pith. machine review for the scientific record. sign in

arxiv: 2604.26510 · v1 · submitted 2026-04-29 · ❄️ cond-mat.mes-hall

Recognition: unknown

Influence of a graphene substrate on the stabilization of molecular systems with hydrogen bonds

Alexander V. Savin
Authors on Pith no claims yet

Pith reviewed 2026-05-07 12:57 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords grapheneKevlarhydrogen bondsthermal stabilitymolecular dynamicspolyglycinebeta sheetsaramid
0
0 comments X

The pith

A graphene substrate stabilizes hydrogen-bonded molecular structures such as Kevlar up to temperatures of 800 K and higher.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper simulates the behavior of polyglycine β-sheets and parallel Kevlar molecules placed on a graphene sheet using molecular dynamics. The simulations reveal that the graphene helps keep the parallel hydrogen bond chains intact, allowing the structures to maintain their form at high temperatures. The authors conclude from this that graphene can be used to enhance the thermal stability of Kevlar fibers. A reader would care because Kevlar is a key material in protective gear and composites, and better heat resistance expands its uses.

Core claim

Numerical simulation of the dynamics shows that planar two- and three-layer molecular structures of β-sheets from polyglycine peptide chains and parallel Kevlar molecules on graphene retain their shape due to parallel chains of hydrogen bonds up to a temperature of 800 K. The system of parallel Kevlar molecules exhibits even higher stability, with the hydrogen bonds between peptide groups preserved at higher temperatures.

What carries the argument

The graphene sheet serves as a substrate that stabilizes the parallel chains of hydrogen bonds in the molecular layers, preventing their disruption at elevated temperatures.

If this is right

  • The β-sheets of polyglycine retain their shape up to 800 K on graphene.
  • The parallel Kevlar molecules maintain hydrogen bond chains at temperatures above 800 K.
  • Adding graphene to Kevlar fibers can significantly increase their thermal stability.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This stabilization effect might extend to other hydrogen-bonded polymers or biomolecules on graphene surfaces.
  • Composite materials combining graphene with Kevlar could be developed for applications requiring high thermal resistance.
  • Further simulations with different layer numbers or molecular arrangements could refine the optimal configurations for stability.

Load-bearing premise

The chosen molecular-dynamics force fields and simulation parameters correctly reproduce the thermal stability and hydrogen-bond behavior of these systems when supported on graphene.

What would settle it

Heating samples of Kevlar fibers deposited on graphene and comparing their decomposition or softening temperatures to those of pure Kevlar fibers would directly test whether the thermal stability increases as predicted.

Figures

Figures reproduced from arXiv: 2604.26510 by Alexander V. Savin.

Figure 2
Figure 2. Figure 2: Dependence (a) of the fraction of peptide groups view at source ↗
Figure 1
Figure 1. Figure 1: Stationary state of an antiparallel β-sheet of the polypeptide chain (Gly)432 on a graphene sheet G=C3518 of size 9.7 × 9.2 nm2 (two-layer complex (Gly)N /G| with N = 432, Ng = 3518, number of hydrogen bonds Nhb = 391). Graphene sheet atoms are shown in green, peptide group car￾bon atoms in light gray, α-atoms of the peptide chain in dark gray, nitrogen atoms in blue, oxygen in red, hydrogen in white. Hydr… view at source ↗
Figure 3
Figure 3. Figure 3: State of the β-sheet of the polypeptide chain (Gly)432 on a graphene sheet G=C3518 (two-layer complex (Gly)N /G| with N = 432, Ng = 3518) at temperature T = 600 K. 9% of the hydrogen bonds are broken (weak￾ened) (N¯hb = 356.2). The state of a molecular system can be characterized by its dimensionless heat capacity c = 1 3NakB dE¯(T ) dT (8) and the fraction of peptide groups participating in the formation … view at source ↗
Figure 4
Figure 4. Figure 4: State of an isolated three-layer complex view at source ↗
Figure 6
Figure 6. Figure 6: State of an isolated three-layer complex view at source ↗
Figure 5
Figure 5. Figure 5: Stationary state of a system of N1 = 16 paral￾lel para-aramid molecules H(C6H4CONH)14C6H5 lying on a graphene sheet G=C3518 of size 9.7×9.2 nm2 (two-layer com￾plex (AramidN )N1 /G| with N = 14, N1 = 16, Ng = 3518, number of hydrogen bonds Nhb = 210). Graphene sheet atoms are shown in green, carbon atoms of para-aramid molecules in gray, nitrogen atoms in blue, oxygen in red, hy￾drogen in white. Hydrogen bo… view at source ↗
read the original abstract

