Towards Building a Unified Adsorption Model for Goethite Based on Variable Crystal Face Contributions: III Carbonate Adsorption

1. Summary

Thank you very much for taking the time to review this manuscript. Please find the detailed responses below and the corresponding revisions/corrections highlighted/in track changes in the re-submitted files.

2. Questions for General Evaluation

Reviewer’s Evaluation

Response and Revisions

Does the introduction provide sufficient background and include all relevant references?

Can be improved

Is the research design appropriate?

Must be improved

Are the methods adequately described?

Can be improved

Are the results clearly presented?

Can be improved

Are the conclusions supported by the results?

Yes

3. Point-by-point response to Comments and Suggestions for Authors

Comments 1: This study ambitiously extends a unified CD-MUSIC model to carbonate adsorption on goethite, proposing a novel surface complex configuration to resolve discrepancies in prior literature. However, it relies heavily on indirect evidence without direct structural validation (e.g., DFT or in-situ spectroscopy). The lack of computational/experimental confirmation for the surface complexes renders the model speculative. Additionally, the unified parameters obtained lack validation—ternary competition experiments or application to diverse goethite morphologies are absent, undermining claims of universal applicability. Manuscript structure is fragmented, and technical errors require correction. Therefore, major revisions are recommended.

Response 1: We agree that the proposed surface carbonate complex bears a certain degree of speculation, however, we believe the theoretical arguments made are based on solid evidence. In order to be more clear about this evidence we have restructured previous sub-sections 2.3.1 and 2.3.2 to new (cf. TC version) sub-section 2.5 Configuration of the adsorbed carbonate complex, and sub-sections within: 2.5.1. Structural and spatial evidence, 2.5.2. Physico-chemical evidence, 2.5.3. DFT evidence, and 2.5.4. Spectroscopic evidence.

In summary we present the following evidence to justify the new complex proposed: (1) Structurally, the distance between oxygens in the carbonate moiety is 2.22-2.23 Å, which is 0.8 Å smaller than the interatomic distance between adjacent SC oxygens in the {101} crystal face (3.02 Å). This would require extreme bending of the adjacent octahedra to accommodate a bidentate bridged complex, whereas the adjacent TC oxygen sites in the adjoining row of octahedra have a distance of 2.83 Å from the closest SC sites, i.e., 0.2 Å closer than in the former case. (2) The vast majority of TC oxygen sites are predicted by the MUSIC model to be protonated across the normal pH range (4-10), and thus yield a positive charge (cf. Fig. 3b) that would exert a definite attractive electrostatic force towards a negatively charged oxygen of a second C-O^- moiety in the vicinity. (3) The separation distance between the carbonate oxygen and the positive TC OH site would be (2.83 Å – 2.23 Å=) 0.60 Å, which is lower than a covalent O-H bond (typically 0.96 Å), and therefore, formation of an actual bond with this TC OH site can be safely proposed. (3) This bond of the second carbonate anion does not require the breaking of a second Fe-OH bond, as does the formation of a bidentate complex with an adjacent SC site, nor the extreme bending of the adjacent Fe octahedra, therefore, the activation energy for the reaction proposed (1) is expected to be lower than that of a bidentate complex, and thus show faster kinetics and higher stability. (4) Previous DFT work on carbonate adsorption on dioctahedral Fe(III) clusters did not test the extreme bending required for the bidentate bridged complex in larger periodic slabs of Fe(III) octahedra, nor considered the presence of positively-charged TC adjoining sites; (4) The infrared evidence of Dn₃ for carbonate is not unambiguously assigned to a bidentate surface complex, because its value lies somewhere above that of a typical monodentate complex and far below that of a bidentate bridged one.

