Phase Transitions

This article was downloaded by:[Dhar, Ravindra] On: 8 May 2008 Access Details: [subscription number 792956155] Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK

Phase Transitions A Multinational Journal Publication details, including instructions for authors and subscription information: http://www.informaworld.com/smpp/title~content=t713647403

Characteristic dielectric parameters of columnar discotic hexa-n-alkoxyanthraquinones R. Dhar ab; M. Gupta b; V. K. Agrawal b; Sandeep Kumar c a Physics Department, Ewing Christian College, Allahabad 211003, India b Physics Department, University of Allahabad, Allahabad 211002, India c Raman Research Institute, Bangalore 560080, India Online Publication Date: 01 May 2008 To cite this Article: Dhar, R., Gupta, M., Agrawal, V. K. and Kumar, Sandeep (2008) 'Characteristic dielectric parameters of columnar discotic hexa-n-alkoxyanthraquinones', Phase Transitions, 81:5, 459 — 469 To link to this article: DOI: 10.1080/01411590701844392 URL: http://dx.doi.org/10.1080/01411590701844392

PLEASE SCROLL DOWN FOR ARTICLE Full terms and conditions of use: http://www.informaworld.com/terms-and-conditions-of-access.pdf This article maybe used for research, teaching and private study purposes. Any substantial or systematic reproduction, re-distribution, re-selling, loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.

Downloaded By: [Dhar, Ravindra] At: 06:17 8 May 2008

Phase Transitions Vol. 81, No. 5, May 2008, 459–469

Characteristic dielectric parameters of columnar discotic hexa-n-alkoxyanthraquinones R. Dharab*, M. Guptab, V.K. Agrawalb and Sandeep Kumarc a

Physics Department, Ewing Christian College, Allahabad 211003, India; bPhysics Department, University of Allahabad, Allahabad 211002, India; cRaman Research Institute, C. V. Raman Avenue, Bangalore 560080, India (Received 15 October 2007; final version received 3 December 2007) Temperature-dependent dielectric spectroscopy of resynthesized discotic compounds, rufigallol hexa-n-alkoxylates for n ¼ 6, 7, 8, 9 having wide temperature range (470 C) hexagonal columnar mesophase has been carried out in the frequency range of 10 Hz to 10 MHz. The mesophase and their transition temperatures have been determined by using polarizing microscope and differential scanning calorimeter. Dielectric permittivity parallel ("0jj ) and perpendicular ("0? ) to column have been determined. Using these data, dielectric anisotropy (" ¼ "0jj "0? ) has been found to be positive throughout the entire range of the Colh phase for all of the four compounds of this series. No relaxation phenomenon is found in the frequency range of 10 Hz to 10 MHz. The DC conductivity of these compounds has been found to be rather low (1010–1011 S-m1). All the electrical parameters show odd–even effect with the variation of n. Keywords: discotic liquid crystal; permittivity and loss; conductivity

hexagonal

columnar

phase;

dielectric

1. Introduction Liquid Crystals formed by disc-shaped molecules, now commonly referred to as discotic liquid crystals (DLCs), have been of interest since their discovery in 1977 in hexasubstituted benzene derivatives [1]. Since the discovery of mesomorphism in disc-like molecules [1,2] several series of DLCs have been synthesized [3,4] and some structural properties have been examined by X-ray experiments [5] and optical microscopy [6]. This relatively new class of liquid crystals has gained increasing interest, both from a scientific and an application point of view [7–14]. Discotic liquid crystals are, generally, composed of disc-shaped molecules with rigid planar central core that is laterally substituted by multiple flexible tails. The disc-like molecules exhibit two distinct classes of phases, the columnar and the discotic nematic phases [15]. Columnar mesophases are classified according to the symmetry in the packing of the columns. In the columnar structures, the molecules are stacked one upon the other to build columns. The columns itself are arranged in a two-dimensional network leading to columnar phases

*Corresponding author. Email: [email protected] ISSN 0141-1594 print/ISSN 1029-0338 online 2008 Taylor & Francis DOI: 10.1080/01411590701844392 http://www.informaworld.com


