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REVIEW 4 major objections 6 minor 64 references

Depth-resolved measurement of solvation entropy, interfacial transport and charge-transfer kinetics of practical lithium-ion batteries

T0 review · 4 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Thermal ripples from electrochemical heat reveal what happens at each electrode inside a working battery.

desk verdict The depth-resolved 1ω entropy measurement is credible and new, but the paper's headline 2ω claim — separating charge-transfer from transport resistance — is not supported by its own sensitivity analysis. read the letter →

arxiv 2411.10920 v2 pith:WKQZBAAW submitted 2024-11-17 physics.chem-ph

Divya Chalise , Sean D. Lubner , Sumanjeet Kaur , Venkat Srinivasan , Ravi S Prasher This is my paper · ORCID
classification physics.chem-ph PACS 82.47.Aa
keywords METSmulti-harmonicelectro-thermalspectroscopythermalpenetrationdepthsolvationentropycharge-transferresistancesolid-electrolyteinterphaseoperandocharacterizationlithium-ionbatteries
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper claims that the heat a lithium-ion cell produces while an alternating current passes through it can be turned into a depth-resolved, operando probe of each electrode-electrolyte interface. By measuring the resulting temperature oscillations at the first and second harmonics of the current, the authors recover the solvation entropy, interfacial transport resistance, charge-transfer resistance, and SEI resistance separately for the two electrodes in practical cells. This matters because conventional impedance or voltage measurements average over the whole cell or require symmetry assumptions, so they cannot tell which electrode is degrading or how much of the interfacial impedance is transport versus kinetics. The paper demonstrates the method on lithium symmetric, NMC-lithium, and a cell with electrodeposited and foil lithium electrodes, and shows operando SEI growth at one interface.

What carries the argument

Multi-harmonic Electro-Thermal Spectroscopy (METS) uses the thermal penetration depth $\delta = \sqrt{\alpha/\omega}$ as the depth selector and the harmonic order plus current-amplitude scaling as the process selector. Entropic heat at $1\omega$ is measured at high frequencies where only the near-sensor interface contributes, and then at lower frequencies where the second interface contributes; $2\omega$ heat from transport (ohmic, current-squared) and charge transfer (nonlinear, weaker than current-squared) is measured at several current amplitudes to separate the two. Feldman's algorithm for periodic heating in a stratified medium converts the computed heat-generation rates into the surface temperature spectrum that is fitted to the lock-in thermometry data.

What would settle it

A direct test would be two otherwise identical symmetric cells whose exchange current density differs by an order of magnitude, for example through different electrolyte additives, while their SEI transport resistance is the same. If METS $2\omega$ spectra fitted with a small imposed charge-transfer resistance return the same transport resistance in both cells while independent measurements confirm the kinetic difference, the separation holds; if the fitted transport resistance shifts when only kinetics changes, the charge-transfer/transport split is not valid.

Watch

Extended reading notes

Core claim

The central claim is that electrochemical heat sources carry enough information to serve as spatially resolved sensors of their own interfaces. Reversible solvation heat is proportional to current and appears at the first harmonic, while irreversible Ohmic heat from SEI/CEI transport is proportional to current squared and appears at the second harmonic; the nonlinear Butler-Volmer overpotential adds a second-harmonic heat component whose current scaling differs from a pure square law. Because a thermal wave at angular frequency $\omega$ decays over penetration depth $\delta = \sqrt{\alpha/\omega}$, high-frequency signatures come only from the interface nearest the sensor and low-frequency signatures include both interfaces. Fitting the measured in-phase and out-of-phase temperature spectra with a layered heat-diffusion model yields the entropic coefficient at each interface and splits the total interfacial impedance into transport and charge-transfer parts. The authors validate the totals against EIS and demonstrate that two chemically similar lithium electrodes can have very different transport resistances, and that SEI growth can be tracked in real time.

Load-bearing premise

The load-bearing premise is that the charge-transfer resistance is small enough that the second-harmonic signal is insensitive to it: the reported charge-transfer values are imposed rather than measured, so if real kinetics were slow, the transport resistances fitted from the same spectra would be wrong.

