The Unusual Tribological Properties of Graphene/Antimonene Heterojunctions: A First-Principles Investigation

Round 1

Reviewer 1 Report

The authors presented an interesting approach for curing epoxy systems via dynamic crosslinking. The reviewer has few questions which need to be answered before acceptance.

1. Why 180C is chosen for curing the system.
2. Even though the authors presented an interesting approach but it seems the epoxy systems were under cured. How authors will justify this?
3. Have authors tried using different hardener system (apart from using sebacic acid), it would to interesting to compare the use of different hardeners and comparison between the properties of the two different systems.

Authors must cite some recent work related to the same type of work and explain the rationale of their work.

1. https://doi.org/10.1021/acs.macromol.9b02526
2. https://doi.org/10.1007/s10118-020-2479-6

Author Response

The reviewer 1 give the wrong comments for our manuscript. The comments should be for curing epoxy systems via dynamic crosslinking. In this work, we focus on the unusual tribological properties of graphene/antimonene het-erojunctions. Thus, we are hard to response for these comments.

Reviewer 2 Report

See attached document.

Comments for author File: Comments.pdf

Author Response

Reviewer 2

Methods

• Although a subtle point, it behooves the authors to provide a reference for their choice of GGA with Grimme dispersion model (PBE+D), to help ensure that this approach is appropriate for these types of heterojunction/structures.

Responses: Thank you! The reference was added to ensure that this approach is appropriate for these types of heterojunctions.

• The authors did not provide a justification, merit, or details for there choice of alignment in the x-y plane. Given the degrees of freedom present for describing the graphene/antimonene heterostructure the authors should discuss details of incommensurate and commensurate (i.e., moire) lattices between graphene and antimonene. This is important to understand the nature of the potential energy surface structure in the x-y plane.

Responses: Thank you! Periodic boundary conditions are added in the x-y plane, the moving direction is only applied along x direction for calculated the work of separation due to the same potential energy between moving along x and y axis. For instance, the graphene layers coincide exactly calling commensurate, rather incommensurate. Due to difficult to coincide between graphene and antimonene layers, thus, incommensurate could be defined for graphene/antimonene heterojunction.

• There are many typographic errors throughout this section, for example on line 61 "cal-culated" should be calculated.

Responses: Thank you! The typographic errors are carefully corrected in the revised manuscript.

Results

• I found Fig. 2(b) and Fig. 3 to be inconsistent with each other, probablybecause the supporting text is confusing. In Fig. 2(b) it appears thatat 3.2-3.3 A that the PBE+D model employs a spline interpolation and therefore this region is not necessarily physical. However, in Fig. 3 it doesn't seem to be the case. The authors should review the Grimme PBE+D parameter set to ensure this is not the case.

Responses: Thank you! The interface between 3.2 -3.3 Å in Fig 2(b) did not employ any interpolation. The data in Fig. 3 was originated from the partial differential of the calculated van der Waals energy. The Grimme PBE+D parameter was set as 0.75 and 20 for s6 and d. The data in Fig. 2 b were obtained from the energies under PBE+D, the data in Fig. 3 was calculated from the difference between the energies under PBE+D and the ones under PBE. Thus, the calculated results should be accurate.

• Table 1 is at _rst glance confusing; it appears that there are two configurations in the "configuration" column, but this is not so. Additionally is the assessment at a separation distance 3.45 A meaningful given the statement above. I believe the confusion here is that I'm unable to understand if the authors are treating heterojunctions and graphene/antimonene as two different con_gurations. Furthermore, the authors show a continuous curve for Fig. 2 and 3 but yet three values for Table 1.

Responses: Thank you! The table was carefully modified in the revised manuscript. The content in this table was clear and reasonable in the revised manuscript.

• In general these two sections need a great deal of additional explanation.

Responses: Thank you! The additional explanations for these two sections were added in the revised manuscript.

• Fig. 5 labels are difficult to read. This _figure would be better plotted as a contour or color heatmap, unless each point is part of a sequence, then it would be useful to employ color coding to indicate so. A more detailed figure caption is need.

Responses: Thank you! The Fig. 5 was altered to the contour heatmap in the revised manuscript. And the detailed figure caption was added.

• This section should just be combined with previous sections.

Responses: Thank you! The section 3.2 and 3.3 was combined in the revised manuscript.

• What is meant by electron density di_erence in this context, is it the usually meaning? Authors should provide a de_nition (e.g., equation used to calculate it) or expand upon what they mean.

Responses: Electron density difference Dr has often used to analyze electronic transitions between two interfaces. The depletion and accumulation of electron density at atomic interface would closely affect the tribological performance of the tribosystems.

