Incremental Capacity and Voltammetry of Batteries, and Implications for Electrochemical Impedance Spectroscopy
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThis study investigates the interrelationships among cyclic voltammetry (CV), incremental capacity analysis (ICA), and electrochemical impedance spectroscopy (EIS), with particular emphasis on the critical roles of sweep rates in CV and charge/discharge rates in ICA. Furthermore, the implementation of superimposed direct current (DC) bias during EIS measurements demonstrates enhanced equivalent circuit model (ECM) fitting accuracy. However, the following issues require resolution before publication:
1. While the authors acknowledge that previous studies have explored the relationships between cyclic voltammetry (CV) and incremental capacity analysis (ICA), could explicitly elaborate on the novel contributions of this work?
2. The authors are requested to further clarify the significance of CV-ICA correlation.
3. Lines 56-57 (page 2): "...we extend these ideas with an emphasis on the significance of very low sweep/cycling rates, and discuss their relevance to EIS." However, it is counterintuitive that high charge/discharge currents (which induce asymmetry in CV/ICA curves) are claimed to improve the accuracy of equivalent circuit model (ECM) fitting in EIS.
4. Regarding the EIS results under applied working currents described in Lines 244-245 (Page 9), the authors are requested to clarify the novelty of achieving enhanced equivalent circuit model (ECM) fitting accuracy in such operational conditions compared with earlier findings.
5. In Table 1, for the Rs-CPE-CPE equivalent circuits tested under 10 mA and 500 mA square wave currents respectively, the fitted series resistance values (Rs, derived from high-frequency regions) exhibit a significant discrepancy (36.64 mΩ vs. 18.25 mΩ). The authors are requested to address this observed phenomenon.
Author Response
Comment 1. While the authors acknowledge that previous studies have explored the relationships between cyclic voltammetry (CV) and incremental capacity analysis (ICA), could explicitly elaborate on the novel contributions of this work?
Response 1. We thank the reviewer for these helpful comments, which have enabled us to clarify the manuscript in many respects. The novelty of the manuscript lies in our pointing out the underappreciated (or even totally neglected) links between ICA and CV, two techniques that are usually regarded as being entirely unrelated, whereas they can be regarded as being linked by concepts related to rate of charge movement. Indeed, when rate of charge movement (i.e. current) in ICA is small enough, or the voltage ramp in CV gentle enough, and dt is tending towards zero when either dQ/dt or dV/dt is constant, both analyses are equivalent (i.e. will show the investigator the same information). We demonstrate this mathematically and with examples. The fact that peaks corresponding to individual electrode interactions are not normally seen in CV is simply due to the fact that the voltage ramp does not allow the near-equilibrium pseudo-static conditions that we postulate to become apparent because charge is moving much too fast.
We realised when carrying out these experiments that the results had implications for our EIS measurements, which are carried out at extremely low frequencies. To the best of our knowledge we are the only group in the world carrying out such measurements, so it is unlikely that anybody else would have noticed this. We have found in the past that the ECM fitting procedure that we use with our EIS measurements does not work well without the presence of adequate rates of charge movement (the square wave "working current"), and we have been able to relate this to our ICA/CV observations from the cycling experiments.
We appreciate that this may not have been clear in the original as a result of our not providing sufficient background information from previous experiments leading up to this work, and because of the way the paper was structured. To this end, the manuscript has been completely rearranged, considerably more explanatory detail added, and the conclusion partially rewritten. Increased emphasis of the above concepts should, we anticipate, increase the visibility of the novel findings and concepts.
Comment 2. The authors are requested to further clarify the significance of CV-ICA correlation.
Response 2. The reviewer correctly points out that the significance of the correlation may have been lost in the way the manuscript was structured. The mathematics describing the connections between ICA and CV, and the ways in which they might be considered to be related by factors pertaining to rates of charge movement, have been moved down into a new 'Experimental Methods' section where they are closer to the results and discussion, and more explanatory detail has been added to bring home the idea that in CV it is DV/dt that is constant but in ICA dQ/dt is constant. However, when dt becomes small enough, the two become equivalent. Basically, everything comes down to rate of charge movement.
