Light-emitting conjugated molecule containing 1,3,4-oxadiazole, carbazole and naphthalene units

Article abstract of DOI:10.1016/j.saa.2005.04.036

A novel π-conjugated small molecule VNCO, 2,5-bis{3′-[3″-vinyl-9″-(α-naphthyl)carbazolyl]phenyl} -1,3,4-oxadiazole, containing hole-transporting carbazole moieties, electron-injecting 1,3,4-oxadiazole moieties and chromophore naphthalene was designed and synthesized by Wittig reaction of 2,5-bis(3-tolylene-triphenylphosphonium bromide)-1,3,4-oxadiazole and 3-formyl-9-(α-naphthyl)carbazole. The UV-vis absorption, fluorescence excitation and emission spectra have been obtained in solution for VNCO. The photoluminescence (PL) of VNCO were examined in different solvents and the luminescence quantum yield was 0.746 in chloroform. It emitted blue and blue-green light, with the band gap of 3.30 eV estimated from the onset absorption. In addition, the light-emitting can be quenched by both electron donor (N,N-dimethylaniline) and electron acceptor (dimethylterephalate). Furthermore, the molecular interactions of VNCO with fullerene (C₆₀) or carbon nanotubes (CNTs) were also carefully investigated.

Full text of DOI:10.1016/j.saa.2005.04.036

Spectrochimica Acta Part A 63 (2006) 15–20
Light-emitting conjugated molecule containing 1,3,4-oxadiazole,
carbazole and naphthalene units
∗
Liheng Feng, Zhaobin Chen
School of Chemistry and Chemical Engineering, Shanxi University, Taiyuan 030006, PR China
Received 24 January 2005; accepted 6 April 2005
Abstract
ꢀ
ꢀꢀ
ꢀꢀ
A novel ␲-conjugated small molecule VNCO, 2,5-bis{3 -[3 -vinyl-9 -(␣-naphthyl)carbazolyl]phenyl}-1,3,4-oxadiazole, containing hole-
transporting carbazole moieties, electron-injecting 1,3,4-oxadiazole moieties and chromophore naphthalene was designed and synthesized by
Wittig reaction of 2,5-bis(3-tolylene-triphenylphosphonium bromide)-1,3,4-oxadiazole and 3-formyl-9-(␣-naphthyl)carbazole. The UV–vis
absorption, fluorescence excitation and emission spectra have been obtained in solution for VNCO. The photoluminescence (PL) of VNCO
were examined in different solvents and the luminescence quantum yield was 0.746 in chloroform. It emitted blue and blue–green light,
with the band gap of 3.30 eV estimated from the onset absorption. In addition, the light-emitting can be quenched by both electron donor
(
N,N-dimethylaniline) and electron acceptor (dimethylterephalate). Furthermore, the molecular interactions of VNCO with fullerene (C60) or
carbon nanotubes (CNTs) were also carefully investigated.
2005 Elsevier B.V. All rights reserved.
©
Keywords: Light-emitting; Wittig reaction; Fullerene (C60); Carbon nanotubes (CNTs)
1
. Introduction
for combining the electron-injecting group, hole-transporting
group and chromophore in the same molecule.
Organic semiconducting materials including polymers,
oligomers, and small molecules are a subject of high inter-
est as potential active materials in optoelectronic devices
Many researches show that carbazole and its derivatives
are good hole-transport materials and have been used in
construction of light-emitting device (LEDs) [10,11]; several
ꢀ
[
1]. These materials are characterized by a low driving volt-
1,3,4-oxadiazole (OXD) derivatives, such as 2-(4 -biphe-
ꢀ
age, uniform luminance, the manifestation of various colors,
the ability to easily form patterns and nanoscale films, and
the capacity for mass production [2,3]. Since the found of
polymer light-emitting diodes (PLEDs) based on poly (p-
phenylenevinylene) (PPV) by the Cambridge group, many
researchers have made some efforts to develop light-emitting
nylyl)-5-(4 -tert-butylphenyl)-1,3,4-oxadi-azole (PBD) have
been actually used as electron-injection materials to im-
prove the balance of charge carrier and to increase the pho-
ton/electron quantum efficiency [12–15]. In this study, we de-
signed and synthesized ␲-conjugated small molecule VNCO
bearing hole-transporting carbazole moieties, electron-
injecting 1,3,4-oxadiazole moieties and chromophore naph-
thalene. The synthesis was carried out by Wittig reaction of
2,5-bis(3-tolylene-triphenylphosphonium bromide)-1,3,4-
oxadiazole and 3-formyl-9-(␣-naphthyl)carbazole. The
absorption, fluorescence excitation and emission spectra
have been obtained in solution for VNCO. The photolu-
minescence (PL) of VNCO were examined in different
solvents. The quenching processes of VNCO with electron
donor N,N-dimethylaniline (DMA), and electron acceptor,
dimethylterephthalate (DMTP) were studied. Moreover, the
(
LE) molecules that exhibit both high LE efficiency and high
stability, properties that are directly related to the perfor-
mance and reliability of LED [4,5]. Low LE efficiency in
LEDs is attributed mainly to an imbalance in the transporta-
tion rates of the electrons and holes in LE layer [6–9]. To
overcome the problem of low LE efficiency, it is desired
∗
Corresponding author. Tel.: +86 351 7011492; fax: +86 351 7011688.