Numerical simulation of the dynamics of planar two- and three-layer molecular structures formed by $\beta$-sheets of polyglycine peptide chains and systems of parallel Kevlar (para-aramid) molecules placed on a graphene sheet has been performed. It is shown that in these structures the $\beta$-sheets retain their shape, due to the presence of parallel chains of hydrogen bonds, up to a temperature of $T=800$K. An even higher stability is exhibited by the system of parallel Kevlar molecules. Here, the parallel chains of hydrogen bonds between peptide groups of neighboring molecules are preserved even at higher temperatures. The performed modeling allows us to conclude that the addition of graphene to Kevlar fibers can significantly increase their thermal stability.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript reports classical molecular dynamics simulations of two- and three-layer β-sheet structures formed by polyglycine chains and by parallel Kevlar (para-aramid) molecules, both placed on a graphene substrate. The central result is that the parallel hydrogen-bond chains in these assemblies remain intact up to at least 800 K (and higher for the Kevlar system), leading to the claim that addition of a graphene substrate can significantly increase the thermal stability of Kevlar fibers.

Significance. If the reported stability temperatures are shown to be robust with respect to force-field choice and are accompanied by explicit bare-Kevlar control simulations that reproduce known experimental decomposition onsets, the work would provide a concrete computational indication that graphene can stabilize hydrogen-bonded molecular assemblies against thermal disruption. At present the computational evidence is insufficiently anchored to support that inference.

major comments (3)
  1. Methods section: the force field (or combination of force fields) used for the peptide/graphene and Kevlar/graphene interactions is not specified, nor are the system sizes, thermostat/barostat settings, equilibration protocol, or convergence criteria for the reported H-bond persistence temperatures. Without these details the central stability claim cannot be evaluated or reproduced.
  2. Results section (Kevlar paragraph): the manuscript states that parallel H-bond chains are preserved at temperatures above 800 K, yet provides no direct comparison run of the identical Kevlar assembly in the absence of the graphene substrate. The inference that graphene “significantly increase[s]” thermal stability therefore lacks the necessary control simulation that would isolate the substrate effect.
  3. Discussion/Conclusion: the claim that the simulations allow one to conclude that graphene addition improves real Kevlar-fiber thermal stability is not supported by any reproduction of the experimental Kevlar decomposition onset (~670–800 K) or by cross-validation against a second force field. The reported temperatures remain unanchored model outputs.
minor comments (2)
  1. Abstract: the phrase “numerical simulation of the dynamics” should be replaced by the specific method (e.g., classical molecular dynamics) and the temperature range explored should be stated explicitly.
  2. Figure captions: the temperature at which each snapshot is taken and the criterion used to define an intact H-bond chain should be stated.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for the thorough review and insightful comments on our manuscript. We have addressed each major point below and will revise the manuscript to improve clarity, reproducibility, and the strength of our conclusions where possible.

read point-by-point responses

  1. Referee: Methods section: the force field (or combination of force fields) used for the peptide/graphene and Kevlar/graphene interactions is not specified, nor are the system sizes, thermostat/barostat settings, equilibration protocol, or convergence criteria for the reported H-bond persistence temperatures. Without these details the central stability claim cannot be evaluated or reproduced.

