Analysis of radial breathing-mode of nanostructures with various morphologies: a critical review

References

• Sun C. Q.: ‘Size dependence of nanostructures: impact of bond order deficiency’, Prog. Solid State Chem., 2007, 35, 1–159.
   Web of Science ®Google Scholar
• Gao G.: ‘Nanostructures & nanomaterials’, Vol. 3, ; 2004, London, Imperial College Press.
   Google Scholar
• Rao A. M., Richter E., Bandow S., Chase B., Eklund P. C., Williams K. A., Fang S., Subbaswamy K. R., Menon M., Thess A., Smalley R. E., Dresselhaus G. and Dresselhaus M. S.: ‘Diameter-selective Raman scattering from vibrational modes in carbon nanotubes’, Science, 1997, 275, 187–191.
   PubMed Web of Science ®Google Scholar
• Dresselhaus M. S., Dresselhaus G., Saito R. and Jorio A.: ‘Raman spectroscopy of carbon nanotubes’, Phys. Rep., 2005, 409, 47–99.
   Web of Science ®Google Scholar
• Eisler H. J., Gilb S., Hennrich F. H. and Kappes M. M.: ‘Low frequency raman active vibrations in fullerenes. 1. Monopolar modes’, J. Phys. Chem. A, 2000, 104, 1762–1768.
   Web of Science ®Google Scholar
• Portales H., Saviot L., Duval E., Fujii M., Hayashi S., Del Fatti N. and Vallée F.: ‘Resonant Raman scattering by breathing modes of metal nanoparticles’, J. Chem. Phys., 2001, 115, (8), 3444–3447.
   Web of Science ®Google Scholar
• Lange H., Mohr M., Artemyev M., Woggon U. and Thomsen C.: ‘Direct observation of the radial breathing mode in CdSe nanorods’, Nano Lett., 2008, 8, 4614–4617.
   PubMed Web of Science ®Google Scholar
• Yu F., Zhou H., Zhang Z., Tang D., Chen M., Yang H., Wang G., Yang H., Gu C. and Sun L.: ‘Experimental observation of radial breathing-like mode of graphene nanoribbons’, Appl. Phys. Lett., 2012, 100, 101904.
   Google Scholar
• Jorio A., Saito R., Dresselhaus G. and Dresselhaus M. S.: ‘Raman spectroscopy in graphene related systems’; 2009, Singapore, Wiley-VCH.
   Google Scholar
• Thomsen C. and Reich S.: ‘Double resonant Raman scattering in graphite’, Phys. Rev. Lett., 2000, 85, 5214–5217.
   PubMed Web of Science ®Google Scholar
• Li L. and Chang T.: ‘Explicit solution for G-band mode frequency of single-walled carbon nanotubes’, Acta Mech. Solida Sin., 2009, 22, 571–583.
   Web of Science ®Google Scholar
• Dresselhaus M. S. and Eklund P. C.: ‘Phonons in carbon nanotubes’, Adv. Phys., 2000, 49, (6), 705–814.
   Web of Science ®Google Scholar
• Kuzmany H., Plank W., Hulman M., Kramberger C., Grüneis A., Pichler T., Peterlik H., Kataura H. and Achiba Y.: ‘Determination of SWCNT diameters from the Raman response of the radial breathing mode’, Eur. Phys. J. B, 2001, 22, 307–320.
   Web of Science ®Google Scholar
• Maultzsch J., Telg H., Reich S. and Thomsen C.: ‘Radial breathing mode of single-walled carbon nanotubes: optical transition energies and chiral-index assignment’, Phys. Rev. B, 2005, 72, 205438.
   Google Scholar
• Telg H., Thomsen C. and Maultzsch J.: ‘Raman intensities of the radial-breathing mode in carbon nanotubes: the exciton-phonon coupling as a function of (n1, n2)’, J. Nanophotonics, 2010, 4, 041660.
   Google Scholar
• Milošević I., Dobardžić E. and Damnjanović M.: ‘Phonons in narrow carbon nanotubes’, Phys. Rev. B, 2005, 72, 085426.
   Google Scholar
• Cheng H. C., Liu Y. L., Wu C. H. and Chen W. H.: ‘On radial breathing vibration of carbon nanotubes’, Comput. Methods Appl. Mech. Eng., 2010, 199, 2820–2827.
   Web of Science ®Google Scholar
• Araujo P. T., Pesce P. B. C., Dresselhaus M. S., Sato K., Saito R. and Jorio A.: ‘Resonance Raman spectroscopy of the radial breathing modes in carbon nanotubes’, Phys. E, 2010, 42, 1251–1261.
   Web of Science ®Google Scholar
• Popov V. N., Henrard L. and Lambin P.: ‘Resonant Raman intensity of the radial breathing mode of single-walled carbon nanotubes within a nonorthogonal tight-binding model’, Nano Lett., 2004, 4, 1795–1799.