• Fig. 5 is really plotting the partial DOS, text should indicate so.
• Given that the main shift occurs in the Sb 5s valance band, it would be useful to have an additional figure or inset which highlights this. More specifically, just plotting the Sb 5s PDOS on a narrow energy scale, e.g., -2 to 1 eV.

Responses: Thank you! The DOS of Sb 5s between –2 and 1 eV was conducted in the revised manuscript.

• labels in Fig. 5 are difficult to read.

Responses: The labels for all figures are improved in the revised manuscript.

• Its not clear to my from Fig. 9 and eqs. 1-2 how superlubricity is established. Seems unsubstantiated that if the friction coefficient falls within 0.00007-0.0002 x axis location. If this is the case the superlubricity is only valid at certain spatial locations; not sure how to interpret that. Seems like the friction coefficient needs to be plotted against shear velocity or force. Overal I think this needs more details to be clearly understood.

Responses: Thank you! In this work, the static friction force was calculated from the formula (2) in the revised manuscript. We calculated the static friction force at the certain positions. The friction coefficients were calculated by . And the superlow friction was found for graphene and antimonene heterojunctions. We expect to provide positive guidance for the experimental investigations.

Reviewer 3 Report

The English is very poor numerous formulation are difficult to understand; just an example : “We found that work” and there are plenty

The introduction is very brief and do not expose clearly the challenges and the state of art review in details; otherwise the motivation is low seems that is a continuation of a research but there was not resented exactly its scientific purpose
Why you have selected this “the cutoff energy of 420 eV” ???

I suggest presenting the figures after some text in order to understand their context

Figure 5,9 font size of all ordinates and abscissa are very poor ..otherwise I suggest to use an uniform style over the entire paper

Figure 5,7 required detailed evaluation and discussion as now is very poor presented

Legend in Figure 8 is not visible

Please discuss each image from Figure 8

The discussion seems a simple statement not a clear discussion

Otherwise you said that this research is focused in “tribological properties” but they were investigated only partially cause there is no any trial about friction effect between studied parts

The references are little bit out of date, so I suggest to cite some more recent one

Author Response

Reviewer 3

The English is very poor numerous formulation are difficult to understand; just an example : “We found that work” and there are plenty

Responses: Thank you! Work of separation is a physical expression, showing the adhesion strength for two interfaces. And we try our best to improve the English level.

The introduction is very brief and do not expose clearly the challenges and the state of art review in details; otherwise the motivation is low seems that is a continuation of a research but there was not resented exactly its scientific purpose

Responses: Thank you! In this work, we focus on investigating the potential tribological behavior of graphene/antimonene heterojunction, until now, there are rarely reports. Thus, this work has resented its scientific purpose to some extent.

Why you have selected this “the cutoff energy of 420 eV” ???

Responses: Thank you! After the convergence tests, 420 eV with k-point of 25 ´ 25 ´ 1 is probe to be the better parameter for the calculated system.

I suggest presenting the figures after some text in order to understand their context

Responses: Thank you! The figures are listed after the text.

Figure 5,9 font size of all ordinates and abscissa are very poor ..otherwise I suggest to use an uniform style over the entire paper

Responses: The font size of all figures are improved in the revised manuscript.

Figure 5,7 required detailed evaluation and discussion as now is very poor presented

Responses: Thank you! The detailed evaluation and discussion for Figure 5 and 7 was added in the revised manuscript.

 

Legend in Figure 8 is not visible

Responses: Thank you! All figures were well improved in the revised manuscript.

Please discuss each image from Figure 8

Responses: Thank you! Due to adding a figure in the revised manuscript, the figure number of Figure 8 was 9 in the revised manuscript. Figure 9 shows 3D potential energy surfaces. From Figure 9a to 9c, only one low friction path is observed. Last, under the misaligned contacts, potential energy possesses the lowest values as shown in Figure 9, that is, the sys-tem could easily slide over the low friction paths due to the lowest energy barriers. Therefore, we could confirm that the lowest energy barriers should be another factor for structural superlubricity.

The discussion seems a simple statement not a clear discussion

Responses: Thank you! We aimed at illustrating the cause of superlow friction, thus, in discussion section, we probed the mechanism according to three aspects. And although the discussion in this part seemed simple, was enough for illustrating the superlow friction mechanism.  

Otherwise you said that this research is focused in “tribological properties” but they were investigated only partially cause there is no any trial about friction effect between studied parts

Responses: Thank you! We could illustrate this issue in this way. We calculated work of separation for graphene and antimonene heterojunction. In general, adhesion between two solid surfaces was typically characterized by the work of separation. And many published researches have successfully investigated the tribological properties of the tribosystems[1,2]. Thus, in this work, the results of work of separation and PES well probed the superlow friction mechanism.