We consider that the experimental carbonate adsorption conditions of the data modeled is sufficiently variable (in concentrations, types of CO₂ systems – open and closed, two ionic strengths, two electrolyte anions and two goethites of different SSA) to yield reliable unified modeling results. The successful unified Cl^- binding model presented, using the fixed site densities and capacitance values previously obtained from nitrate data modeling [6] is a testament to the gradual construction of a reliable model for the adsorption behavior of goethite. The carbonate adsorption is adequately simulated, reproducing subtle features in the behavior, such as the reversing in the ionic strength behavior at high pH in open systems, where at the higher ionic strength adsorption is higher than at lower ionic strength (Figure 3b,c) (i.e., there was no need to invoke a ternary carbonate-Na⁺ outer-sphere complex as reported in previous work [3,4,27]); or the fact that at higher partial pressure of CO₂ the high SSA goethite adsorbs less carbonate at a pH range of 4-7 than the lower SSA goethite at a lower CO₂ partial pressure (a result of the higher capacitance 1 value of the lower SSA goethite – cf. Table 2).

We agree that ternary experiments where anion competition and possible carbonate-cation ternary surface complex formation would be the next step to follow, in order to continue supporting the unified model proposed, but this endeavor will be undertaken in future work with the results from the different binary systems obtained so far, and including future modeling of the adsorption behavior of major environmental ions.

We hope that the revised version submitted resolve issues of fragmented manuscript structure and technical errors.

Comments 2: Lines 45-46: This statement is too one-sided.

Response 2: We agree with the reviewer, and we have expanded this comment to read (lines 48-53 in the TC version): ”Synthetic goethite particles were reported earlier to have acicular morphologies that expose various crystal faces [1], the most prevalent being {101}, {100}, and {210} (Pnma space group). More recently, using a suite of electron microscopies [5,8,9] and tomography [8], it was found that face {100} is negligible or absent, resulting in a lath morphology for goethite. The other two faces have been typically considered for surface complexation modeling using CD-MUSIC.”

Comments 3: Section 2.3: In this section, additional combinations of carbonate surface complexes for consideration are suggested, including monodentate/bidentate configurations, variations in the state of protonation, and participating sites.

Response 3: All possibilities mentioned by the reviewer were considered in the original manuscript in sub-section 2.3.1, except participation of sites other than SC ones, because doubly-coordinated sites have been consistently considered throughout the article series as non-reactive. TC sites cannot be occupied in an inner-sphere manner because the OH in these sites are already positively-charged and cannot accept an additional proton to dissociate as water and accommodate the binding of a carbonate oxygen moiety to three surface Fe(III) species.

Comments 4: Lines 267-268: Is it possible to form a hydrogen bond?

Response 4: The distance between the carbonate oxygen and the protonated TC site (0.6 Å) is lower than that of a typical O-H covalent bond (0.96 Å), therefore it is highly probable that a covalent bond in this part of the complex is formed [see also bullet (3) in the above Response 1].

Comments 5: Section 2.3.3: This section insufficiently clarifies the fitting procedure.

Response 5: We have improved the description of the fitting procedure in the new sub-section 2.6, lines 346-363 of the TC version. We hope it is clearer now.

Comments 6: Line 288: Log K or log K? Variables should be italicized—please check this throughout the manuscript.

Response 6: We have, accordingly, made the suggested corrections throughout the manuscript text.

Comments 7: Table 3: What is the unit of RMSE?

Response 7: They are mmol/m². This has been added in Table 3.

Comments 8: Figure 4: The unit "uatm” should be μatm?

Response 8: The symbol m has been replaced as the prefix of both atm and of M in Figure 4.

Comments 9: The depth of 4. DISCUSSION needs to be strengthened.

Response 9: We have improved the discussion section making better and clearer statements. However, we believe a very important discussion in the manuscript is also held in a more complete and orderly fashion in the new section 2.5 and sub-sections within, analyzing the evidences for the carbonate complex proposed.

Point 1: The English could be improved to more clearly express the research.

Response 1: We have revised the English throughout the manuscript text and corrected it where necessary to improve the description and discussion of the work.

5. Additional clarifications

We hope that the revised manuscript has improved the introduction section by making it somewhat more succinct, and that the research design, methods, and results are better presented.

1. Summary

Thank you very much for taking the time to review this manuscript. Please find the detailed responses below and the corresponding revisions/corrections highlighted/in track changes in the re-submitted files.

2. Questions for General Evaluation

Reviewer’s Evaluation

Response and Revisions

Does the introduction provide sufficient background and include all relevant references?

Can be improved

Is the research design appropriate?

Can be improved

Are the methods adequately described?