   Web of Science ®Google Scholar
• Ezawa M.: ‘Graphene nanoribbon and graphene nanodisk’, Phys. E, 2008, 40, 1421–1423.
   Google Scholar
• Bischoff D., Güttinger J., Dröscher S., Ihn T., Ensslin K. and Stampfer C.: ‘Raman spectroscopy on etched graphene nanoribbons’, J. Appl. Phys., 2011, 109, 073710.
   Google Scholar
• Shi J. X., Ni Q. Q., Lei X. W. and Natsuki T.: ‘Nonlocal vibration of embedded double-layer graphene nanoribbons in in-phase and anti-phase modes’, Phys. E, 2012, 44, 1136–1141.
   Google Scholar
• Thonhauser T. and Mahan G. D.: ‘Predicted Raman spectra of Si[111] nanowires’, Phys. Rev. B, 2005, 71, 081307(R).
   Google Scholar
• Mankad V., Mishra K. K., Gupta S. K., Ravindran T. R. and Jha P. K.: ‘Low frequency Raman scattering from confined acoustic phonons in freestanding silver nanoparticles’, Vib. Spectrosc., 2012, 61, 183–187.
   Web of Science ®Google Scholar
• Voisin C., Del Fatti N., Christofilos D. and Vallée F.: ‘Time-resolved investigation of the vibrational dynamics of metal nanoparticles’, Appl. Surf. Sci., 2000, 164, 131–139.
   Web of Science ®Google Scholar
• Hartland G. V., Hu M. and Sader J. E.: ‘Softening of the symmetric breathing mode in gold particles by laser-induced heating’, J. Phys. Chem. B, 2003, 107, 7472–7478.
   Web of Science ®Google Scholar
• van Dijk M. A., Lippitz M. and Orrit M.: ‘Detection of acoustic oscillations of single gold nanospheres by time-resolved interferometry’, Phys. Rev. Lett., 2005, 95, 267406.
   PubMed Web of Science ®Google Scholar
• Crut A., Maioli P., Del Fatti N. and Vallée F.: ‘Time-domain investigation of the acoustic vibrations of metal nanoparticles: size and encapsulation effects’, Ultrasonics, 2015, 56, 98–108.
   PubMed Web of Science ®Google Scholar
• Juvé V., Crut A., Maioli P., Pellarin M., Broyer M., Del Fatti N. and Vallée F.: ‘Probing elasticity at the nanoscale: terahertz acoustic vibration of small metal nanoparticles’, Nano Lett., 2010, 10, 1853–1858.
   PubMed Web of Science ®Google Scholar
• Ruijgrok P. V., Zijlstra P., Tchebotareva A. L. and Orrit M.: ‘Damping of acoustic vibrations of single gold nanoparticles optically trapped in water’, Nano Lett., 2012, 12, 1063–1069.
   PubMed Web of Science ®Google Scholar
• Major T. A., Lo S. S., Yu K. and Hartland G. V.: ‘Time-resolved studies of the acoustic vibrational modes of metal and semiconductor nano-objects’, J. Phys. Chem. Lett., 2014, 5, 866–874.
   PubMed Web of Science ®Google Scholar
• White C. T., Robertson D. H. and Mintmire J. W.: ‘Helical and rotational symmetries of nanoscale graphatic tubules’, Phys. Rev. B, 1993, 47, 5485–5488.
   PubMed Web of Science ®Google Scholar
• Rafii-Tabar H.: ‘Computational physics of carbon nanotubes’; 2008, Cambridge, Cambridge University Press.
   Google Scholar
• Jishi R. A., Venkataraman L., Dresselhaus M. S. and Dresselhaus G.: ‘Phonon modes in carbon nanotubules’, Chem. Phys. Lett., 1993, 209, 77.
   Web of Science ®Google Scholar
• Kurti J., Kresse G. and Kuzmany H.: ‘First-principles calculations of the radial breathing mode of single-wall carbon nanotubes’, Phys. Rev. B, 1998, 58, R8869.
   Web of Science ®Google Scholar
• Sanchez-Portal D., Artacho E., Soler J. M., Rubio A. and Ordejon P.: ‘Ab initio structural, elastic, and vibrational properties of carbon nanotubes’, Phys. Rev. B, 1999, 59, 12678–12688.
   Web of Science ®Google Scholar
• Jorio A., Saito R., Hafner J. H., Lieber C. M., Hunter M., McClure T., Dresselhaus G. and Dresselhaus M. S.: ‘Structural (n, m) determination of isolated single wall carbon nanotubes by resonant Raman scattering’, Phys. Rev. Lett., 2001, 86, 1118–1121.