460

R. Dhar et al.

with hexagonal, rectangular or oblique symmetry, whereby tilted variants are also possible [7–14]. Along the axes of the columns, long-range order of the molecules can exist. The several columnar phases are distinguished by the intra and inter column order. Due to their high viscosity in the columnar phases, there are no applications for these materials as such in display devices but the negative birefringence films formed by polymerized nematic DLCs have been commercialized as compensation foils to enlarge the viewing angle of commonly used twisted nematic liquid crystal displays. Nevertheless, they receive increasing attention in the field of one-dimensional conductors [16–18]. Self-organization of discotic molecules into columnar liquid crystalline phases is a subject of great practical interest since these phases do show, for appropriately chemically tailored molecules, specific physical properties such as a good electronic conductivity along the column axes. It has recently been demonstrated that the degree of order determines charge mobility in columnar liquid crystalline materials [19,20]. The potential applications of such one-dimensional organic semiconductors are being explored towards their use as organic field effect transistors and as charge transport or emitting layers in organic light emitting diodes [10]. The practical exploitation of these self-organizing materials requires, moreover, a good control of the spatial alignment of the columns, hence the need of a fundamental understanding of the physical and chemical mechanisms underlying the alignment techniques. Generally, in pure disc like molecules there can be two possibilities to align disc molecules. First, disc column axis in the plane of the electrode i.e., parallel to electrode surface and the other possibility is that disc column axis is perpendicular to the plane of electrode. These two types of alignments are distinguishable as [21,22], when column axis is parallel to electrode surface is called planar alignment (or edge-on) and when column axis is perpendicular to electrode surface is called homeotropic alignment (or face on). The dielectric study of discotic materials is scarce. However, some works on discotic materials give information about the different types of relaxation process present in discotic materials [23–27]. In the present article, we are reporting our experimental results on the dielectric study of the homologous series of aliphatic ethers of rufigallol (short notation En, where n is the number of carbon atoms contained in each aliphatic chain), with n ¼ 6, 7, 8, 9. The members of this series show wide temperature range of hexagonal columnar (Colh) phase [28]. The general structure of these liquid crystalline materials is shown below. O

OR

RO

OR

RO

OR OR

O

In the present work dielectric study has been carried out for R ¼ C6H13, C7H15, C8H17 and C9H19 (E6, E7, E8 and E9, respectively). Initially, Cosimo Carfagna et al. [28] gave the synthesis of this series. They also gave the X-ray diffraction patterns of the mesophase of this series. That study also conforms that all the compounds of this series give enantiotropic, columnar mesophases to a regular stacking of the discs along the columns. Recently, the phase behavior of three homologs of hexa-n-alkoxyanthraquinones under pressure has been described by Maeda et al. [29]. Present study will conclude dielectric properties of the series.

Phase Transitions

461


2. Experimental section Transition temperatures and transition enthalpies have been determined by using a differential scanning calorimeter (DSC) of Perkin-Elmer (model DSC-7 equipped with TAC-7/DX controller and Pyris software) which agrees with the previously reported values [28]. A transmitted light polarizing microscope has been used to identify the mesophase. In order to determine dielectric permittivity ("0 ) and loss ("00 ), capacitance (Cm) and conductance (Gm) of the cell filled with the material have been determined in the frequency range of 10 Hz to 10 MHz using a Solartron SI-1260 impedance/gain phase analyzer, coupled with a Solartron dielectric interface model-1296. Dielectric studies have been carried out by filling the samples in the cell in its isotropic liquid phase by capillarity action. Dielectric cells are parallel plate capacitors made from indium tin oxide (ITO) coated glass plates having resistance less than 25 ohm/œ. Active capacitance (CA) of the cell has been determined by using standard nonpolar liquid cyclohexane as follows. CA ¼

CðchÞ CðaÞ "0 ðchÞ 1

ð1Þ

where C(ch) and C(a) are the capacity of the capacitor with cyclohexane and air, respectively, inside the cell. "0 (ch) is the relative permittivity of the cyclohexane. Complete removal of the cyclohexane (after the calibration) from the cell has been ensured by comparing capacity of the cell before and after filling the cyclohexane. "0 and "00 of the material have been calculated by using following equations. "0 ¼