E-mail address: zchen@sxu.edu.cn (Z. Chen).
1
386-1425/$ – see front matter © 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.saa.2005.04.036

1
6
L. Feng, Z. Chen / Spectrochimica Acta Part A 63 (2006) 15–20
molecular interactions of VNCO with fullerene (C ) or
carbon nanotubes (CNTs) were also investigated.
MS D300. Elemental analyses were performed on a Vario EL
elemental analysis instrument (Elementar Co.) UV–vis and
fluorescence spectra were obtained on a Shimadzu UV-265
spectrophotometer and Shimadzu RF-540 spectrofluorotho-
tometer, respectively. Luminescence spectrometer was with a
xenon lamp as the light source. Both excitation and emission
bands were set at 5 nm. All the experiments were carried out
60
2
. Experimental
2
.1. Materials and instruments
◦
at 15 ± 1 C.
The reagents and chemicals for preparation of com-
pounds were used as received unless noted otherwise.
Ethanol, dichloromethane, toluene, chloroform, ethylacetate,
petroleum ether, etc. were purchased from Beijing Chemical
Plant and treated according to standard methods used before,
which were all applied to measurement of the light-emitting
properties. The synthetic route used is shown in Scheme 1.
Melting points were determined on a Sanyo Gallenkamp
MPD350 melting point apparatus and uncorrected. The IR
spectra were determined on a PE-1700 IR spectrophotome-
2.2. Preparation of materials
2.2.1. Preparation of 9-(α-naphthyl)carbazole [16]
Place 0.05 mol of carbazole, 0.054 mol of ␣-bromo-
naphthanlene, 50 mol of potassium carbonate, 0.008 mol of
copper powder and 100 ml of nitrobenzene in three-necked
flask equipped with a mechanical stirrer, dropping funnel and
a Claisen still-head which was fitted with a thermometer and
a condenser. The reaction mixture was stirred vigorously and
heated on an oil hath to gentle reflux. The water produced
from the reaction together with some nitrobenzene was dis-
tilled from the reaction system. After refluxing for 10 h, the
1
ter by dispersing samples in KBr disks. H NMR spectra were
measured on a Bruker ARX300 spectrometer with DMSO as
solvent. Mass spectrum dates were obtained on a JEOL GC-
Scheme 1. The synthetic routes of compounds.

L. Feng, Z. Chen / Spectrochimica Acta Part A 63 (2006) 15–20
17
reaction mixture was cooled and the solvent, nitrobenzene,
3. Results and discussion
with the unreacted halides were removed by steam distil-
lation. The residue was filtered at the pump, washed well
with water and dried in the air. The crude products were
purified by recrystallization or silica gel column chromatog-
raphy (eluent: ethyl acetate:n-hexane = 1:10). Yield: 71%,
3.1. The synthesis of compounds
9-(␣-Naphthyl)carbazole could be obtained via the
C N coupling reaction, Cu(0) as catalyst, by employ-
ing ␣-bromonaphthanlene and carbazole. 3-Formyl-9-(␣-
naphthyl)carbazole was synthesized by two-step strategy,
and reaction temperature have a significant influence on
the reaction. It have been found by experiment that
◦
−1
m.p. 123–124 C, IR (KBr pellet) cm : 3020, 1600, 1580,
1
1
470, 775, 765, 750,725; H NMR (CDCl3): δ: 6.88–8.24
(
m, 15H). Anal. Calcd for C22H N: C, 90.06; H, 5.16; N,
15
4
.77. Found: C, 89.76; H, 5.03; N, 4.41.
