Mechanical Response of Carbon Nanotube Bundle to Lateral Compression
, Elena A. Korznikova 2,3, Volodymyr I. Dubinko 4, Denis V. Laptev 5, Alexey A. Kudreyko 6, Elvira G. Soboleva 7, Sergey V. Dmitriev 2,3,* and Kun Zhou 8,*
Round 1
Reviewer 1 Report
In this work, Abdullina and coworkers report on mechanical response of carbon nanotube (CNT) bundle under lateral biaxial compression. Numerical calculations are carried out to address the role of van der Waals forces, bending and tension of CNT walls during the deformation process. The presented results seem solid, discussion and main conclusions sound reasonable. However, I find a lack of accuracy in the introduction. Mentioned large number of different publications does not emphasize the value and actuality of the current work. The motivation of authors is not clear, and as a result, a reader may lose interest. In the introduction you need to outline the problems of the field and give a reader a clear understanding of how important this work is. How it will advance the field? The fact that "...little attention was paid to the discussion of structure evolution under lateral compression up to large strain levels." does not explain why it is important to pay this attention.
Thus a revision is requested to improve the quality of the paper and make it suitable for publication in Computation journal.
Author Response
Reviewer 1 wrote:
In this work, Abdullina and coworkers report on mechanical response of carbon nanotube (CNT) bundle under lateral biaxial compression. Numerical calculations are carried out to address the role of van der Waals forces, bending and tension of CNT walls during the deformation process. The presented results seem solid, discussion and main conclusions sound reasonable. However, I find a lack of accuracy in the introduction. Mentioned large number of different publications does not emphasize the value and actuality of the current work. The motivation of authors is not clear, and as a result, a reader may lose interest. In the introduction you need to outline the problems of the field and give a reader a clear understanding of how important this work is. How it will advance the field? The fact that "...little attention was paid to the discussion of structure evolution under lateral compression up to large strain levels." does not explain why it is important to pay this attention.
Thus a revision is requested to improve the quality of the paper and make it suitable for publication in Computation journal.
Our response:
We thank the Reviewer for his/her valuable comments.
In the Introduction, we have added the following:
In the existing works devoted to the mechanics of CNT bundles, little attention was paid to the discussion of structure evolution under lateral compression up to large strain levels. This problem is interesting from the standpoint of fundamental science because materials with highly deformable structural units should have peculiar mechanical properties and CNT bundle is an example of such material, as CNT cross section can obtain various shapes under pressure. Unlike dense materials, CNT crystal can demonstrate very high compressibility in the elastic region and highly stretchable or compressible elastic materials are actively studied in recent years [62-64]. Practically, CNT bundles can be used, e.g., for protection against shocks and vibrations [33,65,66].
Reviewer 2 Report
The manuscript by Abdullina et al. reports a computational study of the mechanical response of a carbon nanotube bundle to lateral biaxial compression. The analysis is performed using the “chain model” developed recently by the authors. It is found that the bundle of nanotubes experiences two consecutive phase transitions with an increase of strain. In the course of these transitions, ideal cylindrical nanotubes first transform into the structures with an ellipsoidal cross section and then fully collapse.
Although the manuscript reports interesting results I feel that it lacks, in its current form, several important aspects that should be thoroughly addressed by the authors:
1) The chain model used in this work is practically not described at all. The authors refer to several earlier publications but it is important to provide at least a brief description of this model in the methodology part without the necessity to surf over other publications.
2) The same concerns different contributions to the r.h.s of Eq. (1). At least a qualitative description of these terms should be added to the manuscript, especially in view of their comparison in Figure 4. Otherwise, the discussion of the results shown in Figure 4 is rather pointless.
3) My main concern regarding the model is that the authors treat each row of atoms oriented along the z-axis as a rigid object. The validity of this assumption needs to be justified and explained. If all atoms in each nanotube are movable (which would be more physically correct to my understanding), will the reported phase transitions and the nanotube collapse also take place?
4) As a follow up to the previous comment: are there any experimental or atomistic-level (based on all-atom MD) proofs of the phenomena reported in this work?
5) Figure 3: Scales should be added to the y-axis in all panels. Then it would be more clear to which extend the behavior shown in panel (a, right) is indeed due to computational noise. To my understanding, if all nanotubes have perfect spherical cross sections, there should be no dependence on orientation and the function should be peaked around one value either 0 or 90 degrees.
Minor comments:
6) Introduction, first paragraph: “Such van der Waals crystals have properties not exhibited by their structural elements” - please provide examples of the properties
7) How the methodology presented will be modified if armchair nanotubes are considered instead of zigzag nanotubes?
8) Abstract, line 2: “with the used of the chain model” -> “using the chain model”
9) Page 5, line 122: “and the other to components” -> “and the other two components”
On the basis of the above-listed comments, I recommend a major revision of the manuscript.
