STATISTICAL PROPERTIES OF DYNAMIC SCATTERING IN MBBA

(1)

HAL Id: jpa-00216223

https://hal.archives-ouvertes.fr/jpa-00216223

Submitted on 1 Jan 1975

HAL is a multi-disciplinary open access

archive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

STATISTICAL PROPERTIES OF DYNAMIC

SCATTERING IN MBBA

M. Zulauf, M. Bertolo’Iti, F. Scudieri

To cite this version:

M. Zulauf, M. Bertolo’Iti, F. Scudieri. STATISTICAL PROPERTIES OF DYNAMIC

(2)

JOURNAL DE PHYSIQUE Colloque C1, supplkment au no 3, Tome 36, Mars 1975, page (21-265

Classification

Physics Abstracts

7.130

STATISTICAL PROPERTIES OF DYNAMIC SCATTERING IN MBBA

(")

M. ZULAUF

Biozentrum der Universitiit-Basel, Switzerland

M. BERTOLOIITI and F. SCUDIERI

Istituto di Fisica, Facolti di Ingegneria, Universitk di Roma, Roma, Italy

RbumB. - L'analyse de la fonction de corr6Iation du second ordre de la lumikre diffuske par le

MBBA en presence d'un champ Blectrique alternatif montre l'existence de diffkrents types de pro- cessus responsables de la diffusion. Nous prbentons une discussion de resultats expQimentaux. Abstract. - The analysis of the second order correlation function of light scattered by a nematic liquid crystal (MBBA) in the presence of a d. c. electric field shows the existence of different kinds of processes responsible for the scattering. Experimental results are presented and discussed,

1. Introduction.

-

Some aspects of motion in volume is of the same order or less than the correlation liquid crystals under the action of an external d. c. length of fluctuations in the material, the scattered field electric field can be studied by means of a correlation looses its gaussian properties, and therefore eq. (3) is technique which consists in measuring the second-order no longer valid.

correlation function g(2)(z) of the scattered light field, The gaussian property is also no longer valid when

defined as the scattering is produced by single centres whose

number at a time in the scattering volume approaches g'"(z) =

<

I(0) I(z)

>

_' ₍₁₎ unity [3]. It is however possible in certain cases to gain information on the gross shape of the spectralline ever where I(t) is the light intensity at time t .

If the statistics of the scattered light is Gaussian one a measurement of gC2)(z) is equivalent to a spectral analysis, g(2)(z) being simply connected to the first order correlation function

by the well-known relation

g'"(r) = 1

+

1

g'l'(z) 12

.

₍₃₎

We recall here that in digital correlation experiments such as the one described here, the quantity determined, in the case of Gaussian statistics, is

Z(')(z) = 1

+

a g'"(z)

i2

,

( 3 4 where a is a constant depending on spatial coherence, etc. [I].

Great care must be taken in using eq. (3) or (3a) due to the fact that its validity is limited to the case of Gaus- sian statistics. It has now been well demonstrated [2] that when the characteristic length of the scattering (*) Work partially supported by the National Research Coun-

cil (CNR) of Italy in the Quantum Electronics Group (GREQP).

when the statistics not ~ a i s s i a n . In ;he following it will be shown that different relaxation processes in the motion of the liquid crystal can be observed through a study of the time behaviour of the function gf2)(r). The experimental results show that the technique employed is very convenient for studying the dynamic flow of material.

2. Experimental apparatous. - The material exa- mined is MBBA [n-p-methoxybenziliden p-n (butil- anyline)]. The liquid crystal is contained in a cell 12 thick, whose details have been described elsewhere [4]. The applied electric field is parallel to the incident light direction and the material is initially in homeotropic configuration. The experimental set-up is shown in figure 1. A polarized laser beam (CRL Krypton gas

L A S E R

T H E R M A L C O N T R O L

FIG. 1.

-

Experimental set up.

(3)

M. ZULAUF, M. BERTOLO'ITI AND F. SCUDIERI

Fro. 2.

-

Plot of - In [&(z)

-

11 vs. z for different applied voltage values.

A

(4)

STATISTICAL PROPERTIES OF D YNAMIC SCATTERING I N MBBA C1-267

laser operated at

A

= 6 471

A

with adjustable power, typically a few mW) is focused, by means of a micro- scope objective (Leitz 20 x), on the thermostated sample cell at 22 OC. The scattering volume has a dimension of

about 80 y. The scattered light is observed in parallel and perpendicular polarization through a pin-hole of 50 p diameter at a distance of roughly 8 cm, by means of a photo-multiplier FW-130. The output signal is autocorrelated (Precision Devices Systems Ltd, Mal- vern) and the normalized second-order correlation function g(2)(z) is plotted versus time at 24 points. The scattering angle was fixed at 25 OC.

3. Experimental results. - A convenient method of interpreting the data consists in plotting

-

In [;(')(z)

-

I] versus z = v T ( v = 1,2,

...,

24). We have collected a few typical experiments in two single graphs with sampling times T = 100 ys and T = 1 ms (Fig. 2 and 3). We concentrate here on the case of ver-

tical polarization.