◦
ꢀ
the suitable reaction temperature was 110 C. 2,5-Bis{3 -
ꢀꢀ ꢀꢀ
[
3 -vinyl-9 -(␣-naphthyl)carbazolyl]-1,3,4-oxadiazole was
2
.2.2. 3-Formyl-9-(α-naphthyl)carbazole [17]
To 0.2 mol of N,N-dimethyl formamide cooled to 0 C
◦
synthesized by 3-formyl-9-(␣-naphthyl)carbazole 2,5-bis(3-
tolylene-triphenylphosphonium bromide)-1,3,4-oxadiazole
via Wittig reaction.
Comparing the IR spectrum of 3-formyl-9-(␣-
naphthyl)carbazole with that of 9-(␣-naphthyl)carbazole
evidences the formation of the aldehyde group. The
most obvious change of the IR after Vilsmeier reaction
was added dropwise 0.2 mol of phosphorous oxychloride.
The mixture was left to stand for 1 h at room temperature
to complete the formation of the complex reagent. 0.02 mol
of 9-(␣-naphthyl)carbazole in the reaction solvent were then
◦
added. The reaction mixture was heated to 110 C with stir-
ring for 24 h and poured into broken ice. After neutraliz-
ing with base, the mixture was extracted with chloroform
and dried with anhydrous magnesium sulfate. The solvent
was removed by distillation in vacuum, giving the solid
residue. The crude product was purified by silica gel col-
umn chromatography (eluent: ethyl acetate:n-hexane = 1:3).
−1
is the appearance of a new peak at 1690 cm , which
indicates that C O structure is introduced into 3-formyl-
9
-(␣-naphthyl)carbazole. In addition, from IR spectrum
ꢀ
ꢀꢀ
ꢀꢀ
of 2,5-bis{3 -[3 -vinyl-9 -(␣-naphthyl)carbazolyl]-1,3,4-
−
1
oxadiazole, the disappearance of 1690 cm (C O) and the
appearance of 1602 cm 1
−
(
) indicate that the target
◦
−1
Yield: 42%, m.p. 168–169 C. IR (KBr pellet) cm : 3015,
2
1
compound VNCO is successfully synthesized by Wittig
reaction.
754, 1690, 1600, 1238, 820, 800, 770. H NMR (CDCl3):
δ 7.5–8.6(m, 14H), 10.05(s, 1H). MS (m/z): 321(M ), 292,
+
1
27.
3.2. UV–vis absorption and fluorescence excitaion and
emission spectrum
2
.2.3. 2,5-Bis(3-tolylene-triphenylphosphonium
bromide)-1,3,4-oxadiazole
,5-Bis(3-tolylene-triphenylphosphonium bromide)-1,3,
-oxadiazole was synthesized by the previous work [18].
Fig. 1 shows the UV–vis absorption, photoluminescence
PL) excitation and the PL emission spectra of VNCO in
dilute chloroform solution. The UV–vis absorption spectra of
2
(
4
VNCO solution in chloroform showed absorption peak (λab)
around 240 nm attributable to the naphthalene, carbazole
ꢀ ꢀꢀ ꢀꢀ
.2.4. 2,5-Bis{3 -[3 -vinyl-9 -(α-
2
naphthyl)carbazolyl]phenyl}-1,3,4-oxadiazole (VNCO)
19]
The freshly prepared sodium ethoxide (0.24 mol) were
and oxadizole rings and a shoulder 273 nm that is assigned
[
*
to the ␲–␲ transition of the conjugation backbone. The
◦
added at 0 C to a well stirred solution of appropriated
-formyl-9-(␣-naphthyl)carbazole (0.04 mol) and 2,5-bis(3-
tolylene-triphenyl-phosphonium bromide)-1,3,4-oxadiazole
3
(
0.02 mol) in anhydrous THF (30 mL) under nitrogen atmo-
◦
sphere. After the resulting suspension was stirred at 0 C
for 1 h, the corresponding reaction mixture was stirred at
◦
7
0 C for 12 h; the solvent was removed under reduced pres-
sure. Then, the mixture was diluted with ethyl acetate and
washed with 1N HCl and water. The organic extract was dried
(MgSO4) and concentrated under reduced pressure. Chro-
matography of the residue eluting with ethyl acetate/hexanes
(
5
1
1:7) mixture gave analytically pure compounds. Yield:
−
1
2%, IR (KBr pellet) cm : 2934, 2865, 1610, 1500, 1480,
1
418, 1074, 804, 696; H NMR (DMSO): δ: 7.54–8.72(m,
aromatic and olefinic). Anal. Calcd for C H40N4O: C,
62
8
6
6.91; H, 4.67; N, 6.55. Found: C, 86.98; H, 4.66; N,
.52.