Author Response
Reviewer 2 wrote:
The manuscript by Abdullina et al. reports a computational study of the mechanical response of a carbon nanotube bundle to lateral biaxial compression. The analysis is performed using the “chain model” developed recently by the authors. It is found that the bundle of nanotubes experiences two consecutive phase transitions with an increase of strain. In the course of these transitions, ideal cylindrical nanotubes first transform into the structures with an ellipsoidal cross section and then fully collapse.
Although the manuscript reports interesting results I feel that it lacks, in its current form, several important aspects that should be thoroughly addressed by the authors:
1) The chain model used in this work is practically not described at all. The authors refer to several earlier publications but it is important to provide at least a brief description of this model in the methodology part without the necessity to surf over other publications.
2) The same concerns different contributions to the r.h.s of Eq. (1). At least a qualitative description of these terms should be added to the manuscript, especially in view of their comparison in Figure 4. Otherwise, the discussion of the results shown in Figure 4 is rather pointless.
3) My main concern regarding the model is that the authors treat each row of atoms oriented along the z-axis as a rigid object. The validity of this assumption needs to be justified and explained. If all atoms in each nanotube are movable (which would be more physically correct to my understanding), will the reported phase transitions and the nanotube collapse also take place?
4) As a follow up to the previous comment: are there any experimental or atomistic-level (based on all-atom MD) proofs of the phenomena reported in this work?
5) Figure 3: Scales should be added to the y-axis in all panels. Then it would be more clear to which extend the behavior shown in panel (a, right) is indeed due to computational noise. To my understanding, if all nanotubes have perfect spherical cross sections, there should be no dependence on orientation and the function should be peaked around one value either 0 or 90 degrees.
Minor comments:
6) Introduction, first paragraph: “Such van der Waals crystals have properties not exhibited by their structural elements” - please provide examples of the properties
7) How the methodology presented will be modified if armchair nanotubes are considered instead of zigzag nanotubes?
8) Abstract, line 2: “with the used of the chain model” -> “using the chain model”
9) Page 5, line 122: “and the other to components” -> “and the other two components”
On the basis of the above-listed comments, I recommend a major revision of the manuscript.
Our response:
We thank the Reviewer for his/her valuable comments.
1) We have extended the description of the chain model. The following was added to Sec. 2:
Much smaller computational cell can be used for simulation of structures with a long-range order, but for irregular structures a representative volume should be considered and, as it will be shown later, the cell with 20x24 CNTs is sufficiently large.
The last line to the caption of Fig. 1 was added.
Equations (2) to (4) were added and explained.
The text explaining what is lost by assuming rigid atomic rows along the armchair direction [see item 3)].
2) We agree. The description of interatomic interactions was added, see Eqs. (1-5).
3) The following discussion was added in relation to what is lost by assuming the rigidity of the atomic rows along the armchair direction (see Conclusions, Sec. 4):
The chain model used in the present study assumes that the atomic rows along the armchair direction are rigid. All structures analyzed here correspond to this assumption and, therefore, can be obtained in case of refusal of plane strain conditions. In the case of full atomic modeling CNTs can collapse in another fashion, by initiation of the local collapsed region and its propagation along the tube. If this scenario is energetically favorable, then the first-order phase transition should happen somewhat earlier than in the case of plane strain conditions. Another limitation of the chain model is related to the simulations at finite temperature. Phonon waves propagating along the CNTs are completely suppressed by the plane strain conditions. All these effects should be addressed in frame of a full atomic model.
4) The following text was added (see Conclusions, Sec. 4):
In the present study full atomic simulations were not conducted, but in the previous works with smaller number of degrees of freedom it was shown that in many cases the chain model gives physically meaningful results close to those obtained in full atomic simulations [67-73].
5) In fact, CNTs in Fig. 2(a), being under biaxial compression, have slightly flattened faces with the cross section resembling hexagonal prisms. The expected long diameters of the prisms have orientations of 30, 90 and 150 degrees. But this effect is very weak and the cross section profiles are perturbed by the discreteness of the CNT wall and we see other peaks in Fig. 3(a), right panel. We believe that the addition of the ordinate scale can be misleading since here we present the normalized histograms and, if the Reviewer would not further insist, we would like to keep Fig. 3 unchanged. In order to clarify these points we add the following text to the description of Fig. 3:
CNTs in Fig. 2(a), being under biaxial compression, have slightly flattened faces with the cross section resembling hexagonal prisms. The expected long diameters of the prisms have orientations of 30, 90 and 150 degrees. But this effect is very weak and the cross section profiles are perturbed by the discreteness of the CNT walls and we see other peaks in Fig. 3(a), right panel.
6) New version of this sentence is: Such van der Waals crystals have properties not exhibited by their structural elements, for example, chemical properties typical for molecular crystals and peculiar mechanical properties related to deformability of the structural units [1-8].
7) The following text was added (see Conclusions, Sec. 4):
Modification of the chain model to the case of the armchair CNT bundle is straightforward but the model parameters will be somewhat different from that for the zigzag CNTs.
8) Corrected.
