Физика твердого тела, 1999, том 41, вып. 5 Electronic and Optical Properties of Fullerene Nanostructures © Yu.I. Prilutski, S.S. Durov Kiev Shevchenko University, 252033 Kiev, Ukraine E-mail: firstname.lastname@example.org Two new types of molecular/electronic fullerene nanostructures are considered: 1) highly stable hydrated clusters (Ih symmetry group) and microcrystals (Th symmetry group) of fullerene C60 in water solution and 2) the single-walled carbon nanotube from C60 fullerenes. The vibrational spectra of these fullerene nanostructures are calculated using the molecular dynamics approach. The electronic properties of a single-walled fullerene nanotube are investigated using the tight-binding method. The obtained theoretical results were compared with available experimental data.
Fullerenes are widely investigated currently and have 1. Study of Vibrational Spectrum potential for various technical applications . In particular, of Fullerene Aggregates C60 in Water for biomedical testing, water-soluble forms of fullerenes are undoubtedly of great interest. Poor solubility in water of Using the atom-atom potential method, the dense-packing fullerenes and their derivatives limits biological and medical and symmetry principles we have calculated the structure of studies, even though there were reports on successfully fullerene aggregates C60 in water solution . The main prepared micro- and macro-colloidal particle solutions in results obtained were as follows: a) the spherical clusters (Ih organic solvents or in water [2–7]. In particular, G.V. An- symmetry group) with the diameter of 3.56 nm containing drievsky with collaborators [5–7] has recently proposed 33 molecules of C60 (see Fig. 1) were shown to be the most a method for obtaining molecular-colloidal dispersions of stable ones among possible hydrated aggregates; b) possible fullerenes in water without any stabilizers and this resulted existence of stable hydrated microcrystals C60 (the space in the generation of solutions with fullerene aggregate sizes group is Th, the lattice parameters are a = 1.002 nm and from several nanometers to 200 nm. These aggregates c = 1.636 nm ) having a linear size of (2.51-5.84) nm have been consisted of more small spherical particles with in water solution of fullerenes was stated; c) the water effect on a geometry of the fullerene aggregates was discussed;
diameter approximately 2-3 nm containing 4-13 molecules d) the obtained theoretical results were experimentally of C60 . The fullerene water solutions (FWS), being confirmed.
molecular-colloidal systems, were found to be stable for more than 12 months at ambient conditions. At present The calculated vibrational frequencies of the most stable time, the highest concentration of C60 achieved in the FWS hydrated fullerene cluster consisted of 33 of C60 molecules is 1.4g/l [5–7]. It should be noted that the formation of ( = (14-152) cm-1) lie significantly lower the fundasimilar fullerene C60 structures in different organic solvents mental intramolecular modes for the individual C60 fullerene ( =(296-1590) cm-1) . The Raman spectrum of this was not observed [2–4] showing an important influence of cluster is represented in table 1.
water on their formation and existence [5–7].
The discovery of single-walled carbon nanotubes [8,9] have provided the opportunity to study their mechanical, Table 1. The calculated Raman frequencies (cm-1) of hydrated optical and electronic properties [10,11]. Specifically, their fullerene cluster consisted of 33 of C60 molecules electronic characteristics are predicted to vary depending upon the nanotube symmetry and diameter, thus giving Theory Theory  Symmetry (cluster C60) (molecule C60) either metallic or semiconducting behaviour . It is very important for the creation of novel materials for Hg 14 nanoengineering.
Hg 28 Ag 33 The geometric structure of possible fullerene aggregates in Hg 58 water was studied in detail in paper . The present paper Hg 63 is devoted to the calculation of the vibrational spectrum of Hg 82 fullerene aggregates in water solution and the structure of a Hg 85 single-walled fullerene nanotube (SWFN), as well as its elecHg 94 tronic and optical properties. The obtained theoretical results Ag 101 Hg 103 were compared with available experimental data [13–15].
886 Yu.I. Prilutski, S.S. Durov 2. Study of Electronic and Vibrational Properties of the SWFN The simulated structure of the SWFN is presented in Fig. 2.
The radius and the length of ideal part of a nanotube are equal to 0.35 nm  and 0.43 nm, correspondingly.
As is known [1,11], the dependence of the gap on the radius R of a single-walled carbon nanotube may be approximately described by the formula dg =.
R In our case, is the average energy of interaction between two -electrons located on the single and double bonds in the C60 molecule; d0 is the average distance between the neighbouring carbon atoms in the C60 molecule.
The numerical calculations carried out by using the tightbinding method  has shown that = 2.35 eV and d0 = 0.14 nm. The presence of a heptagon-heptagon pair as a defect in the structure of the SWFN leads to the change of its radius from 0.35 to 0.38 nm (the average distance between the neighbouring carbon atoms in the heptagon Figure 1. The calculated structure of a fullerene cluster consisted is equal to d0 too). As a result, the decrease of the gap of 33 of C60 molecules.
from 0.94 to 0.87 eV takes place. Thus, the semiconductorsemiconductor heterojunction with different values of the gap is formed. It should be noted that the similar heteroTable 2. The calculated limiting (k = 0) intermolecular frequencies (cm-1) of hygrated microcrystal CTheory Theory  Symmetry (microcrystal C60) (solid C60) Au 21 Eu 27 Fu 23 Fu 30 Ag 13 Figure 2. The calculated structure of a single-walled fullerene Eg 14 nanotube.
