Evidence for cybotactic cluster pretransition formation in TBBA liquid crystal

Solid State Communications, Vol. 24, pp. 433—43 7, 1977.

Pergamon Press

Printed in Great Britain

EVIDENCE FOR CYBOTACTIC CLUSTER PRETRANSITION FORMATION IN TBBA LIQUID CRYSTAL* G. Albertini,t M. Corinaldesi,~S. Mazkedian,1: S. Melone,t M.G. Ponzi-Bossit and F. Rustichellil: §

t

Facolta di Medicina,

1

Facolta di Ingegneria, Università di Ancona, Italy.

§ JRC, EURATOM, Ispra, Italy

(Received 1 July 1977 by R. Fieschi)

We report an investigation by X.ray diffraction of the cybotactic cluster formation near the nematic—smectic A phase transition of TBBA liquid crystal. The results are discussed on the basis of the Landau theory developed by de Gennes and McMillan. The dimensions of the cybotactic clusters are evaluated as a function of the temperature. CYBOTACTIC CLUSTERS were observed for the first time by De Vries[l, 2}in the nematic phase of BACP and DHA, and of BOCP[3] by using X-ray diffraction. These clusters can be roughly imagined as smectic islands imbedded ma nematic sea. But more correctly they can be considered as small nematic regions fluctuating to and from a smectic configuration (order parameter fluctuations). McMilan has observed these fluctuations by X-ray diffraction in cholesteryl nonanoate [4], cholesteryl miristate [4], CBAOB [5], OBT [6] and HAB [7]. In connection with these fluctuations a divergence of the bend elastic constant K33 and of the twist elastic constant K22 was predicted by de Gennes[8, 9} and observed by Rayleigh light scattering[l0, 12], Fredericksz transition[13, 15] and by other methods. The presence of cybotactic clusters has been used to explain anomalous behaviour of the anisotropy of electrical conductivity[l6] and of binary diffusion[l7] near a nematic— smectic transition. Here we report an investigation by X-ray diffraction on the cybotactic cluster formation near the nematic—smectic A transition of TBBA liquid crystal, by following a procedure similar to that of McMillan. Very recent measurements by NMR of diffusion coefficients by Kruger and co-workers[18, 19] on this very interesting substance do not exclude the existence of cybotactic clusters, The experimental apparatus we did use was a conventional vertical X-ray powder diffractometer which was properly modified to allow the insertion of a nearly vertical magnetic field of 1.7 kG. The primary beam of Ni filtered CuKa radiation (X = 1.54 A impinged on the 1 mm thick sample, ______________

*

This wQrk was supported by C.N.R. 433

the temperature of which was controlled electronically to 0.3°C by a hot stage containing electrical resistors. Diffraction patterns were recorded first from the powdered sample at different phases during the heating process under magnetic field, starting from room temperature. 26 scans were performed automatically around the low angle peak position corresponding to the smectic A interplanar distance of 27.6 A, which is approximately the molecular length. As the temperature was progressively raised a sharp increase of the Bragg peak was observed at a certain point, indicating that the molecular alignment was taking place. The sample ‘—

was held under magnetic field at 30°Cabove the transition temperature for 30 m and then progressively cooled until the transition to the smectic A phase took place. Figure 1 shows the scattering (diffraction) peaks obtained in the nematic phase (T = 214°C)and in the smectic A phase (T = 181°C).This kind of diffraction patterns has been recorded throughout the phase transition as a function of temperature. Figure 2 shows the measured peak maximum intensity as a function of the temperature. The temperature scale is referred to the critical temperature 7~,which practically can be assumed to be equal to the transition temperature T = 199 C measured independently by calorimetry and which was assigned to the abscissa scale of Figs. 2—5 by the best fit method discussed below. Figure 3 shows the measured full widths at half maximum of the diffraction peaks as a function of the temperature. Also the corrected widths are reported in the Figure. The correction was performed by ¶ Actually in the nematic phase one should speak of scatteringpeaks rather than diffraction peaks. However, we will use the term diffraction for convenience.

434

EVIDENCE FOR CYBOTACTIC CLUSTER PRETRANSITION 29

800-

SCANS

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8000

>-

T°181°C C)

0

>-

>-

Cl)

‘-,)

w

w

Vol. 24, No.6

TBBA NEMATIC

50

z w

~40 — ~304

I—

N E M A i I C

400

<20-

S M E C T 4000-

0 w

C

U) ) 10 4 w

A

~

‘~

-

OOp I

I

0

10

0

00

20

I

30

Tr 214°C

Fig. 2. Measured peak maximum intensity of the diffraction pattern as a function of the temperature in the nematic phase. The critical temperature T~can be assumed to be equal to T 199°C(see text). I

1°

TAKE

OFF ANGLE

•

~

1° (29)

I

Fig. 1. Diffraction patterns of CuKa radiation (X = 1.54 A) by aligned TBBA in the nematic phase and in the smectic A phase (Bragg angle 1.6°).

