On the importance of the electric double layer structure in aqueous electrocatalysis

To design electrochemical interfaces for efficient electric-chemical energy interconversion, it is critical to reveal the electric double layer (EDL) structure and relate it with electrochemical activity; nonetheless, this has been a long-standing challenge. Of particular, no molecular-level theories have fully explained the characteristic two peaks arising in the potential-dependence of the EDL capacitance, which is sensitively dependent on the EDL structure. We herein demonstrate that our first-principles-based molecular simulation reproduces the experimental capacitance peaks. The origin of two peaks emerging at anodic and cathodic potentials is unveiled to be an electrosorption of ions and a structural phase transition, respectively. We further find a cation complexation gradually modifies the EDL structure and the field strength, which linearly scales the carbon dioxide reduction activity. This study deciphers the complex structural response of the EDL and highlights its catalytic importance, which bridges the mechanistic gap between the EDL structure and electrocatalysis.

The report is a study using mainly computational methods and a few experiments, to study the origin of the electric double layer. The system is a Ag111 surface with water/Na+ or water/F-solution. Several observed effects are very clearly reproduced and a credible molecular explanation is presented for the capacitance peaks. The paper is well-written and the conclusions are clearly presented. However, there are some things to address before the conclusions can be seen as verified. Since the conclusions fully rely on a single computational model which is non-standard and therefore not well tested, it is crucial that this model is benchmarked. Below are some specific points to address.
1. There are some questionable arguments in the molecular origin discussion. It is stated that the cause for F-to adsorb on the surface while Na+ stays further away is due to the smaller hydration energy of anions. In the supporting information the hydration energy for F-is presented as 115-120 kcal/mol, while Na+ has a value of 80-90 kcal/mol. This is precisely opposite to the argument on line 119. It is also stated that the dispersive energy is larger for F-than for Na+, which is likely correct. This should be straight forward to estimate from the Uvdw term. 2. In the parametrization of the Buckingham potential for water, only the geometry with the oxygen adsorbed is probed. However, in the simulations at the cathode most water molecules point the hydrogen towards the surface. This geometry should also be probed, and should probably be tested with a charged Ag cluster. 3. It is not clear if the TIP3P Ag(111) interaction is balanced. I cannot find any benchmark of that. Especially when the surface is charged and the hydrogen points to the surface, the interaction in the presented model seems very strong so that the cations are even pushed out of the first layer. It could be correct, but it could as welle be an artefact from an model that has a too strong interaction between H and Ag. Since TIP3P has an inflated charge distribution to compensate for the lack of anisotropy and other effects, it could lead to the formation of the silver-hydrogen bond formation at the cathode, which in turn seem to completely outcompete the silver cation interaction. I suggest that another water model is tested to see if the electrolyte structure is the same or if it is changed, to avoid the risk of an artefact due to a too simple water model. 4. The interpretation that the electric field difference is the determining factor for the difference in activity when crown-ether is added, could be correct but could as well be incorrect. Direct interaction between the oxygen atoms of -COO at the surface could also stabilize the formation of that adduct, and this interaction would also be limited by addition of crown-ether. There are some recent reports that discuss this phenomenon including Nature Catalysis 2021, 4, 654-662 andJ. Phys. Chem. C 2020, 124, 41, 22479-22487. Overall I believe that this report could provide very interesting and important insight on the catalystsolvent interface under working conditions. There are some questions on the reliability of the method that needs to be addressed and some discussion that could be improved, but the key points of the paper are of high interest. We would like to thank the reviewer for the favorable comments and recognition of the significance of our work.

