Defect configuration, not nitrogen content, governs the mechanical integrity of nitrogen-doped graphene: a molecular dynamics study

A.K.M. Monjur Morshed; Indranil Rudra; Jahid Emon

REVIEW 3 major objections 5 minor 29 references

Defect configuration, not nitrogen content, governs the mechanical integrity of nitrogen-doped graphene: a molecular dynamics study

T0 review · 3 major / 5 minor · reviewed 2026-08-01 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The mechanical strength of nitrogen-doped graphene is set by how the nitrogen is arranged — whether it sits in the lattice or at a vacancy — not by how much nitrogen is present.

desk verdict A clean, well-validated MD comparison that shows defect configuration matters more than N content, but the flagship edge-chemistry result leans on a single unvalidated Tersoff potential and is slightly over-sold. read the letter →

arxiv 2607.18129 v1 pith:JKRDILWM submitted 2026-07-20 cond-mat.mtrl-sci

Indranil Rudra , Jahid Emon , A.K.M. Monjur Morshed This is my paper · ORCID

classification cond-mat.mtrl-sci

keywords nitrogen-dopedgraphenedefectconfigurationmoleculardynamicstensilestrengthpyridinicnitrogengraphiticvoiddefectsfracturemechanism

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper uses molecular dynamics simulations to isolate what actually weakens nitrogen-doped graphene under tension. By comparing three size-matched defects — a graphitic nitrogen cluster, a bare void, and a pyridinic nitrogen cluster — it shows that nitrogen chemistry alone is mechanically benign, while vacancies are the real culprit, and that nitrogen decorating a vacancy makes it even worse. The authors also find that when a nitrogen cluster and a void coexist, their orientation relative to the load matters far more than their separation: defects stacked in-line fail at the weaker member, while side-by-side defects couple through overlapping stress fields and weaken the sheet over surprisingly long ranges. The central claim reframes the mechanical role of nitrogen in graphene from a question of composition to one of local atomic structure.

What carries the argument

Three size-matched defects — a graphitic-nitrogen cluster (chemistry without missing atoms), a circular void (missing atoms without chemistry), and a pyridinic-nitrogen cluster (missing atoms with edge nitrogen) — are compared so that pairwise contrasts isolate the contribution of edge chemistry and of the vacancy independently. Pyridinic nitrogen, defined as nitrogen bonded to two carbon atoms at a vacancy edge, is the mechanically active form. The argument runs on these controlled comparisons plus Tersoff bond-order molecular dynamics, with per-atom stress field visualization showing that the void fails via damage-tolerant sub-critical cracking while the pyridinic rim fails abruptly.

What would settle it

A density-functional-theory or machine-learning-potential calculation of the same three size-matched defects under identical uniaxial tension that finds the pyridinic cluster not weaker than the bare void would falsify the ranking, as would an experiment measuring no strength difference between two nitrogen-doped graphene samples with equal nitrogen content but sharply different pyridinic fractions.

Watch

Extended reading notes

Core claim

The mechanical impact of a nitrogen cluster in graphene is governed almost entirely by whether it carries vacancies, not by the presence of nitrogen itself. Evidence: a graphitic-nitrogen cluster (which substitutes into the intact lattice) leaves strength, stiffness, and fracture strain essentially unchanged (<1% strength reduction), whereas a void of the same footprint degrades ultimate tensile strength by ~23% and a pyridinic cluster — the same void with nitrogen decorating its rim — degrades it by ~30%. Because the pyridinic cluster and the void differ only in edge chemistry, and the graphitic and pyridinic clusters differ only in the presence of the vacancy, the decomposition is direct.

Load-bearing premise

The Tersoff B-C-N interatomic potential correctly represents the relative strength of carbon-nitrogen edge bonds versus reconstructed carbon edges; if it mis-orders that edge chemistry, the central ranking (pyridinic worst, void intermediate, graphitic benign) could change.

