最近運(yùn)氣不錯(cuò)，在 Nano Lett. 發(fā)表了一篇關(guān)于多晶石墨烯熱傳導(dǎo)模擬的論文。

論文題目:Bimodal grain-size scaling of thermal transport in polycrystalline graphene from large-scale molecular dynamics simulations

論文鏈接：http://pubs.acs.org/doi/abs/10.1021/acs.nanolett.7b01742

全文：2017-NL.pdf

在此分享此文的 cover letter、得到的審稿意見(jiàn)以及回復(fù)，希望對(duì)某些讀者有一定的參考價(jià)值。

注：

1）本文中的英文是從 word 文檔直接復(fù)制過(guò)來(lái)的，有些單詞連在一起了，影響閱讀，望讀者見(jiàn)諒。

2）本文的分子動(dòng)力學(xué)模擬（MD）計(jì)算采用的是我寫的GPUMD程序。該程序的下載地址為：https://github.com/brucefan1983/GPUMD

3）本文中使用的多晶石墨烯樣品是用相場(chǎng)晶體法（PFC）產(chǎn)生的，質(zhì)量很高。這些樣品的坐標(biāo)文件都以附加材料的形式發(fā)表在ACS網(wǎng)站（解壓后有幾百兆），需要的可以免費(fèi)下載。

一、cover letter

這個(gè)對(duì)一般的期刊可能不重要，但對(duì) Nano Lett. 這種類型的期刊可能比較重要。如果不用心寫，可能很難過(guò)編輯那一關(guān)。下面是此文的 cover letter（我自己感覺(jué)寫得太啰嗦，但又怕寫得太少讓編輯感覺(jué)不重視。我個(gè)人是反對(duì)在論文中寫一些言過(guò)其實(shí)的話，但給編輯的信可以寫得夸張一點(diǎn)。）：

Dear Editors,

It is our pleasure to submit the manuscript entitled “Bimodal grain-size scaling of thermal transport inpolycrystalline graphene from large-scale molecular dynamics simulations” by Zheyong Fan, Petri Hirvonen, Luiz Felipe C. Pereira, Mikko M. Ervasti, Ken R.Elder, Davide Donadio, Ari Harju, and Tapio Ala-Nissila, for exclusive publication in Nano Letters.

Graphene holds great potential for thermal management applications due to its exceptionally high thermal conductivity (which can exceed 5 000 W/mK) in its pristine form. However, wafer-scale graphene samples needed for industrial applications are usually grown by chemical vapor deposition and are inevitably polycrystalline in nature. Such samples contain grain boundaries which are extended line defects separating grains of different orientations.   It has been known since the seminal 1941 experiments by P. Kapitza in liquid He that interfaces have amajor impact on the heat flow across them. While grain boundary and other interface effects on heat conduction have been extensively studied in 3D systems, their influence on 2D materials such as graphene is much less understood.

The central question for polycrystalline graphene concerns the scaling of the thermal conductivity with the average grain size. To this end, in our work we employ extensive classical molecular dynamics (MD) simulations to quantify the grain-size scaling of thermal transport in large suspended samples prepared by an efficient multiscale approach based on the phase field crystal model, which allows us to consider properly thermalized multigrain configurations up to about 200 nm in linear size.

Our first important result is that in contrast to previous theoretical works, the scaling of the thermal conductivity with the grain size displays bimodal behaviour with two effective Kapitza lengths. Compared to pristine graphene where the thermal conductivity is dominated by flexural modes associated with out-of-plane phonons, in polycrystalline graphene the grain size scaling is dominated by the out-of-plane (flexural) phonons with a Kapitza length that is an order of magnitude larger than that of the in-plane phonons.This result quantifies for the first time the dramatic influence of grain boundaries on heat conduction in 2D materials.

Concerning heat conduction measurements in graphene there is a large variation between results from different experiments. Most recently it has been shown by high-quality experiments that in pristine graphene the heat conductivity can be as high as 5 000 W/mK (as mentioned above). This value is almost 70% higher than that obtained from the most accurate classical MD simulations. This means that quantum effects play an important role. The second important result in our work is that we show that when mode-by-mode quantum corrections are properly applied to our classical MD results (and the pristine case is properly renormalized to the experimental value), we can obtain full agreement with the experimental data for polycrystalline graphene.

To summarize, we think that our results constitute a significant step forward in understanding heat transport in graphene and other two-dimensional materials. Our work should be of broad interest to engineers, chemists and physicists working on nano-structured graphene and related systems in the context of thermal management devices and deserves publication in Nano Letters.