Notes:
-I recommend the authors consider revising the title to be more specific to the impact of the paper. This is a great paper, but it is hard to get excited by the title.
We would like to thank the reviewer for the thoughtful suggestions regarding the title.
Following the recommendations made by the reviewer, we changed the title from "Revealing the significance of the electric double layer structure for electrocatalysis" to "Electric double layer structure in aqueous electrolyte and its electrocatalytic importance" to reflect the impact of the paper more clearly.
-The authors do not provide enough relevant literature as to the recent developments, both experimental and computational, in the field of interfacial electrocatalysis. It is therefore recommended that some of the works listed below be used to motivate the aims of this manuscript. 10.1039/C7CP06087D, doi.org/10.1063/1.5124878, doi.org/10.1039/C9EE01341E, doi.org/10.1021/jacs.6b07612, doi.org/10.1021/jacs.7b06765, doi.org/10.1038/s41929-021-00655-5, doi.org/10.1021 We would like to thank the reviewer suggesting these additional references. We agree that all of the recommended references are important and have added corresponding citations on pages 3 and 12 of the revised manuscript. We appreciate the recognition of the reviewer regarding the importance of the EDL study, which will have a significant impact on the understanding of electrocatalysis. We also would like to thank the reviewer for recommending the publication of our work in Nature We appreciate the efforts made by the reviewer in critiquing our manuscript and providing us with valuable comments. We also would like to thank the reviewer for recognizing the scientific insights that the present work attempted to address. We fully acknowledge and admire the previous research works that have been devoted to electric double layers.
Following the thoughtful suggestion provided by the reviewer, we avoided using unnecessary superlative expressions and revised the title to address the impact of our present work clearly.
We understand that the major concern of the reviewer is the lack of comparison of our results with previous theoretical works, such as the famous Kornyshev model. To the best of our knowledge, there has been no full understanding of the molecular origin of the camel-shaped differential capacitance observed in dilute aqueous electrolyte systems, which we believe warrants the publication of our work in Nature Communications. We further believe that our fundamental understanding of the EDL structure in aqueous electrolytes provides insight into controlling the electrocatalytic reaction that is relevant to modern renewable energy technologies. A more detailed discussion is provided below.

Below I list my major critiques of this work: 1)-Unwarranted Superlatives and Exaggerated Claims:
The paper is replete with unwarranted superlatives. Here are some examples: a)-In the abstract "Unprecedented structural phase transition" Two issues here. First, the structural changes and phase transitions near the electrode as a function of potential is reasonably accepted and is not unprecedented. Second, just from a language point of view even if it were not the case, it is not the structural phase transition that is unprecedent, but rather its explanation. We agree with the reviewer that the word "unprecedented" was unnecessary and thus have removed it from the manuscript. However, we would like to emphasize that the structural phase transition predicted from our cathodic-polarization simulation is different from the previously suggested ones. For example, the first paper that the reviewer mentioned [Electrochm. Acta, 41, 2207-2227, 1996] discussed a phase transition in the adsorbate layer of the ions, and the second paper by Kornyshev et al. [Energy Environ. Mater., 3, 414-420, 2020] described a phase transition from bound cation-anion pairs to free ones in the moderate (or high) ion concentration regime, which cannot be related to the dilute aqueous electrolyte case. Based on the comment provided by the reviewer that "I like the simulations, ionic structure change, and especially the Maxwell construction used by the authors. I think it is a decent explanation amongst many that already exist.", we believe that the reviewer fully acknowledges that our work is distinctive from previous works but has a concern regarding our means of expression. We greatly appreciate the thoughtful suggestion and constructive comments provided by the reviewer and have revised our expressions accordingly.

b)-Another exaggerated claim is the following:
"While the EDL is one of the oldest concepts in electrochemistry1, its significance in controlling electrochemical reactions has been recognized recently 2-7 ." References 2-7 are all published in 2020-2021. Do the authors mean that no one in the last century ever recognized the importance of EDL for electrochemistry? Or they have something more specific in mind.
In continuation of our response in above, we deeply appreciate the constructive comments provided by the reviewer. We clarified the indicated expression as follows: "The EDL is one of the oldest and most fundamental concepts in electrochemistry 1,2 . As a recent example, the electrochemical carbon dioxide reduction reaction (CO2RR) has been suggested to be controlled by the EDL structure 3-10 ."

c)-This one is about spectroscopy of the EDL:
"Nonetheless, to date, the atomic-level details of the EDL still remain unknown because not only the EDL is spatially concealed between the two bulk phases of solid and liquid, impeding spectroscopic measurements,…" Have the authors not found any optical spectroscopic literature dedicated to the EDL structure that they can so confidently say the spectroscopic measurements are impeded at the EDL? There are hundreds, if not thousands of papers on spectroscopy of the electrode-electrolyte interface, including Raman, and IR vibrational spectroscopy dedicated to understanding ionic structure. A quote like this is inaccurate at best.
We agree that the original expressions could have been interpreted as ignoring the importance of spectroscopic dedications given in this field, although that was not our intention. Following the suggestion made by the reviewer, we have revised the indicated text as follows: "Nonetheless, to date, the microscopic structure of the EDL has not been fully resolved not only because the EDL is spatially concealed between the two bulk phases of solid and liquid 11 , but also because the electrochemical signals are highly convoluted by the complex, coupled EDL responses of the multiple components in the electrified interface 12 ."

