RESEARCH COMMUNICA'l'lONS
and double exposure holographic interferometry have
been extensively used in the visualization of structural
deformations and vibrations. The conventional techniques using a two-beam geometry involves the separation
of the transmitted object beam and the image-bearing
diffracted beam. So the quality of the interference
pattern depends heavily on the transmission of the
hologram and the suppression of the background
intensity. The four-wave mixing (FWM) geometry
employed by us helps in obtaining a PC image of the
object which is free from distortions because of its
aberration compensation property. The importance of
the present work lies in the fact that by preparing a
nonlinear medium, in the way suggested by us, one can
attain a contrast of unity.
A new approach to combine the efficiencies of a
photorefractive crystal and the fast response times
offered by dye thin film, is discussed. This novel
composite material gives two phase conjugate signals
differing in their growth and decay times. It has been
exploited in a simple four-wave mixing geometry to
perform phase conjugate interferometry. The technique
is free from the phase change problems associated with
dye thin films alone and a very high contrast interferogram can be obtained by properly choosing suitablc
material and geometric parameters.
1 . Pepper, D. M., Sci. Am., 1989, 254, 56-65.
2. HOpf, F. A,, ,I. Opt. SOC.
i l ~ l . ,1980, 70, 1320-1323.
3. Feinberg, .I., Opt. Lett., 1983, 8 , 569-571.
4. Huignard, J. P.and Marrakchi, A,. Opt. Lett., 1981, 6 , 622-624.
5. Bar-Joseph, I. e t a / , Opt. L e t t . , 1981, 6 , 414-416.
6. Nakagawa, K. and Fujiwara, A,, Opt. Conimun., 1989, 70,73-76.
7. Nakagawa, K. and Fujiwara, I-I., SPIE, 1989, 954, 11-15.
ACKNOWLEDGEMENT This work was carried out under a
research programme sponsored by thc Defence Research and
Development Organization.
Received 7 August 1993; accepted 12 August 1993.
fascinating molecules'~'. A variety of reactions have
been carried out on C60 generally giving rise to a
mixture of products. Birch reduction of CbOhas been
reported3 to yield a mixture of C60H18and C60H36,while
controlled hydroboration4 followed by protonolysis
gives C60H2. Calculations have been carried out on
C60H60, with isolated double bond^^-^. Considering that
several of the derivatives studied so far conform to the
general formula C60X60.e, (X = M, Br, etc), it is
tempting to speculate whether some of these derivatives
consists of n distinct benzene rings distributed in the
fullerene cage9. C6()H36 seems to be the most promising
candidate to adopt such a structure with four isolated
benzenoid rings.
The preparation of fullerene was carried out by contact
arc vapourization. of
Separation and pmification of C60 were accomplished by a simple filtration
technique using a charcoal - silica-gel mixture1?.CbOH36
was obtained by Birch reduction of c60 as follows. To
excess Lilliquid NH,,a solution containing 30 mg of Cho
and 5 ml of tert-butanol in 200 ml methyl cyclohexa~~e
was added and stirred vigorously. The temperature of
the reaction mixture was maintained at minus - 3 3 T for
6-7 h by using a liquid ammonia refluxing condensor,
The product was quenched with excess of ammoniuni
chloride, washed with water, dried over anhydrous
MgS04 and passed tlirough a silica column to remove
possible amine addition products. The new product in
TLC showed a single spot (iodine-active) with an A,.
value of around 0.37 in 30% CH2C12/hexane. After
removing the solvent, a white solid product was
obtained. This product was characterized by FAB and El
mass spectrometry, FTIR, N M R and U V spectroscopy.
Although the FAB and El mass spectra of the purified
pro'duct of Birch reduction show a distribution of mass
peaks, the main line is at mlz 746 (Figure 1 ) corresponding to a hydride C,of-136. There was no Seature to
indicate the presence of a Nl-lz gropp in the F U R
spectrum (KBr pellet). The FTIR spectrum showed
characteristic frequencies associated with aliphatic C-tl
-
Investigations of the fullerene
hydride C60H36
A. Govindaraj
CSIR Center of Excellence in Chemistry, Indian Institute of Sc~ence,
Bangalore 560 012, India
Under Birch reduction conditions, C60 predomiSpectroscopic results a r e connantly forms C60H36.
sistent with the structure predicted by calculations,
involving four benzene rings distributed tetrahedrally in a spheroidal framework.