Editorial extensions

If this is right

Two graphene samples with identical nitrogen content can differ in ultimate tensile strength by up to ~30% depending on whether the nitrogen is graphitic or vacancy-associated.
Graphitic substitution offers a path to chemically functionalize graphene for electronics or catalysis at negligible mechanical cost.
The mechanical penalty of nitrogen doping is carried almost entirely by the pyridinic (and likely pyrrolic) fraction, which nucleates brittle failure at the pore rim.
For multiply defective graphene, defect arrangement relative to the load matters more than defect density: side-by-side defects weaken the sheet far more than in-line ones at the same spacing.
Design rules can use the ~80 Å interaction range to space cross-load defects far enough apart to recover weakest-link behavior.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The same vacancy-dominated logic may extend to other substitutional dopants in graphene (e.g., boron, oxygen); the mechanical penalty of doping may generally be carried by the vacancy-associated fraction, not the substitutional one.
The configuration-based decomposition offers a way to reconcile scatter in reported strengths of nitrogen-doped graphene, which may differ mainly because synthesis routes produce different pyridinic-to-graphitic ratios.
A testable prediction follows: two free-standing nitrogen-doped graphene films with equal total nitrogen content but different pyridinic fractions should exhibit measurably different tensile strengths, with the higher pyridinic fraction failing earlier and more abruptly.
The ~80 Å side-by-side interaction range suggests that defect engineering at nanometre spacings must treat defects as a collective stress-field problem, not as independent contributors.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Two things to know. First, the paper does a genuinely clean job of separating nitrogen chemistry from missing atoms: three size-matched defects, two contrasts, and a pristine baseline that matches experiment. Second, the headline conclusion—configuration matters, not nitrogen content—is directionally right but a bit stronger than the evidence, because the one edge-chemistry result that distinguishes it (pyridinic 8 GPa weaker than void) rests on a single Tersoff parameterization never validated for C–N bond breaking.

The controlled comparison is the real contribution. Graphitic N is mechanically invisible; a void costs ~23% UTS; the pyridinic cluster costs ~30%. The fracture-mechanism contrast—damage-tolerant void vs abrupt rim failure of pyridinic—is nice and supported by stress-field visualization. The orientation-dependent interaction, side-by-side coupling out to ~80 Å, is new to me and would be the most citable piece.

Soft spots, in proportion. The pyridinic-vs-void gap is ~2.8× the combined uncertainty—meaningful, but not a landslide, and it is entirely dependent on how the Kınacı Tersoff potential describes C–N edge bonds at large strain. The paper itself concedes Tersoff-type fracture is only approximate; without DFT edge-energy calculations or a different potential as a check, the quantitative ranking pyridinic < void < graphitic could shift. The ~80 Å range is measured for the pyridinic defect and inherits the same uncertainty. Also, the novelty boundary with the authors' own ref [19] is fuzzy: they don't spell out what's incremental relative to that prior MD study. Minor: single defect size, single strain rate, "data on request" with no deposit, and a writing style that occasionally overstates ("almost entirely").

None of that kills the central claim. The qualitative conclusion that configuration beats content is plausible and well-supported. It just needs a more modest sentence and, ideally, a DFT or MLIP cross-check on the C–N edge. I'd send this to peer review; a good referee would ask for code/data and a tempering of the abstract. If you work on defective 2D materials, worth a read; the interaction range result is the one I'd cite.

Referee Report

3 major / 5 minor

Summary. The paper uses molecular dynamics (LAMMPS, Tersoff B-C-N potential of Kınacı et al.) to study uniaxial tension in graphene containing three size-matched defects: a graphitic-N cluster, a circular void, and a pyridinic-N cluster. By comparing these defects, the authors isolate the effects of nitrogen chemistry versus missing atoms. They report that graphitic N is mechanically benign (<1% strength reduction), a void reduces UTS by ~23%, and a pyridinic N cluster is most damaging (~30% reduction). They further study a pyridinic cluster coexisting with a void, finding that in-line defects behave as a weakest-link system while side-by-side defects interact through overlapping stress fields up to ~80 Å separation. The central claim is that mechanical integrity is governed by defect configuration and arrangement rather than nitrogen content or defect density alone. The pristine-graphene baseline is validated against experiments (E=937±5 GPa, UTS=127.8±0.7 GPa).