CðmÞ CðaÞ þ1 CA

ð2Þ

GðmÞ GðaÞ !CA

ð3Þ

"00 ¼

where C(m) and G(m) are the capacitance and conductance of the cell filled with material (measured in parallel mode), G(a) is the conductance of the cell with air inside the cell and ! (¼2f ) is the angular frequency of the measuring electric field. G(a) is negligible as compared to G(m) in the present case. For the homeotropic (molecular discs parallel to electrodes surfaces) alignment two plates have been separated by teflon spacers of thickness 10 mm to obtain a stable capillary gap between the electrode surfaces. Sample has been cooled slowly to get perfect alignment of the molecules in the Colh phase. Alignment of the molecules with disc perpendicular to substrate is very difficult. Hence, dielectric measurements have been performed for random orientation of the molecules, which yield average value of dielectric parameters. For this purpose a thick cell (100 mm) has been used to get average value of dielectric permittivity and loss. Dielectric data have been acquired in the cooling cycle. A measuring electric field of magnitude 500 mVrms has been applied normal to electrode surfaces while acquiring the electrical data. High frequency effects in the measurement of C and G has been explained earlier by using an appropriate impedance model [30a]. In this model ITO sheet resistance (R) and lead inductance (L) have been taken in series to the parallel combination of C and G. According to this model, C(m) and G(m) vary as follows CðmÞ ¼

Cð1 !2 =!20 Þ LG2 2 1 þ GR !2 =!20 þ !2 ðLG þ CRÞ2

ð4Þ

462

R. Dhar et al.


GðmÞ ¼

Gð1 þ GRÞ þ ð!CRÞ2 =R 2 1 þ GR !2 =!20 þ !2 ðLG þ CRÞ2

ð5Þ

where !20 ¼ 1=ðLCÞ. The reactive cut-off frequency !x0 (corresponding to C(m) ¼ 0) is given as: 1=2 1 LG2 ð6Þ !x0 ¼ !0 C For !4!x0, C(m) is negative i.e., inductive effect dominates. High-frequency parasitic effects on conductance (and hence loss "00 ) contribute nearly one decade earlier than in the case of capacitance. In the present study also conductance data are affected as early as 100 kHz, whereas capacitance data are almost unaffected up to 1 MHz. For these reasons, discussion on the measured data in the high-frequency range has been limited to 1 MHz. Peaks of the mesophase transitions on DSC thermograms have been located with the accuracy of 0.1 C, whereas enthalpies of the transitions (H) have been determined with the accuracy better than 2%. Uncertainty in the determination of dielectric permittivity and loss is less than 2% in the frequency range of 10 Hz to 1 MHz. Other details of the experimental techniques have already been discussed elsewhere [31,32].

3. Results and discussion Optical polarizing microscopy suggests only one wide temperature range mesophase i.e., Colh phase for all the members of aliphatic esters of rufigallol as reported earlier by Cosimo Carfagna et al. [28]. Optical texture for E6 compound at 94.0 C for thick (unaligned molecules) samples has been given in Figure 1. A systematic scanning ratedependent thermodynamic study suggests that peak transition temperatures (TP) as determined by DSC, vary linearly (having opposite slopes in heating and cooling cycles) with the scanning rate of the temperature as shown in Figure 2. Intersections of two straight lines have been observed at about 1.5 C instead at 0 C [32]. From DSC, the values of transition temperature and enthalpy for isotropic phase to hexagonal columnar

Figure 1. Optical texture of columnar phase of unaligned sample between two cover slips at 94.0 C for E6.

463

phase transitions of all the compounds are given in Table 1. As the length of alkyl chain increases, the temperature range of mesophase decreases indicating that the thermal stability of the Colh phase decreases with the length of the flexible alkyl chains. (Table 1). Figure 3 shows variation of dielectric permittivity with frequency for E8 compound at 78.6 C for thin (columns normal to electrode surfaces) and thick (unaligned molecules) samples. The dielectric permittivity value for unaligned sample is given only above 1 kHz. This is because with 100 mm spacer, capacitance value of the cell comes around 10–20 pF and is not precisely measurable by Solartron SI-1260 impedance/gain phase analyzer below 1 kHz. Generally, dielectric data below 1 kHz are affected due to ionic conductance [30b] but in the present samples there is no signature of ionic effects indicating negligibly 109