On behalf of the authors

Sincerely Yours,

Corresponding author: xxx

Mail address: xxx

Phone: xxx

Fax: xxx

Email:xxx

二、第一輪的審稿意見(jiàn)和回復(fù)

文章在編輯手里待了一個(gè)月才送給審稿人。審稿人都很給力，不到三個(gè)星期就得到了第一輪審稿意見(jiàn)?？偟膩?lái)說(shuō)，審稿意見(jiàn)算是比較正面的。第一個(gè)審稿人建議直接接受，那就感謝就是了。第二個(gè)審稿人指出了一些我們的文章忽略了的問(wèn)題。這種情況下，一方面在回復(fù)中解釋，一方面在文章中加一些相關(guān)的討論即可。第三個(gè)審稿人主要認(rèn)為我們應(yīng)該給出更詳細(xì)的計(jì)算數(shù)據(jù)以及全部多晶石墨烯的坐標(biāo)數(shù)據(jù)。我們就老老實(shí)實(shí)弄了附加材料，給出了這些數(shù)據(jù)。三個(gè)審稿意見(jiàn)和我們的回復(fù)如下：

Dear Prof. xxx

Thank you for a rapid processing of our manuscript exclusively submitted for publication in Nano Letters. We hereby submit a revised version of the manuscript “Bimodal grain-size scaling of thermal transport in polycrystalline graphene from large-scale molecular dynamics simulations” by Zheyong Fan, Petri Hirvonen, Luiz Felipe C. Pereira, Mikko Ervasti, Ken Elder, Davide Donadio, Ari Harju, and Tapio Ala-Nissila (Manuscript ID: nl-2017-01742z). We thank the reviewers for their constructive criticism that has helped us to improve themanuscript. Since the changes to the manuscript are relatively minor we hope that our work can now be accepted for publication.

Yours Sincerely,

xxx

On behalf of theco-authors

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Reply to the Commentsfrom the Editorial Office -- nl-2017-01742z

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Commentsfrom the Editorial Office:

-Ref. 20: please update reference with full publication details.

Reply: All the incomplete references have been updated.

-Ref. 30: please provide a date accessed for the URL.

Reply: We have provideda date of accessing the URL.

- Because you answered the Conflict of Interest custom question "No," the following sentence must be added to your manuscript: "The authors declare no competing financial interests."

Reply: We have added this statement.

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Reply to the First Referee --  nl-2017-01742z

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Reviewer’s Comments:

In this manuscript, the authors present a convincing study on thermal conductivity of polycrystalline graphene using molecular dynamics calculations. The novelty of the work is based on the (more than usual) realistic model for samples as well as on the quantum corrections applied on the classical simulations. In my view the article is suitable for publication in Nano Letters as is.

Reply: We thank the referee for supporting our work to be published in Nano Letters.

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Reply to thesecond Referee --  nl-2017-01742z

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Comments:

The authors perform large-scale quantum-corrected MD simulations of polycrystalline graphene. The results are compared to one set of recent experiments and used to explain different gran size scaling trends for in-plane and out-of-plane phonons. The work is quite interesting because it is among the first MD results that accurately predicts Kaptiza resistances at grain boundaries, and as such may be of broad interest. However, there are several questions that arise:

Reply:We thank the Referee for the positive comments.

1)   Ref. 16 clearly shows an angle dependence, but none was discussed in this manuscript. Does the Kapitza resistance depend on mismatch angle in additionto grain size?

Reply:This is an interesting question and the answer is definitely positive -- the Kapitza resistance depends on the misorientation angle if we consider individual grain boundaries (GBs). We have in fact carried out a separate study on this question, and find that when the misorientation angle between two grains is relatively large (around 30 degrees), the Kapitza resistance is relatively weakly dependent on the mismatch angle, with the Kapitza conductance after quantum corrections being about 10 W/m^2/K. This is in excellent agreement with the effective Kapitza conductance (9.5 W/m^2/K) obtained in this work. These results will be discussed in a future publication.

Action: We have added the following sentences to the last paragraph ofpage 10  (Just before the Methods section):

“This argument is further supported by the fact that while the Kapitza conductance of individual grain boundaries depends on the angle of misorientation, for angles between about 20 and 40 degrees, this dependence is rather weak. We have carried out a comprehensive study of the Kapitza conductance for grain boundaries of different orientations and the results will be published elsewhere.”

2)   CVD grow graphene has a broad distribution of grain sizes. How does this work account for the broad non-uniformity of grain sizes? How about anisotropy in grains that are not nearly circular? If there is anisotropy, asingle or even bimodal Kaptiza resistance cannot be extracted.