2)-Lack of Comparison with Previous Models:
One of the best known models of the double hump capacitance is described by Kornyshev's (and cited  First, the lack of comparison of our results with those of the Kornyshev model was an oversight on our part. As the reviewer noted below, the contribution of Kornyshev to the EDL field has been so great and his model is highly important in this field. However, we believe that this model (as well as many other models relying on a coarse-grained description of water as a continuum dielectric) has intrinsic limitations in resolving the microscopic origin of capacitance behavior measured in dilute electrolytes. First, the Kornyshev model is a lattice-gas model that does not include explicit treatment of water molecules. Although we do not criticize such a theoretical setting, as it also provides important insight with analytical convenience, this model cannot fully reflect the response of water molecules to the EDL field.
The role of water molecules in the EDL becomes important for dilute, that is, water-rich electrolytes. Second, as mentioned previously, the essence of the Kornyshev model is the inclusion of ion saturation behavior in the Gouy-Chapman model, and the emergence of a camel shape is ascribed to ion saturation. Thus, a concentrated electrolyte is required to manifest a camel shape, and in the dilute limit, the results of this model simply approach those of the Gouy-Chapman model, predicting a U-shaped capacitance curve. Therefore, the lack of explicit water molecules and the requirement of a finite ion concentration make the Kornyshev model suitable for explaining the camel-shaped capacitance measured in the ionic-liquid electrolyte system, rather than that measured in the dilute aqueous electrolyte system. In addition, owing to the lack of explicit water molecular structures in the model, the phase transition concept discussed based on the Kornyshev model is mostly related to the ion structure changes (e.g., from bound ion pairs to free ions [Energy Environ. Mater., 3, 414-420, 2020]), whereas the phase transition predicted from our cathodic charging simulation has direct implications for the orientation response of the water dipoles in the EDL.
Following the comment made by the reviewer, we added the following paragraph to compare our results with those of the Kornyshev model on pages 11 and 12 of the revised manuscript: "Notably, some theoretical models have predicted the emergence of a camel shape in the capacitance 34,40-42 ; thus, it is useful to compare our approach to the previous model. One of the most recent and elaborate EDL models predicting the camel shape is the Kornyshev model 34,43-47 , which is a lattice-gas model incorporating ion saturation behavior into the Gouy 25 -Chapman 26 theory, where water is coarse-grained as a dielectric. Although our mechanism for the cathodic hump indicates that the key to bistability is orientation polarization of the water molecular dipoles in the EDL, the Kornyshev model ascribes the emergence of the capacitance hump to ion saturation 34 . Thus, a concentrated electrolyte is essential to manifest a camel shape in the Kornyshev model, and in the dilute limit, the results of this model approach those of Gouy 25 -Chapman 26 model. Therefore, the Kornyshev model is suitable for explaining the camel-shaped capacitance measured in a dense Coulomb system such as an ionic-liquid electrolyte 34,43-48 , whereas our mechanism explains the camel-shaped capacitance measured in a dilute aqueous electrolyte 15-19 ." As discussed so far, our results are distinct from those of the previous models, which were mostly based on coarse-grained descriptions and/or intended to explain the camel-shape behavior of ionic-liquid systems. In this regard, to the best of our knowledge, no theory has provided molecular-level understanding of the origin of camel-shaped capacitance characteristically measured from a simple system, such as the interface between a planar metal electrode and dilute aqueous electrolyte. However, we agree with the thoughtful comment provided by the reviewer that some expressions, which sound exaggerated, needed to be toned down and clarified. Therefore, we changed the original text reading "We are now thus ready to address the century-year-long question, unresolved since the development of the early EDL theories in the 1900s: what type of molecular-scale change in the EDL structure is responsible for the two humps of the camel-shaped capacitance curve?