Editorial extensions

If this is right

  • METS can assign the overlapping semicircles of an EIS spectrum to a specific electrode and split each into transport and charge-transfer resistance without assuming equal electrodes.
  • SEI resistance at an individual lithium-electrolyte interface can be followed operando; after cycling at 40 °C, the foil electrode's transport resistance grew from 15.75 $\Omega$ to 32.6 $\Omega$, while the electrodeposited electrode's grew from 1.35 $\Omega$ to 3.26 $\Omega$.
  • Solvation entropy can be measured at the cathode and anode separately inside a working cell, not only as a cell-averaged or symmetric-cell quantity.
  • Because the heat signatures are electrochemical rather than structural, the approach applies to other battery chemistries and to arbitrary sensor positions within multilayer stacks.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If METS is as local as it appears, it could become an early failure-localization tool: a sensor on a cell tab might flag which electrode first develops high SEI resistance or plating-related heating before the cell's global impedance changes, a diagnostic the paper does not demonstrate.
  • The same harmonic-separation logic could be pushed to lower frequencies to capture mass-transport heat, which the authors leave for future work, potentially yielding depth-resolved diffusion properties rather than only resistances.
  • A decisive extension would be to vary exchange current density on purpose, for example with additives or temperature, and check whether METS recovers the expected kinetic change; the paper reports charge-transfer values that are small and effectively imposed in the fits.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper introduces Multi-harmonic Electro-Thermal Spectroscopy (METS), an operando technique in which an AC current drives an electrochemical cell while a lock-in resistance thermometer on the cell exterior records 1ω and 2ω temperature oscillations. Thermal penetration depth is used to attribute heat sources to specific electrode–electrolyte interfaces, and the harmonic content is used to separate reversible entropic heat (1ω) from irreversible ohmic and kinetic heat (2ω). The 1ω spectra are fitted to yield entropic coefficients at each interface (1.2 mV/K for a Li symmetric cell; 1.3 and 1.0 mV/K for an NMC–Li cell; 1.05 and 1.33 mV/K for an NMC–graphite cell), with literature agreement in all three configurations. The 2ω spectra at multiple current amplitudes are fitted to extract interfacial transport and charge-transfer resistances at each electrode and to track SEI growth. The paper claims depth resolution of a few microns and validation against EIS, and it reports the 2ω decomposition as the central new capability.

Significance. The 1ω entropy measurement is the strongest part of the paper: per-interface solvation entropy in an operating cell is a genuinely new observable, and the authors support it with quantitative agreement against literature values in three independent cell configurations, including a falsifiable dual-sensor sign-reversal test in an NMC–graphite cell. The SI also contains a clean control experiment (a serpentine heater with an independently measured resistance, fit to within 5%) that validates the thermal-analysis chain. If the 2ω claims are corrected, the technique still provides per-interface total interfacial resistance without symmetric-electrode assumptions, which is useful for identifying defective electrodes. However, the claimed separation of charge-transfer resistance from interfacial transport resistance is not supported by the paper's own sensitivity analysis and uncertainty quantification: the reported R_CT values are effectively priors. The 'few microns' depth-resolution claim in the abstract is likewise not supported by the demonstrated interface-level attribution.