Reply: We have considered in this work relatively but not exactly uniformgrain sizes generated by the phase-field crystal method, which has been shown to reproduce realistic grain size distributions in the asymptotic limit in two dimensions  [R. Backofen, K. Barmak, K. R. Elder and A. Voigt, Acta Mater. 64, 72 (2014)]. However, we argue that CVD type of non-uniformities and anisotropies could certainly influence theresults quantitatively,  but not qualitatively. If the mismatch angledistribution is such that there’s no abundance of small angle GBs, there’s very little change in the Kapitza conductance as explained above in our reply to the Referee’s first question.We stress that the concept of an effective grain size is very much the same as that of an effective phonon mean free path which, in spite of being a relatively crude estimate, captures the essential physics. Because the in-plane and out-of-plane phonons have drastically distinct transport properties, we expect that the bimodal scaling would survive even if enhanced variations in the non-uniformity and anisotropy of the GBs were considered.

Action: We have added the following sentences to the last paragraph of page 10 (Just before the Methods section):

“Finally, we point out that our samples were generated by the phase field crystal method, which has been shown to reproduce realistic grain size distributions in the asymptotic limit in two dimensions [43]. Such samples may not correspond to those observed in some experiments [18], but additional non-uniformity andanisotropy should influence the results only quantitatively,  not qualitatively.The concept of an effective grain size is analogous to that of an effective phonon mean free path, which, in spite of being a relatively crude estimate, captures the essential physics. Because the in-plane and out-of-plane phonons have drastically distinct transport properties, we expect that the bimodal scaling would survive even if the influence of additional non-uniformity andanisotropy were taken into account.”

3)   Substrate effects are ignored here--most of the time, a CVD grownsample is supported or transferred, and the substrate is known to have adramatic effect on flexural (out of plane) modes. How would your results differ if the simulated samples were on SiO2? If the ZA branch is suppressed by substrate interactions, would the bimodal features nearly disappear?

Reply: We indeed expect that the substrate will have strong effects onthe heat transport in the systems we have studied. When the ZA branch is suppressed by the interactions with the substrate, the bimodal features may be significantly reduced. To figure out whether it will disappear completely requires detailed study and we leave this interesting question for future work. However, we stress that the suspended case is of critical interest and is the starting point for more elaborated studies.

Action: We have added the following sentences to the last paragraph ofpage 10  (Just before the Methods section):

“We note that we have only considered suspended graphene samples in this work.  For supported graphene, heat transport by the out-of-plane phonons will be significantly suppressed. Whether or not the bimodal scaling will survive in the presence of a substrate is an interesting question which requires further study.”

4)   corrugation plays a role, and the corrugation here is natural, caused by strain due to mismatch at the GB. In supported samples, the corrugation is also caused by substrate roughness. How would that effect theoutcome?

Reply: This point is related to the previous question. We agree that corrugation caused by a rough substrate can have significant effects on the results and hope to address this question in the future.

5) quantum corrections are performed for the heat capacity but not for the anharmonic rates. How significant is the role of anharmonicity here? Is grain boundary scattering dominant?

Reply: Actually, we have applied quantum corrections to both the heat capacity in the limit where grain boundary scattering dominates and anharmonicity in the limit where phonon-phonon scattering dominates. The difference is that we used a more rigorous mode-to-mode approach to correct the heat capacity in polycrystalline graphene and hence the Kapitza conductance, but used an empirical way to correct the anharmonicity in pristine graphene by scaling the out-of-plane thermal conductivity such that the total thermal conductivity matches a reference value measured experimentally. The reason is that there is so far no rigorous and practical quantum correction method in the diffusive regime where phonon-phonon scattering dominates. In summary, in the limit of polycrystalline graphene with relatively small grains, the grain boundary scattering dominates and one can apply the mode-to-mode method to properly correct the calculated classical Kapitza conductance; in the limit of pristine graphene, phonon-phonon scattering dominates and we can only correct the classical anharmonicity in an empirical way.

Other than these broad questions, the manuscript is well composed and clear.  It shouldbe published with suitable revisions addressing the above.

Reply: We thank the Referee again for the very insightful comments.

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Reply to theThird Referee --  nl-2017-01742z

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Recommendation: Publish after minor revisions noted.

Comments:

The authors have performed MD-simulations to reveal the scaling of thermal conductivity and kapitza resistance for samples with different crystallitesizes. Their main result, is that the often used formula, equation (1) in their paper, holds for in-plane and out-of-plane modes independently, giving rise to a nonlinear reciprocal scaling with crystallite linear dimension.  This is an interesting and important result that is worthy of publishing.