E6

Colh−I

E7

Tp (°C)

103

E8 E9

97

91

85 −1.5

I− Colh 3.5

8.5

SR

13.5

°C-min–1

Figure 2. Linear dependence of peak temperature of mesophase transitions with the scanning rate. Table 1. Transition temperature (Ti) and enthalpy (Hi) for isotropic - Colh for the rufigallol hexa-n-alkoxylates. Compound E6 E7 E8 E9

Ti ( C)

Hi (J g1)

103.6 99.7 92.9 90.1

13.1 12.5 10.3 9.5

4.5

3.5

Colh

ε′


Phase Transitions

1 2.5

1.5 1.0E+01

2

1.0E+03

1.0E+05

1.0E+07

Frequency (Hz)

Figure 3. Variation of dielectric permittivity with frequency at 78.6 C for E8. Curve-1 is for homeotropic alignment and curve-2 is for unaligned sample.


464

R. Dhar et al.

small ionic conductivity of the samples. However, measured dielectric data above 1 MHz are affected due to ITO resistance and lead inductance [30a]. Constant values of dielectric permittivity in the frequency range of 10 Hz to 1 MHz suggest that there is no relaxation mechanism below 10 MHz in either of the molecular configuration. Same conclusion has been drawn for the other members of the series. As discussed in Section 1, generally two types of alignments are possible for complete disc shape molecules, we believe that in the case of thin sample (10 mm), homeotropic alignment (column axis perpendicular to electrode surface) is possible and therefore dielectric measurement under this condition yield dielectric permittivity parallel to columns axis ("0jj ). Dark field of view obtained under crossed polarizer as shown in Figure 4 confirms our views. However, in the case of thick sample (100 mm) dielectric measurement yields average value of the dielectric permittivity ("0av ) due to the random orientation of the molecules where "0av ¼ (1/3) ("0jj þ 2"0? ). Optical texture of thick sample (100 mm) is shown in Figure 5 and it shows random orientation

Figure 4. Optical texture with almost dark field of view of columnar phase of homeotropic (column axis normal to surface) aligned sample between two ITO coated glass plates (treated for alignment) at 101.9 C for E6.

Figure 5. Optical texture of columnar phase of unaligned sample (100 mm) between two ITO coated glass plates at 82.0 C for E6.

465

of the molecules. "0? is dielectric permittivity normal to columns axes. Using this relation, values of "0? have been obtained by measuring "0jj and "0av . Figure 6 shows variations of the static dielectric permittivity "0jj and "0? (100 kHz) with temperature and hence dielectric anisotropy "0 (¼ "0jj "0? ) for E6, E7, E8 and E9. At isotropic to columnar transition temperature, "0? goes down whereas "0jj goes up showing positive value of "0 for all four members of the series. When samples are further cooled, magnitudes of "0 decrease. This is because, with lowering in temperature, molecules of even thick cells align similar to that of thin cell i.e., plane of the disc parallel to the plane of electrodes. Near room temperature, alignment in both type of cells (thick and thin) are same and hence dielectric permittivity measured in two cells are also same. This is evidenced by the optical texture study as well. As can be seen from Figure 6, dielectric anisotropy for these compounds is low. Due to the elongation of the chain length, the number of molecules per unit volume decreases and hence dielectric anisotropy should decrease [33,34] as observed in Figure 7. Small value of dielectric anisotropy can be related to the presence of aliphatic chains. Figure 6 shows the dependence of the dielectric permittivity of the isotropic phase ("0iso ) on number of carbon atoms attached in compounds (n). Figures 7 and 8 both show the odd–even effect of the dielectric permittivity and anisotropy as observed in several other cases [35].

(a) 2.9

1

ε′

I Colh

2.8

3

2.6 2 2.5 28 (b)

48

68 88 Temperature (°C)

108

2.82 1 I 2.67

Colh

3

ε′


Phase Transitions

2.52

2.37 20

2

40

60 80 Temperature (°C)

100

Figure 6. Variation of dielectric permittivity for homeotropic ("0jj by curve-1), planar ("0? by curve-2) and unaligned sample ("0av by curve-3) with temperature at 100 kHz for E6 (a), E7 (b), E8 (c) and E9 (d). Vertical line shows transition from isotropic phase to hexagonal columnar phase.