Yes

Are the results clearly presented?

Yes

Are the conclusions supported by the results?

Yes

3. Point-by-point response to Comments and Suggestions for Authors

General Comment: The study presents a well-structured application of the CD-MUSIC model to carbonate adsorption on goethite, offering valuable insights into surface complexation mechanisms. The data are robustly analyzed, and the conclusions are largely supported by the results. However, the following issues require clarification and revision to strengthen the manuscript prior to publication:

Response: Thank you for your positive feedback.

Comments 1: The manuscript states that surface site density (e.g., SC and TC sites) varies with goethite particle size but does not explicitly explain the underlying mechanism. This relationship is counterintuitive, as smaller particles (higher surface area) typically expose more reactive sites.

Response 1: If the crystal face proportions remained the same regardless of the particle size, the specific surface area should have no effect on the number of reactive surface sites present per m², i.e. a higher specific surface area exposed would not translate into a higher reactive surface site density. We have expanded the statement in lines 54-59 (in the TC version) with a short phrase to give more clarifying background, which is more detailed in the [8,9] references given: “As their specific surface areas (SSAs) decrease below ca 82 m²/g, they show progressively higher adsorption capacities per surface area due to increasing reactive surface site densities, which in turn is due to a progressive increase in the total proportion of crystal face {210} over {101} (in the form of alternating steps on the {101} face [8,9]), because {210} has more than twice the surface density of singly-coordinated (SC) sites than {101} (7.5 sites/nm² vs. 3.03 sites/nm²).”

Comments 2: The proposed monodentate-SC + TC electrostatic interaction model is innovative but requires spectroscopy or theoretical validation.

Response 2: We believe the theoretical arguments made for the proposed surface complex are based on solid evidence. In order to present this evidence more clearly we have restructured previous sub-sections 2.3.1 and 2.3.2 to new (cf. TC version) sub-section 2.5 Configuration of the adsorbed carbonate complex, and sub-sections within: 2.5.1. Structural and spatial evidence, 2.5.2. Physico-chemical evidence, 2.5.3. DFT evidence, and 2.5.4. Spectroscopic evidence.

In summary we present the following evidence to justify the new complex proposed: (1) Structurally, the distance between oxygens in the carbonate moiety is 2.22-2.23 Å, which is 0.8 Å smaller than the interatomic distance between adjacent SC oxygens in the {101} crystal face (3.02 Å). This would require extreme bending of the adjacent octahedra to accommodate a bidentate bridged complex, whereas the adjacent TC oxygen sites in the adjoining row of octahedra have a distance of 2.83 Å from the closest SC sites, i.e., 0.2 Å closer than in the former case. (2) The vast majority of TC oxygen sites are predicted by the MUSIC model to be protonated across the normal pH range (4-10), and thus as yielding a positive charge (cf. Fig. 3b) that would exert a definite attractive electrostatic force towards a negatively charged oxygen of a second C-O^- moiety in the vicinity. (3) The separation distance between the carbonate oxygen and the positive TC OH site would be (2.83 Å – 2.23 Å=) 0.60 Å, which is shorter than a covalent O-H bond (typically 0.96 Å), and therefore, formation of an actual bond with this TC OH site can be safely proposed. (3) This bond of the second carbonate anion does not require the breaking of a second Fe-OH bond, as does the formation of a bidentate complex with an adjacent SC site, nor the extreme bending of the adjacent Fe octahedra, therefore, the activation energy for the reaction proposed (1) is expected to be lower than that of a bidentate complex, and thus show faster kinetics and higher stability. (4) Previous DFT work on carbonate adsorption on dioctahedral Fe(III) clusters did not test the extreme bending required for the bidentate bridged complex in larger periodic slabs of Fe(III) octahedra, nor considered the presence of positively-charged TC adjoining sites; (4) The infrared evidence of Dn₃ for carbonate is not unambiguously assigned to a bidentate surface complex, because its value lies somewhere above that of a typical monodentate complex and far below that of a bidentate bridged one.

Comments 3: The introduction provides ample background but obscures the study’s key advancements.