   PubMed Web of Science ®Google Scholar
• Dobardzic E., Milosevic I., Nikolic B., Vukovic T. and Damnjanovic M.: ‘Single-wall carbon nanotubes phonon spectra: symmetry-based calculations’, Phys. Rev. B, 2003, 68, 045408.
   Google Scholar
• Longhurst M. J. and Quirke N.: ‘The radial breathing mode of carbon nanotubes’, Mol. Simul., 2005, 31, 135.
   Web of Science ®Google Scholar
• Reich S., Thomsen C. and Maultzsch J.: ‘Carbon nanotubes: basic concepts and physical properties’; 2004, Weinheim, John Wiley & Sons.
   Google Scholar
• Araujo P. T., Maciel I. O., Pesce P. B. C., Pimenta M. A., Doorn S. K., Qian H., Hartschuh A., Steiner M., Grigorian L., Hata K. and Jorio A.: ‘Nature of the constant factor in the relation between radial breathing mode frequency and tube diameter for single-wall carbon nanotubes’, Phys. Rev. B, 2008, 77, 241403(R).
   Google Scholar
• Kürti J., Zólyomi V., Kertesz M. and Sun G. Y.: ‘The geometry and the radial breathing mode of carbon nanotubes: beyond the ideal behaviour’, New J. Phys., 2003, 5, 125.
   Web of Science ®Google Scholar
• Goupalov S., Satishkumar B. and Doorn S. K.: ‘Excitation and chirality dependence of the exciton-phonon coupling in carbon nanotubes’, Phys. Rev. B, 2006, 73, 115401.
   Google Scholar
• Telg H., Maultzsch J., Reich S., Hennrich F. and Thomsen C.: ‘Chirality distribution and transition energies of carbon nanotubes’, Phys. Rev. Lett., 2004, 93, 177401.
   PubMed Web of Science ®Google Scholar
• Meyer J. C., Paillet M., Michel T., Moreac A., Neumann A., Duesberg G. S., Roth S. and Sauvajol J.: ‘Raman modes of index-identified freestanding single-walled carbon nanotubes’, Phys. Rev. Lett., 2005, 95, 217401.
   PubMed Web of Science ®Google Scholar
• Lawler H. M., Areshkin D., Mintmire J. W. and White C. T.: ‘Radial-breathing mode frequencies for single-walled carbon nanotubes of arbitrary chirality: first-principles calculations’, Phys. Rev. B, 2005, 72, 233403.
   Google Scholar
• Xiao Y., Li Z. M., Yan X. H., Zhang Y., Mao Y. L. and Yang Y. R.: ‘Curvature effect on the radial breathing modes of single-walled carbon nanotubes’, Phys. Rev. B, 2005, 71, 233405.
   Google Scholar
• Rols S., Righi A., Alvarez L., Anglaret E., Almairac R., Journet C., Bernier P., Sauvajol J. L., Benito A. M., Maser W. K., Muñoz E., Martinez M. T., de la Fuente G. F., Girard A. and Ameline J. C.: ‘Diameter distribution of single wall carbon nanotubes in nanobundles’, Eur. Phys. J.B, 2000, 18, 201–205.
   Web of Science ®Google Scholar
• Agrawal B. K., Agrawal S. and Srivastava R.: ‘Ab initio study of small diameter (6, 6) armchair carbon nanoropes: orientational dependent properties’, J. Phys. Condens. Matter., 2003, 15, 6931–6942.
   Web of Science ®Google Scholar
• Popov V. N. and Lambin P.: ‘Radius and chirality dependence of the radial breathing mode and the G-band phonon modes of single-walled carbon nanotubes’, Phys. Rev. B, 2006, 73, 085407.
   Google Scholar
• Chang T.: ‘Explicit solution of the radial breathing mode frequency of single-walled carbon nanotubes’, Acta Mech. Sin., 2007, 23, 159–162.
   Web of Science ®Google Scholar
• Chang T.: ‘A molecular based anisotropic shell model for single-walled carbon nanotubes’, J. Mech. Phys. Solids, 2010, 58, 1422–1433.
   Web of Science ®Google Scholar
• Ghavanloo E. and Fazelzadeh S. A.: ‘Vibration characteristics of single-walled carbon nanotubes based on an anisotropic elastic shell model including chirality effect’, Appl. Math. Model., 2012, 36, 4988–5000.
   Web of Science ®Google Scholar
• Basirjafari S., Esmaielzadeh Khadem S. and Malekfar R.: ‘Validation of shell theory for modeling the radial breathing mode of a single-walled carbon nanotube’, Int. J. Eng. Trans. A, 2013, 26, (4), 447–454.
   Google Scholar
• Ebbesen T. W. and Takada T.: ‘Topological and sp3 defect structures in nanotubes’, Carbon, 1995, 33, 973–978.
   Web of Science ®Google Scholar
• Singh D. K., Iyer P. K. and Giri P. K.: ‘Optical signature of structural defects in single walled and multiwalled carbon nanotubes’, J. Nanosci. Nanotechnol., 2009, 9, 1–6.
