Endpoint slippage analysis in the presence of impedance rise and loss of active material

The endpoint slippage analysis can be used to quantify the reduction and oxidation side-reactions occurring in rechargeable batteries. Application of this technique often disregards the interference of additional aging modes, such as impedance rise and loss of active material (LAM). Here, we show that these modes can themselves induce slippage of endpoints, making the direct determination of parasitic reactions more difficult. We provide equations that describe the slippages caused by LAM and impedance rise. We show that these equations can, in principle, account for the contribution of these additional modes to endpoint slippage, enabling correction of testing data to quantify the side-reactions of interest. However, the challenge with this approach is that it requires information about the average Li content of disconnected active material domains, which is, in many cases, unknowable. The present work explores mathematical connections between measurable quantities (such as capacity fade and endpoint slippages) and the extent of LAM or impedance rise endured by the cell, and discuss how the tracking of endpoints can better serve battery diagnostics.

💡 Research Summary

The paper investigates how two common aging mechanisms—impedance rise and loss of active material (LAM)—interfere with the endpoint‑slippage analysis that is routinely used to quantify parasitic reduction and oxidation reactions in rechargeable batteries. Endpoint slippage works by plotting charge and discharge voltage profiles on a cumulative‑capacity axis; the positions where the cell reaches its voltage cut‑offs (end‑of‑charge, EOC, and end‑of‑discharge, EOD) shift when side reactions consume or generate lithium. In an ideal system, a rightward shift of the discharge endpoint indicates reduction‑type parasitic consumption, while a rightward shift of the charge endpoint signals oxidation‑type parasitic generation.

The authors first review the classic picture for graphite‑NMC cells, then introduce four archetypal LAM scenarios defined by Dubarry et al.: loss of lithiated or delithiated material on either electrode, depending on whether disconnection occurs during charge or discharge. Each scenario traps a different amount of Li⁺ in the isolated domains, thereby altering the amount of lithium that can be reversibly shuttled in subsequent cycles. For example, LAM occurring on the negative electrode while the cell is charged (LAMliNE) removes both active sites and the lithium they contain, leading to a rightward shift of the discharge endpoint that mimics reduction‑type slippage, while leaving the charge endpoint unchanged. Conversely, loss of delithiated positive‑electrode material (LAMdePE) initially leaves both endpoints unchanged, but once enough material is lost the discharge endpoint shifts rightward because the remaining positive material becomes the limiting factor.

Impedance rise, typically arising from interfacial thickening on the positive electrode, is modeled as an added over‑potential (e.g., 50 mV). This extra polarization shortens the charge half‑cycle, moving the charge endpoint leftward, while the discharge endpoint is largely unaffected because the steep negative‑electrode voltage rise dominates the determination of EOD.

The core contribution of the work is a set of analytical expressions that relate the measured endpoint shifts (ΔEOC, ΔEOD) to the magnitudes of parasitic reduction, parasitic oxidation, each LAM mode, and impedance rise. The expressions involve two key parameters, α and β, which are the slopes (dV/dQ) of the positive and negative electrode voltage curves at the EOC and EOD, respectively. Because the derived formulas are linear and additive, the total slippage observed between two cycles can be expressed as the sum of the individual contributions. Consequently, if independent measurements of LAM extent (e.g., from differential voltage analysis) and impedance increase are available, one can set up a system of two equations with two unknowns (the true parasitic capacities) and solve for them, effectively “correcting” the raw slippage data.

A practical demonstration using simulated voltage profiles shows that the method can recover the underlying parasitic capacities even when LAM and impedance effects are simultaneously present. However, the authors emphasize a critical limitation: the correction requires knowledge of the average Li⁺ content of the domains that become disconnected during LAM. This quantity is generally not directly measurable, especially in complex electrodes such as silicon, where large volume changes and heterogeneous lithiation make the trapped lithium fraction ambiguous. As a result, the correction can be applied only with assumptions or estimates of this trapped‑Li level, introducing uncertainty into the final parasitic‑reaction rates.

In summary, the study extends the endpoint‑slippage framework to incorporate realistic aging phenomena, provides mathematically rigorous and additive correction formulas, and highlights both the promise and the practical challenges of applying these corrections in real‑world battery diagnostics. Future work will need to develop experimental techniques to estimate trapped lithium in isolated domains, and to validate the theoretical corrections against independent measurements of side‑reaction rates.