Significance. If the configuration-based conclusion holds, the paper provides a practically useful reframing: the mechanical penalty of nitrogen doping is carried by vacancy-associated (pyridinic) nitrogen, not by substitutional graphitic nitrogen, and coexisting-defect interactions are orientation-controlled. The strengths of the manuscript include a clean comparative design with size-matched defects, a validated pristine baseline, and a clear limitation section. The study uses a published potential with no fitting to the target strengths, and the central contrasts are internally consistent. However, the most novel quantitative result — the 8.0 GPa difference between the pyridinic cluster and the size-matched void (Section 3.2, Table 2) — rests entirely on the Tersoff B-C-N parameterization's description of C–N bond breaking at two-fold-coordinated pyridinic edges, which is not validated in the manuscript. This is a correctness-risk concern for the central claim, not a circularity issue.

major comments (3)

[Sections 2.3, 3.2, 4] The central claim that edge nitrogen chemistry itself weakens a pore beyond the vacancy — as opposed to the vacancy alone — rests on the 8.0 GPa difference between the pyridinic cluster (90.0±1.8 GPa) and the void (98.0±2.2 GPa) in Table 2. This difference is statistically suggestive (~2.8σ) but its physical interpretation depends entirely on the Tersoff B-C-N parameterization [12] correctly representing C–N bond dissociation and edge reconstruction at the pore rim. The paper does not validate this against DFT or experiment; Section 4 explicitly concedes that Tersoff-type potentials represent the large-strain fracture regime only approximately. If the potential over- or under-binds C–N relative to C–C at the rim, the ranking pyridinic < void < graphitic could change or the gap could vanish. Please add a validation of C–N bond-breaking energetics or pyridinic-edge stability (e.g., DFT ref
[Section 3.4 and Data availability] The side-by-side interaction range (~80 Å) and the ~13 GPa orientation difference are quantified using the pyridinic defect, so they inherit the same potential-validity concern as the isolated-defect comparison. Additionally, the manuscript provides no input structures, LAMMPS scripts, or processed data: the Data availability statement says only that data will be made available on request. Given that the main quantitative claims are differences of a few GPa and depend on the exact defect construction (60-atom hole, one-sublattice substitution, rim termination), independent reproduction is difficult. Please deposit the initial configurations, the potential parameters, and the simulation scripts, or provide sufficient detail in the text to reproduce the exact defect geometries.
[Sections 3.2 and 4] The conclusion that the mechanical impact is governed 'almost entirely' by whether the cluster carries vacancies is stronger than the data support. The vacancy contribution (void vs pristine) is ~30 GPa, while the edge-chemistry contribution (pyridinic vs void) is 8.0 GPa, i.e., about a quarter of the vacancy effect, not negligible. With only three independent runs per configuration, the 8.0 GPa gap is a 2.8σ effect. Please temper the wording to 'primarily' or 'dominantly' rather than 'almost entirely,' and discuss the finite-statistics and finite-cell-size uncertainties in the decomposition.

minor comments (5)

[Table 2 and Section 2.3] Table 2 lists graphitic-N UTS as 127.8±0.7 GPa, while the text in Section 3.2 states 127.5±0.8 GPa. Please make these consistent.
[Section 3.4] In the perpendicular orientation, the 5 Å gap UTS is reported as 77.4 GPa without an uncertainty, whereas other values in the same sentence report standard deviations. Please provide the uncertainty for all reported coupled strengths.
[Figure 5] The figure caption/plot should indicate whether the reported points include error bars; if they are too small to see, state that explicitly.
[References] Reference [2] cites a ResearchGate URL; a permanent journal article or DOI would be more appropriate. Reference [19] is the authors' own related work; please check that it is cited in a context that does not overstate external support.
[Section 2.2] The graphitic-N cluster is described as occupying the same 'circular footprint of approximately 7 Å radius' as the void, but it contains 30 substituted atoms while the void removes 60 atoms. Please clarify whether 'size-matched' means footprint-matched or atom-count-matched, as the two differ.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; all results are forward MD simulations with a fixed published potential, validated against independent literature values.