SINCEthe discovery of the fullerene, there has been
considerable effort to study the chemistry of these
F i g 1. e
c
I
das
spcctra o ~ ' C ~ ~ N ; ,
CURREN 1 bCIENCE, VOL. 65, NO. 1 I , 10 DECEMBER 1993
RESEARCH COMMUNICATIONS
W a v e length,nm
3500
2500
1500
Wave number c ~ '
500
F i g u r e 2. Experimental infrared spectru~n(FT) of C,,lH,, along w ~ t h
the spectra predictcd for T and TI, structures (scaled by 0.9).
1~igul.e4 . Elcctronic absorption spectru~nof (u)C,,I-l;, alonz \\ ill1
( b ) the spectra of TCNE and the c o ~ n p i e swith TCNE. Inset shows
the "C N M I i spectrum in CDCI,. ('The askrisk indicates thc signal
d u e to the solvent.)
F i g u r e 3 . Proton N M R spectrum ofC6,tIi, (in CDCI3).
stretching as well as aromatic C=C skeletal vibrations
(Figure 2). The IH NMR spectrum in CDCI3 (Figure 3)
showed a broad band in the 2.5-4.3 ppm range. The
NMR spectrum showed distinct bands around
140 ppm and 40 ppm which can be assigned respectively
to benzenoid and saturated carbons (insert of Figure 4).
The signal due to the benzenoid carbons is weak
because of the quaternary nature of these carbons.
Although the NMR signals are relatively broad, their
positions support the structure to be discussed later. The
hydrocarbon showed a band at 2 18 nm and another
around 275 nm in the UV spectrum (in cyclohexane
solution), characteristic of benzenoid rings (Figure 4 a).
All these spectroscopic data of CG0H36are consistent
with a structure containing isolated benzene rings.
Further evidence for the presence of benzene rings
comes from the observation of a charge-transfer band
of C60H36 with tetracyanoethylene around 305 nm
(Figure 4 b). The benzene - TCNE systemI3 shows a
charge transfer band at 300 nm.
C U R R E N T SCIENCE. VOL. 6 5 , NO. 11, 10 DECEMBER 1993
F i g u r e 5 . I'rqjection ol'C,,,l 13,
(T)structure down a thrcc-Sold nsis.
MNDO calculation^^^ have shown that a structure with
four tetrahedrally disposed benzene rings as shown in
Figure 5 (T symmetry) is more stable for C,oH3(,than
that with isolated double bonds (TI, symmetry). MNDO
calculations distinguished the T structure with benzenoid rings from the TI, structure with isolated double
bonds in terms of vibrational frequencies. The observed
IR spectrum of C60H36is compared with the spectra
structure. The
predicted by calculation for the T and Ti,
experimental spectrum seems to correspond more
closely to the spectrum of the T rather than the TI,
structure (Figure 2). This structure of CGoH3(,suggests
that factors such as angle strain, degree of conjugation,
the number and magnitude of eclipsing interactions as
RESEARCH COMMUNICATIONS
well as the strain associated with cage distortions are
Evolution of basin boundaries during
important factors in the reduction of C,& The simple
explanation offered earliervor the structure of CBOH36 onset of chaos
was based on the consideration that 36 is the number of
6. Ambika"
hydrogens required to leave a single unconjugated
Department of P h y s ~ c s , Cochin University of Scicncc and
double bond in each pentagon of CbO.We feel that it is
Technology, Cocliin 682 022, India
not unreasonable to postulate a structure of C60H36as
one with four tetrahedrally disposed benzene rings. It is
The evolution of basin boundaries in a system with
possible that a structure with isolated double bonds first
multiple attractors is analysed numerically as the
formed transforms to the therniodynamically more stable
system
develops period doublings, crises and tangles.
structure with the benzenoid rings via sigmatropic shifts.
The
disappearance
of the basin o f attraction of a
TIILISwith the tbur symmetrically spaced betlzene units
chaotic attractor during a boundary crisis as well as
in the spheroid, the shape o[ the cage permits an
the erosion of the bounded basin by the escaping
effective elimination of angle strain at both the sp2 and
basin due to a heteroclinic tangle are displayed in a
sp3carbon atoms. The overall angular distortions are
series of basin portraits.
marginally higher for the T isomer than the TI, form. It
appears that the aromatic character of the benzenoid
IN the study o f nonlinear systems, we often come across
units is responsible for the greater stabilization of the
systems
with multiple attractors, i.e. wit11 more than one
former isomer. It is also likely that under conditions of
asymptotically
stable states coexisting for one particular
Birch reduction with tcrt-butan01 as the proton source
set
of
system
parameters.
