Multiscale Simulation of Graphene Growth on Cu(111): Insights from DFT, MD, KMC, and Thermodynamic Analyses

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper provides a coherent study on the thermodynamic and kinetic mechanisms of graphene growth on Cu(111) via chemical vapor deposition (CVD) using density functional theory (DFT), molecular dynamics (MD), and kinetic Monte Carlo (KMC) simulations. The authors analyse methane dehydrogenation energetics, carbon cluster adsorption, and the effects of temperature, pressure, and CH₄/H₂ ratio on deposition rates. Key findings include the high energy demand for methane dissociation (particularly the CH→C step at 1.23 eV), optimal growth conditions (e.g., 1310 K, low pressure), and the role of gas-phase composition in carbon yield

• The computational details on the DFT part should be elaborated on more — energy convergence criteria, specifying the DFT package name, type of pseudopotentials, and Vxc approximations.

• The adsorption energies of carbon clusters (e.g., C₆: -6.54 eV) should be compared to the literature values. It will help to enhance results' significance.

• The simplified mass transport model (e.g., fixed δ=0.02 m) may not capture pressure-dependent boundary layer. A comprehensive analysis for δ-dependence would improve results robustness.

• Font style and their size on pictures are incoherent through the whole paper. In some cases, the font size is so small that it is hard to read the text; in some cases is too big.

Author Response

Comments 1:The computational details on the DFT part should be elaborated on more — energy convergence criteria, specifying the DFT package name, type of pseudopotentials, and Vxc approximations.

Response 1: Thank you for pointing this out. We agree with this comment. Therefore, we have added more detailed descriptions of the DFT calculation settings, including the energy convergence criterion, the name of the DFT package (VASP), the type of pseudopotentials (PAW), and the exchange–correlation functional (PBE-GGA).The revisions have been made in the red-marked text corresponding to lines 88–99.

Comments 2: The adsorption energies of carbon clusters (e.g., C₆: -6.54 eV) should be compared to the literature values. It will help to enhance results' significance.

Response 2: Thank you for pointing this out. We agree with this comment. Therefore, we have compared the adsorption energy of representative carbon clusters (e.g., C₆: -6.54 eV) with values reported in relevant literature to enhance the credibility and significance of our results.The revisions have been made in the red-marked text corresponding to lines 179–184.

Comments 3:The simplified mass transport model (e.g., fixed δ=0.02 m) may not capture pressure-dependent boundary layer. A comprehensive analysis for δ-dependence would improve results robustness.

Response3: Thank you for pointing this out. We agree with this comment. Therefore, we have added a δ-dependence analysis to assess its impact on mass transfer under different pressures, enhancing the robustness of the results. Corresponding modifications have been made to the red-highlighted content in lines 239–248.

Comments 4:Font style and their size on pictures are incoherent through the whole paper. In some cases, the font size is so small that it is hard to read the text; in some cases is too big.

Response 4: Thank you for pointing this out. We agree with this comment. Therefore, we have adjusted the font style and size in all figures for consistency and readability. The content corresponding to lines 249–260 and 270–271 marked in red has been revised.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This article studies the growth kinetics of graphene on Cu(111) surfaces by means of first-principles calculations and transition state search methods applied to determine the energy barriers associated with methane dehydrogenation. Also, the influence of key operating parameters - temperature, pressure, and CH4/H2 partial pressure ratio - on graphene deposition by chemical vapor deposition (CVD) was investigated based on thermo- dynamic equilibrium analysis.

The manuscript needs to be deeply revised, and it is mandatory that all the following main points be carefully addressed before it can be considered for publication:

1. First, the presentation needs to be improved. The abstract wrongly reports the words “in this chapter …”, suggesting that the manuscript was initially written as a chapter of a volume.
2. Then, the added value of this paper should be clearly enlightened in the introduction of the manuscript, considering the large literature in the field.
3. The title appears to be limited to the MD while the article includes also other methods used, as DFT and MC simulations. Therefore, the title should be rewritten/improved. To give a more comprehensive view of the paper content.
4. The introduction needs to be improved too. For the sake of completeness and to broaden/complete the discussion, it should be reported/commented on the most recent studies in the current literature regarding the formation of graphene from aromatic hydrocarbons, their adsorption on Cu substrate and decomposition steps, as described in this remarkable article that deserves to be mentioned [https://doi.org/10.1016/j.carbon.2023.02.011].
5. To improve the readability of the paper, which is 18 pages long, it is suggested to insert at the end of the introduction a short list of the following paragraphs to indicate how the article is organized, giving the reader an immediate overview of its content.
6. Fig. 3: for increasing the readability, the different energy levels should be reported by using different colors.
7. Regarding the comment of Fig. 12, some significant decreases are reported: “the content of H2 increased slightly with increasing temperature, while the contents of CH4 and C2H6 decreased significantly. The content of C2H4 increased very slowly …”. I do not agree with such comments, the H2 behaviour appears constant and the CH4 only slowly decreases, while the C2H4 trend is almost constant, and so on. Therefore, the authors should deeply revise and rewrite all the discussion of this point.
8. At lines 358-360, in the comment of Fig. 13 is reported that: “when the temperature exceeds 1310 K, the curve levels off and begins to decrease.” Honestly, I can't see any decrease in the trend that continues, even if slightly, to increase anyway. The authors should clarify/correct.
9. It would be very interesting to compare the theoretical results with experimental data, if any. The author should carefully comment on this inside the manuscript.
10. Furthermore, the conclusions should be completed by highlighting the value that the manuscript adds to the current literature in the field and outlining some perspectives opened by this study.
11. All references need to be completed with DOI.