Reply: We thank the Referee for the positive comments.

The authors then proceed to compare their results with experimental and numerical results of other authors. Since their classical MD cannot account for possible quantum effects they then make corrections. Here I think the authors risk making too strong statements in regards to both the uncertainties in the reported experiments and lack of data points, as well as in regard to the applicability of the rather crude quantum corrections.For instance, on line 53, end of page 7, they claim "The only possible reason for the discrepancy must be the use of classical statistics in view of the Debye temperature..."This is a very strong statement that does not at all take into account possible experimental errors not accounted for, neither for other effects such as finite sample sizes or specific details of the samples. I agree that it is a very likely cause.To account for the quantitative disagreement the authors apply two different corrections. First a mode-by-mode quantum correction, and then a scaling to match with previously known results for pristine graphene. Both corrections are rather crude, and I think the authors risk overselling the agreement. In particular as the main message of the paper, the bimodality, seems not to be confirmed by the numerics-experimental comparison.

Reply: We thank the Referee for pointing this out. We agree thatthe statement: “The only possible reason for the discrepancy must be the use ofclassical statistics in view of the Debye temperature...” is too strong. We have changed this to read: “One reason for the discrepancy is the use of classical statistics in view of the high Debye temperature ...”. However, we argue that the bimodal grain-size scaling is supported by the experimental data. Using the single-parameter fitting formula [Eq. (1) in the manuscript] without considering the in-out decomposition [Eqs. (2) and (3) in the manuscript], the experimentally extracted Kapitza conductance (3.8 GW/m^2/K) is significantly smaller than the correct one (about 10 GW/m^2/K). In the formalism of the in-out decomposition, the out-of-plane component has a smaller Kapitza conductance (2.5 GW/m^2/K) but  a much larger Kapitza length, and thus dominates the grain-size scaling. The in-plane component has weaker influence on the grain-size scaling, but contributes a larger Kapitza conductance (7 GW/m^2/K). Only by considering the in-out decomposition, can one obtain the correct grain-size scaling of the thermal conductivity and at the same time obtain the correct magnitude of the Kapitza conductance.

Action: We have properly modified the statement about quantum corrections as explained above.

Inconclusion, I think the paper is worthy of publication provided the author sclarify the following points.

* How many different disorder realization were averaged over for different sizes?

* How large was the spread from realization to realization for the data points in Fig. 3a-3c?

Finally, for comparisons with other approaches, and for others to be able to reproduce data, I strongly encourage the authors to make the numerical samples used available online. This facilitates fair comparisons and bench marking with other methods.

Reply: We thank the Referee for suggesting these. For each effective grain size, we have averaged the results over 2 to 7 independent realizations. The spread from realization to realization is reasonably small.

Action:We have provided the following data in the Supporting Information:(1) All the numerical samples.(2) Detailed results regarding Fig. 3 in the manuscript. We have also published the GPUMD code used in this work and provided a reference (https://github.com/brucefan1983/GPUMD) to the code in the revised manuscript.


三、第二輪審稿意見(jiàn)和回復(fù)

文章二審又用了一個(gè)月左右。這次第三個(gè)審稿人沒(méi)有意見(jiàn)了，但第二個(gè)審稿人又提出了幾個(gè)新的問(wèn)題（這些問(wèn)題是在第一輪審稿中沒(méi)有涉及的）。我們認(rèn)為這是不合理的，所以在提交修改稿的時(shí)候順便給編輯寫了個(gè)私信。在提交第二個(gè)修改稿之后，當(dāng)天就接受了。也許給編輯寫的私信起到了一定作用? 

給編輯的私信內(nèi)容如下：

We would like to draw your attention to the second report from Referee 2. In this report the Referee asks us to make small but nevertheless mandatory changes that he/she did not require or even mention in the first report. To our understanding it is not proper to keep on asking new changes in subsequent reports.

第二輪審稿意見(jiàn)和我們的回復(fù)如下：

Nano Letters

The Editors

Attn: prof. xxx

Dear Prof. xxx

Thank you for a rapid processing of our manuscript exclusively submitted for publication in Nano Letters. We hereby submit the second revised version of the manuscript “Bimodal grain-size scaling of thermal transport in polycrystalline graphene from large-scale  molecular dynamics simulations” by  Zheyong Fan, Petri Hirvonen, Luiz Felipe C. Pereira, Mikko Ervasti,  Ken Elder, Davide Donadio, Ari Harju, and Tapio Ala-Nissila (Manuscript ID: nl-2017-01742z.R1).  We thank the reviewers for their constructive criticism that has helped us to improve the manuscript. Since the changes to the manuscript are relatively minor we hope that our work can now be accepted for publication.