    Authors: We agree that these methodological details are essential and were inadvertently omitted. In the revised manuscript, we will expand the Methods section to fully specify the force fields and interaction parameters used for the peptide/graphene and Kevlar/graphene systems, the dimensions and composition of all simulated systems, the thermostat and barostat algorithms and coupling times, the equilibration protocol including heating and relaxation steps, and the precise geometric criteria (distance and angle thresholds) together with the time-window analysis used to determine persistence of the parallel hydrogen-bond chains. revision: yes

  2. Referee: Results section (Kevlar paragraph): the manuscript states that parallel H-bond chains are preserved at temperatures above 800 K, yet provides no direct comparison run of the identical Kevlar assembly in the absence of the graphene substrate. The inference that graphene “significantly increase[s]” thermal stability therefore lacks the necessary control simulation that would isolate the substrate effect.

    Authors: We acknowledge that an explicit control simulation of the bare Kevlar assembly is required to isolate the substrate contribution. Although the present study focused on the graphene-supported configurations, we will perform and report additional simulations of the identical Kevlar multilayer system without the graphene sheet under the same simulation conditions. These new results will be added to the Results section to provide a direct, quantitative comparison of hydrogen-bond persistence with and without the substrate. revision: yes

  3. Referee: Discussion/Conclusion: the claim that the simulations allow one to conclude that graphene addition improves real Kevlar-fiber thermal stability is not supported by any reproduction of the experimental Kevlar decomposition onset (~670–800 K) or by cross-validation against a second force field. The reported temperatures remain unanchored model outputs.

    Authors: We will revise the Discussion and Conclusion to moderate the language, stating that the simulations provide computational evidence that the graphene substrate can enhance the thermal persistence of the hydrogen-bonded Kevlar assembly relative to the temperatures at which bare assemblies are expected to lose order. We will explicitly reference the experimental decomposition range for context while clarifying the limitations of classical force-field models in quantitatively reproducing experimental onset temperatures. Cross-validation against a second force field lies outside the scope of the present work and would require substantial additional resources; we therefore note this as a direction for future study rather than a revision that can be completed at this stage. revision: partial

standing simulated objections not resolved
  • Cross-validation of the reported stability temperatures against a second, independent force field

Circularity Check

0 steps flagged

No circularity: stability temperatures obtained from direct MD forward simulation

full rationale

The paper reports results from numerical molecular-dynamics simulations of β-sheet and Kevlar structures on graphene. Stability up to 800 K (and higher for Kevlar) is stated as an observed outcome of the runs, not derived by fitting parameters to the target quantity or by any self-referential equation. No load-bearing step reduces to a definition, a fitted input renamed as prediction, or a self-citation chain. The modeling chain is self-contained against external benchmarks once the force-field choice is accepted; the circularity analysis therefore finds none.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available, so the ledger is limited to standard assumptions of molecular-dynamics modeling; no explicit free parameters, invented entities, or paper-specific axioms are stated.

axioms (1)
  • domain assumption Standard molecular-dynamics force fields correctly capture hydrogen-bond energetics and thermal fluctuations in peptide and aramid systems.
    Implicit in any such simulation; not verified or cited in the abstract.

pith-pipeline@v0.9.0 · 5415 in / 1279 out tokens · 67156 ms · 2026-05-07T12:57:35.313785+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

50 extracted references · 35 canonical work pages

  1. [1]

    Such a two-layer structure can be denoted by the formula (Gly) N /G|, where the vertical line denotes a solid flat substrate on which the graphene sheet G lies

    An- tiparallel sheets are more stable than parallel sheets, in which all hydrogen bonds are directed in the same di- rection. Such a two-layer structure can be denoted by the formula (Gly) N /G|, where the vertical line denotes a solid flat substrate on which the graphene sheet G lies. We also consider an isolated three-layer structure (Gly)N /G/(Gly)N , i...