466

R. Dhar et al. (c) 1 I

Colh ε′

2.63 3 2.53

2.43 26

2 46

66 Temperature (°C)

86

106

(d) 1 2.65 Colh ε′

I 3

2.55

2 2.45 24

44

64 Temperature (°C)

84

104

7.5 n

8.5

9.5

Figure 6. Continued. 2.80

2.70 εiso′


2.73

2.60

2.50 5.5

6.5

Figure 7. Variation of dielectric permittivity in isotropic phase (data for 102.0 C) with n (number of carbon atoms attached to aliphatic chain).

Conductivity of these materials is very low. The variation of conductivity with frequency is shown in Figure 9 for E6 compound in Colh phase at 98.0 C. Total conductivity of the dielectric cell follows general equation [36] ðtÞ ¼ ðdcÞ þ A!m

ð7Þ

467

Phase Transitions

∆ε′

0.25

0.15

0.05 5.5

6.5

7.5 n

8.5

9.5

Figure 8. Variation of dielectric anisotropy in columnar phase with n (number of carbon atoms attached to aliphatic chain) at TI-Colh3 C.

0

Log (σ(t))

−2 −4 −6 −8 −10 −12

1

2

3

4

5

6

7

Log (Frequency (Hz))

Figure 9. Variation of log of conductivity with log of frequency for E6 in Colh phase at 98.0 C.

2.10E-10

σdc(S-m−1)


0.35

1.40E-10

7.00E-11

0.00E+00 5.5

6.5

7.5 n

8.5

9.5

Figure 10. Variation of dc conductivity in columnar phase with n (number of carbon atoms attached to aliphatic chain) at TI-Col-3 C for homeotropic aligned sample.

468

R. Dhar et al.

Colh σac/(S-m−1)


4.9E-05

I

3.6E-05

2.3E-05

1.0E-05 30

45

60

75

90

105

Temperature (°C)

Figure 11. The variation of ac conductivity for E6 for homeotropic alignment at 1 MHz frequency with temperature. Vertical line shows transition from isotropic phase to hexagonal columnar phase.

At low frequencies (51 kHz), second part (ac conductivity) is negligible and hence total conductivity is composed of only dc part i.e., (dc). However, above 1 kHz, ac part i.e., A!m starts to contribute in total conductivity. At and above 100 kHz, A!m term dominates over (dc) term. The plot of log( (t)) against log( f ) gives (dc) at different temperatures which are of the order of 1010–1011 S-m1 for all compounds of this series. Variation of (dc) with n is shown in Figure 10 for homeotropic aligned sample. As seen from Figure 10, (dc) also shows odd–even effect. AC conductivity (A!m) for these samples is of the order of 105–106 S-m1. Variation of ac conductivity with temperature for E6 compound at 1 MHz is shown in Figure 11. Generally in discotic materials, doping can increase conductivity. With a small concentration of dopant like electron acceptor trinitrofluorenone (TNF), conductivity can be increased by a factor of 107 or more relative to that in undoped samples [37].

4. Conclusions Compounds of presented series (Rufigallol hexa-n-alkoxylates) have wide temperature range hexagonal columnar mesophase. Dielectric studies have been performed for thin (columns normal to electrode surfaces i.e., homeotropic alignment) and thick (unaligned molecules) samples. At the isotropic to columnar transition temperature, "0jj goes up, whereas "0? goes down showing positive value of "0 for all the four members of the series. When samples are further cooled, magnitudes of "0 decrease. This is because, with lowering in temperature, molecules of even thick cells align similar to that of thin cell i.e., plane of the disc parallel to the plane of electrodes. Low value of positive dielectric anisotropy is found throughout hexagonal columnar phase for all the compounds of this series. The DC conductivity for all the members of this series has been found to be of the order of 1010–1011 S-m1. Dielectric permittivity, anisotropy, and DC conductivity show odd–even effect with the variation of n.

Acknowledgements Authors wish to thank Department of Science and Technology, New Delhi, for providing financial assistance under a research project.

