# Vibrational properties of nanographene

Sandeep Kumar Singh; F.M. Peeters

Nanoscale Systems: Mathematical Modeling, Theory and Applications (2013)

- Volume: 2, page 10-29
- ISSN: 2299-3290

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topSandeep Kumar Singh, and F.M. Peeters. "Vibrational properties of nanographene." Nanoscale Systems: Mathematical Modeling, Theory and Applications 2 (2013): 10-29. <http://eudml.org/doc/266621>.

@article{SandeepKumarSingh2013,

abstract = {The eigenmodes and the vibrational density of states of the ground state configuration of graphene clusters are calculated using atomistic simulations. The modified Brenner potential is used to describe the carbon-carbon interaction and carbon-hydrogen interaction in case of H-passivated edges. For a given configuration of the C-atoms the eigenvectors and eigenfrequencies of the normal modes are obtained after diagonalisation of the dynamical matrix whose elements are the second derivative of the potential energy. The compressional and shear properties are obtained from the divergence and rotation of the velocity field. For symmetric and defective clusters with pentagon arrangement on the edge, the highest frequency modes are shear modes. The specific heat of the clusters is also calculated within the harmonic approximation and the convergence to the result for bulk graphene is investigated.},

author = {Sandeep Kumar Singh, F.M. Peeters},

journal = {Nanoscale Systems: Mathematical Modeling, Theory and Applications},

keywords = {Carbon clusters; nanographene; Molecular dynamics simulation; Normal modes; phonon spectrum; phonon density of states; Specific heat; carbon clusters; molecular dynamics simulation; normal modes; specific heat},

language = {eng},

pages = {10-29},

title = {Vibrational properties of nanographene},

url = {http://eudml.org/doc/266621},

volume = {2},

year = {2013},

}

TY - JOUR

AU - Sandeep Kumar Singh

AU - F.M. Peeters

TI - Vibrational properties of nanographene

JO - Nanoscale Systems: Mathematical Modeling, Theory and Applications

PY - 2013

VL - 2

SP - 10

EP - 29

AB - The eigenmodes and the vibrational density of states of the ground state configuration of graphene clusters are calculated using atomistic simulations. The modified Brenner potential is used to describe the carbon-carbon interaction and carbon-hydrogen interaction in case of H-passivated edges. For a given configuration of the C-atoms the eigenvectors and eigenfrequencies of the normal modes are obtained after diagonalisation of the dynamical matrix whose elements are the second derivative of the potential energy. The compressional and shear properties are obtained from the divergence and rotation of the velocity field. For symmetric and defective clusters with pentagon arrangement on the edge, the highest frequency modes are shear modes. The specific heat of the clusters is also calculated within the harmonic approximation and the convergence to the result for bulk graphene is investigated.

LA - eng

KW - Carbon clusters; nanographene; Molecular dynamics simulation; Normal modes; phonon spectrum; phonon density of states; Specific heat; carbon clusters; molecular dynamics simulation; normal modes; specific heat