   Web of Science ®Google Scholar
• Saidi W. A.: ‘Effects of topological defects and diatom vacancies on characteristic vibration modes and Raman intensities of zigzag single-walled carbon nanotubes’, J. Phys. Chem. A, 2014, 118, 7235–7241.
   PubMed Web of Science ®Google Scholar
• Saidi W. A. and Norman P.: ‘Spectroscopic signatures of topological and diatom-vacancy defects in single-walled carbon nanotubes’, Phys. Chem. Chem. Phys., 2014, 16, 1479.
   PubMed Web of Science ®Google Scholar
• Saidi W. A. and Norman P.: ‘Probing single-walled carbon nanotube defect chemistry using resonance Raman spectroscopy’, Carbon, 2014, 67, 17–26.
   Web of Science ®Google Scholar
• Wang Y. F., Cao X. W., Hu S. F., Liu Y. Y. and Lan G. X.: ‘Graphical method for assigning Raman peaks of radial breathing modes of single-wall carbon nanotubes’, Chem. Phys. Lett., 2001, 336, 47–52.
   Web of Science ®Google Scholar
• Bandow S., Asaka S., Saito Y., Rao A. M., Grigorian L., Richter E. and Eklund P. C.: ‘Effect of the growth temperature on the diameter distribution and chirality of single-wall carbon nanotubes’, Phys. Rev. Lett., 1998, 80, 3779–3782.
   Web of Science ®Google Scholar
• Saito R., Takcya T., Kimiira T., Dresselhaus G. and Drcsselhaus M. S.: ‘Raman intensity of single-wall carbon nanotubes’, Phys. Rev. B, 1998, 57, 4145.
   Web of Science ®Google Scholar
• ánchez-Portall D. S., Artacho E. and Soler J. M.: ‘Ab initio structural, elastic, and vibrational properties of carbon nanotubes’, Phys. Rev. B, 1999, 59, 12678–12688.
   Web of Science ®Google Scholar
• Gupta S. S. and Batra R. C.: ‘Continuum structures equivalent in normal mode vibrations to single-walled carbon nanotubes’, Comput. Mater. Sci., 2008, 43, 715–723.
   Web of Science ®Google Scholar
• Batra R. C. and Gupta S. S.: ‘Wall thickness and radial breathing modes of single-walled carbon nanotubes’, J. Appl. Mech., 2008, 75, 061010.
   Google Scholar
• Lei X. W., Ni Q. Q., Shi J. X. and Natsuki T.: ‘Radial breathing mode of carbon nanotubes subjected to axial pressure’, Nanoscale Res. Lett., 2011, 6, 492.
   PubMedGoogle Scholar
• Basirjafari S., Esmaeilzadeh Khadem S. and Malekfar R.: ‘Radial breathing mode frequencies of carbon nanotubes for determination of their diameters’, Curr. Appl. Phys., 2013, 13, 599–609.
   Web of Science ®Google Scholar
• Longhurst M. J. and Quirke N.: ‘The environmental effect on the radial breathing mode of carbon nanotubes in water’, J. Chem. Phys., 2006, 124, 234708.
   PubMed Web of Science ®Google Scholar
• Longhurst M. J. and Quirke N.: ‘The environmental effect on the radial breathing mode of carbon nanotubes. II. Shell model approximation for internally and externally adsorbed fluids’, J. Chem. Phys., 2006, 125, 184705.
   PubMed Web of Science ®Google Scholar
• Araujo P. T. and Jorio A.: ‘The role of environmental effects on the optical transition energies and radial breathing mode frequency of single wall carbon nanotubes’, Phys. Status Solidi B, 2008, 245, (10), 2201–2204.
   Google Scholar
• Araujo P. T., Fantini C., Lucchese M. M., Dresselhaus M. S. and Jorio A.: ‘The effect of environment on the radial breathing mode of super growth single wall carbon nanotubes’, Appl. Phys. Lett., 2009, 95, 261902.
   Web of Science ®Google Scholar
• Bachilo S. M., Balzano L., Herrera J. E., Pompeo F., Resasco D. E. and Weisman R. B.: ‘Narrow (n,m)-distribution of single-walled carbon nanotubes grown using a solid supported catalyst’, J. Am. Chem. Soc., 2003, 125, 11186–11187.
   PubMed Web of Science ®Google Scholar
• Araujo P. T., Doorn S. K., Kilina S., Tretiak S., Einarsson E., Maruyama S., Chacham H., Pimenta M. A. and Jorio A.: ‘Third and fourth optical transitions in semiconducting carbon nanotubes’, Phys. Rev. Lett., 2007, 98, 067401.