Fg 9 Fg 11 Fg 18 The limiting intermolecular spectrum of hydrated microcrystal C60 is represented in table 2. As we can see the Table 3. The calculated and experimental Raman-active vibracalculated vibrational frequencies lie lower the fundamental tional frequencies (cm-1) for the single-walled nanotube modes for solid C60 .
Symmetry Theory Experiment  It should be noted that low vibrational frequencies of fullerene cluster C60 (2Hg and Ag modes, see table 1) can coHg 119 incide with some intermolecular frequencies of microcrystal Hg 190 C60 (Eg, Eu and Fu modes, see table 2). Ag 396 Hg 770 The numerical calculations were carried out in the apHg 885 proximation of a Lennard-Jones (12-6) atom-atom potential Hg 1356 only (the entropy factor did not consider because an assumpHg 1525 tion was made that the formation of orientationally ordered Hg 1549 structures in water takes place ) using the proposed Ag 1583 Hg 1606 molecular dynamics model for a fullerene crystal C60 .
Физика твердого тела, 1999, том 41, вып. Electronic and Optical Properties of Fullerene Nanostructures junction was really observed in the experiment [13,14] for  Yu.I. Prilutski. Ukr. Fiz. Zhurn. 43, 12, 1245 (1998).
 R. Saito, G. Dresselhaus, M.S. Dresselhaus. Phys. Rev. B53, 4, the single-walled carbon nanotube with a pentagon-heptagon 2044 (1996).
 P. Lauginie, J. Conard. J. Phys. Chem. Solids 58, 9, The calculated vibrational frequencies of the SWFN (1997).
(in the framework of the proposed molecular dynamics  A.M. Rao, E. Richter, S. Bandow, B. Chase, P.C. Eklund, model ) lie in the range of =(49-1744) cm-1. The K.A. Williams, S. Fang, K.R. Subbaswamy, M. Menon, Raman spectrum of this nanotube is represented in table 3.
A. Thess, R.E. Smalley, G. Dresselhaus, M.S. Dresselhaus.
As we can see, they are in a satisfactory agreement with Science 275, 5235, 187 (1997).
the available experimental results  for the single-walled  W. Kraetschmer, L.D. Lamb, K. Fostiropoulos, D.R. Huffman.
carbon nanotube of ”armchair” configuration.
Nature 347, 6291, 354 (1990).
 Yu.I. Prilutski, V.O. Gubanov, S.S. Durov. Ukr. Fiz. Zhurn. 42, 9, 1143 (1997).
3. Conclusion  Yu.I. Prilutski, G.G. Shapovalov. Phys. Stat. Sol. (b) 201, 2, 361 (1997).
The main results obtained are as follows.
 H.W. Kroto, J.R. Health, S.C. O’Breine, R.F. Curl, R.E. Smalley.
1) The vibrational spectra of possible fullerene aggregates Nature 318, 6042, 162 (1985).
C60 in water (clusters (Ih symmetry group) and microcrys-  J.Q. You, F. Nori, Y.L. Lin. Solid State Commun. 91, 2, (1994).
tals (Th symmetry group)) are calculated using the molecular dynamics approach . The obtained theoretical results can be useful for the further optical experiments;
2) As a model for the calculation of electronic and optical of a single-walled carbon nanotube, the nanotube formed of the C60 molecules was proposed. The presence of a heptagon-heptagon pair as a defect in the structure of this nanotube leads to the formation of the semiconductorsemiconductor heterojunction with the different value of gap. The electronic characteristics and vibrational spectrum of a single-walled fullerene nanotube are investigated using the molecular dynamics model  and the tight-binding method . The obtained theoretical results are in a good agreement with the available experimental data [13–15].
References  M.S. Dresselhaus, G. Dresselhaus, P.C. Eklund. Science of Fullerenes and Carbon Nanotubes. Academic Press, N. Y.
 T. Anderson, K. Nilsson, M. Sundahl, G. Westman, O. Wennerstrom. J. Chem. Soc., Chem. Commun. 8, 604 (1992).
 R.S. Ruoff, D.S. Tse, M. Malhotra, D.C. Lorents. J. Phys. Chem.
97, 13, 3379 (1993).
 W.A. Scrivens, J.M. Tour, K.F. Creek, L. Pirisi. J. Am. Chem.
Soc. 116, 10, 4517 (1994).
 G.V. Andrievsky, M.V. Kosevich, O.M. Vovk, V.S. Shelkovsky, L.A. Vashchenko. J. Chem. Soc., Chem. Commun. 12, (1995).
 G.V. Andrievsky, V.K. Klochkov, A.D. Roslyakov, A.Yu. Platov. International Workshop ”Fullerenes and Atomic clusters”. Abstracts of invited lectures and contributed papers.
St.etersburg, Russia (1977). P. 262.
 N.O. Mchedlov-Petrossyan, V.K. Klochkov, G.V. Andrievsky.
J. Chem. Soc. Faraday Trans. 93, 24, 4343 (1997).
 S. Iijima, T. Ichihashi. Nature 363, 6351, 603 (1993).
 D.S. Bethune, C.H. Kiang, M.S. de Vries, G. Gorman, R. Savoy, J. Vazquez, R. Beyers. Nature 363, 6351, 605 (1993).
 N. Hamada, S.I. Sawada, A. Oshiyama. Phys. Rev. Lett. 68, 12, 1579 (1992).
 C.T. White, D.H. Robertson, J.W. Mintemire. Phys. Rev. B47, 2, 5485 (1993).
Физика твердого тела, 1999, том 41, вып.