In such cases, each attractor
only partial reduction of C , o occurs leaving four liexawill
be
having
its
own
separate
basin o f attraction. the
s~~bstituted
benzene rings.
basin being the set of initial points that lead to the
attractor as time t -+ m. The boundary of the closure of
I . Special issue on 13i1ckrninsler-1'~1Ilcre1ic.,
:lc,c. Clioil, 1te.r.. 1992.
this region can in general be smooth or fractal. As the
25, 9 9 .
attractor undergoes a bifurcation, the basin boundary
2 . Spccinl issuc on Fullcre~lcs~n.
Indiuti .I. ('IIcII~.,
1992, 31 h % 13.
evolves, either going from a smooth to a fractal or
]:I.
3. Ilwllcr, I<. I:, ct nl.1, /'!ij'.s. C h e ~ v . 1990,
,
94. 8634.
disappearing. Therefore, studies related to the location
4. Ilcndcrson. l i . G. and i'aliill, P. A,. Scie17ce. 1993. 259. 1885.
as well as the nature of these boundaries and their
5. Saundcrs, PI., Scie17rc. 101. 253. 330.
changes as the system parameters evolve have signi6. Dl~lilnp.13. I.. Ilrcnncr. 11. W., Mintmire, .I. W.. Mowrcy, R. C .
ficance because of their implications in the onset of
:uid Wl~ilc,C,', 'l'.> ,I, /J/iyxC'/IL>/X. I99 I * 95, 5763,
7 . (iuo. 'I'. i ~ n dS~uscriii,G.G., (:helli. /.'/iq'.v, Idel/,.1097, 191, 527
chaos in the system' 4. An a p r i w i knowledge about
8. Bako~vics.I). arid Tliicl, W.,
C'iietlr, l'i~,.s. i.erl., 1992, 193, 236.
how the attractor basins evolve can be of use when we
9. Taylor. I<., .I. ('iiei~~.
Soc. Perkilt Titzns. 2, 1992, 1067; Austin.
address the question of control mechanisms too, since
S. .I. cr o/.:..l. ('lrcill. Soc. Perkill Trc~~is.
2. 1W3. 1383.
suitable control is normally applied to bring the system
10. K r : ~ t s c l i ~ ~W..
w . I.mib. I,, I)., I:ostiropoulous, I<, nrid Ilull'inan,
within the basin of a periodic artractors. So, also the.
I). 12.. .\'orrim, 1090, 347. 3 5 4 .
1 1 . l'ratlccp. T.i)'Souza, F.. Subbatinn. C;. N..Krishnan, V , and
extent of basin erosion due t o forcing can tell 11show far
Rno, C'. lu'. R.. /'roc, itrdiilrl .,lc~ci.Sci. (('/icni. Sci.), 1991. 103,
a system has chances of remaining constrained in a
685.
noisy environment, and this is a useful criterion in
12. (iovi~idaraj,A. : a d llao C'. N.I<.. Puil. Sci. Tcch~zol.,I993 ( in
engineering
and applied sciences" 77.
press).
13. IZao, C'. N,12.. Bhal. S. n. and Dwivcdi. P. C.,
Ajil,!. Spcc. Rev.
In this communication, a detailed display of the
1071.5. 1.
evolution of basin boundaries of a system with multiple
attractors is presented. By concentrating on parameter
regimes where interesting phenomena like crises and
tangles occur, we study nu~nericallythe reorganization
ACKN0Wl,lif>CiliMIJNNII. I thank Prof. C. N. R. Rao and Prof. .I.
of the basin structure as the parameters pass through
Cliandrasekhar Ibr guidancc and advice.
their critical values. In this context, we note that basin
boundary analysis has been carried out extensively in
l<cccivcd 20 August 1993; revised accepted 27 September 1993.
discrete dynamical ~ y s t e r n s ~ - ' ~The
.
attractor-basin
portraits have been explored in detail recently by Ueda"
for the Duffing equation, while Thompson et
Notc ndded in proyj: After completing this work, we have become
have analysed basin organization prior to escape in a
w a r e of a mass spcctrometric study of product distributions of C,, single-well or double-well oscillator.
13irch reduction (Banks, M. R . et al., J. C h e m Soc. Chenz. Commzm.,
1993, 1149).
*On leave from Department of Physics, Maharaja's College, Cochin
682 Ol 1, India
CURRENT SCIENCE, VOL. 65, NO. 1 I , 10 DECEMBER 1993
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