Electric Field-Dependence of Double Layer Capacitances by Current-Controlled Charge-Discharge Steps

Round 1

Reviewer 1 Report

The authors investigated voltage curves as a function of double-layer capacitance time (DLC) by current-controlled charge and discharge steps

The results obtained clarify and confirm the phenomena known so far. The tests were conducted in a limited voltage range. The results should be presented in comparison to the state of the art.

Author Response

[1] The first reviewer

The reviewer has agreed on our presentation.

Reviewer 2 Report

In the manuscript “Field-dependence of double-layer capacitances by current-controlled charge-discharge steps” by He et al. The present work deals with the time- and the voltage-dependence of a DLC by applying constant currents to a platinum electrode in KCl solution.

This article is interesting. However, there are some general points and some additional remarks in the text which need to addressed before publication:

1. The Introduction needs improvement, taking into account previous work and existing literature, the Authors should emphasize why current work is necessary.

Additional remarks on the manuscript:

Page 2 – Materials and Methods section

- laconic description of the experiment. How many times has the experiment been performed? What is its repeatability?

- the reagents used were not accurately described, e.g. no KCl concentration or deionized water specification.

Figure 2,3,4,5 and 6 - What is the error of the obtained experimental values?

 

The article is clearly written, the illustrations are understandable. I believe that this manuscript will be interesting for all scientists involved in such studies and I suggest publication after minor revision of the manuscript.

Author Response

(1) The Introduction needs improvement, taking into account previous work and existing literature, the Authors should emphasize why current work is necessary.

The reviewer recommended us to improve Introduction by the necessity of the present work. Our aim is to reveal the voltage-dependence. This dependence is important industrially because it varies the electric energy through ∫CVdV/2. We would like to address this fact for the necessity of this work. Therefore, we added to the end of the third paragraph (line 55)

"It is important industrially for designing supercapacitors because it varies the electric energy through ∫CVdV/2."

(2) How many times has the experiment been performed? What is its repeatability?

We checked the reproducibility of our voltage-time curves at three runs. We would like to add to the end of 2. Materials and Methods section (line 74)

"Reproducibility of our voltage-time curves was examined at three runs to be within 5 % errors."

(3)  the reagents used were not accurately described, e.g. no KCl concentration or deionized water specification.

We revised "Aqueous solution of KCl was prepared with the analytical grade of KCl and distilled and deionized water. " at line 71 as

"Aqueous solution of KCl was prepared with the analytical grade of KCl (Wako) to be 0.1 M and distilled and deionized water prepared by CPW-100(Advantec, Tokyo). "

(4) Figure 2,3,4,5 and 6 - What is the error of the obtained experimental values?

We added an error bar in Fig. 2. The caption was revised by adding " 'I' means the error bar."

Errors in the other figures are close to the sizes of marks of the plots. We described this point in the final line (line 74) of 2. Materials and Methods section as

"Errors in the most graphs were close to the sizes of marks of the plots."

 

Author Response File: Author Response.pdf

Reviewer 3 Report

The authors investigated field-dependence of double layer capacitances by current-controlled charge-discharge steps. The paper was well organized and discussed. Minor revision is suggested due to a technical problem found in "Conclusions" part, where there is no conclusion and the first paragraph of "Results and Discussion" was pasted there. 

Author Response

[3] The third reviewer

The authors investigated field-dependence of double layer capacitances by current-controlled charge-discharge steps. The paper was well organized and discussed. Minor revision is suggested due to a technical problem found in "Conclusions" part, where there is no conclusion and the first paragraph of "Results and Discussion" was pasted there. 

We have to apologize to the reviewer. We made a mistake in editing the submitted manuscript. The mistake lies just in a copying process. We revised it as

" The DLC obtained by the constant current-control includes not only the time-dependence of the power law but also the electric field-dependence. The latter is much larger than the former for the constant current-control. It is revealed in the convex deviation of the voltage-time curve from the line. It is not noticeable for results by the ac-impedance measurements because the applied voltage is too small to be detected. Since the current-controlled measurement provides as large voltages as 0.3 V, it makes the field effect distinct.

