Effect of Dielectric Constant on Interaction Between Charged Macroions in Asymmetric Electrolyte

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

I have reviewed the manuscript titled "Effect of Dielectric Constant on the Interaction Between Charged Macroions in Asymmetric Electrolyte", in which the author use Monte Carlo simulations to investigate how the dielectric constant of the solvent affects charge inversion between two highly charged colloidal particles immersed in an asymmetric electrolyte solution. The study contributes to the discussion on how dielectric effects influence the effective interactions in charged systems. However, a number of clarifications and revisions are necessary to improve clarity and presentation. Below, I provide detailed comments and suggestions. These issues should be addressed before the manuscript can be considered for publication.

Abstract

The definition of the parameter β is unclear. It currently reads as if β is simply the ratio of counterion charge to macroion charge. However, it is actually the ratio of the total counterion charge to the total macroion charge, which is a function of concentration as well. This should be clearly stated to avoid misinterpretation.

Introduction

-The introduction includes excessive self-citation ([2–8]). It would be more appropriate to also cite classical and foundational works in colloidal science and electrostatics, such as (J. W. Verwey and J. T. G. Overbeek, Theory of the Stability of Lyophobic Colloids (Elsevier, Amsterdam, 1948), J.-P. Hansen and H. Löwen, “Effective interactions between electric double layers,” Annu. Rev. Phys. Chem. 51, 209 (2000)).

-Please check the reference numbering. For instance, what is cited as [18] should be [19], and [19] should be [20], and so on.

Lines 98–103: The description is repetitive and confusing. Please rewrite this section for clarity.

Line 106: The statement that β determines the salt concentration is only valid if the particle concentration is held fixed. This assumption should be explicitly stated.

Line 107: The use of a cylindrical cell has been used in previous works. Please cite them.

Line 129: The term “macroion volume charge fraction” is unclear. Does it refer to the volume fraction occupied by the macroions or to a volumetric charge density? Please clarify the meaning.

Table 1.

-Rewrite the caption. “lists the Bjerrum lengths and dielectric constants of the solvents used.” Is incomplete.

-Indicate the temperature at which the dielectric constant values are given. Include references for the dielectric constants.

-As far as I am concerned, methanol and methyl alcohol refer to the same substance. Could the author check on this?

Table 2.

-In the third column, the solvent name corresponding to a dielectric constant of 68 is missing.

-Again, clarify the possible redundancy between methanol and methyl alcohol.

-Consider adding a comment on the limitations of treating the solvent as a continuous medium. In some cases, the molecular size of the solvent is comparable to the macroion size used in simulations, challenging the validity of the continuum assumption.

Lines 245–246: The claim that counterion adhesion to the macroion surface lowers the dielectric constant is confusing. Please elaborate on the mechanism or provide a citation that supports this statement.

Figures:

Figures 2g and 2h appear to be identical. Please verify and correct if necessary.

Figure 3 has already been published in Molecules 2024, 29(11), 2484; https://doi.org/10.3390/molecules29112484. I think it is not essential to include this figure again. If the figure is retained, the author must cite the original source and explicitly state that it has been reused.

 