21-30 "
to "Therefore, we are now ready to elucidate the microscopic structural details of the EDL, which have been questioned but not fully resolved since the development of the early EDL theories in the 1900s 2 . In particular, we focus on what type of molecular structural response in the EDL is responsible for the two humps in the camel-shaped capacitance curves that have been measured from simple systems, such as the interfaces between planar metal electrodes and dilute aqueous electrolytes 25-34 ." I do like the explanations given the paper under review on the origin of the double hump capacitance. I like the simulations, ionic structure change, and especially the Maxwell construction used by the authors. I think it is a decent explanation amongst many that already exist.
We would like to thank the reviewer for recognizing the significance of our work. We sincerely appreciate the efforts made by the reviewer in critiquing our manuscript and providing constructive comments. Thanks to the thoughtful comments provided by the reviewer, our manuscript has been greatly improved and the distinct points of our study have been well clarified.

3)-Relation to CO2 reduction: The authors efforts in relating this work to CO2 reduction is appreciated. However, it is done in passing and without much depth. Perhaps it can be done in a separate paper. The explanation in the manuscript is not in depth enough.
We appreciate the reviewer for noting this issue. Indeed, after the submission of our manuscript, we became aware of the paper by Koper et al., suggesting the importance of short-range electrostatic interactions between cations and adsorbed CO2 [Nat. Catal., 4, 654-

(2021)]. Thus, we further performed DFT-CES simulations to understand the interaction between the cation and adsorbed CO2 in a bent form (*CO2). Our DFT-CES simulation
revealed that the cation can coordinate to the *CO2 and that the coordinating ability of the cation to *CO2 is weakened when the cation is chelated by the crown ether. Specifically, the coordination number of cation to *CO2 decreases from 1.0 to 0.3 when the cation is chelated ( Figure R1). This finding suggests that the linear dependence of the CO2RR activity on the crown ether concentration can also be explained using a mechanism based on a direct cation-*CO2 interaction. However, as described in the original manuscript, the linear dependence of the CO2RR activity on the crown ether concentration can also be explained in terms of the weakened electric field in the EDL. Thus, we believe that it is more appropriate to address both mechanistic possibilities in the present study than to close the discussion, which will inspire many other researchers to study the mechanism of CO2RR further. Indeed, we are also conducting a theoretical-experimental joint study to identify the mechanistic role of cations during CO2RR, which will be presented in a future paper.
To address both possibilities based on short-range direct and long-range field-dipole interactions equally, we modified Figure 4c in the revised manuscript as shown in Figure R2. Figure R2. DFT-CES snapshots showing that uncomplexed Na + develops a more direct interaction with the adsorbed CO2 than 15C5-complexed Na + , forming a compact EDL structure with a stronger field.
We also added Figure R1 into to the supporting information and appended below discussion to page 12 of the revised manuscript: "Not only the long-range dipole-field interaction, but also the short-range direct interaction of the cation with the adsorbate CO2 has been highlighted recently 10,53 . Our DFT-CES simulation further revealed that the coordination number of Na + to the adsorbed CO2 decreases from 1.0 to 0.3 when the cation is complexed with 15C5 ( Supplementary Fig. 12).
Thus, the decrease in the CO2RR activity can also be explained in terms of the decrease in the coordinating ability of a cation to the adsorbed CO2. In both mechanistic possibilities, our work demonstrates the importance of identifying the EDL structure for controlling the electrocatalytic activity."

Minor problems 1)-There are numerous English grammar and style problems in the manuscript.
A couple of examples are below. In the abstract: "As based on first principles." "that linearly scales the carbon dioxide reduction activity" 2)-The references section is split by the figures

section. 3)-The unit Angstrom is missing in several places.
We properly revised the grammatical errors and carefully proof-read the manuscript.

