argue that this approach could lead to inaccuracies when applied to certain systems, which includes Si electrodes in Li-ion batteries and hard carbon in Na-ion batteries. We analyze this issue in quantitative terms and propose equations that can provide true rates of parasitic processes from experimental endpoint slippage data. This work shows that, in battery science, well-established analytical approaches may not be directly transferrable to new electrode systems.

💡 Research Summary

The paper critically examines the widely used endpoint‑slippage method for quantifying parasitic oxidation and reduction reactions in rechargeable batteries. Traditionally, this technique assumes that in a graphite‑based negative electrode the charge is limited by the positive electrode (PE) and discharge is limited by the negative electrode (NE). Under this assumption, reduction side‑reactions (e.g., SEI formation) shift only the discharge endpoint, while oxidation side‑reactions shift only the charge endpoint, allowing a direct mapping of endpoint shifts to the rates ΔQ_red and ΔQ_ox.

The authors demonstrate that this simple mapping breaks down for electrode systems whose voltage‑capacity curves lack flat plateaus and exhibit gentle slopes, such as silicon‑based anodes in Li‑ion cells and hard‑carbon anodes in Na‑ion cells. In these cases, a reduction reaction raises the NE potential, forcing the PE to delithiate further to reach the voltage cutoff; consequently the charge endpoint also moves. Likewise, oxidation can cause a modest shift of the discharge endpoint. The magnitude of these cross‑effects depends on the local voltage gradients of the PE and NE at the end‑of‑charge (EOC) and end‑of‑discharge (EOD) points.

To capture this behavior, the authors introduce two correction coefficients, α and β, derived from the slopes ∂V/∂Q of the PE and NE at EOC and EOD and the imposed voltage limits. The generalized relationships become:

ΔQ_c = α·ΔQ_ox + β·ΔQ_red
ΔQ_d = α·ΔQ_red + β·ΔQ_ox

When α = β = 0 the classic equations are recovered; otherwise the measured slippage must be de‑convoluted using the above formulas to obtain the true parasitic rates.

The paper validates the theory through extensive simulations. Voltage profiles from half‑cells (NMC811, NMC532, graphite, Si, hard carbon) were combined with controlled shifts representing oxidation or reduction. By varying Si content, voltage cut‑offs, and electrode loadings, the authors map how α and β evolve. They find that for Si fractions above ~30 wt % or for narrow voltage windows, α and β become significant, leading to up to 20 % error if uncorrected. Conversely, low Si content (<10 wt %) or wide voltage windows render the correction negligible. Similar trends are observed for Na‑ion cells with hard‑carbon anodes, where the PE’s steep voltage rise yields a non‑zero α.

A practical workflow is proposed: (1) extract the local voltage slopes at EOC/EOD from experimental dV/dQ curves; (2) compute α and β using the known voltage limits; (3) apply the correction equations to measured endpoint shifts to retrieve ΔQ_ox and ΔQ_red. This enables accurate quantification of parasitic processes from routine cycling data, even for emerging electrode chemistries.

In summary, the work reveals that endpoint‑slippage analysis is not universally transferable; its reliability hinges on electrode voltage characteristics. By introducing analytically derived correction factors, the authors provide a robust method to extract true oxidation and reduction rates across a broad range of battery chemistries, improving electrolyte screening, electrode design, and lifetime prediction.