  2. [2]

    Problem (

    58 nm 2 consisting of Ng = 12670 carbon atoms (G=C12670), and a polypeptide chain of N = 1584 PGs. Problem (

  3. [3]

    The solution of the problem showed that in the ground stationary state, the polypep- tide chain lies in a plane parallel to the graphene sheet at a distance h ≈ 3

    was solved numerically using the conjugate gradient method [ 33, 34]. The solution of the problem showed that in the ground stationary state, the polypep- tide chain lies in a plane parallel to the graphene sheet at a distance h ≈ 3. 33 ˚ A. In the most energetically fa- vorable packing, the β -sheet has the shape of a rect- angle of size 15 . 9 × 16. 7 n...

  4. [4]

    The average hydrogen bond energy is Ehb = 0. 304 eV. To model the dynamics of two- and three-layer struc- tures (Gly)N /G|and (Gly)N /G/(Gly)N , we first find the ground stationary state of the molecular system by nu- merically solving the problem of minimizing its potential energy ( 6). Then we place the resulting stationary state of the molecular system i...

  5. [5]

    flat β -sheet

    was integrated numerically using the velocity Verlet method [ 35] with an integration step of ∆ t = 1 fs. After a time t = 10 tr, the molecular system reaches equilibrium with the thermostat at temperature T . Fur- ther integration of the system of equations of motion ( 7) over a time of t = 2 ns allows us to find the average energy of the system ¯E(T ) an...

  6. [6]

    H(C6H4CONH)N C6H5 – see Fig

    can also form parallel linear Kevlar molecules (para-aramid – polyterephthalamide) (a) (b) Figure 6: State of an isolated three-layer complex (AramidN )N1 /G/(AramidN )N1 (N = 24, N1 = 32, Ng = 12670) at temperatures (a) T = 600 and (b) 1200 K. H(C6H4CONH)N C6H5 – see Fig

  7. [7]

    According to [ 3], hydro- gen bonds account for approximately 60% of the trans- verse strength of Kevlar fiber

    Analysis of the Kevlar molecular structure shows that the high elastic modulus of Kevlar fibers stems from the rigidity of the aromatic polyamide chains and the high density of in- terchain hydrogen bonds [ 36]. According to [ 3], hydro- gen bonds account for approximately 60% of the trans- verse strength of Kevlar fiber. We will show that placing Kevlar mo...

  8. [8]

    56 × 18. 58 nm 2. We place on the sheet a system of 32 parallel para-aramid molecules H(C 6H4CONH)24C6H5. Such a two-layer structure can be described by the for- mula (AramidN )N1/G|, where the number of links in one para-aramid molecule (number of PGs) is N = 24, the number of molecules is N1 = 32, and the number of car- bon atoms in the graphene sheet i...

  9. [9]

    30 ˚ A from its surface

    showed that in the ground stationary state, all para-aramid molecules lie in a single plane parallel to the graphene sheet at a distance of h ≈ 3. 30 ˚ A from its surface. The molecules lie parallel to each other, forming N transverse lines of hydrogen bonds – see Fig

  10. [10]

    The total number of hy- drogen bonds is Nhb = N (N1 − 1) = 744, and the av- erage hydrogen bond energy is Ehb = 0 . 179 eV. The reduced hydrogen bond energy in comparison with the polyglycine β -sheet arises because the benzene rings of adjacent molecules sterically hinder the close approach of the hydrogen-bonding peptide groups. To model the dynamics of...

  11. [11]

    with the initial condition corresponding to the stationary state of the molecular structure. After reaching a state in equilibrium with the thermostat, we find the average energy of the system ¯E(T ) and the average number of hydrogen bonds ¯Nhb(T ) at temperature T (we assume that two peptide groups form a hydrogen bond if their interaction energy E > 0. ...

