najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/22208054201785635640najo-685Research ArticleCHEMISTRY AND MATERIALS SCIENCEХИМИЯ И НАУКА О МАТЕРИАЛАХEnergetics of carbon nanotubes with open edges: Modeling and experimentZavodinskyV. G.

153, Tikhookeanskaya st., 680042, Khabarovsk

vzavod@mail.ruGorkushaO. A.

54, Dzerzhinskogo st., 680000, Khabarovsk

o_garok@rambler.ruKuz’menkoA. P.

94, 50 let Oktyabrya st., 305040 Kursk

apk3527@mail.ruInstitute for Material ScienceRussian FederationKhabarovsk Department, Institute of Applied MathematicsRussian FederationSouthWest State UniversityRussian Federation20171208202585635–640Copyright © Zavodinsky V.G., Gorkusha O.A., Kuz’menko A.P., 20252025Zavodinsky V.G., Gorkusha O.A., Kuz’menko A.P.Zavodinsky V.G., Gorkusha O.A., Kuz’menko A.P.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/685

Modeling approaches based on the density functional theory (DFT): the Kohn–Sham (KS) method and orbitalfree (OF) method are used to for calculation of the binding energies per atom as functions of the diameter of singlewall carbon nanotubes (SWCNTs) with the open ends. It is shown that this energy has a minimum at a diameter of about 1.1 – 1.2 nm. The experiments made by means of Raman spectroscopy have shown that diameters of SWCNTs mainly lie in the range of 1 – 1.5 nm.