Comment 3. Lines 56-57 (page 2): "...we extend these ideas with an emphasis on the significance of very low sweep/cycling rates, and discuss their relevance to EIS." However, it is counterintuitive that high charge/discharge currents (which induce asymmetry in CV/ICA curves) are claimed to improve the accuracy of equivalent circuit model (ECM) fitting in EIS.
Response 3. We thank the reviewer for this observation, and agree that this would normally be the case in most laboratories. However, our EIS method is unique, and is carried out at extremely low frequencies. We have discovered that our extra-low frequency sinusoidal stimuli are associated with only very small and gradual charge movements, and these allow equilibrium-like conditions to prevail at the electrode (which would not be the case in a working battery). Electrochemical phenomena (which we would want to see when conducting ICA) taking place at these EIS frequencies interfere with the impedance data, and we see inconsistencies and 'drift' between consecutive measurements - two new figures have been added to the manuscript to illustrate this. We have found through experience that the addition of a working square-wave current stabilises impedance measurements and renders them reproducible, with any drift between runs being attributable to battery ageing. We have hypothesised that this is because the working current pushes the cell out of the near-equilibrium electrode state (which we term 'pseudo-static'). While at first glance this may seem counterintuitive in terms of conventional EIS, we have added further detail to the manuscript to emphasise the difference in our approach and why this matters.
Comment 4. Regarding the EIS results under applied working currents described in Lines 244-245 (Page 9), the authors are requested to clarify the novelty of achieving enhanced equivalent circuit model (ECM) fitting accuracy in such operational conditions compared with earlier findings.
Response 4. Again, we thank the reviewer for this comment, and agree that further clarification is required. In the original version of the manuscript we had provided insufficient information on our ECM fitting procedure. We have now remedied this, and greatly expanded the 'ECM Fitting' part of the Methods section. This includes an explanation, with mathematics, of the CPE, and how this relates to our model-fitting method. We know from experience that this works, and we now clearly state in the paper that the findings presented replicate previously reported work in a different battery chemistry. We also describe in the 'Conclusion' section in a way that may have not been apparent previously how the battery ECM is traditionally seen as elements representing individual cell components. This conventional view, which is driven by 'traditional' EIS at frequencies too high to represent the normal cycling of a rechargeable battery, results in excessively complicated and unhelpful ECMs. We assert much more clearly in the revised paper that the simple three-element ECM is sufficient, and the novelty of this is implicit in the statement that we can only derive it by performing EIS at extra-low frequencies. We now state this clearly in the conclusion.
Comment 5. Table 1, for the Rs-CPE-CPE equivalent circuits tested under 10 mA and 500 mA square wave currents respectively, the fitted series resistance values (Rs, derived from high-frequency regions) exhibit a significant discrepancy (36.64 mΩ vs. 18.25 mΩ). The authors are requested to address this observed phenomenon.
Response 5. We have dealt with this in part above. The series resistance value noted in the presence of the negligible square wave is unreliable because of impedance 'drift' phenomena related to pseudo-static conditions at the electrode, further explanation of which we have now added (with figures) to the manuscript. If we ran the measurement again we would almost certainly get another value - we can see this unreliability in what was Figure 4(a) and is now Figure 6(a), where the series resistance drops to a minimum at around 0.1Hz but then rises again sharply at 1Hz.
Reviewer 2 Report
Comments and Suggestions for AuthorsDear authors,
Thank you for the very nicely written and clearly presented article discussing the relationship between the different electrical characterization techniques for batteries. The background theory is very clearly written, and the results are clearly presented and overall easy to follow for the reader. I would already recommend this manuscript for publication as is.
