SPECTRAL MEASUREMENTS OF THE DEPOLARIZED SCATTERED LIGHT FROM A BINARY MIXTURE NEAR ITS CRITICAL POINT

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SPECTRAL MEASUREMENTS OF THE DEPOLARIZED SCATTERED LIGHT FROM A BINARY MIXTURE NEAR ITS CRITICAL POINT

D. Beysens, A. Bourgou, G. Zalczer

To cite this version:

D. Beysens, A. Bourgou, G. Zalczer. SPECTRAL MEASUREMENTS OF THE DEPOLARIZED

SCATTERED LIGHT FROM A BINARY MIXTURE NEAR ITS CRITICAL POINT. Journal de

Physique Colloques, 1976, 37 (C1), pp.C1-225-C1-232. �10.1051/jphyscol:1976135�. �jpa-00216463�

SPECTRAL MEASUREMENTS OF THE DEPOLARIZED SCATTERED LIGHT FROM A BINARY MIXTURE NEAR ITS CRITICAL POINT

D. BEYSENS, A. BOURGOU

(*)

and G. ZALCZER Laboratoire de Diffusion Intlastique de la Lumi&re Service de Physique du Solide et de Rtsonance Magnttique

Centres d'Etudes Nucltaires de Saclay, BP no 2, 91 190 Gif-sur-Yvette, France

RBsumB. -

Nous presentons ici des mesures spectrales de la lumiere depolarisee diffuske par un melange binaire (nitrobenzkne et n-hexane) pres de son point critique de demixion.

La lumikre diffusee dkpolariske est due principalement aux fluctuations d'orientation et aux rediffu- sions multiples. Un Fabry-Pkrot de

60

GHz d'intervalle spectral libre permet de separer spectrale- ment ces deux contributions. La largeur de la raie de reorientation se comporte comme la viscosite.

Suffisamment loin du point critique, la variation spatiale et la dkpendance en temperature de l'inten- sit6 de diffusion multiple sont bien expliqukes par un calcul invoquant un processus de double diffu- sion, en bon accord avec la r6cente thkorie d'Oxtoby et Gelbart, Q condition de prendre en compte le phenomene de turbidite.

Abstract. -

We report spectral measurements of the depolarized light scattered from a binary mixture (nitrobenzene and n-hexane) near its critical mixing point.

The depolarized scattered light is mainly related to orientation fluctuations and multiple scatter- ing.

A

spectral analysis performed with a

60

GHz free spectral range Fabry-Perot spectrometer allows a rigorous separation of these two contributions to be made. The temperature dependance of the width of the reorientational spectrum is seen to behave in the same manner as the viscosity.

Both the spatial and the temperature dependence of the multiple scattered light are well explained by a double scattering calculation when

T

is not too close to

Tc,

and are in good agreement with a recent theory given by Oxtoby and Gelbart if however one takes the turbidity into account.

1. Introduction.

-

I t has been well known for a long time that the depolarization factor of binary mixtures drastically increases near the critical mixing point. A similar behaviour is seen in pure fluids near their liquid-vapour critical point. This general trend leads one t o ask certain questions

:

i) Is there any coupling in a binary mixture between the concentration fluctuations (the concentration is the order parameter of a binary system) and the reorien- tation fluctuations

?

ii) To what amount does the multiple scattered light contribute t o the total depolarized light

?

Does the study of the corresponding multiple intensity allow us t o experimentally obtain the 3-body, 4-body, ..., n-body correlation function

?

In order t o try and answer these questions we have performed spectral intensity measurements in the well known [I] binary mixture of nitrobenzene and n-hexane. What is the reason t o do spectral measure- ments

?

As is shown in figure 1 the spectrum of the polarized and depolarized light scattered by a binary mixture is ccmposed of lines which can be easily separated by a Fabry-Ptrot. The polarized spectrum is always dominated by the critical divergence (expo-

(*)

Ecole Normale Suptrieure,

43,

rue

^de

la Libertt,

Le

Bardo, Tunis, Tunisie.

Polarized Spectrum

concentration (-1) entropy(- a) brillouin

---

^{kHz I MHz GHz IO~,GHZ}

^--Y

multiple reorientation induced

scattering (?) (? anisotropy

apparatus function: 1.5 GHz background

- --

^{free I}

-

spectral range ^.-I

---

60 GHz Depolarized Spectrum

-

FIG. 1. -

The frequency range of the spectral lines scattered

by

a binary mixture is compared

with the

main spectral characteristics

of

a

Fabry-Perot interferometer.

nent

:

y) of the intensity related to concentration fluctuations. One can distinguish three parts in the depolarized spectrum

:

i) The reorientation spectrum, which is due t o the strongly anisotropic molecules of nitrobenzene (in solution). The order of magnitude of the corresponding half-width is typically 5 GHz. A 60 GHz free spectral range Fabry-Ptrot allows us t o resolve this spectrum.

ii) The broad depolarized components, like the induced anisotropic spectrum [27] whose half-width is

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1976135

C1-226 D. BEYSENS, A. BOURGOU AND G. ZALCZER

typically 1000 GHz. This line is present as a flat

background, owing to the Fabry-PCrot overlapping orders.

iii) The multiple scattered light. The corresponding half-width should be of the same order of magnitude as the linewidth of light singly scattered by the concen- tration fluctuation, i. e. lower than a few kHz. The corresponding spectrum will not be resolved by the Fabry-PCrot, and therefore will be seen as an apparatus function (half-width 1.5 GHz). Its intensity will be then given by the height - or the integral

²

of this peak.