Yours Sincerely,

Zheyong Fan

On behalf of the co-authors

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Reply to the second Referee -- nl-2017-01742z.R1

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The authors use Molecular Dynamics to study heat transport in polycrystalline graphene. This is an important topic as all 2-dimensional materials grown wafer-scale by CVD are going to be polycrystalline and grain boundaries are well known to impede heat removal. The study is thorough and timely, focusing on size scaling of thermal conductivity vs. grain size. The conclusion that Kaptiza resistance is bimodal seems novel and useful to a broad community. I support publication with the following corrections/questions:

Reply:We thank the Referee for the positive comments.

1) The extraction of the Kaptiza resistance strongly relies on two things:

   a) that the length scaling in Eqn. 1 (or similar form Eqn. 2 and 3) is correct; however, this has been cast into question by some early and recent work showing that the size scaling ispartially logarithmic. Klemens called this the problem of long waves (Int. J.Thermophys. 22, 265 (2001)) and it was further elaborated recently by separating the diffusive and hydrodynamic components (see Majee and Aksamija, PRB 93, 235423 (2016)). It appears that the simple ballistic-to-diffusive scaling is there, but there is a logarithmic component due to phonon hydrodynamics.

 Reply: Whether Eqs. (2) and (3) apply or not depends on whether the thermal conductivity of pristine graphene is upper bounded or not. In our previous work [Fan et al., Phys.Rev. B 95, 144309 (2017)], we have in fact studied this question in quantitative detail using both EMD and NEMD simulations. The unequivocal conclusion from our work is that the thermal conductivity of pristine graphene is finite when the in-plane strain  is zero while it diverges logarithmically when a sufficiently large in-plane strain is applied.  In our present manuscript, we consider unstrained polycrystalline graphene for which the thermal  conductivity in the limit ofinfinite grain size is thus certainly finite. Equations (2) and (3) in thecurrent work  are similar to Eq. (33) in Fan et al. [Phys. Rev. B 95, 144309 (2017)],  whose validity has been numerically demonstrated. We also point out that the in-plane and the out-of-plane  components in our formalism are similar to the diffusive and the hydrodynamics components as mentioned by the Referee, which have quite different length dependence in pristine graphene. As mentioned in our last reply to the Referee, the Kapitza conductance extracted by fitting with the Eqs. (2) and (3) is very close to  that calculated using individual grain boundaries.

b) that there is a Kaptiza contribution in the kappa^cross component, which is lumped with the in-plane  contribution. While it's clear what G^in means, what happens to the G^cross when the kappa^cross is added to kappa^in?

2) there are only in-plane and out-of-plane phonons. what is the physical mechanism of heat  transfer underlying  kappa^cross? I can see the in and out of plane phonons coupling to each other, but only one or the other is carrying the heat at anytime. What is the intuitive meaning of kappa^cross?

Reply: The appearance of kappa^cross is intrinsic to the standard Green-Kubo correlation function – linear  response formalism. We have found inour earlier paper  [Fan et al., Phys.Rev. B 95, 144309 (2017)] that  kappa_cross is almost zero in pristine graphene. However, in polycrystalline graphene there is significant  surface corrugation (as can be seen from Fig. 1 of the current manuscript), and the definitions of the in-plane (xy) direction and the out-of-plane (z) direction are not ideal throughout the whole sample. Thus, it is expected that there is some degree of correlation or coupling between the in-plane and  out-of-plane modes (the Green-Kubo cross-correlation function measures the degree of such coupling by definition). We have already commented this point in the manuscript by stating that “This is due to  enhanced coupling between the out-of-plane and in-plane phonon modes in the presence of larger surface  corrugation.”. Attributing the small kappa_cross to the in-plane component is just a choice to simplify the discussion.  We have also tried attributing the small kappa_cross evenly to the in-plane and the out-of-plane components, or simply discarding it. We found out that both of these approximations lead to very little difference in the extracted Kapitza conductance and the bimodal grain-size scaling. That is, this technical issue is irrelevant to the conclusions in the manuscript.

3) the authors cite only one paper (Ref. 42) for previous results based on lattice dynamics calculations; however, there have been several other,earlier, papers showing this result (PRBs from Linsday, Balandin, an APL from Knezevic, and several others) that should be cited.

Reply: We agree that the citation here is not complete. In the revised manuscript, we have cited a few relevant papers from the authors as suggested by the Referee.