Author Response
Comment 1. Thank you for the very nicely written and clearly presented article discussing the relationship between the different electrical characterization techniques for batteries. The background theory is very clearly written, and the results are clearly presented and overall easy to follow for the reader. I would already recommend this manuscript for publication as is.
Response 1. We thank the reviewer for their encouraging comments. The manuscript has in fact undergone revision, but all the original elements are still in place. The additions have been extra background information, clarifications and reinforcement of key points. There has also been rearrangement of content, but nothing that was in the original has been removed.
Reviewer 3 Report
Comments and Suggestions for AuthorsAuthors present ICA as a method to complement CV measurements, and EIS, at low sweep rate cycling experiments and extra-low frequencies.
Its seems that ICA response is just a scaled CV response, by a factor of k (fig. 2 and fig. 3). Authors confirm this fact themselves in section 4. of the manuscript. Only relevant conclusion is made in the end where they criticize overfitting of EIS data. However, they themselves give no corresponding physical process for CPE1 and CPE2 in their Equivalent circuit model.
Presented method might have some value in testing full cell setup but it doesn't come across the way it is written. Authors should state more clearly what is the novelty here and present in in less convoluted way.
Author Response
Comment 1.
Authors present ICA as a method to complement CV measurements, and EIS, at low sweep rate cycling experiments and extra-low frequencies.
Its seems that ICA response is just a scaled CV response, by a factor of k (fig. 2 and fig. 3). Authors confirm this fact themselves in section 4. of the manuscript. Only relevant conclusion is made in the end where they criticize overfitting of EIS data. However, they themselves give no corresponding physical process for CPE1 and CPE2 in their Equivalent circuit model.
Presented method might have some value in testing full cell setup but it doesn't come across the way it is written. Authors should state more clearly what is the novelty here and present in in less convoluted way.
Response 1. We thank the reviewer for their comments, and agree that rearrangement and clarification of the manuscript was required. The conclusions relating to the overfitting of EIS data were not fact the real point of the manuscript, and we accept that the original did not convey the findings that we wanted to emphasise. As a result, the concluding section has been partially rewritten, and the results and discussion expanded and clarified. The revised manuscript has a much stronger focus on the novelty and uniqueness of our extra-low frequency EIS technique and its utility.
The reviewer is correct that the ICA plots we describe are effectively scaled 'CV-type' measurements, and we have added additional explanation around the mathematical treatment to make this clearer. We reiterate that we have not carried out true CV on this cell because at no time did we apply a voltage ramp and measure the currents generated - the manuscript makes this clear - but we have used a novel analysis to look at the data in different ways. Also, we wish to stress the importance of rate of charge movement because this (rather than simply application of constant current or a constant voltage ramp) is what finally determines what the investigator sees (i.e. something that looks like ICA or CV) and explains why we need a "working" square-wave current to get repeatable and reliable results in our EIS measurements. Nobody else will have reported problems like this because no other laboratories make measurements at such low frequencies.
We would like to address specifically the topic of the physical processes behind the CPEs, because this is what the overfitting of ECMs refers to. ECM fitting based on conventional EIS focuses on patterns in Nyquist plots that supposedly reveal individual electrochemical processes. This approach tends to introduce unmanageable and unnecessary complexity into circuit models, and we state this in the manuscript. We have tried to make clearer the point that the ECM fitting procedure that we use is dependent on data obtained by extra-low frequency EIS and presented in Bode plots, which we believe is unique to our laboratory, and that under these conditions we are able to generate a 3-element CPE that is agnostic to electrochemical processes but that nevertheless models the cell's behaviour accurately. Essentially, the process sees the battery as a 'black box', with behaviour described by the resistor and two CPEs. The CPEs do not represent specific processes, but their fractional characteristics combine to represent the battery reliably.
Comment 2. Presented method might have some value in testing full cell setup but it doesn't come across the way it is written. Authors should state more clearly what is the novelty here and present in in less convoluted way.