UR - http://eudml.org/doc/266621

ER -

## References

top- J. Zimmermann, P. Pavone, and G. Cuniberti. Vibrational modes and low-temperature thermal properties of graphene and carbon nanotubes: Minimal force-constant model. Phys. Rev. B, 78 (4), 045410 (2008). [Crossref]
- J. Maultzsch, S. Reich, C. Thomsen, H. Requardt, and P. Ordejón. Phonon Dispersion in Graphite. Phys. Rev. Lett., 92 (7), 075501 (2004).
- J. Zhou and J. Dong. Vibrational property and Raman spectrum of carbon nanoribbon. Appl. Phys. Lett., 91, 173108 (2007). [WoS]
- R. Gillen, M. Mohr, C. Thomsen, and J. Maultzsch. Vibrational properties of graphene nanoribbons by first-principles calculations. Phys. Rev. B, 80, 155418 (2009).
- G. Gao, T. Çaˇgin, and W. A. Goddard III. Energetics, structure, mechanical and vibrational properties of single-walled carbon nanotubes. Nanotechnology, 9, 184-191 (1998). [Crossref]
- R. Saito, T. Takeya, T. Kimura, G. Dresselhaus, and M. S. Dresselhaus. Raman intensity of single-wall carbon nanotubes. Phys. Rev. B, 57 (7), 4145 (1998). [Crossref]
- M. Menon, E. Richter, and K. R. Subbaswamy. Structural and vibrational properties of fullerenes and nanotubes in a nonorthogonal tight−binding scheme. J. Chem. Phys., 104 (15), 5875-5882 (1996).
- B. Barszcz, B. Laskowska, A. Graja, E. Y. Park, T. Kim, and K. Lee. Vibrational properties of two fullerene-thiophenebased dyads. Synth. Met., 159 (23-24), 2539-2543 (2009). [WoS]
- E. Malolepsza, H. A. Witek, and S. Irle. Comparison of Geometric, Electronic, and Vibrational Properties for Isomers of Small Fullerenes C20−C36 . J. Phys. Chem. A., 111 (29), 6649 (2007).
- S. Bera, A. Arnold, F. Evers, R. Narayanan, and P. W¨olfle. Elastic properties of graphene flakes: Boundary effects and lattice vibrations. Phys. Rev. B, 82 (19), 195445 (2010). [WoS]
- B. K. Agrawal, S. Agrawal, and S. Singh. Structural and vibrational properties of small carbon clusters. J. Nanosci. Nanotechnol., 5 (3), 442-448 (2005).
- N. Breda, G. Onida, G. Benedek, G. Col`o, and R. A. Broglia. Bond-charge-model calculation of vibrational properties in small carbon aggregates: From spherical clusters to linear chains. Phys. Rev. B, 58 (16), 11000 (1998). [Crossref]
- R. Saito, M. Hofmann, G. Dresselhaus, A. Jorio, and M. S. Dresselhaus. Raman Spectroscopy of Graphene and Carbon Nanotubes. Advances in Physics, 60 (3), 413-550 (2011). [WoS][Crossref]
- A. Eckmann, A. Felten, A. Mishchenko, L. Britnell, R. Krupke, K. S. Novoselov, and Cinzia Casiraghi. Probing the Nature of Defects in Graphene by Raman Spectroscopy. Nano Lett., 12 (8), 3925-3930 (2012). [WoS][PubMed][Crossref]
- A. K. Geim and K. S. Novoselov, The Rise of Graphene, Nat. Mater., 6), 183-191 (2007).
- A. M. Rao, E. Richter, S. Bandow, B. Chase, P. C. Eklund, K. A. Williams, S. Fang, K. R. Subbaswamy, M. Menon, A. Thess, R. E. Smalley, G. Dresselhaus, and M. S. Dresselhaus. Diameter-Selective Raman Scattering from Vibrational Modes in Carbon Nanotubes. Science, 275 (5297), 187-190 (1997).
- L. Venkataraman. Massachusetts Institute of Technology, PhD-thesis(1993).
- R. A. Jishi, L. Venkataraman, M. S. Dresselhaus, and G. Dresselhaus. Phonon Modes in Carbon Nanotubules. Chem. Phys. Lett., 209 (1-2), 77-82 (1993).
- M. Tommasini, C. Castiglioni, and G. Zerbi. Raman Scattering of Molecular Graphene. Phys. Chem. Chem. Phys., 11), 10185-10194 (2009). [PubMed][Crossref]