major comments (4)
  1. [2ω analysis; Fig. 6(c)–(d); Table 1; SI §12] The decomposition of the 2ω interfacial impedance into charge-transfer and transport components is not identifiable in the reported operating regime, and the paper's own diagnostics confirm the reviewer's concern. The Figure 6 caption states that 'both in-phase and out-of-phase temperature measurements are also not very sensitive to the exchange current density (conversely the charge-transfer resistance) at both interfaces,' and the main text states that sensitivities to charge-transfer resistance are small compared with those to transport resistance. This is expected from the operating point: with R_CT ≈ 0.2–0.5 Ω and I0 = 12–22 mA, the peak overpotential is 2.4–11 mV, well below RT/F ≈ 25.7 mV, so the Butler–Volmer relation is in its linear regime and kinetic heat I²R_CT is functionally identical to ohmic transport heat I²R_SEI; the sub-quadratic nonlinearity invoked for separation is a correction of order (Fη/2RT)² ≈ 1%, far below the ~10% measurement noise. Consistent with this, the reported R_CT values are identical at both electrodes in every cell (0.5/0.5 Ω in Tables 1 and 2; 0.2/0.2 Ω in the NMC row), carry uncertainties that include zero (0.5 ± 0.88 Ω in Table 1), and are explicitly imposed in SI §12 ('assuming a small charge-transfer resistance for both (0.2 Ω)'). The four-component resolution claimed in the abstract and Introduction is therefore a model prior, not a measurement outcome; if the true R_CT were non-negligible, the reported transport resistances would shift by the same amount. The 2ω analysis should be reframed to report per-interface total resistance (R_SEI + R_CT) with R_CT given as an upper bound, or the nonlinear-regime operation (η ~ RT/F) must be demonstrated with a control in which R_CT is independently varied.
  2. [Table 1, NMC–Lithium row] The claim that EIS provides independent per-interface validation is not supported by Table 1. For the NMC–Li cell, EIS attributes 2.26 ± 0.23 Ω to the lithium interface and 10.1 ± 1.0 Ω to the cathode, whereas METS yields 0.5 + 0.2 = 0.7 Ω and 12.2 + 0.2 = 12.4 Ω for the same two interfaces. The anode discrepancy of ~1.56 Ω is about 5σ with respect to the combined uncertainties and is not discussed; only the totals agree (13.1 vs 12.36 Ω). The same direction of bias appears in the post-SEI electrodeposited cell, where METS assigns 3.26 + 0.5 = 3.76 Ω to the near electrode versus 4.6 ± 0.46 Ω from EIS, but 32.6 + 0.5 = 33.1 Ω to the far electrode versus 22.3 ± 2.23 Ω from EIS. This systematic pattern of over-attributing resistance to the far interface suggests a depth-attribution or heat-source-modeling issue (for example, in the uniform volumetric-heating assumption for the porous cathode or in the thermal interface resistance inputs) and must be explained or quantified before the per-interface claims can be regarded as validated.
  3. [Abstract; SI §5] The abstract's claim of 'depth resolution of a few microns' is not supported by the demonstrated capability or by the paper's own statements. SI §5 states that the measurement cannot significantly differentiate the spatial distribution of heat within the 60-µm porous cathode, and that the assumed interfacial heat-generation location (15 nm versus 1 µm) does not affect the results. At the highest measured frequency (30 Hz), the thermal penetration depth in the electrode materials is of order 0.5 mm, larger than the ~100–200 µm stack, so the measurements discriminate heat sources at two interfaces separated by roughly 100 µm rather than localizing heat to micron scales. The abstract should be reworded to claim interface-level attribution within a known stack geometry, or a dedicated resolution test should be provided.
  4. [Table 2, post-SEI growth row] The consistency between the METS and EIS totals is marginal in the post-SEI electrodeposited cell and is not addressed. Table 2 reports a METS total of 35.8 ± 6.28 Ω versus an EIS total of 26.9 ± 2.7 Ω; the 8.9 Ω difference is about 33% of the EIS value and exceeds the combined 1σ uncertainty. In addition, the pre-SEI total (18.1 Ω) includes the two 0.5 Ω charge-transfer contributions, while the post-SEI total (35.8 Ω) excludes them (3.26 + 32.6 = 35.86), so the table is arithmetically inconsistent in how the reported 'Total' is formed. The growth in discrepancy after SEI growth should be quantified and explained, since the SEI-growth demonstration is a headline application.
minor comments (6)
  1. [Figure 2 discussion, main text] The sign-convention discussion around Figure 2 is internally contradictory: the text first states 'at higher frequencies (>1 Hz) ... the in-phase temperature rise is positive for a positive entropic heating at Interface 1' and then, a few sentences later, 'for Interface 1, at higher frequencies (>1Hz, short penetration depth), the in-phase temperature rise is negative while at lower frequencies ... the in-phase temperature rise is positive'; the intervening sentence invoking Feldman's solution also mixes the in-phase and out-of-phase terms ('the out-of-phase temperature rise is negative'). These statements should be corrected and made consistent with the figures and with SI §9.
  2. [Figure 2(b) discussion, main text] In the NMC–Li description, the sentence 'the out-of-phase temperature is not cancelled at lower frequencies (<1Hz), and theoretically keeps rising as the frequency increases' appears to mean 'as the frequency decreases'; the direction of the frequency sweep should be corrected.
  3. [Figure and table cross-references] Several cross-references are inconsistent: the post-SEI paragraph cites 'Figure 5 (b)' for the EIS spectrum that is shown in Figure 4(b); the comparison table for the electrodeposited cell is called 'Table 3' in the text but is captioned 'Table 2'; and the main-text paragraph refers to 'Table 3' where Table 2 is evidently meant. These should be reconciled.
  4. [Abstract and Introduction] The acronym expansion is inconsistent: the abstract defines METS as 'Modulated Electrothermal Sensing' while the Introduction defines it as 'Multi-harmonic Electro-Thermal Spectroscopy'; the header title of the manuscript also differs from the arXiv title. The terminology should be unified.
  5. [Data and Code Availability] The manuscript states that data and MATLAB code are available 'upon request'; for a measurement technique whose central claims rest on non-unique fitting, depositing the fitting code and representative raw spectra in a public repository would substantially strengthen the paper and is recommended.
  6. [Figures 5 and S12] Because the R_CT/R_SEI separation is claimed to rest on the sub-quadratic current scaling of the kinetic heat, the authors should add a plot of the 2ω temperature amplitude normalized by I0² against I0² (or against a dimensionless overpotential) for the three current amplitudes; the present presentation cannot visually demonstrate the effect on which the separation claim depends.