  12. [12]

    showed that two- and three-layer structures (AramidN )N1/G| and (Aramid N )N1 /G/(AramidN )N1 are stable against thermal fluctuations at all considered temperatures T ≤ 1600 K – see Fig

  13. [13]

    dimensionality reduc- tion

    The dimension- less heat capacity of the two- and three-layer structure always remains equal to unity ( c = 1). With increas- ing temperature, only a slow decrease in the fraction of peptide groups participating in the formation of hydro- gen bonds occurs. Here, in contrast to the β -sheet of the polyglycine chain, destruction of the planar struc- ture of...

  14. [14]

    Careri, U

    G. Careri, U. Buontempo, F. Galluzzi, A. C. Scott, E. Gratton, E. Shyamsunder. Spectroscopic evidence for Davydov-like solitons in acetanilide. Phys. Rev. B 30(8), 4689-4702 (1984). DOI: 10.1103/PhysRevB.30.4689

    work page doi:10.1103/physrevb.30.4689 1984

  15. [15]

    J. C. Eilbeck, P. S. Lomdahl, A. C. Scott. Soliton struc- ture in crystalline acetanilide. Phys. Rev. B. 30(8), 4703- 4712 (1984). DOI: 10.1103/PhysRevB.30.4703

    work page doi:10.1103/physrevb.30.4703 1984

  16. [16]

    S. C. Chowdhury, J. W. Gillespie Jr. A molecu- lar dynamics study of the effects of hydrogen bonds on mechanical properties of Kevlar crystal. Compu- tational Materials Science 148, 286-300 (2018). DOI: 10.1016/j.commatsci.2018.02.055 7

    work page doi:10.1016/j.commatsci.2018.02.055 2018

  17. [17]

    J. F. Nagle, S. Tristram-Nagle. Hydrogen bonded chain mechanisms for proton conduction and proton pumping. J. Membrane Biol. 74, 1-14 (1983). DOI: 10.1007/bf01870590

    work page doi:10.1007/bf01870590 1983

  18. [18]

    K.-D. Kreuer. Proton conductivity: materials and ap- plications. Chem. Mater. 8(3), 610-641 (1996). DOI: 10.1021/cm950192a

    work page doi:10.1021/cm950192a 1996

  19. [19]

    I. A. Kaliman, A. A. Moskovsky, S. S. Konyukhov, A. V. Nemukhin. Modeling of proton transport in the grami- cidin A channel. Moscow Univ. Chem. Bull. 49(5), 291- 294 (2008)

    2008

  20. [20]

    Nagamani, U

    C. Nagamani, U. Viswanathan, C. Versek, M. T. Tuomi- nen, S. M. Auerbach, S. Thayumanavan. Importance of dynamic hydrogen bonds and reorientation barriers in proton transport. Chem. Commun. 47, 6638-6640 (2011). DOI: 10.1039/C1CC11207D

    work page doi:10.1039/c1cc11207d 2011

  21. [21]

    R. W. Jansen, R. Bertoncini, D. A. Pinnick, A. I. Katz, R. C. Hanson, O. F. Sonkey, M. O’Keeffe. Theoretical aspects of solid hydrogen halides under pressure. Phys. Rev. B 35(18), 9830-9840 (1987). DOI: 10.1103/Phys- RevB.35.9830

    work page doi:10.1103/phys- 1987

  22. [22]

    Springborg

    M. Springborg. Energy surfaces and electronic proper- ties of hydrogen fluoride. Phys Rev. B 38(2), 1483-1503 (1988). DOI: 10.1103/PhysRevB.38.1483

    work page doi:10.1103/physrevb.38.1483 1988

  23. [23]

    A. S. Davydov, N. I. Kislukha. Solitary excitations in one-dimensional molecular chains. Phys. Status Solidi B 59(2), 465-470 (1973). DOI: 10.1002/pssb.2220590212

    work page doi:10.1002/pssb.2220590212 1973

  24. [24]