Response 3: We agree, thank you for pointing this out. We left important general background of the previous work on goethite modeling from this article series, but moved Table 1 with the text referring to it to a new sub-section in the Materials and Methods section, entitled “2.2 Goethite site densities for CD-MUSIC modeling”

Comments 4: The distinction between the standard and extended CD-MUSIC model is unclear.

Response 4: Although we use more realistic site densities based on structural and electron microscopy data, the model used is actually the standard CD-MUSIC model. This has been corrected (“extended” deleted) in all instances mentioned in the revised version.

Comments 5: How goethite surface area (particle size) impacts face distribution and site density?

Response 5: We have expanded the statement in lines 54-59 (in the TC version) with a short phrase to give more clarifying background, which is more detailed in the [8,9] references given: “As their specific surface areas (SSAs) decrease below ca 82 m²/g, they show progressively higher adsorption capacities per surface area due to increasing reactive surface site densities, which in turn is due to a progressive increase in the total proportion of crystal face {210} over {101} (in the form of alternating steps on the {101} face [8,9]), because {210} has more than twice the surface density of singly-coordinated (SC) sites than {101} (7.5 sites/nm² vs. 3.03 sites/nm²).”

Point 1: The English is fine and does not require any improvement.

Response 1: Thank you for your positive feedback.

5. Additional clarifications

We hope that the revised manuscript has improved the introduction section by making it somewhat more succinct, and that the research design is better presented.

1. Summary

Thank you very much for taking the time to review this manuscript. Please find the detailed responses below and the corresponding revisions/corrections highlighted/in track changes in the re-submitted files.

2. Questions for General Evaluation

Reviewer’s Evaluation

Response and Revisions

Does the introduction provide sufficient background and include all relevant references?

Can be improved

Is the research design appropriate?

Yes

Are the methods adequately described?

Can be improved

Are the results clearly presented?

Can be improved

Are the conclusions supported by the results?

Can be improved

3. Point-by-point response to Comments and Suggestions for Authors

General Comment: The document discusses the development of a unified adsorption model for goethite, focusing on the interfacial behavior and adsorption of carbonate ions in relation to particle size and surface site density.  The authors are using a previous dataset for carbonate adsorption in open and closed atmosphere. The authors claim that the only carbonate complex formed when binding with the goethite surface is a configuration between a monodentate and bidentate binuclear, binding to adjacent singly coordinated and triply coordinated sites. They support this hypothesis based on the O-O distance of carbonate with evidence from infrared spectroscopy. Overall, the study is up to publication standards and suitable for publication in Colloids and Interfaces with some revisions and a better explanation of the unique configuration they propose for carbonate.

Response: Thank you for your positive feedback.

Comments 1: The overall structure of the manuscript could be improved. The Introduction currently includes detailed information on goethite types and modeling results, which is uncommon. Typically, these details are more appropriate for the methods or results/discussion sections. The authors are encouraged to restructure the manuscript accordingly to enhance clarity.

Response 1: We agree, thank you for pointing this out. We left in the Introduction Section important general background of the previous work on goethite modeling, from this article series, but moved Table 1 with the text referring to it to a new sub-section in the Materials and Methods section, entitled “2.2 Goethite site densities for CD-MUSIC modeling”

Comments 2: Line 36: The statement regarding cation adsorption could be clarified. Cation adsorption is less significant than anion adsorption due to the surface charge of goethite, this explanation should be expanded in the introduction.

Response 2: Cation adsorption on goethite is very important despite the fact that below pH 9 its net surface charge is positive; this is because there are still plenty of negatively-charged sites below this pH; in fact, the net charge of singly-coordinated (SC) sites is predicted by the model to become progressively negative from pH values as low as 4-5. This is later explained in the manuscript’s new sub-section 2.4.1 (old sub-section 2.3.1) and Fig. 3a. There is general agreement among modelers of the goethite surface acidity that monoprotonated positively-charged triply-coordinated sites have a considerably lower acidity than biprotonated positively-charged SC sites, therefore, the former would stay mostly positively charged across the normal pH range (4-10), while the latter would become progressively negatively charged above pH 4-5.

Comments 3: Lines 45–53: If the site densities for the different goethite crystal faces are taken from previous studies, the authors should provide appropriate citations.

