The Measurement Challenge:
Decoupling Intercalation Kinetics from Chemical Capacitance

In my previous essay on Chemical Capacitance, I concluded with a fundamental question: if an intercalation material remembers every charge-transfer event through a continuous shift in its thermodynamic state, how can we hope to isolate and measure the charge-transfer kinetics themselves?

This question lies at the heart of our recently published Viewpoint in ACS Energy Letters: "Charge-Transfer Kinetics of Intercalation Reactions: A Measurement Challenge" (Choi et al. 2026). In this paper, we pinpoint the root cause of why the academic community remains deeply divided over how battery intercalation kinetics should be modeled. While some argue a standard Butler-Volmer (BV) model is sufficient, others claim a film resistor is necessary, and recent high-profile work suggests that coupled ion-electron transfer (CIET) theory is required.

Our core premise is that this disagreement is not necessarily a reflection of differing materials physics, but rather a direct consequence of methodological limitations. Because intercalation materials store charges inside their host lattice, redox potentials shift during transient measurements, rendering the resulting kinetic parameters highly model-dependent.

Dissecting the Literature: Where Common Methods Diverge

To prove this point, we performed a rigorous numerical audit of three major electroanalytical methods proposed in recent literature. By setting an arbitrarily assumed "truth" (such as a standard symmetric Butler-Volmer equation) in a simulated electrochemical cell, we tested whether each method could successfully recover the underlying parameters.

Method 1: Linear Extrapolation to t = 0

One common approach is to apply a current step-up to a single-particle electrode and record the voltage response. To filter out the slow redox potential shift, researchers fit a linear function to the voltage transient (typically between 2 and 10 seconds) and extrapolate back to t = 0 to obtain the "instantaneous" overvoltage.

Our numerical audit showed that while this method is highly accurate in the linear low-overpotential regime (η < k_BT/e), it systematically deviates at larger overpotentials (η > 3 k_BT/e). Because reaction currents scale exponentially with overpotential in the non-linear regime, any linear extrapolation error is amplified. Consequently, the method overestimates the reaction overvoltage, misinterpreting the dynamic stoichiometry changes as film-resistor resistance.

Method 2: Time-Readout at Resonant Frequency τ

Another prominent method applies a voltage step-up and measures the current response at a specific time τ, which is identified from the resonant frequency of the charge-transfer semicircle in EIS. The goal is to measure after double-layer charging has decayed but before significant stoichiometry drift occurs.

When we simulated this protocol, we made a striking discovery: the recovered current-potential curve became almost completely flattened, mimicking a linear resistor even though the true input kinetics were highly non-linear.

This artifact occurs for two reasons:

1. Bias Partitioning to Warburg Pseudocapacitance: Even at the short time τ, the diffusive chemical capacitance (modeled by a Warburg impedance) takes up a significant portion of the applied voltage (often over 10%), leading to an overestimation of the actual reaction overvoltage.
2. Charging Timescale Mismatch: The resonance timescale τ = R_CTC_DL is not the physical timescale that governs double-layer charging, which is instead determined by R₀C_DL. Measuring at τ is somewhat arbitrary and fails to isolate clean charge-transfer current.

Method 3: Large-Amplitude and Operando GEIS

A third method attempts to bypass transient shifts by using frequency-domain analysis under large-amplitude sinusoidal excitations. However, our simulations showed that even under an idealized, zero-redox-shift scenario, the harmonic interference in the frequency domain misidentifies the charge-transfer symmetry factor (α). A true symmetric barrier (α = 0.5) was recovered as highly asymmetric (α ≈ 0.7), indicating that the method introduces intrinsic mathematical artifacts.

Toward Verifiable Battery Kinetics

These findings lead to a sobering conclusion: currently popular electroanalytical methods are insufficient to confidently determine the charge-transfer kinetics of Li intercalation. The very property that makes batteries useful—their high chemical capacitance—is what prevents us from obtaining clean kinetic measurements.

Any adjustment method that attempts to correct for the redox potential shift must assume a specific model beforehand. But in the highly non-linear Tafel regime, even minor errors in the assumed model are exponentially amplified, creating a circular logic loop where the measured kinetics simply reflect the assumptions of the correction model.

To break this circularity, we must move away from standard transient correction schemes. Instead, we anticipate that the path to a truly verifiable measurement lies in decoupling the thermodynamic shift from the kinetic signal.

By exploring alternative measurement environments that can manage or bypass local state evolution during the active charge-transfer process, we hope to establish a cleaner observation window. If we can minimize or mathematically isolate the dynamic potential shifts, we will be able to probe the charge-transfer kinetics more directly. Redefining this measurement environment is the challenge we must tackle next.