[1] Surface & Coatings Technology 283 (2015) 129–134

[2] ACS Appl. Mater. Interfaces 5 (2013) 5889–5893.

The references are little bit out of date, so I suggest to cite some more recent one

Responses: Thank you! The recent references are cited in the revised manuscript.

Round 2

Reviewer 1 Report

Can be accepted in present form.

 

Author Response

Thank you very much! Englishi level was carefully improved in the manuscript. 

Reviewer 2 Report

I appreciate that the authors have taken the time to reply to the various comments I have provided and have improved the quality of the manuscript, however, I still think there is some confusion and authors may want to consider trying to expand the level of details. Below are the follow-up comments to the authors replies.

 

• The authors did not provide a justification, merit, or details for there choice of alignment in the x-y plane. Given the degrees of freedom present for describing the graphene/antimonene heterostructure the authors should discuss details of incommensurate and commensurate (i.e., moire) lattices between graphene and antimonene. This is important to understand the nature of the potential energy surface structure in the x-y plane.

Responses: Thank you! Periodic boundary conditions are added in the x-y plane, the moving direction is only applied along x direction for calculated the work of separation due to the same potential energy between moving along x and y axis. For instance, the graphene layers coincide exactly calling commensurate, rather incommensurate. Due to difficult to coincide between graphene and antimonene layers, thus, incommensurate could be defined for graphene/antimonene heterojunction.

I appreciate the additional details about periodic boundary conditions is good to note however I assumed this since the work is on 2D crystalline material. What I think the authors are missing to describe is why they choose the specific orientation between graphene and antimonene as shown in Fig. 1. For example see

• • M Le Ster et al., 2D Mater. 7 011005, 2020
  • Jun Kang, et al., Nano Letters 13 (11), 5485-5490, 2013 

• I found Fig. 2(b) and Fig. 3 to be inconsistent with each other, probablybecause the supporting text is confusing. In Fig. 2(b) it appears thatat 3.2-3.3 A that the PBE+D model employs a spline interpolation and therefore this region is not necessarily physical. However, in Fig. 3 it doesn't seem to be the case. The authors should review the Grimme PBE+D parameter set to ensure this is not the case.

Responses: Thank you! The interface between 3.2 -3.3 Å in Fig 2(b) did not employ any interpolation. The data in Fig. 3 was originated from the partial differential of the calculated van der Waals energy. The Grimme PBE+D parameter was set as 0.75 and 20 for s6 and d. The data in Fig. 2 b were obtained from the energies under PBE+D, the data in Fig. 3 was calculated from the difference between the energies under PBE+D and the ones under PBE. Thus, the calculated results should be accurate.

Unfortunately this is still unclear to me, should one expect an abrupt flattening of dispersion curve? Its my impression this should be a smooth and continuous curve. Basically whats going on in the regions circled in red (see attached file). I'm pretty sure this is related to the damping function used in DFT+D, which depends on the vdW radii and decay parameter.

 

• Table 1 is at _rst glance confusing; it appears that there are two configurations in the "configuration" column, but this is not so. Additionally is the assessment at a separation distance 3.45 A meaningful given the statement above. I believe the confusion here is that I'm unable to understand if the authors are treating heterojunctions and graphene/antimonene as two different con_gurations. Furthermore, the authors show a continuous curve for Fig. 2 and 3 but yet three values for Table 1.

Responses: Thank you! The table was carefully modified in the revised manuscript. The content in this table was clear and reasonable in the revised manuscript.

Now that its clear to what the authors are using "graphene/antimonene heterojunctions" as the descriptor. This table should drop the configuration column since the table caption already states this. Thank you for this.

• Its not clear to my from Fig. 9 and eqs. 1-2 how superlubricity is established. Seems unsubstantiated that if the friction coefficient falls within 0.00007-0.0002 x axis location. If this is the case the superlubricity is only valid at certain spatial locations; not sure how to interpret that. Seems like the friction coefficient needs to be plotted against shear velocity or force. Overal I think this needs more details to be clearly understood.

Responses: Thank you! In this work, the static friction force was calculated from the formula (2) in the revised manuscript. We calculated the static friction force at the certain positions. The friction coefficients were calculated by . And the superlow friction was found for graphene and antimonene heterojunctions. We expect to provide positive guidance for the experimental investigations.

I appreciate the response however this analysis is still confusing to me. How is superlubricity classified? Is it an intensive (i.e. bulk) or extensive (i.e. system additive) quantity. if its intensive then how can one claim that this heterojunction is superlubricity if it has values at certain locations that do not fall within range. If superlubricity is a intensive quantity, what is the criteria/definition for superlubricity if one is calculating the static friction coefficient as a function of spatial location. Just seems that the manuscript doesn't specifically address this, just mentions:

line 156 "It implies that the structural superlubricity is achieved for gra-
phene/antimonene heterojunctions."