Fig. 1. The UV–vis absorption and fluorescence excitation, emission spec-
trum of VNCO.

1
8
L. Feng, Z. Chen / Spectrochimica Acta Part A 63 (2006) 15–20
Fig. 2. The emission spectra of VNCO in different solvents.
Fig. 3. Fluorescence spectra of VNCO at different concentration of
−
6
DMA. Concentration of VNCO, 8.63 × 10 mol/L; concentration of DMA
−
5
−5
−5
(
1
mol/L), 0, 0.00; (1) 1.34 × 10 ; (2) 3.36 × 10 ; (3) 7.39 × 10 ; (4)
PL excitation spectra were overlapped with the absorption
spectra and displayed maximum (λex,max) at 283 nm. VNCO
emitted blue and blue–green light with emission maximum
−
4
−4
.
.55 × 10 ; (5) 3.13 × 10
3.5. The quenching processes of fluorescence of VNCO
(
λ
f,max) at 375 nm.
with N,N-dimethylaniline (DMA) and
dimethylterephthalate (DMTP)
3
.3. Solvent effects on photoluminescence (PL)
The compound VNCO has good solubility in common
organic solvents, such as ethanol, acetonitrile, chloroform,
toluene, etc. The emission spectra of VNCO are investigated
in different solvents and all results are showed in Fig. 2. It
can be seen from Fig. 2 that with the increase of the solvents
polarity, the emission spectra of VNCO are red shift from
N,N-dimethylaniline (DMA) is a typical electron donor
and dimethylterephalate (DMTP) is a typical electron accep-
tor. When DMA is added to a solution of VNCO in chloro-
form, the fluorescence of VNCO is efficiently quenched and
the quenching process follows the Stern–Volmer equation.
4
−1
The apparent quenching coefficient, Ksv, is 1.46 × 10 M
(as shown in Fig. 3). In order to go further into the fluores-
3
64 to 394 nm and half-peak breadth are gradually widened.
cence quenching of VNCO, the quenching process of VNCO
with DMTP is also examined and shown in Fig. 4. It can be
seen that the emission intensity of fluorescence are initially
increased and then decreased with gradual increasing in con-
centration of VNCO in chloroform. Meanwhile, the emission
peaks show red-shifted about 15 nm. From the experimental
facts and references, an explanation is proposed: carbazole
It is well known that the emission spectra of chromophore
red shift with the increase of the solvents polarity due to the
dipole–dipole interaction of the excited state.
3
gap
.4. Quantum yield of photoluminescence and the band
The fluorescence quantum yield was measured by relative
method using the quinine sulfate as the standard (0.546 in
−
1
0
.5 mol L H2SO4) [20]. The quantum yield was calculated
from the following equation:
ꢀ
ꢁ
2
Fs Ar nr
Φs = Φr
Fr As ns
In the above expression, Φs is the fluorescent quantum
yield, F is the integration of the emission intensities, n
is the index of refraction of the solution, and A is the
absorbance of the solution at the exciting wavelength. The
subscripts r and s denote the reference and unknown sam-
ples, respectively. The value of quantum yield of VNCO
opt
in chloroform is 0.746. The band gap (Eg ) of the VNCO
can be estimated from the onset absorption (UVonset) with
opt
Fig. 4. Fluorescence spectra of VNCO at different concentration of DMTP.