- M. A. Pimenta, G. Dresselhaus, M. S. Dresselhaus, L. G. Cançado, A. Jorio, and R. Saito. Studying disorder in graphite-based systems by Raman spectroscopy. Phys. Chem. Chem. Phys., 9, 1276-1291 (2007). [PubMed][Crossref][WoS]
- A. G. Ryabenko, N. A. Kiselev, J. L. Hutchison, T. N. Moroz, S. S. Bukalov, L. A. Mikhalitsyn, et al. Spectral properties of single-walled carbon nanotubes encapsulating fullerenes. Carbon, 45 (7), 1492-1505 (2007). [Crossref][WoS]
- K. H. Michel and B. Verberck. Theory of the evolution of phonon spectra and elastic constants from graphene to graphite. Phys. Rev. B, 78 (8), 085424 (2008). [Crossref]
- M. Mohr, J. Maultzsch, E. Dobardžic, S. Reich, I. Miloševic, M. Damnjanovic, et al. Phonon dispersion of graphite by inelastic x-ray scattering. Phys. Rev. B, 76 (3), 035439 (2007).
- B. Partoens and F. M. Peeters. From graphene to graphite: Electronic structure around the K point. Phys. Rev. B, 74 (7), 075404 (2006). [Crossref]
- N. Mounet and N. Marzari. First-principles determination of the structural, vibrational and thermodynamic properties of diamond, graphite, and derivatives. Phys. Rev. B, 71 (20), 205214 (2005).
- W. An, Y. Gao, S. Bulusu, and X. C. Zeng. Ab initio calculation of bowl, cage, and ring isomers of C20 and C20− . J. Chem. Phys., 122 (20), 204109-204116 (2005).
- D. P. Kosimov, A. A. Dzhurakhalov, and F. M. Peeters. Carbon clusters: From ring structures to nanographene. Phys. Rev. B, 81 (19), 195414 (2010). [Crossref][WoS]
- D. P. Kosimov, A. A. Dzhurakhalov, and F. M. Peeters. Theoretical study of the stable states of small carbon clusters Cn (n=2-10). Phys. Rev. B, 78 (23), 235433 (2008). [WoS][Crossref]
- M. Ezawa. Metallic graphene nanodisks: electric and magnetic properties. Phys. Rev. B, 76 (24), 245415 (2007). [WoS]
- J. Fernandez-Rossier and J. J. Palacios. Magnetism in graphene nanoislands. Phys. Rev. Lett., 99 (17), 177204 (2007). [Crossref]
- D. W. Brenner, O. A. Shenderova, J. A. Harrison, S. J. Stuart, B. Ni, and S. B. Sinnott. A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons. J. Phys.: Condens. Matter, 14 (4), 783-802 (2002). [Crossref]
- J. D. Louck. Exact normal modes of oscillation of a linear chain of identicalatoms. Am. J. Phys., 30, 585 (1962). Zbl0129.43805
- J. H. Eggert. One-dimensional lattice dynamics with periodic boundary conditions: An analog demonstration. Am. J. Phys., 65, 108 (1997).
- T. Zhou, C. Xu, X. Zhang, C. Cheng, L. Chen, and Y. Xu. A simple theoretical model for ring and nanotube radial breathing mode. Acta Phys. -Chim. Sin., 24 (9), 1579-1583 (2008). [WoS][Crossref]
- M. Vandescuren, P. Hermet, V. Meunier, L. Henrard, and Ph. Lambin. Theoretical study of the vibrational edge modes in graphene nanoribbons. Phys. Rev. B, 78 (19), 195401 (2008). [Crossref]
- V. A. Schweigert and F. M. Peeters. Spectral properties of classical two-dimensional clusters. Phys. Rev. B, 51 (12), 7700 (1995). [Crossref]
- L. X. Benedict, S. G. Louie, and M. L. Cohen. Heat capacity of carbon nanotubes. Solid State Commun., 100 (3), 177-179 (1996).
- A. A. Maradudin, E. W. Montroll, G. H. Weiss, and I. P. Ipatova. Theory of the vibrational frequency spectra of solids. In: H. E. Ehrenreich, F. Seitz, and D. Turnbull (ed.). Solid State Physics, Academic, New York, pp. 129-188 (1971).
- J. Zimmermann, P. Pavone, and G. Cuniberti. Vibrational modes and low-temperature thermal properties of graphene and carbon nanotubes: Minimal force-constant model. Phys. Rev. B, 78 (4), 045410 (2008). [Crossref]