assuming that the angular instrumental resolution coincides with the 0.4°value of the full width at half maximum measured in the smectic A phase and reported in Fig. 1. Furthermore it was assumed that the resolution is of triangular shape, as appears evident from the figure, and that the shape of the intrinsic diffraction pattern is Lorentzian [4,7]. Then a deconvolution calculation allowed an evaluation of the corrected full width at halfmaximum and of the corrected peak maximum intensity. The diffraction patterns were recorded by moving the detector in the scattering plane containing the direction of molecules and of the magnetic field. Therefore the measured momentum transfer hq11, where q11 = (4ir/X) sin 0, is as a consequence parallel to the magnetic field direction and is equal to hq11 defined in [5] A scale in q1~units is reported in Fig. 3. In the following we will neglect, as McMillan does [61, the variation of the molecular structure factor over .

0

j5

I

•°

-

MEASURED CORRECTED

I

TB BA

I

NEMATIC 0.10 A

Q 1°

o-1

W

az Q I— 0 ~ Q5 a

0.05A

LL

a

Ic 0

I

10

20

30

[T—T~](°C)—-

Fig. 3. Measured and corrected full width at half maximum of the diffraction pattern as a function of the temperature in the nematic isphase. The correction the instrumental resolution discussed in the text.for The unit of the right side scale is q( 1 = (4ir/X) sin 0. the region of q space corresponding to the diffraction peak. The points reported in Fig. 4 represent the corrected values of the peak maximum intensity. The scale is in arbitrary units and is independent of the scale

Vol. 24, No.6

EVIDENCE FOR CYBOTACTIC CLUSTER PRETRANSITION

I

I

I

I

I

TBBA NEMATIC 1—40-

— i=1.35~0.15 BEST FIT FOR

z

~

used in Fig. 2. The large errors in the points at low ternperatures are due to the big corrections introduced. Pretransition effects are clearly visible, as in the substances investigated by McMillan[4, 7], in the form of a continuous increase of the intensity as the critical temperature is approached. The phenomenon observed by McMillan was described theoretically by a Landau theory of the phase transition developed by McMillan [4] and by de Gennes[8, 91. The theory, which calculates the scattering due to order parameter fluctuations, predicts that the maximum X-ray intensity of the Lorentzian peak should vary as (T— T,,)~’,where T~ is a critical temperature somewhat below the transition temperature. The McMillan theory predicts that y should be equal to I, and the de Gennes theory, based on an analogy to the normal metal—superconductor phase transition and a Wilson calculation, predicts that y should be equal to 1.30. Experimentally McMfflan found for y a value of 1 in the nematic—smectic A first order phase transition of OBT[6] and a value of 1.49 in the nematic— smectic A second order phase transition of CBAOB. The critical temperature T~was in the OBT 1°Cbelow the transition temperature. The solid line shown in Fig. 4 represents the best fit of the experimental data obtained for the value y = 1.35 ±0.15 and for the assignment of the critical temperature T~shown in the figure with an uncertainty

— BEST FIT FOR ~=0.45± 0.15

11

-~

-250 ~

-200~ 450

‘~

20

[T T~](’C)~

—

0<

~:

30

Fig. 4. Best fit of the corrected peak maximum intensity as a function of the temperature, according to the dependence (T 1~)~ and the value of y = 1.35 ±0.15.

I I

~8c-I~ z ( w

-

20-

I

TBBA NEMATIC

~-1~-~

-

-

~30-

10-

~12O-

435

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10 20 [T—Tc](~C)—’

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~

30

Fig. 5. The longitudinal coherence length ~ of cybotactic clusters and their equivalent thickness L as a function of the temperature. The best fit of the experimental data according to the dependence (T— 7~)~ was obtained for v = 0.45 ±0.15. of ±0.3°C.Due to the uncertainty in the absolute temperature scale of the X-ray hot stage and to the small difference between the critical temperature and the transition temperature observed by McMillan, one can attribute to 7~the transition temperature value T = 199°C,which we have obtained by calorimetric technique. They value found for TBBA agrees quite well with the de Gennes predictions and with the McMillan experimental values. In fact, being the nematic—smecticA transition of TBBA slightly of first order [20], it is reasonable to get a y value between the first order and the second order phase transition values obtained by McMillan. From the corrected diffraction peak widths reported in Fig. 3 it was possible to calculate the longitudinal coherence length [7,9] ~ through the equation [9] =

.~

(1)

where ~q1)is the full width at half maximum of the Lorentzian curve, reported in Fig. 3*~The ~ values ___________

*

Actually the ~.K values mentioned in [9] are equal to our (z~q11/2)values.