full rationale

All quantitative outputs (UTS, fracture strain, modulus) are produced by forward LAMMPS simulations using the published Kınacı et al. Tersoff B-C-N parameterization [12], with no parameter fitted to the target strengths. The size-matched defect construction (void vs pyridinic, graphitic vs pyridinic) provides controlled contrasts; each comparison is a simulation outcome, not an input definition. The pristine validation (937 GPa, 127.8 GPa, 0.254 strain) is checked against independent experimental and computational references [1], [17], so the baseline is not defined by the paper's own results. The self-citation [19] is used only as corroborating background for vacancy-type degradation, which the present paper itself computes (void UTS 98 GPa, -23%), and [10] concerns electronic/magnetic properties, not mechanical claims. The acknowledged Tersoff limitation is a potential-accuracy caveat, not an input that determines the conclusion. No load-bearing step reduces to its own inputs; hence no circularity.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

No new physical entities are postulated. The load-bearing assumptions are the empirical potential's fidelity, the adequacy of the finite-cell/image-separation choices, and the representativeness of a single 7 Å defect geometry.

free parameters (2)

Strain rate = 1×10^9 s⁻¹
Chosen as a typical MD loading rate; the paper notes it is far from experimental conditions and is known to influence strength and ductility (ref [26]).
Defect footprint radius = ≈7 Å (60-atom hole / 30 N substitution)
Single fixed defect size/shape; the central claim may not generalize to other sizes, shapes, or edge reconstructions.

assumptions (4)

domain assumption Tersoff B-C-N potential (Kınacı et al. / Lindsay-Broido) faithfully represents C-C, C-N, and N-N bond breaking and relative edge energetics.
Invoked in Section 2.3; the paper relies on comparative cancellation of systematic errors.
domain assumption Periodic images do not interact: defect-image separation of at least ~50 Å is sufficient for stress fields not to overlap.
Section 2.1; assumed rather than demonstrated by convergence tests.
domain assumption Three independent velocity seeds are sufficient to estimate run-to-run variability and to support the reported differences.
Section 2.4/2.5; no statistical power analysis is provided.
domain assumption The choice of one sublattice for graphitic N substitution produces a representative graphitic cluster without N-N nearest neighbours.
Section 2.2; the mechanical invisibility of this particular cluster is used to conclude that substitutional N is benign.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Defect configuration, not nitrogen content, governs the mechanical integrity of nitrogen-doped graphene: a molecular dynamics study." pith.science (2026). https://pith.science/paper/JKRDILWM

@misc{pith2026260718129,
  author       = {Pith},
  title        = {Pith review of: Defect configuration, not nitrogen content, governs the mechanical integrity of nitrogen-doped graphene: a molecular dynamics study},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JKRDILWM}},
  note         = {Machine review of arXiv:2607.18129}
}

read the original abstract

The mechanical reliability of nitrogen-doped graphene is often attributed to its nitrogen content, yet nitrogen occurs in chemically distinct configurations whose individual mechanical roles, and whose interactions with other defects, remain unresolved. Here, molecular dynamics simulations of uniaxial tension are used to separate the contributions of nitrogen chemistry, missing atoms, and defect arrangement to the strength and fracture of graphene. Three size-matched defects, a graphitic-nitrogen cluster, a void, and a pyridinic-nitrogen cluster, are compared so that two controlled contrasts isolate the effects of edge chemistry and of the vacancy independently. The graphitic cluster leaves the mechanical properties essentially unchanged (a strength reduction of <1 %), whereas the void degrades the ultimate strength by ~23 % and the pyridinic cluster, which combines the same vacancy with edge nitrogen, is the most damaging (~30 %), failing abruptly from its nitrogen-decorated rim rather than through the damage-tolerant process of the bare void. The mechanical impact of a nitrogen cluster is therefore governed by whether it carries vacancies, not by nitrogen itself. When a nitrogen cluster and a void coexist, their interaction is controlled by orientation relative to the load: in-line defects interact negligibly and fail at the more severe member, whereas side-by-side defects couple through overlapping stress fields and weaken the sheet progressively as they approach, an interaction that persists to separations of ~80 {\AA}. These results establish that the mechanical integrity of nitrogen-modified graphene is determined by the configuration of defects, the bonding environment of nitrogen, and the arrangement of coexisting defects relative to the load, rather than by nitrogen content or defect density alone, thereby providing a basis for defect-tolerant design.