    A. S. Davydov, N. I. Kislukha. Solitons in one- dimensional molecular chains. Phys. Status Solidi B 75(2), 735-742 (1976). DOI: 10.1002/pssb.2220750238

    work page doi:10.1002/pssb.2220750238 1976

  25. [25]

    A. S. Davydov. Solitons in molecular systems. Phys. Scr . 20, 387-394 (1979). DOI: 10.1088/0031-8949/20/3-4/013

    work page doi:10.1088/0031-8949/20/3-4/013 1979

  26. [26]

    A. S. Davydov. The role of solitons in the energy and electron transfer in one-dimensional molecular sys- tems. Physica D 3, 1-22 (1981). DOI: 10.1016/0167- 2789(81)90116-0

    work page doi:10.1016/0167- 1981

  27. [27]

    J. M. Hyman, D. W. McLaughlin, A. C. Scott. On Davydov’s alpha-helix solitons. Physica D 3(1-2), 23-44 (1981). DOI: 10.1016/0167-2789(81)90117-2

    work page doi:10.1016/0167-2789(81)90117-2 1981

  28. [28]

    A. C. Scott. Dynamics of Davydov solitons. Phys. Rev. A 26, 578-595 (1982). DOI: 10.1103/PhysRevA.26.578

    work page doi:10.1103/physreva.26.578 1982

  29. [29]

    A. C. Scott. Davydov solitons in polypeptides. Philos. Trans. R. Soc. London A 315, 423-436 (1985). DOI: 10.1098/RSTA.1985.0049

    work page doi:10.1098/rsta.1985.0049 1985

  30. [30]

    A. C. Scott. Davydov’s soliton. Phys. Rep. 217, 1-67 (1992). DOI: 10.1016/0370-1573(92)90093-F

    work page doi:10.1016/0370-1573(92)90093-f 1992

  31. [31]

    D. D. Georgiev, J. F. Glazebrook. Launching of Davydov solitons in protein α -helix spines. Physica E 124, 114332 (2020). DOI: 10.1016/j.physe.2020.114332

    work page doi:10.1016/j.physe.2020.114332 2020

  32. [32]

    D. D. Georgiev, J. F. Glazebrook. Thermal stability of solitons in protein α -helices. Chaos, Solitons and Fractals 155, 111644 (2022). DOI: 10.1016/j.chaos.2021.111644

    work page doi:10.1016/j.chaos.2021.111644 2022

  33. [33]

    Cruzeiro

    L. Cruzeiro. The VES Hypothesis and Protein Confor- mational Changes. Z. Phys. Chem. 230(5-7), 743-776 (2016). DOI: 10.1515/zpch-2015-0714

    work page doi:10.1515/zpch-2015-0714 2016

  34. [34]

    Cruzeiro

    L. Cruzeiro. The VES KM: a pathway for protein folding in vivo. Pure Appl. Chem. 92(1), 179-191 (2020). DOI: 10.1515/pac-2019-0301

    work page doi:10.1515/pac-2019-0301 2020

  35. [35]

    Cruzeiro

    L. Cruzeiro. Knowns and unknowns in the Davydov model for energy transfer in proteins. Low Temp. Phys. 48, 973-994 (2022). DOI: 10.1063/10.0015107

    work page doi:10.1063/10.0015107 2022

  36. [36]

    A. S. Davydov. Influence of electron-phonon interac- tion on electron motion in a one-dimensional molecular chain. Theor. Math. Phys. 40(3), 408-421 (1979). DOI: 10.1007/BF01032070

    work page doi:10.1007/bf01032070 1979

  37. [37]

    A. S. Davydov, A. V. Zolotaryuk. Subsonic and supersonic solitons in nonlinear molecular chains. Phys. Scripta. 30, 426-430 (1984). DOI: 10.1088/0031- 8949/30/6/010

    work page doi:10.1088/0031- 1984

  38. [38]

    A. S. Davydov. Solitons in Molecular Systems. Kluwer Academic Publishers, Dordrecht, 1991

    1991

  39. [39]