436

EVIDENCE FOR CYBOTACTIC CLUSTER PRETRANSITION

obtained are reported in Fig. 5 as a function of the ternperature. Pretransition effects are visible in the form of a progressive increase of the coherence length, as the temperature is reduced, up to a divergence near the critical temperature. The minimum ~ value is 23 A at T = 27°C.At first sight it could seem astonishing that the coherence length, which measures the dimension of the cybotactic cluster [9], is smaller than the molecular length (—‘ 27.6 A). We believe that it is due to the definition of ~I(’ on statistical mechanics basis, more than on crystallographic basis, so that one should expect that ~ gives merely an order of magnitude, more than the effective cybotactic cluster dimension. In order to have a more realistic evaluation of the thickness L of the cybotactic clusters, we have used the approximated Scherrer equation valid for single crystals and reported as equation (5.3) in [21] —

~ (20)

0.9X =

LCOSOB

(2)

where X is the wavelength of the diffracted radiation, 0B is the Bragg angle, and ~ (20) is the full width at half maximum of the diffraction peak, i.e. the quantity reported in Fig. 3. By using equation(2) one obtains the scale for L shown on the right side of Fig. 5. Clearly this procedure is approximated (for instance the shape of diffraction pattern by single crystals is not a Lorentzian) and gives only an equivalent thickness of cybotactic clusters, which however seems to be more realistic, from a pictorial point of view, than the coherence length In fact the minimum value of L is 60 A, which corresponds to at least two molecular lengths. The ratio between L and ~ is about a factor three.

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Theory [9] predicts that ~ should vary as (T-— ~ where v is about one half of y. The best fit of the experimental data reported in Fig. 5 yields a value of v = 0.45 ±0.15. This value appears to be lower than one half of the y value. McMillan obtained [5] two different values for v in CBAOB, i.e. v = 0.75 for the longitudinal coherence length ~ and v = 0.6 for. the transverse coherence length From the divergence of the bend elastic constant a value of v = 0.65 ±0.05 was obtained[13j in the similar material CBOOA and a value of v = 0.66 by Rayleigh scattering[l0j, whereas Cladis [15] obtained v = 0.5. Ribotta and Durand found by investigating the mechanical instabilities of CBOOA in the smectic A phase under dilative instability, that the dilative instability threshold was divergent with an apparent critical exponent (0.16) significantly smaller than the expected v/2 value. The critical exponents arising from our work should be taken with caution as the results are very preliminary. A much more accurate determination of their values in TBBA will be undertaken ~.

as soon as a new experimental apparatus, allowing higher resolution and precision is ready. In conclusion, however, the evidence can be stated for the progressive formation, as a pretransition phenomenon, of cybotactic clusters in TBBA. The thickness of clusters, of the order of few molecular lengths about 30°Cabove the nematic—smectic A transition ternperature, increases progressively as the temperature is reduced, until it diverges near the transition.

~.

Acknowledgements It is a pleasure to thank P. Detourbet, L. Ferrantini and L. Tontodonati for their valuable technical assistance. —

REFERENCES 1.

DE VRIES A., Acta Ciyst. A25, S 135 (1969).

2.

DEVRIESA.,Mol. Cryst.Liq. Cryst. 10,31 (1970).

3. 4

DE VRIES A.,Mol. Cryst. Liq. Cryst. 10, 219 (1970). MCMILLAN W.L., Phys. Rev. 6A, 936, (1972).

5.

MCMILLAN W.L.,Phys. Rev. 7A, 1419, (1973).

6. 7. 8. 9.

MCMILLAN W.L., Phys. Rev. 7A, 1673, (1973). MCMILLAN W.L., Phys. Rev. 8A, 928, (1973). DE GENNES P.G., Solid State Commun. 10, 753, (1972). DE GENNES P.G.,Mol. Cryst. Liq. Cryst. 21,49, (1973).

10. DELAYE M., RIBOTTA R. & DURAND G., Phys. Rev. Lett. 31,443 (1973). 11. SALIN D., SMITH I.W. & DURAND G., .1. de Phys. 35, L-165 (1974). 12. CHU K.C. & MCMILLAN W.L.,Phys. Rev. hA, 1059 (1975).

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EVIDENCE FOR CYBOTACTIC CLUSTER PRETRANSITION

13. CHEUNG L., MEYER R.B. & GRULER H.,Phys. Rev. Lett. 31, 349 (1973). 14. LEGER L.,Phys. Lett. 44A, 535, (1973). 15. CLADIS P.E.,Phys. Rev. Lett. 31, 1200 (1973). 16.

MIRCEA-ROUSSELA.& RONDELEZ F.,J. Chem. Phys. 63, 2311 (1975).

17. RONDELEZ F. & MIRCEA-ROUSSEL A., (Unpublished results). 18. KRUGER G.J., SPIESECKE H. & VAN STEENWINKEL R., J. dePhys. Coil. 37, C3.l23, (1976). 19. KRUGER G.J. & WEISS R.,J. dePhys. 38, 353 (1977). 20. LUZ Z. & MEIBOOM S., J. Chem. Phys. 59, 275 (1973). 21. GUINIER A., X-ray Diffraction, Freeman, San Francisco (1963). 22. RIBOTTA R. & DURAND G.,J. dePhys. 38, 179 (1977).

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