Figures

Figures reproduced from arXiv: 2607.18129 by the authors.

**Figure 1.** Atomic configurations of the defect models used in this study. (a) Graphitic-nitrogen cluster, (b) circular void, and (c) pyridinic-nitrogen cluster, each introduced at the centre of a graphene sheet of dimensions 169.7 × 170.4 Å (carbon shown in grey, nitrogen in blue). (d) Representative coupled configuration containing a nitrogen cluster and a void separated by an edge-to-edge gap, with the loading direction indi… view at source ↗

**Figure 2.** Mechanical properties of pristine graphene and the three isolated defects: (a) ultimate tensile strength, (b) fracture strain, and (c) Young's modulus. Error bars denote the standard deviation over three independent simulations [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗

**Figure 3.** Representative stress–strain curves of pristine graphene and the graphitic-nitrogen cluster, void, and pyridinic-nitrogen cluster under uniaxial tension. The graphitic-nitrogen cluster is mechanically almost indistinguishable from pristine graphene: its UTS (127.5 ± 0.8 GPa) and fracture strain (0.252 ± 0.003) differ from the pristine values by less than the run-to-run scatter, and its modulus is likewise unchanged.… view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: Per-atom stress fields during deformation and fracture, coloured by the stress component along the loading direction, for (top row) the void and (bottom row) the pyridinicnitrogen cluster at successive stages of loading: (a) incipient/peak loading, (b) crack initiatio…

**Figure 5.** Figure 5: Coupled (a) ultimate tensile strength and (b) fracture strain of a nitrogen cluster and a void as a function of edge-to-edge gap, for the parallel (in-line) and perpendicular (side-by-side) orientations. Dotted lines indicate the corresponding single-defect reference v…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

29 extracted references · 17 canonical work pages

[19]

Impact of nitrogen atom clusters and void defects on graphene: a molecular dynamics investigation,

I. Rudra, Md. M. B. Tahmid, J. Emon, and M. J. A. Khan, “Impact of nitrogen atom clusters and void defects on graphene: a molecular dynamics investigation,” J. Mater. Sci., May 2026, doi: 10.1007/s10853-026-13042-x

work page doi:10.1007/s10853-026-13042-x 2026
[12]

Thermal conductivity of BN-C nanostructures,

A. Kınacı, J. B. Haskins, C. Sevik, and T. Çağın, “Thermal conductivity of BN-C nanostructures,” Phys. Rev. B, vol. 86, no. 11, p. 115410, Sep. 2012, doi: 10.1103/PhysRevB.86.115410

work page doi:10.1103/physrevb.86.115410 2012
[1]

Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene,

C. Lee, X. Wei, J. W. Kysar, and J. Hone, “Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene,” Science, vol. 321, no. 5887, pp. 385–388, Jul. 2008, doi: 10.1126/science.1157996

doi:10.1126/science.1157996 2008
[2]

Enhanced mechanical properties of polymer-Matrix nanocomposites reinforced by graphene inclusions: A review

“Enhanced mechanical properties of polymer-Matrix nanocomposites reinforced by graphene inclusions: A review.” Accessed: Jun. 20, 2026. [Online]. Available: https://www.researchgate.net/publication/286386607_Enhanced_mechanical_properties_of_poly mer-Matrix_nanocomposites_reinforced_by_graphene_inclusions_A_review

arXiv 2026
[3]

Structural Defects in Graphene,

F. Banhart, J. Kotakoski, and A. V. Krasheninnikov, “Structural Defects in Graphene,” ACS Nano, vol. 5, no. 1, pp. 26–41, Jan. 2011, doi: 10.1021/nn102598m

doi:10.1021/nn102598m 2011
[4]

Effects of vacancy defect on the tensile behavior of graphene,

X. Sun, Z. Fu, M. Xia, and Y. Xu, “Effects of vacancy defect on the tensile behavior of graphene,” Theor. Appl. Mech. Lett., vol. 4, no. 5, p. 051002, 2014, doi: 10.1063/2.1405102

work page doi:10.1063/2.1405102 2014
[5]