All the issues raised need to be addressed according to the suggested changes, for the manuscript to become suitable for publication in the journal.

Author Response

Comments 1:First, the presentation needs to be improved. The abstract wrongly reports the words “in this chapter …”, suggesting that the manuscript was initially written as a chapter of a volume.

Response 1: Thank you for pointing this out. I/We agree with this comment. Therefore, we have revised the abstract to remove the inappropriate phrase “in this chapter” and adjusted the wording to reflect a standalone journal article format. The content corresponding to lines 17–18 marked in red has been revised.

Comments 2:Then, the added value of this paper should be clearly enlightened in the introduction of the manuscript, considering the large literature in the field.

Response 2: Thank you for pointing this out. We agree with this comment. Therefore, we have revised the introduction to clearly highlight the added value of this study in light of the extensive existing literature in the field. The content corresponding to lines 67–75 marked in red has been revised.

Comments 3:The title appears to be limited to the MD while the article includes also other methods used, as DFT and MC simulations. Therefore, the title should be rewritten/improved. To give a more comprehensive view of the paper content.

Response 3: Thank you for pointing this out. We agree with this comment. Therefore, we have revised the title of the manuscript to:"Multiscale Simulation of Graphene Growth on Cu(111): Insights from DFT, MD, KMC, and Thermodynamic Analysis." The content corresponding to the red-marked section in item 2-3 accordingly.

Comments 4:The introduction needs to be improved too. For the sake of completeness and to broaden/complete the discussion, it should be reported/commented on the most recent studies in the current literature regarding the formation of graphene from aromatic hydrocarbons, their adsorption on Cu substrate and decomposition steps, as described in this remarkable article that deserves to be mentioned [https://doi.org/10.1016/j.carbon.2023.02.011].

Response 4: Thank you for pointing this out. We agree with this comment. Therefore, we have revised the introduction to include recent studies on the formation of graphene from aromatic hydrocarbons and their adsorption and decomposition on Cu substrates. The recommended article [https://doi.org/10.1016/…] has been cited. The text corresponding to lines 57–59 has been modified accordingly.

Comments 5:To improve the readability of the paper, which is 18 pages long, it is suggested to insert at the end of the introduction a short list of the following paragraphs to indicate how the article is organized, giving the reader an immediate overview of its content.

Response 5: Thank you for pointing this out. We agree with this comment. Therefore, we have provided a table of contents before the introduction to improve the readability of the manuscript and help readers quickly understand its organization and content.The revisions have been made in the red-marked text corresponding to lines 30–45.

Comments 6:for increasing the readability, the different energy levels should be reported by using different colors.

Response 6: Thank you for pointing this out. I/We agree with this comment. Therefore, we have adjusted the color scheme in Figure 3 to use distinct colors for representing different energy levels, which improves readability. The content corresponding to lines 165–166 marked in red has been revised.

Comments 7:Regarding the comment of Fig. 12, some significant decreases are reported: “the content of H₂ increased slightly with increasing temperature, while the contents of CH₄ and C₂H₆ decreased significantly. The content of C₂H₄ increased very slowly …”. I do not agree with such comments, the H₂ behaviour appears constant and the CH₄ only slowly decreases, while the C₂H₄ trend is almost constant, and so on. Therefore, the authors should deeply revise and rewrite all the discussion of this point.

Response 7: Thank you for pointing this out. We agree with this comment. Therefore, we have revised all the discussions related to Figure 12 to accurately reflect the observed behaviors. The revisions have been made in the red-marked text corresponding to lines 384–388.

Comments 8:At lines 358-360, in the comment of Fig. 13 is reported that: “when the temperature exceeds 1310 K, the curve levels off and begins to decrease.” Honestly, I can't see any decrease in the trend that continues, even if slightly, to increase anyway. The authors should clarify/correct.

Response 8: Thank you for pointing this out. We agree with this comment. Therefore, we have clarified and corrected the discussion regarding Figure 13, specifically addressing the trend beyond 1310 K. The revisions have been made in the red-marked text corresponding to lines 405–406.

Comments 9:It would be very interesting to compare the theoretical results with experimental data, if any. The author should carefully comment on this inside the manuscript.

Response 9: Thank you for pointing this out. We agree with this comment. Therefore, we have added a discussion comparing our theoretical results with available experimental data, highlighting qualitative agreement and noting the need for further experimental validation. The content corresponding to lines 539–542 marked in red has been revised.

Comments 10:Furthermore, the conclusions should be completed by highlighting the value that the manuscript adds to the current literature in the field and outlining some perspectives opened by this study.

Response 10: Thank you for pointing this out. We agree with this comment. Therefore, we have revised the conclusion to emphasize the added value of this manuscript to the current literature and outlined some new perspectives opened by this study.The revisions have been made in the red-marked text corresponding to lines 531–538.

Comments 11:All references need to be completed with DOI.

Response 11: Thank you for pointing this out. We agree with this comment. Therefore, we have completed all references by adding the corresponding DOIs.The revisions have been made in the red-marked text corresponding to lines 562–610.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

I think the paper is ready to go. 

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have made the required changes improving the manuscript, therefore it is now eligible for publication.