   Web of Science ®Google Scholar
• Chiashi S., Murakami Y., Miyauchi Y. and Maruyama S.: ‘Temperature dependence of Raman scattering from single-walled carbon nanotubes: undefined radial breathing mode peaks at high temperatures’, Jpn. J. Appl. Phys., 2008, 47, 2010–2015.
   Web of Science ®Google Scholar
• Raravikar N. R., Keblinski P., Rao A. M., Dresselhaus M. S., Schadler L. S. and Ajayan P. M.: ‘Temperature dependence of radial breathing mode Raman frequency of single-walled carbon nanotubes’, Phys. Rev. B, 2002, 66, 235424.
   Web of Science ®Google Scholar
• Uchida T., Tazawa M., Sakai H., Yamazaki A. and Kobayashi Y.: ‘Radial breathing modes of single-walled carbon nanotubes in resonance Raman spectra at high temperature and their chiral index assignment’, Appl. Surf. Sci., 2008, 254, 7591–7595.
   Web of Science ®Google Scholar
• Ghavanloo E. and Fazelzadeh S. A.: ‘Effect of temperature change on the radial breathing mode frequency of single-walled carbon nanotubes’, Nano, 2013, 8, 1350057.
   Google Scholar
• Lucas M. and Young R. J.: ‘Effect of uniaxial strain deformation upon the Raman radial breathing modes of single-wall carbon nanotubes in composites’, Phys. Rev. B, 2004, 69, 085405.
   Google Scholar
• Lucas M. and Young R. J.: ‘Raman spectroscopic study of the effect of strain on the radial breathing modes of carbon nanotubes in epoxy/SWNT composites’, Compos. Sci. Technol., 2004, 64, 2297–2302.
   Web of Science ®Google Scholar
• Lucas M. and Young R. J.: ‘Unique identification of single-walled carbon nanotubes in composites’, Compos. Sci. Technol., 2007, 67, 2135–2149.
   Web of Science ®Google Scholar
• Lucas M. and Young R. J.: ‘Effect of residual stresses upon the Raman radial breathing modes of nanotubes in epoxy composites’, Compos. Sci. Technol., 2007, 67, 840–843.
   Web of Science ®Google Scholar
• Chang T.: ‘Radial breathing mode frequency of single-walled carbon nanotubes under strain’, Appl. Phys. Lett., 2008, 93, 061901.
   Google Scholar
• Nikolic B., Milosevic I. and Damnjanovic M.: ‘Raman intensities of totally symmetrical modes of homogeneously deformed single-walled carbon nanotubes’, J. Phys. Chem. C, 2014, 118, 20576–20584.
   Web of Science ®Google Scholar
• Rafii-Tabar H.: ‘Computational modelling of thermo-mechanical and transport properties of carbon nanotubes’, Phys. Rep., 2004, 390, 235–452.
   Web of Science ®Google Scholar
• Zhao X., Ando Y., Qin L. C., Kataura H., Maniwa Y. and Saito R.: ‘Radial breathing modes of multiwalled carbon nanotubes’, Chem. Phys. Lett., 2002, 361, 169–174.
   Web of Science ®Google Scholar
• Li F., Chou S. G., Ren W., Gardecki J. A., Swan A. K., Ünlü M. S., Goldberg B. B., Cheng H. M. and Dresselhaus M. S.: ‘Identification of the constituents of double-walled carbon nanotubes using Raman spectra taken with different laser-excitation energies’, J. Mater. Res., 2003, 18, 1251–1258.
   Web of Science ®Google Scholar
• Pfeiffer R., Simon F., Kuzmany H., Popov V. N., Zólyomi V. and Kürti J.: ‘Tube-tube interaction in double-wall carbon nanotubes’, Phys. Status Solidi B, 2006, 243, 3268–3272.
   Google Scholar
• Spudat C., Müller M., Houben L., Maultzsch J., Goss K., Thomsen C., Schneider C. M. and Meyer C.: ‘Observation of breathing-like modes in an individual multiwalled carbon nanotube’, Nano Lett., 2010, 10, 4470–4474.
   PubMed Web of Science ®Google Scholar
• Levshov D., Than T. X., Arenal R., Popov V. N., Parret R., Paillet M., Jourdain V., Zahab A. A., Michel T., Yuzyuk Y. I. and Sauvajol J. L.: ‘Experimental evidence of a mechanical coupling between layers in an individual double-walled carbon nanotube’, Nano Lett., 2011, 11, 4800–4804.
   PubMed Web of Science ®Google Scholar
• Liu K., Hong X., Wu M., Xiao F., Wang W., Bai X., Ager J. W., Aloni S., Zettl A., Wang E. and Wang F.: ‘Quantum-coupled radial-breathing oscillations in double-walled carbon nanotubes’, Nat. Commun., 2013, 4, 1375.