    Both effects are included in Eq. (5), which is a solution of the kinetic equation for the orientation of interactive dipoles. The field effect is represented in terms of the exponential form of the voltage. The form implies that the voltage can be regarded as a kind of the activation energy of causing the capacitance. "

 

Author Response File: Author Response.docx

Reviewer 4 Report

This document tries to evaluate the deviation from linearity shown by the voltage of supercapacitors using capacitance. Authors have taken platinum electrode in KCl as research system, and finally, they have also analysed a commercial supercapacitor of 1 F. They have fitted some equations of the literature (power law and logarithmic relation) to check the capacitance behaviour.

The main objective of the research remains not clear, and conclusions are not appropriately explained in the document. I think there is a lack of a guiding line in the structure of the document.

General remarks

The calculation/measurement of capacitance is a controversial subject. There are many procedures to define/calculate/measure it. Some standard and manufacturer procedures to calculate capacitance of EDLCs and LICs are the next ones: IEC 62576, IEC TC40-2151, Kamcap procedure, JM Energy procedure,… You can check also the excellent review work of S. Zhang and N. Pan (Adv. Energy Mater. 2014, 1401401). Each of the procedures has slight differences. Moreover, authors have used other procedures to calculate capacitance different to equation (1) (see Ref. 25, 26 and 30). Therefore, it would be interesting to say something about the capacitance evaluation procedures, and compare them with equation (1). Additionally, do the capacitances calculated with all these procedures fulfil in the same manner the power and logarithmic laws?

In the document, the word “field” is profusely used (it is the first word of the title), and only in two times the “field” is described as “electric field”. This can cause confusion between the readers, because, although, the electric field is the usual field inside the supercapacitors, the effect of magnetic field can be also analysed. Authors have to be more explicit.

Electric double layer capacitors (EDLCs), or briefly named supercapacitors, are very interesting energy storage devices because their power density is high (adequate for fast charging processes). However, their energy density is small to be used in most of the market applications. Nowadays, hybrid supercapacitors are replacing EDLCs, because they have high power density, and also greater energy density than standard EDLCs (but lower than lithium batteries yet). Ref. 1 and 2 are related to these hybrid devices, instead of the usual EDLCs, but the platinum electrode in KCl is not a hybrid device, nor is the commercial supercapacitor analysed. A useful classification of supercapacitors appears in this work:

http://www.gecarbon.org/boletines/articulos/BoletinGEC_037_art3.pdf

Therefore, this point has to be clarified: EDLCs, hybrid supercapacitors. Which is the research subject? Is the behaviour identical for all kind of supercapacitors?

1. Introduction

- I don’t understand the second and third phrases of the introduction. Please, could you explain them better?

- (30 line) The “line” can be straight or curved….

- (49 line) Ref. 29 does not explain anything about capacitance of EDLCs and any relation with voltage. It explains the polarization caused by an external electric field on an ideal gas of dipolar molecules. It has no sense at all.

- There are some expressions that I do not understand: “variations of dielectrics of polymers”, “the time- and the voltage-dependence of a DLC”,…

2. Materials and Methods

- It is not clear why do you have chosen the platinum electrode in KCl for the research. Previous research/results on this system have to be mentioned.

3. Results and Discussion

- (84 line) At what potential does the faradaic reactions appear? Add a reference, please.

- All the magnitudes related to the equations used in the document need units. For example, which kind of capacitance can be calculated with (1) equation? Specific capacitance (F g^-1)? Volumetric capacitance (F cm^-3)? Areal capacitance (F cm^-2)? Do all these capacitances show the same non-linearity?

- (line 88) How is defined current density for the wire? And for the commercial supercapacitor?

- Figure 2. Which is the meaning of each colour in the graphic? It has to be more explicit.

- Technical details of the 1 F supercapacitor have to be provided. Moreover, it will be important to know the chemistry, electrolyte,… Is the “cell resistance” the supercapacitor ESR? Measured at what frequency?

Conclusions

- Conclusions section does not resume correctly the achievements of the research work. It is a description of some results of the measurements.

Small corrections:

• Some Refs. appear in a non-correct form: (line 26) [³], (line 33) [⁴],…

 

Author Response

[4] The fourth reviewer

General remarks

The reviewer presented some definitions of capacitances. This manuscript does not aim at comparing definitions and measurements, being different from reviews such as Adv. Energy Mater. 2014, 1401401. We here address capacitances defined electromagnetics in physics. The scientific definition is unique: the ratio of electric charge to voltage, regardless of geometry of capacitances. In order to restrict the definition, we revised

"the definition of the capacitance, C = q/V = It/V for the charge q." in line 31 as

"the definition of the capacitance, C = q/V = It/V for the charge q in the sense of electromagnetics."