SWCNTenergydiametermodelingKohn–Shamorbital freeRaman spectroscopyThis work is performed with financial support of the Ministry of Education and Science of the Russian Federation within the task No. 16.2814.2017/PCh. One of authors (A. P. Kuz’menko) expresses gratitude to employees of the SouthWest State University (Kursk, Russia) A. E. Kuzko, Thet Phyo Naing, and Myo Min Than.ReferencesLee K., Chong Rae Park. Effects of chirality and diameter of singlewalled carbon nanotubes on their structural stability and solubility parameters. Royal Society of Chemistry Advances, 2014, 4, P. 33578–33581.Lee K., Chong Rae Park. Effects of chirality and diameter of singlewalled carbon nanotubes on their structural stability and solubility parameters. Royal Society of Chemistry Advances, 2014, 4, P. 33578–33581.Chin Li Cheung, Andrea Kurtz, Hongkun Park, Charles M. Lieber. DiameterControlled Synthesis of Carbon Nanotubes. J. Phys. Chem. B, 2002, 106, P. 2429–2433.Chin Li Cheung, Andrea Kurtz, Hongkun Park, Charles M. Lieber. DiameterControlled Synthesis of Carbon Nanotubes. J. Phys. Chem. B, 2002, 106, P. 2429–2433.Eletskiy A.V. Carbon nanotubes. Uspekhi Fizicheskikh Nauk, 1997, 167 (9), P. 945–972 (in Russian).Eletskiy A.V. Carbon nanotubes. Uspekhi Fizicheskikh Nauk, 1997, 167 (9), P. 945–972 (in Russian).Kiang C.H., Goddard III W.A., Beyers R., Bethune D.S. Carbon nanotubes with singlelayer walls. Carbon, 33 (7), P. 903–914.Kiang C.H., Goddard III W.A., Beyers R., Bethune D.S. Carbon nanotubes with singlelayer walls. Carbon, 33 (7), P. 903–914.Boguslavskaya E.S., Bazhin I.V. Mechanical properties of carbon nanotubes and of their contacts. Fazovye perekhody, uporyadochennye sostoyaniya i novye materialy, 2009, 11, 4 p. (in Russian).Boguslavskaya E.S., Bazhin I.V. Mechanical properties of carbon nanotubes and of their contacts. Fazovye perekhody, uporyadochennye sostoyaniya i novye materialy, 2009, 11, 4 p. (in Russian).Hohenberg H., Kohn W. Inhomogeneous electron gas. Phys. Rev. B, 1964, 136, P. 864–871.Hohenberg H., Kohn W. Inhomogeneous electron gas. Phys. Rev. B, 1964, 136, P. 864–871.Kohn W., Sham J.L. Selfconsistent equations including exchange and correlation effects. Phys. Rev. A, 1965, 140, P. 1133–1138.Kohn W., Sham J.L. Selfconsistent equations including exchange and correlation effects. Phys. Rev. A, 1965, 140, P. 1133–1138.Beckstedte M., Kley A., Neugebauer J., Scheffler M. Density functional theory calculations for polyatomic systems: electronic structure, static and elastic properties and ab initio molecular dynamics. Comp. Phys. Commun., 1997, 107, P. 187–205.Beckstedte M., Kley A., Neugebauer J., Scheffler M. Density functional theory calculations for polyatomic systems: electronic structure, static and elastic properties and ab initio molecular dynamics. Comp. Phys. Commun., 1997, 107, P. 187–205.Zavodinsky V.G., Gorkusha O.A. A simple quantummechanics way to simulate nanoparticles and nanosystems without calculation of wave functions. International Scholarly Research Network Nanomaterials, 2012, 531965, 3 p.Zavodinsky V.G., Gorkusha O.A. A simple quantummechanics way to simulate nanoparticles and nanosystems without calculation of wave functions. International Scholarly Research Network Nanomaterials, 2012, 531965, 3 p.Zavodinsky V.G., Gorkusha O.A. QuantumMechanical Modeling without Wave Functions. Physics of the Solid States, 2014, 56 (11), P. 2329–2335.Zavodinsky V.G., Gorkusha O.A. QuantumMechanical Modeling without Wave Functions. Physics of the Solid States, 2014, 56 (11), P. 2329–2335.Zavodinsky V.G., Gorkusha O.A. Development of an orbital free approach for simulation of multiatomic nanosystems with covalent bonds. Nanosystems: Physics, Chemistry, Mathematics, 2016, 7 (3), P. 427–432.Zavodinsky V.G., Gorkusha O.A. Development of an orbital free approach for simulation of multiatomic nanosystems with covalent bonds. Nanosystems: Physics, Chemistry, Mathematics, 2016, 7 (3), P. 427–432.Zavodinsky V.G., Gorkusha O.A. Development of the orbital free approach for heteroatomic systems. Nanosystems: Physics, Chemistry, Mathematics, 2016, 7 (6), P. 1010–1016.Zavodinsky V.G., Gorkusha O.A. Development of the orbital free approach for heteroatomic systems. Nanosystems: Physics, Chemistry, Mathematics, 2016, 7 (6), P. 1010–1016.Wang Y.A., Carter E.A. Theoretical Methods in Condensed Phase Chemistry. In Progress in Theoretical Chemistry and Physics, Kluwer, Dordrecht, 