   PubMed Web of Science ®Google Scholar
• Ch Hirschmann T., Araujo P. T., Muramatsu H., Zhang X., Nielsch K., Kim Y. A. and Dresselhaus M. S.: ‘Characterization of bundled and individual triple-walled carbon nanotubes by resonant Raman spectroscopy’, ACS Nano, 2013, 7, 2381–2387.
   PubMed Web of Science ®Google Scholar
• Gupta R., Singh B. P., Singh V. N., Gupta T. K. and Mathur R. B.: ‘Origin of radial breathing mode in multiwall carbon nanotubes synthesized by catalytic chemical vapor deposition’, Carbon, 2014, 66, 724–726.
   Web of Science ®Google Scholar
• Popov V. N. and Henrard L.: ‘Breathinglike phonon modes of multiwalled carbon nanotubes’, Phys. Rev. B, 2002, 65, 235415.
   Web of Science ®Google Scholar
• Dobardžić E., Maultzsch J., Milošević I., Thomsen C. and Damnjanović M.: ‘The radial breathing mode frequencyin double-walled carbon nanotubes: an analytical approximation’, Phys. Status Solidi B, 2003, 237, R7–R10.
   Google Scholar
• Wu G., Zhou J. and Dong J.: ‘Radial-breathing-like phonon modes of double-walled carbon nanotubes’, Phys. Rev. B, 2005, 72, 115418.
   Google Scholar
• Wu G. and Dong J.: ‘Anomalous heat conduction in a carbon nanowire: molecular dynamics calculations’, Phys. Rev. B, 2005, 71, 115410.
   Google Scholar
• Xu C. L. and Wang X.: ‘Matrix effects on the breathing modes of multiwall carbon nanotubes’, Compos. Struct., 2007, 80, 73–81.
   Web of Science ®Google Scholar
• Han S. and Goddard W. A.: ‘Coupling of Raman radial breathing modes in double-wall carbon nanotubes and bundles of nanotubes’, J. Phys. Chem. B, 2009, 113, 7199–7204.
   PubMed Web of Science ®Google Scholar
• Ghavanloo E. and Fazelzadeh S. A.: ‘Prediction of radial breathing-like modes of double-walled carbon nanotubes with arbitrary chirality’, Phys. B, 2014, 451, 34–38.
   Web of Science ®Google Scholar
• Lei X. W., Natsuki T., Shi J. X. and Ni Q. Q.: ‘Radial breathing vibration of double-walled carbon nanotubes subjected to pressure’, Phys. Lett. A, 2011, 375, 2416–2421.
   Web of Science ®Google Scholar
• Miao C. Y., Li H. J. and Guo W. L.: ‘Radial breathing modes of multi-walled carbon nanotubes by anatomic beam-spring model’, Sci. China Phys. Mech. Astron., 2012, 55, 940–946.
   Web of Science ®Google Scholar
• Sbai K., Rahmani A., Fakrach B., Chadli H. and Benhamou M.: ‘Modeling and simulation of vibrational breathing-like modes in individual multiwalled carbon nanotubes’, Phys. E, 2014, 56, 312–318.
   Google Scholar
• Yoshida M. and Fowler P. W.: ‘Dihedral fullerenes of threefold symmetry with and without face spirals’, J. Chem. Soc. Faraday Trans., 1997, 93, 3289–3294.
   Google Scholar
• Adhikari S. and Chowdhury R.: ‘Vibration spectra of fullerene family’, Phys. Lett. A, 2011, 375, 2166–2170.
   Web of Science ®Google Scholar
• Jishi R. A., Mirie R. M. and Dresselhaus M. S.: ‘Force-constant model for the vibrational modes in C60’, Phys. Rev. B, 1992, 45, 13685–13689.
   PubMed Web of Science ®Google Scholar
• Chadderton L.: ‘Axisymmetric vibrational modes of fullerene C60’, J. Phys. Chem. Solids, 1993, 54, 1027–1033.
   Web of Science ®Google Scholar
• Kahn D., Kim K. and Stroscio M.: ‘Quantized vibrational modes of nanospheres and nanotubes in the elastic continuum model’, J. Appl. Phys., 2001, 89, 5107–5111.
   Web of Science ®Google Scholar
• Ghavanloo E. and Fazelzadeh S. A.: ‘Nonlocal shell model for predicting axisymmetric vibration of spherical shell-like nanostructures’, Mech. Adv. Mater. Struct., 2015, 22, 597–603.
   Web of Science ®Google Scholar
• Zhou J. and Dong J.: ‘Vibrational property and Raman spectrum of carbon nanoribbon’, Appl. Phys. Lett., 2007, 91, 173108.
   Google Scholar
• Zhou J. and Dong J.: ‘Radial breathing-like mode of wide carbon nanoribbon’, Phys. Lett. A, 2008, 372, 7183–7186.
