Parallel Combination of Inner Capacitance and Ionic Capacitance, Apparently Inconsistent with Stern’s Model

Round 1

Reviewer 1 Report

The paper is well organized and presented.

My only minor comment is to suggest the authors to re-arrange some subscripts e.g., in eq.16 and 17, the "_av" subscript is confusing and mixed with the other subscripts.

Maybe the authors can clarify it as denotation in context if multiple subscripts appear in the same place. Other than that,  I think it should be ready to go. 

Author Response

Response to Reviewer 1

Comments and Suggestions for Authors

The paper is well organized and presented.

My only minor comment is to suggest the authors to re-arrange some subscripts e.g., in eq.16 and 17, the "_av" subscript is confusing and mixed with the other subscripts.

Maybe the authors can clarify it as denotation in context if multiple subscripts appear in the same place. Other than that, I think it should be ready to go. 

 

We agree on the suggestion. A double subscript causes confusion at a sight, as the reviewer addressed. We revised the double subscript as the upper bar, as a conventional sign, ¯X_a.

Author Response File: Author Response.docx

Reviewer 2 Report

The paper is very poorly written. The language needs a considerable editing. The overall presentation is unclear and the reader has to guess what exactly was meant by the authors, which is unacceptable. 

The overall scientific merit of the paper is not high. Unless of course I missed something due to the lack of clarity. The Stern model is known to be an oversimplification and nowadays no one expects it to be quantitative. On the other hand combining the Stern layer with the Gouy Chapman model is not novel, so it is hard for me to see the value of the work. 

I have no reason to doubt the experimental part of the paper but the conclusions seem trivial to me. 

Therefore I cannot recommend the publication of the paper in Electrochemistry.

Author Response

Since the reviewer did not specify any points to be "poorly written" or "unclear", we cannot understand the criticism.

Although the reviewer said "The Stern model is known to be an oversimplification and nowadays no one expects it to be quantitative.", a number of scientists have used the Stern model in reality, especially in applications of supercapacitors. Our aim is opposite to the criticism "combining the Stern layer with the Gouy Chapman model is not novel ", but we addresses the conceptual validity of the Stern model. However, the Stern model cannot be directly applied to the capacitance data. Please try to understand meaning of experimental results from Fig. 1 to Fig. 5, which are novel results.

Author Response File: Author Response.docx

Reviewer 3 Report

In this work, the authors have introduced a model of double layer capacitance (DLC) in which the DLC at platinum electrode in KCl and HCl solutions can be represented as a simple sum the Helmholtz capacitance and the ionic contribution. Theoretical predictions were verified by experiments at concentrations higher than 1 M. 

The manuscript is generally well written but could be improved with clarity about its true novelty results and how they relate to existing theories of electric double layers. In this sense, the text could be made more clear and less dense, perhaps by differentiating between theoretical and experimental parts.

There is little reference, for example, to existing models that include steric effects (see for example Electrochimica Acta 46 (2001) 3033–3040 or Electrochimica Acta 178 (2015) 541–545) and effect of orientational ordering of solvent water dipoles that render the permittivity to vary in the vicinity of the charged plates (Bioelectrochemistry 87 (2012) 199–203 or Acta Chim. Slov. 66, 534–541, 2019.). It should be stressed how the presented model differs from 

The differential capacitance is usually calculated as the derivative of the mean-field potential with respect to sigma, the surface charge, C = d\phi/d\sigma. How does this relate to the results obtained in the paper? The authors do not take a mean-field approach, but should provide comment on the distinctions between the mean-field, and their model.

Furthermore, how do findings reported in the paper relate to existing theory? It should be made clear what the main contributions of the paper are. To what other systems is the theory applicable? 

 

 

 

  

 

 

Author Response

The reviewer recommended us to clarify novel results. We agree on this criticism. By adding some statements at a given line (numbers in the parentheses in the mark-revised revision), we revised the following points:

1. We added to the line 154^th (153): Our new finding is that the extracted ionic capacitance is proportional to the surface concentration (c^2/3).
2. We added to the line 170^th (170): The Stern model should include at least the linear relation of 1/C with c^-1/2. However, there is no report of such plots to our knowledge.
3. We added to the line 179^th (183): The magnitude of the slopes of the lines in Fig. 5 increased linearly with an increase in the concentration. The increase suggests the attribution of the slopes to ionic effects, being our finding in this report.
4. We added to the line 189th: (192) Frequency-dispersion is caused by long-term molecular interactions, which can be regarded as belonging to a cooperative phenomenon [16]. The frequency dispersion in the Helmholtz layer occurs through solvent interactions while that in the diffuse layer does by ionic diffusion. The common values of l in spite of the difference in origins mean that two interactions are related each other.

 

There is little reference, for example, to existing models that include steric effects (see for example Electrochimica Acta 46 (2001) 3033–3040 or Electrochimica Acta 178 (2015) 541–545) and effect of orientational ordering of solvent water dipoles that render the permittivity to vary in the vicinity of the charged plates (Bioelectrochemistry 87 (2012) 199–203 or Acta Chim. Slov. 66, 534–541, 2019.). It should be stressed how the presented model differs from 

We agree on the criticism of a loss of citing some references.