Reviewer: 3
The report is a study using mainly computational methods and a few experiments, to study the origin of the electric double layer. The system is a Ag111 surface with water/Na+ or water/Fsolution. Several observed effects are very clearly reproduced and a credible molecular explanation is presented for the capacitance peaks. The paper is well-written and the conclusions are clearly presented. However, there are some things to address before the conclusions can be seen as verified. Since the conclusions fully rely on a single computational model which is nonstandard and therefore not well tested, it is crucial that this model is benchmarked. Below are some specific points to address.
We would like to thank the reviewer for the favorable comments and recognition of the significance of our present work. Following the valuable comments provided, we additionally performed an extensive benchmark study of our model, concluding that our findings are not parameter-or model-specific, but rather can be reproduced well in general. A more detailed discussion is provided below.
1. There are some questionable arguments in the molecular origin discussion. It is stated that the cause for Fto adsorb on the surface while Na + stays further away is due to the smaller hydration energy of anions. In the supporting information the hydration energy for Fis presented as 115-120 kcal/mol, while Na + has a value of 80-90 kcal/mol. This is precisely opposite to the argument on line 119. It is also stated that the dispersive energy is larger for Fthan for Na + , which is likely correct. This should be straight forward to estimate from the Uvdw term.
We agree with the reviewer that the adsorption behavior of F − can be ascribed to the fact that its dispersive energy is larger than that of Na + . Indeed, the dispersion coefficients (i.e., We would like to thank the reviewer for validating our FF parameters. To respond to the question posed by the reviewer, we refitted our interfacial FF parameters to reproduce both

Ag-Owater interactions, but new FF parameters include both Ag-Owater and Ag-Hwater
interactions using Buckingham potentials (see Table R1  We firstly note that the original FF parameters predicted nearly the same binding energy of water to the Ag surface for the H-head configuration but that the separation distance was slightly underestimated ( Figure R3). Thus, very strong binding of water to the surface is unlikely to occur even when using the original FF parameters.
By using the new FF parameters, which were fitted to reproduce the Ag-H and Ag-O interactions equally, we also found that the first-coordination shell of the cation remained intact even for the highly charged Ag surface case, in agreement with the results obtained using the previous FF parameters ( Figure R6). We thus concluded that our finding is not an artefact caused by a specific choice of model parameters, but rather is physically sound.

Thus, we further performed DFT-CES simulations to understand the interaction between the cation and adsorbed CO2 in a bent form (*CO2). Our DFT-CES simulation revealed that
the cation can coordinate to the *CO2 and that the coordinating ability of the cation to *CO2 is weakened when the cation is chelated by the crown ether; the coordination number of cation to *CO2 decreases from 1.0 to 0.3 when the cation is chelated ( Figure R8). This finding suggests that the linear dependence of the CO2RR activity on the crown ether concentration can also be explained using a mechanism based on a direct cation-*CO2 interaction. However, as described in the original manuscript, the linear dependence of the CO2RR activity on the crown ether concentration can also be explained in terms of the weakened electric field in the EDL. Thus, we believe that it is more appropriate to address both mechanistic possibilities in the present study than to close the discussion, which will inspire many other researchers to study the mechanism of CO2RR further. Indeed, we are also conducting a theoretical-experimental joint study to identify the mechanistic role of cations during CO2RR, which will be presented in a future paper.
To discuss both possibilities based on short-range direct and long-range field-dipole interactions equally, we modified Figure 4c in the revised manuscript as shown in Figure R9. Figure R9. DFT-CES snapshots showing that uncomplexed Na + develops a more direct interaction with the adsorbed CO2 than 15C5-complexed Na + , forming a compact EDL structure with a stronger field.
"Not only the long-range dipole-field interaction, but also the short-range direct interaction of the cation with the adsorbate CO2 has been highlighted recently 10,53 . Our DFT-CES simulation also revealed that the coordination number of Na + to the adsorbed CO2 decreased from 1.0 to 0.3 when the cation was complexed with 15C5 ( Supplementary Fig. 12). Thus, the decrease in the CO2RR activity can also be explained in terms of the decrease in the coordinating ability of a cation to the adsorbed CO2. In both mechanistic possibilities, our work demonstrates the importance of identifying the EDL structure for controlling the electrocatalytic activity." Overall I believe that this report could provide very interesting and important insight on the catalyst-solvent interface under working conditions. There are some questions on the reliability of the method that needs to be addressed and some discussion that could be improved, but the key points of the paper are of high interest.
We would like to thank the reviewer for recognizing the significance of our work. We sincerely appreciate the efforts made by the reviewer in critiquing our manuscript and providing constructive comments. Thanks to the thoughtful comments provided by the reviewer, our manuscript has been greatly improved and clarified.