−
34
17
Eg (eV) = hc/λ (h = 6.626 × 10
J s, c = 3 × 10 nm/s,
−
6
Concentration of VNCO, 3.72 × 10 mol/L; concentration of DMTP
19
1
3
eV = 1.602 × 10− J). The band gap of the VNCO is
−4
−4
−2
(
mol/L), 0, 0.00; (1) 5.88 × 10 ; (2) 8.76 × 10 ; (3) 5.52 × 10 ; (4),
−
2
−2
−2
.
.30 eV.
6.93 × 10 ; (5) 8.32 × 10 ; (6) 9.22 × 10

L. Feng, Z. Chen / Spectrochimica Acta Part A 63 (2006) 15–20
19
unit is an electron donor group and a typical hole-transporting
molecule while dimethylterephalate (DMTP) is a good elec-
tron acceptor, so the strong interaction between carbazole
and DMTP happens when DMTP is gradually added into
the solution of VNCO, the potential energy of VNCO that
results from the action between VNCO and solvent is deliv-
ered, which would lead to increasing of fluorescence intensity
of carbazole units. When the concentration of DMTP goes
beyond a certain scope, the excess DMTP units would act as
quencher to quench gradually the fluorescence of VNCO.
3
.6. Interaction between VNCO and fullerene (C )
60
C60 bears many unusual electrochemical and electronic
properties. One of the most remarkable properties of C60
related to electron transfer phenomena is that it can effi-
ciently induce a rapid charge separation and a further slow
chargerecombination[21]. Intheexperiment, theinteractions
of VNCO with C60 are examined. The results are shown in
Fig. 5. As we have seen in Fig. 5, ‘0’ is VNCO in concen-
0
Fig. 6. Dependence of F /F on concentration of C60. Concentration of
−
6
VNCO 5.89 × 10 mol/L.
−
6
tration (5.89 × 10 mol/L) without C , ‘1–5’ are VNCO in
60
the present in different concentration of C . With the grad-
60
ual increasing of concentration of C , the fluorescence of
60
VNCO is quenched efficiently and the process is also fol-
lowing the Stern–Volmer equation (Fig. 6). The apparent
5
−1
quenching constant is 3.52 × 10 M , which suggests that
the strong interactions between VNCO and C60 happen in
the excited state. The interactions are mainly coming from
the stronger charge-transfer process of the long ␲ electron
system (VNCO) with the electron acceptor (C ).
60
3
.7. Interaction between VNCO and carbon nanotubes
(
CNTs)
Fig. 7. Fluorescence spectra of VNCO at different concentration of
−
6
Carbon nanotubes are unique tubular structures of
nanometer diameter and have large length/diameter ratio
22]. It shows promise for a wide range of applications due
CNTs. Concentration of VNCO, 8.63 × 10 mol/L; concentration of CNTs
−
6
−6
−5
(mg/ml), 0, 0.00; (1) 2.10 × 10 ; (2) 4.22 × 10 ; (3) 7.32 × 10 ; (4)
−
5
9.15 × 10
.
[
to a combination of their unusual structural, mechanical and
electronic properties [23]. The investigation on the interac-
tion between VNCO and carbon nanotubes (CNTs) is helpful
to understand the optical property of VNCO and apply it
to LEDs. The quenching process of VNCO with carbon
nanotubes is shown in Fig. 7. It can be seen that the fluores-
cence of VNCO is quenched. Similarly, the strong interacting
between VNCO and CNTs are initiated in the excited state.
The strong interaction may be caused by the photoinduced
charge transfer and stacking processes of initiated ␲–␲ sys-
tem. Further research toward a better understanding of this
action is currently in progress.
4
. Conclusions
Fig. 5. Fluorescence spectra of VNCO at different concentration of C60.
−6
Concentration of VNCO, 5.89 × 10 mol/L; concentration of C60 (mol/L),
ꢀ
ꢀꢀ
ꢀꢀ
−6
−6
−6
−6
;
A new ␲-conjugated VNCO, 2,5-bis{3 -[3 -vinyl-9 -
(␣-naphthyl)carbazolyl]phenyl}-1,3,4-oxadiazole, bearing
0
, 0.00; (1) 1.39 × 10 ; (2) 2.32 × 10 ; (3) 3.24 × 10 ; (4) 4.63 × 10
−6
(5) 6.02 × 10
.

2
0
L. Feng, Z. Chen / Spectrochimica Acta Part A 63 (2006) 15–20
hole-transporting carbazole moieties, electron-injecting
,3,4-oxadiazole moieties and chromophore naphthalene
[4] C. Adach, S. Tokoto, T. Tsutsui, S. Saito, Jpn. J. Appl. Phys. 27
1998) 713.