We revised similarly at line 86

"the definition of the capacitance, q = CV for a charge q" as

"the definition of the capacitance, q = CV for a charge q in electromagnetics"

As the reviewer pointed out, there are some methods of measurements of capacitances. Since we have specified a method of measurement (a constant current) and the definition of the capacitance (C=q/V), Eq. (1) has no ambiguity.

We should have cited reviews on industrial criteria of supercapacitances, such as Adv. Energy Mater. 2014, 1401401 in order to remark the presence of industrially various definitions and measurements of supercapacitors. We would like to address this reference paper by adding to line 61

"Our discussion will be directed to the two kinds of the dependence from physical viewpoints, which cover in principle properties of industrially applied capacitances [31]."

Reference [31] Zhang, S.; N. Pan. Supercapacitors Performance Evaluation, Adv. Energy Mater. 2015, 5, 1401401, DOI: 10.1002/aenm.201401401.

Reviewer's question, "Additionally, do the capacitances calculated with all these procedures fulfil in the same manner the power and logarithmic laws?" is not within our work in this manuscript. It is really impossible to obtain the validity of the power law by other techniques. The techniques that reviewer addressed are industrially useful but are not suitable for discussing scientific properties.

In the document, the word “field” is profusely used (it is the first word of the title), and only in two times the “field” is described as “electric field”. This can cause confusion between the readers, because, although, the electric field is the usual field inside the supercapacitors, the effect of magnetic field can be also analysed. Authors have to be more explicit.

We agree on the criticism. We rewrote "field" as "electric field" in the title and abstract. We revised "electric field" at line 50 as

"electric field (abbreviated as "field")" at line 50.

All the documents after line 50, "electric filed" was replaced by "field".

Electric double layer capacitors (EDLCs), or briefly named supercapacitors, are very interesting energy storage devices because their power density is high (adequate for fast charging processes). However, their energy density is small to be used in most of the market applications. Nowadays, hybrid supercapacitors are replacing EDLCs, because they have high power density, and also greater energy density than standard EDLCs (but lower than lithium batteries yet). Ref. 1 and 2 are related to these hybrid devices, instead of the usual EDLCs, but the platinum electrode in KCl is not a hybrid device, nor is the commercial supercapacitor analysed. A useful classification of supercapacitors appears in this work: http://www.gecarbon.org/boletines/articulos/BoletinGEC_037_art3.pdf Therefore, this point has to be clarified: EDLCs, hybrid supercapacitors. Which is the research subject? Is the behaviour identical for all kind of supercapacitors?

We pay attention to EDLCs rather than hybrid supercapacitors. In order specify our concern, we have already written "The present work deals with the time- and the voltage-dependence of a DLC by applying constant currents ..." at line 56 in Introduction.

1. Introduction

- I don’t understand the second and third phrases of the introduction. Please, could you explain them better?

We guess that the question lies in the cooperative phenomena. This is the well-known behavior in statistical physics. In order to help the understanding, we insert to line 45

"Microscopic time scale is expanded to observed macroscopic one, in accord with the expansion of domains of the orientation."

 (30 line) The “line” can be straight or curved….

A line should be straight, and there is no curved line. In order to avoid the confusion, we replaced

"should be a line" by "should take a line segment".

- (49 line) Ref. 29 does not explain anything about capacitance of EDLCs and any relation with voltage. It explains the polarization caused by an external electric field on an ideal gas of dipolar molecules. It has no sense at all.

A degree of polarization is equivalent to an amount of capacitances, regardless of phases of liquid or gas. Therefore, ref. 29 is correct for the citation. In order to avoid readers' misleading, we rewrote

"In contrast, the voltage-dependence is caused theoretically by voltage-change of a degree of the orientation of dipoles [29] as well as the number of oriented dipoles. With an increase in the electric field, the former provides a constant value of the capacitance until a saturated value. The latter increases the capacitance obviously." in line 49

as

"An increase in the field enhances orientation of dipoles or capacitance values."

We deleted ref. 29.

- There are some expressions that I do not understand: “variations of dielectrics of polymers”, “the time- and the voltage-dependence of a DLC”,…

Since the former is due to the author's opinion in ref. 14 and 15, we do not say anything. 

As for the latter, we replace "the time- and the voltage-dependence" as

"the time-dependence and/or the voltage-dependence" at line 56.