Circularity Check

1 steps flagged · score 6.0 of 10

2ω charge-transfer/transport decomposition reduces to an assumed R_CT: the paper's own sensitivity analysis shows the signal is insensitive to R_CT, and SI fits assume 0.2 Ω.

  1. fitted input called prediction [Figure 6 caption; supported by SI Section 12 ('assuming a small charge-transfer resistance for both (0.2 Ω)')]
    "Because of the fast-charge transfer kinetics (small charge-transfer resistance), both in-phase and out-of-phase temperature measurements are also not very sensitive to the exchange current density (conversely the charge-transfer resistance) at both interfaces."

    The paper claims the 2ω spectra at multiple current amplitudes separate R_CT from R_transport because Butler-Volmer nonlinearity makes kinetic heat scale sub-quadratically with current. But the same paper states the 2ω signal is insensitive to R_CT. In the fitted regime (reported R_CT ~0.2–0.5 Ω, currents 12–22 mA), the overpotential is ~4–11 mV, well below RT/F, so Butler-Volmer is effectively linear and kinetic heat is Q = I^2·R_CT, with exactly the same I^2 dependence and 2ω in-phase/out-of-phase form as ohmic SEI transport heat (SI Eqs. S20–S25). Changing current amplitude therefore changes both terms identically, so the fit cannot identify R_CT.

full rationale

The 1ω entropy measurement is self-contained: the entropic coefficients are fit from the 1ω thermal spectra and then cross-checked against independent literature values (Wang et al., Cahill et al.), so that part of the derivation is not circular. The spatial attribution of transport resistances is also partially constrained by the thermal penetration depth argument and by the total-resistance check against EIS. However, the paper's central 2ω claim—that interfacial impedance is uniquely resolved into charge-transfer and transport components—does not survive inspection. The paper's own Figure 6 caption says the 2ω measurement is not sensitive to R_CT, and the SI multilayer analysis explicitly assumes R_CT = 0.2 Ω. In the small-overpotential regime used here, the charge-transfer heat generation is functionally identical to ohmic SEI heat generation (both scale as I^2 at 2ω), so the multi-current fitting cannot separate them. Thus the reported charge-transfer resistances are model priors presented as measured quantities. This is a partial circularity of the central claim, not a full collapse: the transport resistances, SEI growth, and entropy results retain independent content and are benchmarked against EIS and literature. Score 6 reflects one load-bearing 'prediction' (R_CT) that reduces by construction to an assumed input.

Assumptions & free parameters 7 free parameters · 7 assumptions · 0 invented entities

The central electrochemical parameters (entropic coefficients, transport and charge-transfer resistances) are fit outputs from the METS spectra. The thermal model requires assumptions about heat source geometry and thermal properties. No new physical entities are introduced.

free parameters (7)
  • Entropic coefficient at Interface 1 (closest to sensor) = 1.2 mV/K (Li symmetric); 1.3 mV/K (NMC-Li); 1.05 mV/K (NMC-graphite)
    Fitted to high-frequency 1ω in-phase and out-of-phase spectrum; validated against literature values.
  • Entropic coefficient at Interface 2 (further from sensor) = 1.2 mV/K (Li symmetric); 1.0 mV/K (NMC-Li); 1.33 mV/K (NMC-graphite)
    Fitted to low-frequency 1ω out-of-phase spectrum after fixing Interface 1.
  • Interfacial transport resistance at Interface 1 = 9.02 Ω (Li symmetric); 0.5 Ω (NMC-Li); 1.35 Ω (electrodeposited Li pre-SEI)
    Fitted to 2ω spectrum at multiple current amplitudes.
  • Interfacial transport resistance at Interface 2 = 13.75 Ω (Li symmetric); 12.2 Ω (NMC-Li); 15.75 Ω (foil Li pre-SEI)
    Fitted to 2ω spectrum; sum matches EIS within uncertainty except post-SEI case.
  • Charge-transfer resistance at Interface 1 = 0.5 Ω (Li symmetric); 0.2 Ω (NMC-Li)
    Fitted but with very low sensitivity, effectively set by the assumption of fast kinetics.
  • Charge-transfer resistance at Interface 2 = 0.5 Ω (Li symmetric); 0.2 Ω (NMC-Li)
    Same as above; not determined by the data because of insensitivity.
  • Electrode-separator thermal interface resistances (from 3ω fits) = e.g., 5 cm2K/W (Li symmetric); 0.02 and 12.5 cm2K/W (electrodeposited-foil)
    Fitted to separate 3ω measurements and used as thermal inputs to the METS model.
assumptions (7)
  • domain assumption Butler-Volmer kinetics with symmetry factor α = 0.5
    Used to model charge-transfer overpotential and its harmonic content; SI Section 2, Eq S4.
  • domain assumption Ideal double-layer capacitance with no leakage
    Capacitive branch stores no energy and generates no 2ω heat; SI Section 2.
  • domain assumption Neglect of concentration (Warburg) effects via Sand's time criterion
    Justified by operating at frequencies f ≥ 10/τ; SI Eqs S1-S3.
  • standard math Feldman's layered thermal diffusion solution
    Used to compute surface temperature from distributed heat sources; validated by a heater experiment within 5%.
  • ad hoc to paper Interfacial heat generation confined to a thin layer (1 nm) or the first 15 nm of the electrode
    The choice of thickness does not significantly affect results if thin; SI Section 5.
  • ad hoc to paper Uniform volumetric heat generation in the porous cathode
    Porous electrode is homogenized; non-uniform current distribution is not resolved at 0.1-30 Hz; SI Section 5.
  • domain assumption Thermal properties of layers known from 3ω, DSC, and literature, with some estimated values
    Uncertainties in thermal properties propagate into the METS fit; Table S4.