Phase Transitions

469


References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23]

[24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37]

S. Chandrasekhar, B.K. Sadashiva, and K.A. Suresh, Pramana 9 (1977), p. 471. J. Billard et al., Nouv. J. de. Ch. 2 (1978), p. 535. Nguyen Huu Tinh, C. Destrade, and H. Gasparoux, Phys. Lett. 72A (1979), p. 251. A. Queguiner et al., Bangalore-Conference 1979. A.M. Levelut, J. Phys. Lett. 40 (1979), p. 81. C. Vauchier et al., Mol. Cryst. Liq. Cryst. 59 (1980), p. 63. S. Chandrasekhar and S. Kumar, Sci. Spec. 66 (1997), p. 66. D. Demus, et al. (eds), Handbook of Liquid Crystals, Vol. 2B, Wiley-VCH, Weinheim, 2, 1998. C. Tschierske, Annu. Rep. Prog. Chem. Sect. C97 (2001), p. 191. R.J. Bushby and O.R. Lozman, Curr. Opin. Colloid, Interface Sci. 7 (2002), p. 343. B. Donnio et al., Compr. Coord. Chem. 7 (2003), p. 357. S. Kumar, Liq. Cryst. 31 (2004), p. 1037. S Kumar, Liq. Cryst. 32 (2005), p. 1089. S. Kumar, Chem. Soc. Rev. (2006), p. 83. S. Chandrasekhar and G.S. Ranganath, Rep. Prog. Phys. 53 (1990), p. 57. N. Boden, R.J. Bushby, and J.J. Clements, Chem. Phys. 98 (1992), p. 5920. P.G. Schouten et al., J. Am. Chem. Soc. 114 (1992), p. 9028. D. Adam et al., Phys. Rev. Lett. 70 (1993), p. 457. D. Adam et al., Nature 371 (1994), p. 141. A.M. vande Craats et al., Adv. Mater. 8 (1996), p. 823. K. Hatsusaka et al., J. Mater. Chem. 11 (2001), p. 423. L. Bellier-Castella, D. Caprion, and J.-P. Ryckaert, J. Chem. Phys. 121 (2004), p. 4874. W. Haase et al., Calamatic and discotic metallomesogens, in Relaxation Phenomena: Liquid Crystals, Magnetic Systems, Polymers, High-Tc Superconductors, Metallic Glasses, W. Haase and S. Wrobel, eds., Springer-Verlag, Berlin Heidelberg, 2003. Herbert Groothues et al., Liq. Cryst. 18 (1995), p. 117. U. Dahn et al., Liq. Cryst. 19 (1995), p. 759. B. Glusen, W. Heitz, A. Kettner and J.H. Wendorff, Liq. Cryst. 20 (1996), p. 627, 1996. Beatriz Palacios and M. Rosario De La Fuente, Miguel Angel Perez Jubindo, Liq. Cryst. 25 (1988), p. 481. C. Carfagna et al., Liq. Cryst. 2 (1987), p. 611. Yoji Maeda, Hiroshi Yokoyama and Sandeep Kumar, Liq. Cryst. 32 (2005), p. 833. (a) R. Dhar, Indian J. Pure Appl. Phys. 42 (2004), p. 56; (b) S.L. Srivastava and R. Dhar, Indian J. Pure and Appl. Phys. 29 (1991), p. 745. M. Gupta et al., Phys. Rev. E. 72 (2005), p. 021703; M.B. Pandey et al., J. Phys.: Condens. Matter Phys. 19 (2007), p. 436219. S.L. Srivastava, R. Dhar, and M.V. Kurik, Mol. Mat. 2 (1993), p. 261. S.L. Srivastava and R. Dhar, Mol. Cryst. Liq. Cryst. 317 (1997), p. 23. H. Kresse, Advances in Liquid Crystals, Vol. 6, Academic Press, Inc. New York, 1983, p. 109. J. Przemyslaw and J. Jadz´yn, Mol. Cryst. Liq. Cryst. 249 (1994), p. 105. A.K. Johnscher, Nature 269 (1977), p. 673. V.S.K. Balagurusamy et al., Pramana 53 (1999), p. 3.