Its my impression that this needs to b ·e represented differently. It seems that it would make more sense to show the friction coefficient as a function of a Virial stress (or pressure) in Fig. 10 rather than position which would be simply :

σ = 1⁄2 V^-1  ∑ (r_i - r_j) F_ij

with V, r, and F, being the volume, position, and force respectively where i and j are species indices. If the authors have other references besides there own showing that there definition is standard or suitable then my comments on this are mute. The authors may be able to find guidance in Fig. 8 of reference:

• • V. Claerbout, et al., Superlubricity achieved for commensurate sliding: MoS₂ frictional anisotropy in silico, Comp. Materials Sci., 163, 17-23, 2019.

Comments for author File: Comments.pdf

Author Response

Dear reviewers,

Thank you for your meaning suggestions! We carefully modified the manuscript according to these comments. And all modified terms were marked as red color in the revised manuscript. And the point-to-point for responses were listed as follows:

1. I appreciate the additional details about periodic boundary conditions is good to note however I assumed this since the work is on 2D crystalline material. What I think the authors are missing to describe is why they choose the specific orientation between graphene and antimonene as shown in Fig. 1. For example see [15] M Le Ster et al., 2D Mater. 7 011005, 2020 [16] Jun Kang, et al., Nano Letters 13 (11), 5485-5490, 2013

Responses: Thank you! According to the match methods in Ref. [15,16], there is only one possible Moiré pattern graphene (0 0 -1) surface with a 3 × 3 supercell (7.38 Å × 7.38 Å) and antimonene (0 0 -1) surface with a 1 × 1 unit cell (7.3 Å × 7.3 Å) as displayed in Figure 1 with in-plane hexagonal edges aligned in the same orientation and with less than 1% lattice mismatch.

2. Unfortunately this is still unclear to me, should one expect an abrupt flattening of dispersion curve? Its my impression this should be a smooth and continuous curve. Basically whats going on in the regions circled in red (see attached file). I'm pretty sure this is related to the damping function used in DFT+D, which depends on the vdW radii and decay parameter.

Responses: Thank you! I am sorry about this mistake that I deal with these data with a wrong method. Now I correct it with the right method as shown in Figure 2 in the revised manuscript. Moreover, Figure 4 in the revised manuscript was reconducted using the corrected method. In Ortmann, Bechstedt, and Schmidt (OBS) scheme, RvdW was set as 0.77 (alpha = 1.76 Å3) and 1.38 Å (alpha = 6.6 Å3) for carbon and antimony, the n = 8 and damping constant  = 7.5  10-4 was chosen in this work[17]. [17] 15. Ortmann, F.; Bechstedt, F.; Schmidt, W.G. Semiempirical van der Waals correction to the density functional description of solids and molecular structures. Phys. Rev. B 2006, 73, 205101.

3. I appreciate the response however this analysis is still confusing to me. How is superlubricity classified? Is it an intensive (i.e. bulk) or extensive (i.e. system additive) quantity. if its intensive then how can one claim that this heterojunction is superlubricity if it has values at certain locations that do not fall within range. If superlubricity is a intensive quantity, what is the criteria/definition for superlubricity if one is calculating the static friction coefficient as a function of spatial location. Just seems that the manuscript doesn't specifically address this, just mentions: line 156 "It implies that the structural superlubricity is achieved for graphene/antimonene heterojunctions." Its my impression that this needs to b ·e represented differently. It seems that it would make more sense to show the friction coefficient as a function of a Virial stress (or pressure) in Fig. 10 rather than position which would be simply : σ = 1⁄2 V-1 ∑ (ri - rj) Fij with V, r, and F, being the volume, position, and force respectively where i and j are species indices. If the authors have other references besides there own showing that there definition is standard or suitable then my comments on this are mute. The authors may be able to find guidance in Fig. 8 of reference: V. Claerbout, et al., Superlubricity achieved for commensurate sliding: MoS2 frictional anisotropy in silico, Comp. Materials Sci., 163, 17-23, 2019.

Responses: Thank you! In this work, we just only found the potential superlubricity for graphene/antimonene heterojunctions, the reviewer focused on the sliding tribological behaviors of this heterojunction and gave some useful references for us guiding the further investigations about the sliding superlubricity of this heterojunction. Thank you very much again.

Reviewer 3 Report

.

Author Response

Thank you! English level was well improved in the revised manuscript. And the content in the revised manuscript was well riched in the revised manuscript.

Round 3

Reviewer 2 Report

The authors have taken the time to  clarify or correct issues raised the different reviewers and therefore the manuscript is suitable for publication. I do think given the significant improvement and removal of errors the authors should add a acknowledgements toward the reviewers.