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Cite this review

Pith. "Pith review of Depth-resolved measurement of solvation entropy, interfacial transport and charge-transfer kinetics of practical lithium-ion batteries." pith.science (2026). https://pith.science/paper/WKQZBAAW

@misc{pith2026241110920,
  author       = {Pith},
  title        = {Pith review of: Depth-resolved measurement of solvation entropy, interfacial transport and charge-transfer kinetics of practical lithium-ion batteries},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WKQZBAAW}},
  note         = {Machine review of arXiv:2411.10920}
}
read the original abstract

Understanding the performance of electrochemical energy storage systems requires probing the electrochemical properties at each layer and interface during cell operation. While traditional onboard and operando methods can measure impedance, voltage, or capacity, they lack spatial resolution to pinpoint the properties to specific layers and interfaces. In this work, we describe an approach of using thermal waves to measure entropy change, transport resistance, and charge-transfer resistance with depth resolution of a few microns within an electrochemical cell. We achieve this by relating heat generation at multiple harmonics of an AC current to electrochemical processes and leveraging frequency dependence of thermal penetration depth for spatial resolution. We name this frequency domain spectroscopy of the thermal signatures of the electrochemical processes measured at multiple harmonics of the alternating current as Multi-harmonic ElectroThermal Spectroscopy (METS). This technique enables isolation and measurement of solvation entropy at individual electrode-electrolyte interfaces from the first harmonic (1{\omega}) thermal signature and resolution of the overall interfacial impedance into charge-transfer and interface transport resistance components from the second harmonic (2{\omega}) thermal signature. From this, we also demonstrate an operando measurement of the growth of the solid-electrolyte interphase (SEI) layer at the lithium-electrolyte interface and show that two chemically similar electrodes can have significantly different interfacial transport resistance based on the preparation of the electrodes. Additionally, the method is not specific to lithium-ion chemistry and can therefore be generalized for all electrochemical systems of interest.

Figures

Figures reproduced from arXiv: 2411.10920 by the authors.

Figure 1
Figure 1. (a) Schematic of the symmetric lithium-ion cell with heat generated at the two electrode￾electrolyte interfaces when an alternating current is passed through the cell. The expanded view illustrates the electrochemical processes leading to the heat generation at the electrode-electrolyte interface in the cell. The process of charge transfer at the interface generates irreversible heat which is non-Ohmic in nature. Ad… view at source ↗
Figure 2
Figure 2. (a) 1𝜔 temperature spectrum of the symmetric lithium cell plotted with the in-phase (red crosses) and out-of-phase (green circles) components of the temperature oscillation with respect to the alternating current passing through the cell. Going from higher frequency (30 Hz) to a lower frequency (1 Hz), the out￾of-phase temperature, corresponding to the sensible heat, increases as the thermal penetration depth increa… view at source ↗
Figure 3
Figure 3. Thermal penetration depth and entropic coefficient interplay in an NMC523-graphite cell with dual-side sensors at 50% SOC with the measurement from the cathode side sensor (a) and from the anode side sensor (b). Experimental best-fit entropic coefficients are obtained at 1.05 ± 0.14 mV/K for anode and 1.33 ± 0.09 mV/K for cathode. Low-frequency measurements show cathode-side dominance (positive temperature rise at t… view at source ↗

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.