Intrinsic Strength and Failure Behaviors of Graphene Grain Boundaries,

J. Zhang, J. Zhao, and J. Lu, “Intrinsic Strength and Failure Behaviors of Graphene Grain Boundaries,” ACS Nano, vol. 6, no. 3, pp. 2704–2711, Mar. 2012, doi: 10.1021/nn3001356

work page doi:10.1021/nn3001356 2012
[6]

Mechanical properties of graphene and graphene-based nanocomposites,

D. G. Papageorgiou, I. A. Kinloch, and R. J. Young, “Mechanical properties of graphene and graphene-based nanocomposites,” Prog. Mater. Sci., vol. 90, pp. 75–127, Oct. 2017, doi: 10.1016/j.pmatsci.2017.07.004

doi:10.1016/j.pmatsci.2017.07.004 2017

Show all 29 references

[7]

Nitrogen doping and vacancy effects on the mechanical properties of graphene: A molecular dynamics study,

B. Mortazavi, S. Ahzi, V. Toniazzo, and Y. Rémond, “Nitrogen doping and vacancy effects on the mechanical properties of graphene: A molecular dynamics study,” Phys. Lett. A, vol. 376, no. 12– 13, pp. 1146–1153, Feb. 2012, doi: 10.1016/j.physleta.2011.11.034

2012 doi
[8]

Stress Field Characteristics and Collective Mechanical Properties of Defective Graphene,

B. Zheng and G. X. Gu, “Stress Field Characteristics and Collective Mechanical Properties of Defective Graphene,” J. Phys. Chem. C, vol. 124, no. 13, pp. 7421–7431, Apr. 2020, doi: 10.1021/acs.jpcc.9b11027

2020 doi
[9]

A new parallel method for molecular dynamics simulation of macromolecular systems,

S. Plimpton and B. Hendrickson, “A new parallel method for molecular dynamics simulation of macromolecular systems,” J. Comput. Chem., vol. 17, no. 3, pp. 326–337, Feb. 1996, doi: 10.1002/(SICI)1096-987X(199602)17:3<326::AID-JCC7>3.0.CO;2-X. 20

1996 doi
[10]

Md. M. B. Tahmid, I. Rudra, J. Emon, and M. J. A. Khan, “Peripheral Nitrogen Topology as a Defect- Chemical Switch for Electronic and Magnetic States in Graphene: A First-Principles Study of Pyridinic, Pyridazinic, Pyrrolic, and Pyrazolic Configurations,” 2026, arXiv. doi: 10....

2026 doi arXiv
[11]

Atomsk: A tool for manipulating and converting atomic data files,

P. Hirel, “Atomsk: A tool for manipulating and converting atomic data files,” Comput. Phys. Commun., vol. 197, pp. 212–219, Dec. 2015, doi: 10.1016/j.cpc.2015.07.012

2015 doi
[13]

Optimized Tersoff and Brenner empirical potential parameters for lattice dynamics and phonon thermal transport in carbon nanotubes and graphene,

L. Lindsay and D. A. Broido, “Optimized Tersoff and Brenner empirical potential parameters for lattice dynamics and phonon thermal transport in carbon nanotubes and graphene,” Phys. Rev. B, vol. 81, no. 20, p. 205441, May 2010, doi: 10.1103/PhysRevB.81.205441

2010 doi
[14]

A unified formulation of the constant temperature molecular dynamics methods,

S. Nosé, “A unified formulation of the constant temperature molecular dynamics methods,” J. Chem. Phys., vol. 81, no. 1, pp. 511–519, Jul. 1984, doi: 10.1063/1.447334

1984 doi
[15]

Canonical dynamics: Equilibrium phase-space distributions,

W. G. Hoover, “Canonical dynamics: Equilibrium phase-space distributions,” Phys. Rev. A, vol. 31, no. 3, pp. 1695–1697, Mar. 1985, doi: 10.1103/PhysRevA.31.1695

1985 doi
[16]

Visualization and analysis of atomistic simulation data with OVITO–the Open Visualization Tool,