(
1
[5] X.C. Li, G.C.W. Spencer, A.B. Holmes, S.C. Moratti, F. Cacialli,
R.H. Friend, Synth. Met. 76 (1996) 153.
was successfully synthesized by Wittig reaction. The optics
researches showed VNCO emitted blue and blue–green light,
with the band gap of 3.30 eV estimated from the onset absorp-
tion, the luminescence quantum yield was 0.746 in chlo-
roform, and displayed the emission spectra are red-shifted
with the increase of the solvents polarity. Moreover, the
light-emitting can be quenched by both electron donor (N,N-
dimethylaniline) and electron acceptor (dimethylterepha-
late), the molecular interactions of VNCO with fullerene
[6] D.D.C. Bradley, Synth. Met. 54 (1993) 401.
[7] G.M. Wang, C.W. Yuan, H.W. Wu, Y. Wei, J. Appl. Phys. 78 (1995)
2679.
[8] A.R. Brown, D.D.C. Bradley, J.H. Burrouthes, R.H. Friend, N.C.
Greenham, P.L. Burn, A.B. Holmes, A. Kraft, Appl. Phys. Lett. 61
(
1992) 2793.
9] C. Adachi, S. Tokito, T. Tsutsui, S. Satio, Jpn. J. Appl. Phys. 31
1992) 1812.
[10] F.L. Bai, M. Zheng, G. Yu, D.B. Zhu, Thin Solid Films 363 (2000)
18–121.
[
(
1
(
C ) or carbon nanotubes happened in the excited state.
60
[
[
[
11] D.B. Romero, M. Schaer, M. Leclerc, D. Ades, A. Siove, L. Zup-
piroli, Synth. Met. 80 (1996) 271.
12] S. Aratani, C. Zhang, K. Palbaz, S. Hoger, F. Wudl, A.J. Heeger, J.
Electron. Mater. 23 (1994) 453.
13] C. Zhang, H. von Seggern, K. Pakbaz, B. Kraabel, H.W. Schmidt,
A.J. Heeger, Synth. Met. 62 (1994) 35.
14] Y.Q. Liu, X.Z. Jiang, Q.L. Li, D.B. Zhu, Synth. Met. 4 (1997) 36.
15] C. Hosokawa, N. Kawasaki, S. Sakamoto, T. Kusumoto, Appl. Phys.
Lett. 61 (1992) 2503.
Acknowledgements
The present work was supported by the Natural Science
Foundation of China (30000112); Laboratory of Organic
Solid, Chinese Academy of Sciences and The Returned Stu-
dent Science Foundation of Shanxi Province of China.
[
[
[
[
16] T. Ahn, H.K. Shim, Macromol. Chem. Phys. 202 (2001) 3180.
17] Z. Arnold, A. Hoy, Collection Czech. Chem. Commun. 27 (1962)
2886.
[
18] S.Y. Song, M.S. Jang, H.K. Shim, D.H. Hwang, T. Zyung, Macro-
References
molecules 32 (1999) 1482.
[19] Y.L. Lin, H.S. Kuo, Y.W. Wang, S.T. Huang, Tetrahedron 59 (2003)
1277.
[1] J.H. Burroughes, D.D.C. Bradley, A.R. Brown, R.N. Marks, K.
Mackay, R.H. Friend, P.L. Burn, A.B. Holmes, Nature 347 (1990)
[20] J.N. Dmas, G.A. Crobys, J. Phys. Chem. 71 (1971) 991.
[21] B.W. Jing, D.Q. Zhang, D.B. Zhu, Tetrahedron Lett. 41 (2000) 8559.
[22] H.W. Kroto, J.R. Heath, S.C. O’Brien, R.F. Curl, R.E. Smalley,
Nature 318 (1985) 162.
5
39.
2] A. Kraft, A.C. Grimsdale, A.B. Holmes, Angew. Chem. Int. Ed. 37
1998) 402.
3] D.Y. Kim, H.N. Cho, C.Y. Kim, Prog. Polym. Sci. 25 (2000) 1089.
[
[
(
[23] M.S. Dresselhaus, G. Dresselhaus, R. Saito, Carbon 33 (1995) 883.