 

2. Materials and Methods

- It is not clear why do you have chosen the platinum electrode in KCl for the research. Previous research/results on this system have to be mentioned.

There are a number of reports on DLCs at Pt. However, this work does not aim at new materials or new combinations, but aims at data analysis for finding time-variations as well as voltage variations of DLCs. Complicated materials would prevent evaluation of the time-variations and the voltage-variations, and hence the electrochemically well-known Pt in KCl was chosen here. The choice lies in the conventional direction in science.

In order to stress this point, we revised at line 58:

"the dependence are revealed in the charging and discharging curves"

as

"the dependence are revealed in the charging and discharging curves in conventional voltammetry at platinum in KCl solution."

 

3. Results and Discussion

- (84 line) At what potential does the faradaic reactions appear? Add a reference, please.

We replaced "faradaic reactions" by "formation of platinum oxide [30]".

Although the oxidation wave is small, it prevent us analyzing data accurately.

The reference is given by

[30] HeydDavid, D.V.; Harrington, A.; Platinum oxide growth kinetics for cyclic voltammetry, J. Electroanal. Chem. 1992, 15, 19-31, doi.org/10.1016/0022-0728(92)80229-W

 

- All the magnitudes related to the equations used in the document need units. For example, which kind of capacitance can be calculated with (1) equation? Specific capacitance (F g^-1)? Volumetric capacitance (F cm^-3)? Areal capacitance (F cm^-2)? Do all these capacitances show the same non-linearity?

It is not allowed to specify units in general equations without numerical values. This is a common rule in sciences such as physics and chemistry. However, the rule has not been applied to industrial technology. Our paper aims at science rather than industrial technology.

 

- (line 88) How is defined current density for the wire? And for the commercial supercapacitor?

Eq. (1) is valid for any kind of electrode surface because it has no numerical value. Reviewer's question is effective in Fig. 1(b), where numerical values were applied. We would like to revise

"evaluated from Eq. (1) on the time" at line 89 as

"evaluated from Eq. (1) on the time for the geometrical surface area of the immersed part of the wire".

As for the supercapacitors, we did not use any surface area in Fig. 5.

 

- Figure 2. Which is the meaning of each colour in the graphic? It has to be more explicit.

Blue and red colors in Fig. 2 mean, respectively the charging step and the discharging one. We revised " the (a,c) charging (t_n = 3 s) and the (b,d) discharging" in the caption as

"the (a,c, blue)) charging (t_n = 3 s) and the (b,d, red) discharging".

 

- Technical details of the 1 F supercapacitor have to be provided. Moreover, it will be important to know the chemistry, electrolyte,… Is the “cell resistance” the supercapacitor ESR? Measured at what frequency?

We added some features of the supercapacitor by replacing at line 73

"available with nominal values of 1 F capacitance and 5.5 V maximum voltage" by

"available (part number SE-5R5-D105VYV) with nominal values of 1 F capacitance, 5.5 V maximum voltage, and equivalent series resistance 22 W at 1 kHz "

Other data such as electrolytes and electrode materials are not available. The specification of the supercapacitor says that the solution is KCl aqueous solution. However, this should be a mistake because it is impossible to maintain such a large voltage as 5.5 V in aqueous solution.

 

Conclusions

- Conclusions section does not resume correctly the achievements of the research work. It is a description of some results of the measurements.

We have to apologize to the reviewer. We made a mistake in editing the submitted manuscript. We revised it as

"  The DLC obtained by the constant current-control includes not only the time-dependence of the power law but also the electric field-dependence. The latter is much larger than the former for the constant current-control. It is revealed in the convex deviation of the voltage-time curve from the line. It is not noticeable for results by the ac-impedance measurements because the applied voltage is too small to be detected. Since the current-controlled measurement provides as large voltages as 0.3 V, it makes the field effect distinct.

    Both effects are included in Eq. (5), which is a solution of the kinetic equation for the orientation of interactive dipoles. The field effect is represented in terms of the exponential form of the voltage. The form implies that the voltage can be regarded as a kind of the activation energy of causing the capacitance. "

 

Small corrections:

• Some Refs. appear in a non-correct form: (line 26) [³], (line 33) [⁴],…

 We changed the scripts.

Author Response File: Author Response.pdf

Round 2

Reviewer 4 Report

I have no more comments. Authors have answered clearly my questions.