In order to explain the decrease in the relative permittivity of solvents by the field, we rewrote "close to 6 in the Helmholtz layers [18,38,39]" in the line 311th as

"close to 6 in the Helmholtz layers [18,38,39], which has been demonstrated to be the field effect [40].

[40] Gongadze, E.; Iglic, A.; Decrease of permittivity of an electrolyte solution near a charged surface due to saturation and excluded volume effects, Bioelectrochem. 2012, 87, 199-203, doi.org/10.1016/j.bioelechem.2011.12.001.

 

We added to the line 315th (at the end of section 4) (319) the following paragraph:

    Our model is to make the field effect on ions only in the direction normal to the electrode and to keep the ionic concentration in planes parallel to the electrode. It actually corresponds to size effects of ions by occupying ions to give lattice sizes [41], by taking into account the orientational ordering of water dipoles [42], by introducing interaction between the field and hydrostatic pressure [43], and by using molecular dynamics to predict detailed ionic distribution near the point of zero charge [44].

 

[41] Bohinc, K,; Kralj-Iglič, V.; Iglič, A. Thickness of electrical double layer. Effect of ion size, Electrochim. Acta, 2001, 46, 3033-3040, doi.org/10.1016/S0013-4686(01)00525-4.

[42] Gongadze, E.; Iglič, A. Asymmetric size of ions and orientational ordering of water dipoles in electric double layer model - an analytical mean-field approach, Electrochim. Acta, 2015, 178, 541-545, doi.org/10.1016/j.electacta.2015.07.179.

[43] Shapovalov, V.L.; The interaction of electric field and hydrostatic pressure in an electrical double layer: A simple “first principle” model that accounts for the finite sizes of counterions, J. Colloid Interface Sci. 2015, 454, 187-191, doi.org/10.1016/j.jcis.2015.05.018.

[44] Wang, Z.-Y.; Xie, Y.-P.; Liang, Q.; Ma, Z.; Wei, J.; Looking deeper into the structure of mixed electric double layers near the point of zero charge, J. Chem. Phys. 2012, 137, 174707, doi.org/10.1063/1.4765101.

 

The differential capacitance is usually calculated as the derivative of the mean-field potential with respect to sigma, the surface charge, C = d\phi/d\sigma. How does this relate to the results obtained in the paper? The authors do not take a mean-field approach, but should provide comment on the distinctions between the mean-field, and their model.

The electric field at a given location in this report is not mean-field, but we took average of fields to evaluate the capacitance. The field estimated from the capacitance becoms an mean-field. We would like to describe this comment, and added to line 280^th (287)

" Eq. (15) means the location of the anion averaged over 0 to L, which provides the anionic capacitance. The observed capacitance is the sum of the anionic capacitance and the cationic one. If the voltage is estimated from the differential capacitance through dV/ds for the surface charge density s, it is actually a mean-field voltage in the context of the derivation of the capacitance."

 

 Furthermore, how do findings reported in the paper relate to existing theory? It should be made clear what the main contributions of the paper are. To what other systems is the theory applicable? 

This paper directs mainly to experimental results of variation of the DLC with ionic concentrations and time-dependence, given by Fig. 1 - Fig. 5. Since the theory is one of explanations, there may be possibly other interpretations. If the present theory is applied to other combinations of solvents and ions, it is impossible to describe the results in this report. This report is an article rather than a review. In order to stress this point, we added to the end of Conclusion

"The present theory is one of explanations, and hence there may be other possible interpretations."

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

I do feel that the author's revision led to any improvement of the manuscript. It is poorly written and is sprinkled all over with sentences that sound awkward. I did not point specific examples, because that whole text needs heavy revision by a language expert. For example the first sentence in the abstract reads

"A double layer capacitance (DLC) has mainly been brought about by in the Helmholtz layer rather than in the diffuse layer, as was demonstrated with the invariance of DLC to salt concentration, c, less than 0.5 M (M = mol dm-3) (Univ. J. Chem. 1 (2013) 162)." 

This sounds clumsy and weird. Another example is 

"Our model is to make the field effect on ions only in the direction normal to the electrode and to keep the ionic concentration in planes parallel to the electrode." 

Not sure what is meant here.

The final sentence:

"The present theory is one of explanations, and hence there may be other possible interpretations."

actually undermines that value of the whole work. 

Also I do not argue that the data presented are novel. What I struggle with is the novelty of teh scientific conclusions. And yes the fact that the Stern model is insufficient, and the contribution of the Gouy-Chapman component has to be added is known for about 100 years. It was my understanding that this is one of teh main claims if not the main one in the paper. If not, this has to be made clear, but as I mentioned above, reading the paper in its present form is not enjoyable. 

Therefore, I do cannot revise my original recommendation. 

Author Response

Since the reviewer did not specify any points to be "poorly written" or "unclear", we cannot understand the criticism. Please explain the points courteously, and we will accept them.

Although the reviewer said "The Stern model is known to be an oversimplification and nowadays no one expects it to be quantitative.", a number of scientists have used the Stern model in reality, especially in applications of supercapacitors. Our aim is opposite to the criticism "combining the Stern layer with the Gouy Chapman model is not novel ", but we addresses the conceptual validity of the Stern model. However, the Stern model cannot be directly applied to the capacitance data. Please try to understand meaning of experimental results from Fig. 1 to Fig. 5, which are novel results.

Author Response File: Author Response.docx