2000, P. 117–184.Wang Y.A., Carter E.A. Theoretical Methods in Condensed Phase Chemistry. In Progress in Theoretical Chemistry and Physics, Kluwer, Dordrecht, 2000, P. 117–184.Huajie Chen, Aihui Zhou. Orbitalfree density functional theory for molecular structure calculations. Numerical Mathematics: Theory, Methods and Applications, 2008, 1 (1), P. 1–28.Huajie Chen, Aihui Zhou. Orbitalfree density functional theory for molecular structure calculations. Numerical Mathematics: Theory, Methods and Applications, 2008, 1 (1), P. 1–28.Karasiev V.V., Jones R.S., Trickey S.B., Harris F.E. Recent advances in developing orbitalfree kinetic energy functionals. In New Developments in Quantum Chemistry, 2009, P. 25–54.Karasiev V.V., Jones R.S., Trickey S.B., Harris F.E. Recent advances in developing orbitalfree kinetic energy functionals. In New Developments in Quantum Chemistry, 2009, P. 25–54.Chakraborty D. Computing the kinetic energy from electron distribution functions. Ph.D. (Chemistry) Thesis, McMaster University, Hamilton, Ontario, Canada, 2011.Chakraborty D. Computing the kinetic energy from electron distribution functions. Ph.D. (Chemistry) Thesis, McMaster University, Hamilton, Ontario, Canada, 2011.Huang C., Carter E.A. Nonlocal orbitalfree kinetic energy density functional for semiconductors. Phys. Rev. B, 2010, 81, 045206–15.Huang C., Carter E.A. Nonlocal orbitalfree kinetic energy density functional for semiconductors. Phys. Rev. B, 2010, 81, 045206–15.Ho G.S., Ligneres V.L., Carter E.A. Introducing PROFESS: A new program for orbitalfree density functional theory calculations. Comp. Phys. Commun., 2008, 179, P. 839–854.Ho G.S., Ligneres V.L., Carter E.A. Introducing PROFESS: A new program for orbitalfree density functional theory calculations. Comp. Phys. Commun., 2008, 179, P. 839–854.Sarry A.M., Sarry M.F. On the density functional theory. Fizika Tverdogo Tela, 2012, 54 (6), P. 1237–1243 (in Russian).Sarry A.M., Sarry M.F. On the density functional theory. Fizika Tverdogo Tela, 2012, 54 (6), P. 1237–1243 (in Russian).Bobrov V.B., Trigger S.A. The problem of the universal density functional and the density matrix functional theory. J. Exper. Theor. Phys., 2013, 116 (4), P. 635–640.Bobrov V.B., Trigger S.A. The problem of the universal density functional and the density matrix functional theory. J. Exper. Theor. Phys., 2013, 116 (4), P. 635–640.Perdew J.P., Wang Y.A. Accurate and simple density functional for the electronic exchange energy. Phys. Rev. B, 1986, 33, P. 8800–8802.Perdew J.P., Wang Y.A. Accurate and simple density functional for the electronic exchange energy. Phys. Rev. B, 1986, 33, P. 8800–8802.Huhtala M., Kuronen A., Kimmo Kaski. Computational studies of carbon nanotube structures. Computer Physics Communications, 2002, 147, P. 91–96.Huhtala M., Kuronen A., Kimmo Kaski. Computational studies of carbon nanotube structures. Computer Physics Communications, 2002, 147, P. 91–96.Danilov C.V. Simulation of atomic structure and the XRay structure analysis of carbon nanotubes. PhD Thesis, Petrozavodsk State University, Petrozavodsk, Russia, 2013 (in Russian).Danilov C.V. Simulation of atomic structure and the XRay structure analysis of carbon nanotubes. PhD Thesis, Petrozavodsk State University, Petrozavodsk, Russia, 2013 (in Russian).Barnard A.S., Russo S.P., Snook I.K. Surface structure of cubic diamond nanowires. Surf. Sci., 2003, 538, P. 204–210.Barnard A.S., Russo S.P., Snook I.K. Surface structure of cubic diamond nanowires. Surf. Sci., 2003, 538, P. 204–210.Cheng Yang, H. Chuan Kang. Cluster study of the dimer geometry on the C(100) surface. Surf. Sci., 1998, 409, P. 521–527.Cheng Yang, H. Chuan Kang. Cluster study of the dimer geometry on the C(100) surface. Surf. Sci., 1998, 409, P. 521–527.Kuzmenko A.P., Thet Phyo Naing, et al. Selfassembly and Selforganization Processes of Carbon Nanotubes in the Colloidal Systems. J. of Nanoand Electronic Physics, 2015, 7 (4), P. 04014(3).Kuzmenko A.P., Thet Phyo Naing, et al. Selfassembly and Selforganization Processes of Carbon Nanotubes in the Colloidal Systems. J. of Nanoand Electronic Physics, 2015, 7 (4), P. 04014(3).Thomsen C., Reich S. Raman scattering in carbon nanotubes. Topics Appl. Physics, 2007, 108, P. 115–232.Thomsen C., Reich S. Raman scattering in carbon nanotubes. Topics Appl. Physics, 2007, 108, P. 115–232.

The authors declare that there are no conflicts of interest present.