Comments on the Quality of English Language

Revise carefully and correct typographical errors

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

In this work, the author perform Monte Carlo simulations to calculate the mean force and potential of mean force between highly charged macroions in the presence of multivalent ions using the MOLSIM package. There are several technical issues that must be clarified: 1) The mean force associated to the hs contribution is calculated from eqs. 3) and 12), which is by definition infinite. How was calculated numerically this contribution?; 2) What is the meaning of P_i in eq. 11); 3) The author states: "In contrast, E. Allahyarov et al. [18] found that, in the absence of salt, weakly charged colloids interacted repulsively with monovalent counterions in liquids with moderate and low dielectric constants. The charged surface's counterion-counterion coupling parameter, Γ, was less than two in their system." However, the ref [18] does not belong to Allahyarov: 18. Besteman, K.; Zevenbergen, M.A.G.; Lemay, S.G. Charge inversion by multivalent ions: Dependence on
429 dielectric constant and surface-charge density. Phys. Rev. E 2005, 72, 061501.
430 https://doi.org/10.1103/PhysRevE.72.061501.; 4) can the authors elaborate/explain in physical grounds their definition of a_z and Γ: "the average distance between two nearby counterions on a surface with a surface charge density of σ is denoted by 𝑎𝑍 = [𝑍𝐼/(𝜎/𝑒)]^1/2 and 𝛤 = 𝑍𝐼^2*𝑙𝑏/𝑎, both definitions are confusing and their explanation is not found in the references mentioned by the author; 5) What are physical counterions with valence +5?; 6) it seems that the cyindrical cell simulations does not include Ewald sums, are equivalent the current simulations to simulations in a cubic box including Ewald sums to take into account properly long-range interactions?, 7) in physical systems counterions usually are usually monovalent, as OH- or H+, not multivalent, how does the curves of  mean force and potential of mean force change when counterions are monovalent at the same bulk concentration for the bulk multivalent salts, that is, 2:1, 3:1, 5:1?. 8) What is the quantitative connection between the inversion of the force and potential of mean force with the overcharging and inversion of the electrophoretic mobility mentioned by the author?

Author Response

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Reviewer 3 Report

Comments and Suggestions for Authors

In the work “Effect of dielectric constant on the interaction between charged
Macroions in asymmetric electrolyte”,  Khawla Naim Qamhieh determines the effective force of interaction between two multiply charged ions immersed in electrolytes of different composition and density.  It is shown (as previously published works [22], [23]) that at certain combinations of external parameters (density of monovalent counterions, added multivalent salt, dielectric constant, etc.) this force demonstrates attraction.

The change in the sign of the interaction appears to be an unexpected and interesting qualitative factor compared to the predictions of the well-developed interaction theory of so-called  DLVO colloids.  In the DLVO theory, as detailed, for example, in the work of Alexander et all,  J. Chem. Phys. 80, 5776 (1984) “Charge renormalization, osmotic pressure, and bulk modulus of colloidal crystals: Theory“, the pairwise interaction between colloids is always positive.

Note that the dielectric constant of the solvent cannot be an independent parameter. Added multivalent salt changes the dielectric constant of the electrolyte. In addition, the proposed calculations do not take into account the image forces between colloids and counterions of the electrolyte.

The main disadvantage of this work is its incompleteness.    The presentation of results with interesting physical findings should end with suggestions for observing the detected effect. As discussed by Alexander et al., the focus for DLVO colloids is on osmotic pressure or the phenomenon of Coulomb crystallisation in polyelectrolytes. The calculations in this work should be brought to the same level.

Comments for author File: Comments.pdf

Author Response

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Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

After reviewing the author's responses and the revised manuscript, I believe that the author has adequately addressed most of my comments and the paper is now suitable for publication 

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

See the attached file Review_mdpi.pdf

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

From the first Review:

“The main drawback of the manuscript is that it is incomplete. The formalisation of results with physically interesting findings should, as a rule, conclude with suggestions for observing the detected effect.”

In the new version of the manuscript, the question of whether the effects discovered by the author are observable is presented in the conclusion (lines 387–400 and 429–462). 

The proposals include: a.) the sensitivity of the electrophoretic mobility of different clusters to the sign of the interaction between charged clusters;  b.) the effect of aggregation in dilute colloidal solutions.

• a) The electrophoretic mobility of various clusters is independent of charge. These are massive neutral particles that can move in an electrolyte when exposed to an external electric field. This effect is out of manuscript results.
• b)  According to the author’s presentation, the problem of aggregation in colloidal dilute solutions is in generally resolved, as referenced in [10] and [29]. It is therefore easier to explain to readers the quantitative side of the aggregation problem taking into account the author’s own results.  This possibility is not realised.

The manuscript's main weakness remains its incompleteness.

Author Response

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