Application of Thomas-Fermi model to fullerene molecule and nanotube

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.U ovom radu su primenom poluklasicnog pristupa zasnovanog na elektrostatickom i Thomas- Fermijevom modelu izracunate dimenzije elektronske ljuske molekula fulerena i nanotuba. Izracunata vrednost unutrasnjeg poluprecnika elektronske ljuske molekula fulerena je 0.2808 nm, a spoljasnjeg 0.4182 nm. Odgovarajuce eksperimentalno odredjene vrednosti su 0.279 nm i 0.429 nm. Ovo slaganje pokazuje da poluklasican pristup dobro opisuje velicinu elektronske ljuske molekula fulerena. Razmatrana su i dva tipa dipolnih oscilacija u tim molekulima i izracunate su njihove frekvencije. Slicni proracuni su primenjeni i za nanotubu. Za nanotubu sa poluprecnikom jonskog cilindra Rn = 0.7 nm, unutrasnji poluprecnik elektronske ljuske izracunat na osnovu ovog modela je 0.577 nm, a spoljasnji 0.816 nm. Takodje su razmatrana i tri tipa dipolnih oscilacija nanotube i izracunate su njihove frekvencije.