A. Stukowski, “Visualization and analysis of atomistic simulation data with OVITO–the Open Visualization Tool,” Model. Simul. Mater. Sci. Eng., vol. 18, no. 1, p. 015012, Jan. 2010, doi: 10.1088/0965-0393/18/1/015012

2010 doi
[17]

Molecular dynamics investigation on edge stress and shape transition in graphene nanoribbons,

M. C. Wang, C. Yan, L. Ma, and N. Hu, “Molecular dynamics investigation on edge stress and shape transition in graphene nanoribbons,” Comput. Mater. Sci., vol. 68, pp. 138–141, Feb. 2013, doi: 10.1016/j.commatsci.2012.09.035

2013 doi
[18]

Effect of the number of nitrogen dopants on the electronic and magnetic properties of graphitic and pyridinic N-doped graphene – a density- functional study,

E. B. Yutomo, F. A. Noor, and T. Winata, “Effect of the number of nitrogen dopants on the electronic and magnetic properties of graphitic and pyridinic N-doped graphene – a density- functional study,” RSC Adv., vol. 11, no. 30, pp. 18371–18380, 2021, doi: 10.1039/D1RA01095F

2021 doi
[20]

Mechanical properties of defective single-layered graphene sheets via molecular dynamics simulation,

R. Ansari, S. Ajori, and B. Motevalli, “Mechanical properties of defective single-layered graphene sheets via molecular dynamics simulation,” Superlattices Microstruct., vol. 51, no. 2, pp. 274–289, Feb. 2012, doi: 10.1016/j.spmi.2011.11.019

2012 doi
[21]

Fracture toughness of graphene,

P. Zhang et al., “Fracture toughness of graphene,” Nat. Commun., vol. 5, no. 1, p. 3782, Apr. 2014, doi: 10.1038/ncomms4782

2014 doi
[22]

The role of vacancy defects and holes in the fracture of carbon nanotubes,

S. L. Mielke et al., “The role of vacancy defects and holes in the fracture of carbon nanotubes,” Chem. Phys. Lett., vol. 390, no. 4, pp. 413–420, Jun. 2004, doi: 10.1016/j.cplett.2004.04.054

2004 doi
[23]

N-doped graphene: Polarization effects and structural properties,

H. Ghorbanfekr-Kalashami, M. Neek-Amal, and F. M. Peeters, “N-doped graphene: Polarization effects and structural properties,” Phys. Rev. B, vol. 93, no. 17, p. 174112, May 2016, doi: 10.1103/PhysRevB.93.174112

2016 doi
[24]

Review on Recent Progress in Nitrogen-Doped Graphene: Synthesis, Characterization, and Its Potential Applications,

H. Wang, T. Maiyalagan, and X. Wang, “Review on Recent Progress in Nitrogen-Doped Graphene: Synthesis, Characterization, and Its Potential Applications,” ACS Catal., vol. 2, no. 5, pp. 781–794, May 2012, doi: 10.1021/cs200652y

2012 doi
[25]

Graphitization of amorphous carbons: A comparative study of interatomic potentials,

C. de Tomas, I. Suarez-Martinez, and N. A. Marks, “Graphitization of amorphous carbons: A comparative study of interatomic potentials,” Carbon, vol. 109, pp. 681–693, Nov. 2016, doi: 10.1016/j.carbon.2016.08.024

2016 doi
[26]

Molecular Dynamics Simulations and Continuum Modeling of Temperature and Strain Rate Dependent Fracture Strength of Graphene With Vacancy Defects,

M. A. N. Dewapriya and R. K. N. D. Rajapakse, “Molecular Dynamics Simulations and Continuum Modeling of Temperature and Strain Rate Dependent Fracture Strength of Graphene With Vacancy Defects,” J. Appl. Mech., vol. 81, no. 8, p. 081010, Aug. 2014, doi: 10.1115/1.4027681. 21

2014 doi
[27]

An accurate and transferable machine learning potential for carbon,

P. Rowe, V. L. Deringer, P. Gasparotto, G. Csányi, and A. Michaelides, “An accurate and transferable machine learning potential for carbon,” J. Chem. Phys., vol. 153, no. 3, p. 034702, Jul. 2020, doi: 10.1063/5.0005084