   Web of Science ®Google Scholar
• Sanders G. D., Nugraha A. R. T., Saito R. and Stanton C. J.: ‘Coherent radial-breathing-like phonons in graphene nanoribbons’, Phys. Rev. B, 2012, 85, 205401.
   Google Scholar
• Xia M., Su Z., Song Y., Han J., Zhang S. and Li B.: ‘Localized vibrational, edges and breathing modes of graphene nanoribbons with topological line defects’, Eur. Phys. J.B, 2013, 86, 344.
   Google Scholar
• Jiang J. W., Wang B. S. and Rabczuk T.: ‘Acoustic and breathing phonon modes in bilayer graphene with Moiré patterns’, Appl. Phys. Lett., 2012, 101, 023113.
   Google Scholar
• Lui C. H., Malard L. M., Kim S., Lantz G., Laverge F. E., Saito R. and Heinz T. F.: ‘Observation of layer-breathing mode vibrations in few-layer graphene through combination Raman scattering’, Nano Lett., 2012, 12, 5539–5544.
   PubMed Web of Science ®Google Scholar
• Lui C. H. and Heinz T. F.: ‘Measurement of layer breathing mode vibrations in few-layer graphene’, Phys. Rev. B, 2013, 87, 121404(R).
   Google Scholar
• Ng M. Y. and Chang Y. C.: ‘Laser-induced breathing modes in metallic nanoparticles: a symmetric molecular dynamics study’, J. Chem. Phys., 2011, 134, 094116.
   Web of Science ®Google Scholar
• Gupta S. K., Sahoo S., Jha P. K., Arora A. K. and Azhniuk Y. M.: ‘Observation of torsional mode in CdS1-xSex nanoparticles in a borosilicate glass’, J. Appl. Phys., 2009, 106, 024307.
   Web of Science ®Google Scholar
• Zhang X., Han W. P., Wu J. B., Milana S., Lu Y., Li Q. Q., Ferrari A. C. and Tan P. H.: ‘Raman spectroscopy of shear and layer breathing modes in multilayer MoS2’, Phys. Rev. B, 2013, 87, 115413.
   Web of Science ®Google Scholar
• Montagna M.: ‘Brillouin and Raman scattering from the acoustic vibrations of spherical particles with a size comparable to the wavelength of the light’, Phys. Rev. B, 2008, 77, 045418.
   Google Scholar
• Voisin C., Del Fatti N., Christofilos D. and Vallée F.: ‘Ultrafast electron dynamics and optical nonlinearities in metal nanoparticles’, J. Phys. Chem. B, 2001, 105, 2264–2280.
   Web of Science ®Google Scholar
• Voisin C., Christofilo D., Del Fatti N. and Vallée F.: ‘Environment effect on the acoustic vibration of metal nanoparticles’, Phys. B, 2002, 31, (6–317), 89–94.
   Google Scholar
• Dubrovskiy V. A. and Morochnik V. S.: ‘Natural vibrations of a spherical inhomogeneity in an elastic medium’, Earth Phys., 1981, 17, 494–504.
   Google Scholar
• Nelet A., Crut A., Arbouet A., Del Fatti N., Vallée F., Portalès H., Saviot L. and Duval E.: ‘Acoustic vibrations of metal nanoparticles: high order radial mode detection’, Appl. Surf. Sci., 2004, 226, 209–215.
   Web of Science ®Google Scholar
• Cheng W., Ren S. F. and Yu P. Y.: ‘Microscopic theory of the low frequency Raman modes in germanium nanocrystals’, Phys. Rev. B, 2005, 71, 174305.
   Google Scholar
• Lamb H.: ‘On the vibrations of a spherical shell’, Proc. Lond. Math. Soc., 1883, 14, 50–56.
   Google Scholar
• Combe N., Huntzinger J. R. and Mlayah A.: ‘Vibrations of quantum dots and light scattering properties: atomistic versus continuous models’, Phys. Rev. B, 2007, 76, 205425.
   Google Scholar
• Mongin D., Juvé V., Maioli P., Crut A., Del Fatti N., Vallée F., ánchez-Iglesias A. S., Pastoriza-Santos I. and Liz-Marzán L. M.: ‘Acoustic vibrations of metal-dielectric core-shell nanoparticles’, Nano Lett., 2011, 11, 3016–3021.
   PubMed Web of Science ®Google Scholar
• Sauceda H. E., Mongin D., Maioli P., Crut A., Pellarin M., Del Fatti N., Vallée F. and Garzón I. L.: ‘Vibrational properties of metal nanoparticles: atomistic simulation and comparison with time-resolved investigation’, J. Phys. Chem. C, 2012, 116, 25147–25156.
   Web of Science ®Google Scholar
• Huang G. Y. and Liu J. P.: ‘Effect of surface stress and surface mass on elastic vibrations of nanoparticles’, Acta Mech., 2013, 224, 985–994.