    A. V. Savin, O. I. Savina, The structure and dy- namics of the chains of hydrogen bonds of hy- drogen fluoride molecules inside carbon nanotubes. Phys. Solid State 62(11), 2217-2223 (2020). DOI: 10.1134/S1063783420110281

    work page doi:10.1134/s1063783420110281 2020

  40. [40]

    A. V. Savin, Y. S. Kivshar. Stabilization of hydrogen- bonded molecular chains by carbon nanotubes. Chaos 34, 043111 (2024). DOI: 10.1063/5.0197401

    work page doi:10.1063/5.0197401 2024

  41. [41]

    W. D. Cornell, P. Cieplak, C. I. Bayly, I. R. Gould, K. M. Merz, D. M. Ferguson, D. C. Spellmeyer, T. Fox, J. W. Caldwell, P. A. Kollman. A second generation force field for the simulation of proteins, nucleic acids, and organic molecules. J. Am. Chem. Soc. 117, 5179-5197 (1995). DOI: 10.1021/ja00124a002

    work page doi:10.1021/ja00124a002 1995

  42. [42]

    A. V. Savin, Y. S. Kivshar, and B. Hu. Suppression of thermal conductivity in graphene nanoribbons with rough edges. Phys. Rev. B 82, 195422 (2010). DOI: 10.1103/PhysRevB.82.195422

    work page doi:10.1103/physrevb.82.195422 2010

  43. [43]

    A. V. Savin and Y. S. Kivshar. Phononic Fano resonances in graphene nanoribbons with local defects. Sci. Rep. 7, 4668 (2017). DOI: 10.1038/s41598-017-04987-w

    work page doi:10.1038/s41598-017-04987-w 2017

  44. [44]

    A. V. Savin, O. I. Savina. Dynamics of carbon nanotube chains placed on flat substrates. Phys. Solid State 63(1), 145-153 (2021). DOI: 10.1134/S1063783421010194

    work page doi:10.1134/s1063783421010194 2021

  45. [45]

    A. V. Savin. Eigenmodes and resonance vibrations of graphene nanomembranes. Phys. Rev. B 103, 195435 (2021). DOI: 10.1103/PhysRevB.103.195435

    work page doi:10.1103/physrevb.103.195435 2021

  46. [46]

    Fletcher and C

    R. Fletcher and C. Reeves. Function Minimization by Conjugate Gradients. Comput. J. 7(2), 149-154 (1964). DOI: 10.1093/comjnl/7.2.149

    work page doi:10.1093/comjnl/7.2.149 1964

  47. [47]

    D. F. Shanno, K. H. Phua. Algorithm 500: Mini- mization of Unconstrained Multivariate Functions [E4]. ACM Trans. Math. Softw. 2(1), 87-94 (1976). DOI: 10.1145/355666.355673

    work page doi:10.1145/355666.355673 1976

  48. [48]

    Experiments

    L. Verlet. Computer “Experiments” on Classical Fluids. I. Thermodynamical Properties of Lennard- Jones Molecules. Phys. Rev. 159, 98 (1967). DOI: 10.1103/PhysRev.159.98

    work page doi:10.1103/physrev.159.98 1967

  49. [49]

    B. Wang, Z. Mao, D. Li, K. Zhang, C. Zhou, M. Ren, T. Li. Multiscale insights into the stretching behavior of Kevlar fiber. Comput. Mater. Sci. 185, 109957 (2020). DOI: 10.1016/j.commatsci.2020.109957

    work page doi:10.1016/j.commatsci.2020.109957 2020

  50. [50]

    J. Lian, J. Fan, Z. Shi, H. Li, and J. Yin. Kevlar- functionalized graphene nanoribbon for polymer rein- forcement. Polymer 55(10), 2578-2587 (2014). DOI: 10.1016/j.polymer.2014.03.059

    work page doi:10.1016/j.polymer.2014.03.059 2014