Response 2. The novelty lies in the use of the observations with very slow cycling and extra-low frequency EIS to simplify ECM fitting and to relate CV and ICA. Conventional CV classically involves a working electrode, a counter electrode and a reference electrode in a configuration which eliminates or minimises IR drop, which would be hard to realise with a battery. Rather than risking a voltage sweep we suggest that a constant-current method involving very small currents produces a plot similar to that which might be seen if a voltage ramp were applied - 'equivalence' of constant-current and a constant-voltage ramp is only achievable at sufficiently low rates of movement of charge. We note here that since the submission of the first draft we have come across a paper in which authors claim to have applied a very gentle voltage ramp to an NCA battery - their CV plot matches the result that we obtained using a very small constant current to charge and discharge across a similar voltage range. The manuscript has been comprehensively updated in all respects (including expansion of the concluding section with additional explanation) to make all this clearer to the reader.
Reviewer 4 Report
Comments and Suggestions for AuthorsSome points need to be highlighted for a better understanding of the experimental results and to improve the readability of the manuscript:
According to Figure 2a, the voltage response in the initial and final regions of the charge and discharge processes tends to be more vertical (higher slope). Increasing the rate (Figure 3a) resulted in an initial vertical voltage response. What is the reason for the acceleration and further deceleration of the voltage response in these examples? And why is there no vertical behavior in the final regions in the case of Figure 3a? The corresponding explanation should be added to manuscript.
The physical meaning of each ECM component should be revealed, as well as the alpha slopes (including a discussion of the significant difference between alphas).
Reproducibility data is highly desirable, as well as data for the next ECM (R-CPE-CPE).
Author Response
Comment 1. According to Figure 2a, the voltage response in the initial and final regions of the charge and discharge processes tends to be more vertical (higher slope). Increasing the rate (Figure 3a) resulted in an initial vertical voltage response. What is the reason for the acceleration and further deceleration of the voltage response in these examples? And why is there no vertical behavior in the final regions in the case of Figure 3a? The corresponding explanation should be added to manuscript.
Response 1. The shapes of the charging curves reflect the rate of movement of charge (i.e. the size of the current). In Figure 3(a) (now Figure 5(a) in the revised manuscript) the vertical jump in voltage follows the sudden change from -5A to 5A (i.e. 10A total) in discharge/charge current. As V = IR, the I term becomes large, and the instantaneous change over the resistive component of the battery's internal chemistry manifests as a vertical voltage increase. We do not see this with the 100mA scenario in Figure 2(a) (now Figure 4(a)) because the change in current from discharge to charge is only 0.2A. We have added this explanation to the Results and Discussion section.
Comment 2. The physical meaning of each ECM component should be revealed, as well as the alpha slopes (including a discussion of the significant difference between alphas).
Response 2. We have included additional discussion to explain more clearly that the ECM components do not represent individual internal battery processes, but rather that they describe the resistive component and fractional capacitance of the battery. We cross reference back to the 5A cycling plot to show how the ECM relates to the charge/discharge behaviour. We have also added some discussion to clarify the difference between the alpha values. The first value (10mA square wave scenario) results from the inability of the software to fit the second CPE; hence it tries to fit a single CPE using a 'compromise' value that attempts to take in the entire region of the plot that describes the fractional capacitance. The 500mA square wave, however, reveals the second CPE and allows the software to include its contribution. This means that two CPEs, each with an accurate and distinct alpha value, can be used to describe this region of the plot.
Comment 3. Reproducibility data is highly desirable, as well as data for the next ECM (R-CPE-CPE).
Response 3. We can demonstrate reproducibility, and do so by referring back to our previous publication (Dunn C, Scott J. IEEE Trans Instrum Meas 2022;71:1-8) in which we showed success of exactly the same measurement and ECM fitting technique in a different battery chemistry.
