Vol.5, No 1, 2007 pp. 11 - 18
DOI 10.2298/FUPCT0701011K
UDC 547
APPLICATION OF THOMAS-FERMI MODEL TO
FULLERENE MOLECULE AND NANOTUBE
Yuri Kornyushin
Maître Jean Brunschvig Research Unit Chalet Shalva, Randogne, CH-3975
Abstract. Semiclassical description, based on electrostatics and Thomas-Fermi model is applied here to calculate dimensions of the electronic shell of a fullerene molecule and a nanotube. The internal radius of the electronic shell of a fullerene molecule, calculated within the framework of the model is 0.2808 nm. The external radius is 0.4182 nm. The experimental values are 0.279 nm and 0.429 nm correspondingly. This shows that semiclassical approach provides rather good description of the dimensions of the electronic shell in a fullerene molecule. Two types of dipole oscillations in a fullerene molecule are considered and their frequencies are calculated. Similar calculations are performed for a nanotube also. For a nanotube with a radius of the cylinder of the ions, Rn = 0.7 nm, the internal radius of the electronic shell, calculated within the framework of the model is 0.577 nm. The external radius is 0.816 nm. Three types of dipole oscillations in nanotube are considered and their frequencies are calculated.
PRIMENA THOMAS-FERMIJEVOG MODELA NA
MOLEKULE FULERENA I NANOTUBE
U ovom radu su primenom poluklasičnog pristupa zasnovanog na elektrostatičkom i Thomas-Fermijevom modelu izračunate dimenzije elektronske ljuske molekula fulerena i nanotuba. Izračunata vrednost unutrašnjeg poluprečnika elektronske ljuske molekula fulerena je 0.2808 nm, a spoljašnjeg 0.4182 nm. Odgovarajuće eksperimentalno određene vrednosti su 0.279 nm i 0.429 nm. Ovo slaganje pokazuje da poluklasičan pristup dobro opisuje veličinu elektronske ljuske molekula fulerena. Razmatrana su i dva tipa dipolnih oscilacija u tim molekulima i izračunate su njihove frekvencije. Slični proračuni su primenjeni i za nanotubu. Za nanotubu sa poluprečnikom jonskog cilindra Rn = 0.7 nm, unutrašnji poluprečnik elektronske ljuske izračunat na osnovu ovog modela je 0.577 nm, a spoljašni 0.816 nm. Takođe su razmatrana i tri tipa dipolnih oscilacija nanotube i izračunate su njihove frekvencije.