Response 3: We have, accordingly, added citation [6] to this statement, but it is also further described in Table 1, which has now been moved together with the text that makes reference to it, to new sub-section “2. 2 Goethite site densities for CD-MUSIC modeling” in the Materials and Methods section.

Comments 4: Table 1: The surface areas of the goethite samples should be explicitly stated in the table. While the names imply surface area differences, this information should also be included in parentheses or an additional column.

Response 4: We have modified the title of the first column of Table 1 to:
”GoethiteSSA (m²/g)”

Comments 5: Lines 55–57: Please clarify whether this is based on the surface depletion model.

Response 5: These calculations are only the total available reactive site densities and are based on crystallographic information and Pauling bond strength and bond-valence, as well as hydrogen bonding considerations. The surface depletion model is embedded in the MUSIC model framework, but it applies to actual adsorption reactions. Total reactive site densities provide the model with a base for mass balance calculations.

Comments 6: Optimized log K for Cl⁻: How does the optimized log K value for chloride compare with previously reported values? A discussion or comparison with existing literature is needed here.

Response 6: This discussion and comparison were provided previously in sub-section 4.1, second paragraph.

Comments 7: The CD values for the monodentate complex should be better explained. How did the authors allocate the charge for this unique configuration? There was previous spectroscopic evidence showing both a monodentate and bidentate forming (Hausner 2009; Bargar 2005; Su and Suarez 1997, Villalobos 2001) – the authors need to better explain why they adopted the new configuration besides the O-O distance.

Response 7: Allocation of the CD for the proposed complex was previously explained in the paragraph following equation (1). It is the same as that of the bidentate bridged complex.

In order to present the evidence for the proposed complex more clearly we have restructured previous sub-sections 2.3.1 and 2.3.2 to new (cf. TC version) sub-section 2.5 Configuration of the adsorbed carbonate complex, and sub-sections within: 2.5.1. Structural and spatial evidence, 2.5.2. Physico-chemical evidence, 2.5.3. DFT evidence, and 2.5.4. Spectroscopic evidence.

In summary we present the following evidence to justify the new complex proposed: (1) Structurally, the distance between oxygens in the carbonate moiety is 2.22-2.23 Å, which is 0.8 Å smaller than the interatomic distance between adjacent SC oxygens in the {101} crystal face (3.02 Å). This would require extreme bending of the adjacent octahedra to accommodate a bidentate bridged complex, whereas the adjacent TC oxygen sites in the adjoining row of octahedra have a distance of 2.83 Å from the closest SC sites, i.e., 0.2 Å closer than in the former case. (2) The vast majority of TC oxygen sites are predicted by the MUSIC model to be protonated across the normal pH range (4-10 – see also, response 2 above), and thus as yielding a positive charge (cf. Fig. 3b) that would exert a definite attractive electrostatic force towards a negatively charged oxygen of a second C-O^- moiety in the vicinity. (3) The separation distance between the carbonate oxygen and the positive TC OH site would be (2.83 Å – 2.23 Å=) 0.60 Å, which is lower than a covalent O-H bond (typically 0.96 Å), and therefore, formation of an actual bond with this TC OH site can be safely proposed. (3) This bond of the second carbonate anion does not require the breaking of a second Fe-OH bond, as does the formation of a bidentate complex with an adjacent SC site, nor the extreme bending of the adjacent Fe octahedra, therefore, the activation energy for the reaction proposed (1) is expected to be lower than that of a bidentate complex, and thus show faster kinetics and higher stability. (4) Previous DFT work on carbonate adsorption on dioctahedral Fe(III) clusters did not test the extreme bending required for the bidentate bridged complex in larger periodic slabs of Fe(III) octahedra, nor considered the presence of positively-charged TC adjoining sites; (4) The infrared evidence of Dn₃ for carbonate is not unambiguously assigned to a bidentate surface complex, because its value lies somewhere above that of a typical monodentate complex and far below that of a bidentate bridged one.

Point 1: The English is fine and does not require any improvement.

Response 1: Thank you for your positive feedback.

5. Additional clarifications

We hope that the revised manuscript has improved the introduction section by making it somewhat more succinct, and that the methods, results, discussions and conclusions are better presented.