Qualitatively, the shape of the correlation function in terms of its dependence on the applied electric fields shows clearly visible trends : at low voltage, below the Helfrich threshold (- 5.5 V), there is a single exponential relaxation corresponding to the slow mode of thermal orientation fluctuations of the molecules as described by de Gennes [5]. Above the Helfrich threshold and below the threshold U , for turbulence

(< 11 V ) , hydrodynamic motion of the molecules can be seen in the correlation function by the appearance of a curvature in the shape of the

-

In [if2)(z)

-

11 function. For increasing voltages (> 12 V), turbulent motion of the material shows up by an increase of the intensity of scattered light and the onset ,of a new type of curvature in In [&z)

-

11.

4. Discussion. - The results obtained show clearly the pure de Gennes mode at voltages below the Helfrich threshold :

In the intermediate range, between the Helfrich threshold and the threshold for turbulent motion, the presence of a curvature in the

-

In [;(')(z)

-

11 function shows that new processes are taking place. We have tentatively tried to fit the data by the sum of two exponentials in the form

The decay time P - l of the second exponential, as well as the relative amplitudes, depends on the strength of the field : with increasing applied voltage the orientational mode a becomes less and less pronounced. When the electric field is larger than the threshold U, for turbulent motion, the orientational mode of the molecular motion is negligible and there appears a polynomial dependence on z, where the various powers of z may enter with weights depending on the strength

of the applied field. At high field values the experimental data can be fitted by the simple function

if an exponentially decaying background at large z values is subtracted.

It is beyond the scope of the present experiments to describe the observed correlation function by a full calculation of the combined thermal and hydrodynamic modes of motion of the molecules. Instead, we propose a heuristic model which seems to describe the data reasonably well. In this model the motion of the material in the scattering volume is assumed to be similar to the motion of massive scattering centres in a turbulent flow. The light scattered from a seeded turbulent fluid has been described previously [2] and application to the liquid crystal case has been consi- dered [6]. The two processes giving rise to the scatter- ing, i. e. the slow mode described by de Gennes and the scattering by massive particles, are assumed to be statistically independent. The scattered electric field can then be written as the sum of the scattered fields produced by these two different mechanisms. Eq. (5)

can be very simply interpreted in this scheme as giving proof of the growth of a new mode (which can be tentatively associated to orientational fluctuations of the scattering centres) when the field is above the Helfrich threshold. The successive smooth passage to eq. (6), when the field increases, is a proof of the setting up of a turbulent motion of centres as described in reference [6]. a S p o t size 80 pm I

.,

9 0 P m

*

I a 105Pm A I : 130Pm r I 1 9 0 P m a

.,

430 pm A I I 6 7 0 P m A

(5)

C1-268 M. ZULAUF, M. BERTOLOTTI AND F. SCUDIERI

The presence of an exponentially decaying background is in agreement with the fact that the assump- tion of Gaussian statistics for the scattered field is not valid, and is connected to the smallness of the spot size used in the present experiment. Figure 4 shows h

g ( ' ) ( ~ )

-

1 taken for different values of the spot size at an applied voltage of 17 V.

It is evident that when the spot size is increased the background disappears, as must be expected from the preceding considerations.

Furthermore, figure 4 gives evidence of a departure from gaussian statistics of the scattered light when the spot size is under about 100 p for an applied voltage of

17 V. The presence of a background as shown in figure 4 supports a model in which large objects are supposed to scatter light besides the small massive scattering centres previously considered. These large objects could tentatively be identified with disincli- nation lines [7].

Conclusions. - In conclusion we can say that a Acknowledgment. - Discussion of the present expe- measurement of g(2)(z) can allow us to detect the diffe- riment with Prof. P. G. de Gennes, Dr. G. Durand rent kinds of motions that appear in the liquid crystal and Prof. P. Di Porto and B. Crosignani is gratefully when a d. c. electric field is applied. acknowledged.

References

[I] See for example, JAKEMAN, E., in Photon Correlation and [5] DE GENNES, P. G., C . R. Hebd. Se'an. Acad. Sci. 266B (1968)

Light Beating Spectroscopy, edited by H . Z. Cummins 15 ;

and E. R. Pike (plenum Press. New York) 1974, _GROUPE_{D'E?TUDE DES CRISTAUX LIQUIDES}_(Orsay),_J._Clzem. pp. 75 ff.

121 DI PORTO, P., CROSIGNANI, B., BERTOLOTTI, M., J. Appl. Phys. 51 (1969) 816.

Phys. 40 (1969) 5083. [6] BERTOLOTTI, M., DAINO, B., DI PORTO, P., SCUDIERI, F., 131 SCHAEFER.

-

- D. W. ~ ~ ~ B E R N E . B. J.. , Phvs. Rev. Lett.

-

28 (1972) . , SETTE, D., J. Phys. A (Gen. Phys.) 4 (1971) L 97.

475. [7] A first approach to light scattering by disinclination

[4] BARTOLINO, R., BERTOUITTI, M., SCUDIERI, F. and SETTE, D., lines is due to P. G. DE GENNES (private communica-

Appl. Opt. 12 (1973) 2917. tion).

Editorial Comment

The problem attacked in this paper is interesting, In our opinion, the results of such an experiment will but extremely intricate, and the intensity-intensity always be rather difficult to unravel. In the future, it correlation method chosen adds its own complica- might help to work with a scattering region smaller tions. The size of the probed regions is small, but than one Williams domain.