9) Corrected.
Reviewer 3 Report
I belive the paper including a detailed theoretical study is suitable for publication in computation.
Author Response
Reviewer 3 wrote:
I believe the paper including a detailed theoretical study is suitable for publication in computation.
Our response:
We are grateful to the Reviewer for the positive assessment of our work.
Reviewer 4 Report
In this manuscript, the structure evolution and mechanical response of the carbon nanotube bundle under lateral biaxial compression is investigated. The model takes into account tensile and bending rigidity of carbon nanotubes and van der Waals interactions between them. Mechanical response of the carbon nanotube bundle to lateral biaxial compression under plane strain condition is evaluated using the perturbation-relaxation molecular dynamics simulations at zero temperature. Several structural transformations are observed with increasing strain control compression. I think this work could be of interest to readers of Computation. However, the manuscript needs a thorough editing; taking into account the comments below, before I could recommend its publication.
Several important issues should be clarified.
1. A very large cell (14400 atoms) is used in the work. What for? Figure 1 shows a cell (120 atoms), which can be calculated by periodic DFT methods.
2. The temperature effect in the study is not taken into account. For what purpose is kinetic energy given in equation (1)?
3. Parameters of the chain models are given in Ref. 63. How will the slight changes in the values of these parameters affect the results of simulations?
Author Response
Reviewer 4 wrote:
In this manuscript, the structure evolution and mechanical response of the carbon nanotube bundle under lateral biaxial compression is investigated. The model takes into account tensile and bending rigidity of carbon nanotubes and van der Waals interactions between them. Mechanical response of the carbon nanotube bundle to lateral biaxial compression under plane strain condition is evaluated using the perturbation-relaxation molecular dynamics simulations at zero temperature. Several structural transformations are observed with increasing strain control compression. I think this work could be of interest to readers of Computation. However, the manuscript needs a thorough editing; taking into account the comments below, before I could recommend its publication.
Several important issues should be clarified.
- A very large cell (14400 atoms) is used in the work. What for? Figure 1 shows a cell (120 atoms), which can be calculated by periodic DFT methods.
- The temperature effect in the study is not taken into account. For what purpose is kinetic energy given in equation (1)?
- Parameters of the chain models are given in Ref. 63. How will the slight changes in the values of these parameters affect the results of simulations?
Our response:
We thank the Reviewer for his/her valuable comments.
1. Indeed, the crystalline structures such as those shown in Fig. 2 (a) and (b) can be addressed with a much smaller computational cell and even DFT simulations are possible for them. On the other hand, consideration of the irregular structures [Fig. 2 (c) and (d)] requires a larger cell in order to correctly estimate the averaged mechanical properties. The cell size of 20x24 CNTs is sufficient for solving this problem because, as Fig. 5 suggests, the expected isotropy of the irregular structure is preserved.
We have made the following additions to support our choice of the computational cell size:
Much smaller computational cell can be used for simulation of structures with a long-range order, but for irregular structures a representative volume should be considered and, as it will be shown later, the cell with 20x24 CNTs is sufficiently large. (In Sec. 2.)
For simulation of the crystalline structures shown in Figure 2(a) and (b) a much smaller computational cell can be used and even DFT simulations are possible for these cases. For the irregular structures presented in Figure 2(c) and (d), a computational cell with a few CNTs is insufficient for evaluation of the averaged mechanical properties. (In Sec. 3.1, in relation to Fig. 2.)
2. Below Eq. (2) we add:
We note that the kinetic energy term is not taken into account in this work, since only the relaxational dynamics of atoms is considered, but we present it for completeness of the description of the model.
3. The following text was added in Sec. 2:
In the course of fitting the model parameters, strong sensitivity of the simulation results to small changes in the parameters was not observed.
Round 2
Reviewer 2 Report
The authors have responded to my earlier comments and made corresponding modifications to the manuscript.
I have the only remaining question that the authors may address before the manuscript is accepted.
What was the motivation for defining the vdW interaction in a rather unusual form of the (5,11) LJ potential rather than using more conventional (6,12) or (6,9) LJ potentials?
Once this question is addressed, I recommend the publication of this manuscript.
Author Response
Thank you for this question, indeed, this point should be clarified in the description of the model.
In fact, the van der Waals interactions between carbon atoms are
described by the (6,12) Lennard-Jones potential, but when we make summations to describe the interactions between rigid atomic chains then the best fit is obtained with the (5,11) potential [67]. Below Eq. (5) we have added:
Note that the summands in Eq. (5) give the interaction potentials between pairs of rigid atomic rows oriented along the $z$-axis. This potential was obtained by summation of the C-C interatomic energies described by the (6,12) Lennard-Jones potential. The net interaction energy between two atomic rows is best fitted by the (5,11) Lennard-Jones potential [67].
Reviewer 4 Report
The authors took into consideration my suggestions. The manuscript may be recommended for publication.
Author Response
We thank the Reviewer for his/her valuable comments and for the positive final decision.