2020 doi
[28]

A molecular dynamics study of mechanical behavior of vertically stacked NbSe2/MoS2 and WS2/MoS2 van der Waals heterostructures,

P. S. Sourov, S. K. Biswas, B. Kar, and M. J. A. Khan, “A molecular dynamics study of mechanical behavior of vertically stacked NbSe2/MoS2 and WS2/MoS2 van der Waals heterostructures,” Mech. Mater., vol. 216, p. 105642, May 2026, doi: 10.1016/j.mechmat.2026.105642

2026
[29]

Graphene related materials for thermal management,

Y. Fu et al., “Graphene related materials for thermal management,” 2D Mater., vol. 7, no. 1, p. 012001, Oct. 2019, doi: 10.1088/2053-1583/ab48d9

2019 doi

Pith tools

Reviewed August 1, 2026 · model on record in the stance chip above.

[1] [19]

Impact of nitrogen atom clusters and void defects on graphene: a molecular dynamics investigation,

I. Rudra, Md. M. B. Tahmid, J. Emon, and M. J. A. Khan, “Impact of nitrogen atom clusters and void defects on graphene: a molecular dynamics investigation,” J. Mater. Sci., May 2026, doi: 10.1007/s10853-026-13042-x

work page doi:10.1007/s10853-026-13042-x 2026

[2] [12]

Thermal conductivity of BN-C nanostructures,

A. Kınacı, J. B. Haskins, C. Sevik, and T. Çağın, “Thermal conductivity of BN-C nanostructures,” Phys. Rev. B, vol. 86, no. 11, p. 115410, Sep. 2012, doi: 10.1103/PhysRevB.86.115410

work page doi:10.1103/physrevb.86.115410 2012

[3] [1]

Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene,

C. Lee, X. Wei, J. W. Kysar, and J. Hone, “Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene,” Science, vol. 321, no. 5887, pp. 385–388, Jul. 2008, doi: 10.1126/science.1157996

doi:10.1126/science.1157996 2008

[4] [2]

Enhanced mechanical properties of polymer-Matrix nanocomposites reinforced by graphene inclusions: A review

“Enhanced mechanical properties of polymer-Matrix nanocomposites reinforced by graphene inclusions: A review.” Accessed: Jun. 20, 2026. [Online]. Available: https://www.researchgate.net/publication/286386607_Enhanced_mechanical_properties_of_poly mer-Matrix_nanocomposites_reinforced_by_graphene_inclusions_A_review

arXiv 2026

[5] [3]

Structural Defects in Graphene,

F. Banhart, J. Kotakoski, and A. V. Krasheninnikov, “Structural Defects in Graphene,” ACS Nano, vol. 5, no. 1, pp. 26–41, Jan. 2011, doi: 10.1021/nn102598m

doi:10.1021/nn102598m 2011

[6] [4]

Effects of vacancy defect on the tensile behavior of graphene,

X. Sun, Z. Fu, M. Xia, and Y. Xu, “Effects of vacancy defect on the tensile behavior of graphene,” Theor. Appl. Mech. Lett., vol. 4, no. 5, p. 051002, 2014, doi: 10.1063/2.1405102

work page doi:10.1063/2.1405102 2014

[7] [5]

Intrinsic Strength and Failure Behaviors of Graphene Grain Boundaries,

J. Zhang, J. Zhao, and J. Lu, “Intrinsic Strength and Failure Behaviors of Graphene Grain Boundaries,” ACS Nano, vol. 6, no. 3, pp. 2704–2711, Mar. 2012, doi: 10.1021/nn3001356

work page doi:10.1021/nn3001356 2012

[8] [6]

Mechanical properties of graphene and graphene-based nanocomposites,

D. G. Papageorgiou, I. A. Kinloch, and R. J. Young, “Mechanical properties of graphene and graphene-based nanocomposites,” Prog. Mater. Sci., vol. 90, pp. 75–127, Oct. 2017, doi: 10.1016/j.pmatsci.2017.07.004

doi:10.1016/j.pmatsci.2017.07.004 2017