   Web of Science ®Google Scholar
• Sastry M., Swami A., Mandal S. and Selvakannan P. R.: ‘New approaches to the synthesis of anisotropic, core-shell and hollow metal nanostructures’, J. Mater. Chem., 2005, 15, 3161–3174.
   Web of Science ®Google Scholar
• Portalès H., Goubet N., Saviot L., Adichtchev S., Murray D. B., Mermet A., Duval E. and Piléni M. P.: ‘Probing atomic ordering and multiple twinning in metal nanocrystals through their vibrations’, Proc. Natl. Acad. Sci. U.S.A., 2008, 105, 14784–14789.
   PubMed Web of Science ®Google Scholar
• Saviot L. and Murray D. B.: ‘Acoustic vibrations of anisotropic nanoparticles’, Phys. Rev. B, 2009, 79, 214101.
   Google Scholar
• Saviot L., Murray D. B., Duval E., Mermet A., Sirotkin S. and Marco de Lucas M. C.: ‘Simple model for the vibrations of embedded elastically cubic nanocrystals’, Phys. Rev. B, 2010, 82, 115450.
   Google Scholar
• Ghavanloo E. and Fazelzadeh S. A.: ‘Radial vibration of free anisotropic nanoparticles based on nonlocal continuum mechanics’, Nanotechnology, 2013, 24, 075702.
   Google Scholar
• Fazelzadeh S. A. and Ghavanloo E.: ‘Radial vibration characteristics of spherical nanoparticles immersed in fluid medium’, Mod. Phys. Lett. B, 2013, 27, 1350186.
   Web of Science ®Google Scholar
• Ghavanloo E., Fazelzadeh S. A., Murmu T. and Adhikari S.: ‘Radial breathing-mode frequency of elastically confined spherical nanoparticles subjected to circumferential magnetic field’, Phys. E, 2015, 66, 228–233.
   Google Scholar
• Dresselhaus M. S., Lin Y. M., Rabin O., Jorio A., Souza Filho A. G., Pimenta M. A. and Saito R.: ‘Nanowires and nanotubes’, Mater. Sci. Eng. C, 2003, 23, 129–140.
   Web of Science ®Google Scholar
• Utama M. I. B., Zhang J., Chen R., Xu X., Li D., Sun H. and Xiong Q.: ‘Synthesis and optical properties of II-VI 1D nanostructures’, Nanoscale, 2012, 4, 1422–1435.
   PubMed Web of Science ®Google Scholar
• Hu M., Wang X., Hartland G. V., Mulvaney P., Juste J. P. and Sader J. E.: ‘Vibrational response of nanorods to ultrafast laser induced heating: theoretical and experimental analysis’, J. Am. Chem. Soc., 2003, 125, 14925–14933.
   PubMed Web of Science ®Google Scholar
• Pokatilov E. P., Nika D. L. and Balandin A. A.: ‘Acoustic phonon engineering in coated cylindrical nanowires’, Superlattices Microstruct., 2005, 38, 168–183.
   Web of Science ®Google Scholar
• Staleva H. and Hartland G. V.: ‘Vibrational dynamics of silver nanocubes and nanowires studied by single-particle transient absorption spectroscopy’, Adv. Funct. Mater., 2008, 18, 3809–3817.
   Web of Science ®Google Scholar
• Bourgeois E., Fernández-Serra M. V. and Blasé X.: ‘Radial breathing mode in silicon nanowires: an ab initio study’, Phys. Rev. B, 2010, 81, 193410.
   Google Scholar
• Mitran T. L., Nicolaev A., Nemnes G. A., Ion L. and Antohe S.: ‘Ab initio vibrational and thermal properties of AlN nanowires under axial stress’, Comput. Mater. Sci., 2011, 50, 2955–2959.
   Web of Science ®Google Scholar
• Trejo A., Vazquez-Medina R., Duchen G. I. and Cruz-Irisson M.: ‘Anisotropic effects on the radial breathing mode of silicon nanowires: an ab initio study’, Phys. E, 2013, 51, 10–14.
   Google Scholar
• Martínez-Gutiérrez D. and Velasco V. R.: ‘Acoustic breathing mode frequencies in cylinders, cylindrical shells and composite cylinders of general anisotropic crystals: application to nanowires’, Phys. E, 2013, 54, 86–92.
   Google Scholar
• Huang G. Y. and Kang Y. L.: ‘Acoustic vibrations of a circular nanowire by considering the effect of surface’, J. Appl. Phys., 2011, 110, 023526.
   Google Scholar
• Ghavanloo E., Fazelzadeh S. A. and Rafii-Tabar H.: ‘Nonlocal continuum-based modeling of breathing mode of nanowires including surface stress and surface inertia effects’, Phys. B, 2014, 440, 43–47.
   Web of Science ®Google Scholar