We will describe first the experimental set-up

;

then we will deal with polarized intensity and turbidity measurements. Afterwards we will show the results concerning the reorientation spectrum and finally the spatial and temperature dependence of the multiple scattered light.

2. Experimental arrangement.

-

The liquids which we have used were of spectroscopic grade and carefully filtered through 0.2 p teflon filters in order to avoid dust particles. The binary mixture has a critical concen- tration of 0.42 mole fraction of njtrobenzene (0.51, by weight) [I]. Meniscus appeared at

The experimental set-up is shown in figure 2. The temperature of the scattering cell was maintained at a constant level within 0.005

O C

by circulating water from a thermostatic bath. Both transmitted and inci- dent intensity were recorded.

temp potent8ometrlc

photod~ode. 2 control recorder 1

quartz X12 + ottenuotot

thermometer

1'

recorder.2

I

pressure

Av=SOGHz

He-Ne

IHrd

^{recorder ampllfler}

^:i:F u

HV supply

EP

extinction ratio was only restricted by the aperture angle of the Fabry-PCrot

;

this ratio is about

Near the critical point we used an attenuator in order to avoid additional heating by the laser beam.

Both polarized and depolarized spectra were record- ed. As we have pointed out, the polarized intensity is always dominated by the concentration fluctuations whose spectrum is seen as an apparatus function.

Figure 3 shows the depolarized spectrum at various temperatures. One can see a background plus a Lorent- zian line which corresponds to the reorientation contributions, and superimposed on it, a peak which has the apparatus function shape and whose intensity is related to multiple scattering.

anisotropic Line

2

e

----

polarized Line = apparatus function

t o t a t spectrum 10 GHz

FIG. 2. -Experimental arrangement. The collecting lens (L)

can be moved vertically. FIG. 3. - Depolarized spectra obtained a t various T- Tc.

In order to detect the depolarized light, the axis of the Fabry-Ptrot spectrometer was carefully crossed with the laser beam (angle 0

=

90 f 0.020). The polarization of the incoming beam was then adjusted by means of a 4 2 plate

(I).

We have checked that the

(1) The rotation of this 112 plate makes the incident field vertical (polirized scattering) or horizontal (depolarized scatter- ing) ^: see figure 7.

A program of statistical refining due to M. Tour- narie [2,

31

allows us to deconvolute the spectra and gives

:

-

the integrated intensity of the peak, i. e. the mul- tiple scattering intensity,

-

the integrated intensity of the reorientation spectrum,

-

the half-width of the reorientation spectrum.

Let us now consider the results.

3. Polarized intensity and turbidity.

-

In order to to T, is well explained by the increase of the turbi- interpret our results we had to study the temperature dity

(2) :

Figure 5 shows the temperature dependence of dependence of the polarized intensity scattered at 900 the turbidity (z) deduced from the transmitted light and the transmitted light variations near the critical and from the discrepancy between theoretical and

point. experimental polarized intensity.

FIG. 4. - Temperature dependence of the polarized intensity Ill scattered at 90°. In order to show a power law dependence, Ill had to be divided by the (7') smooth temperature dependence factor.

The solid line represents the corresponding theoretical behaviour when assuming an Ornstein-Zernicke form for the pair correla-

tion function. 10 sets of experiments are shown.

Figure 4 shows the polarized intensity divided by the absolute temperature

:

III/T. This quantity is almost entirely due to the concentration fluctuations :

if one assumes an Ornstein-Zernicke form for the pair correlation function. 5 is the correlation length, Kis the transfer wave vector

:

at a scattering angle of 90°, K

=

KO J2, where KO is the, incident wavevector in the medium. The following numerical values are used

:

The to-value is readily obtained by measuring the line- width of the polarized spectrum [28] (light-beating spectroscopy). The agreement with the intensity measurements [I] of Lai and Chen (5,

=

3.64 A) is poor, but linewidth measurements are generally considered as a much more direct way of obtaining 1291 Furthermore, our value of 2.3 A is consistent with that deduced from linewidth measurements performed by Chen and Polonsky [I].

From the linear part of the log-log plot we can easily infer the critical exponent

y =

1.22 5 0.01. The result is in very good agreement with the values obtain- ed in reference [I].

The discrepancy between an Ornstein-Zernicke variation (solid line) and the experimental values close

1

b.%

..

Transmlssnn m e

-

^Theory

FIG. 5.

-

Temperature dependence of the turbidity (7) deduced from transmission measurements and discrepancy between ZII/T and the theoretical curve close to Te. The solid line is the theore-

tical variation (see text).

An analytic form of z [4, 51 may be given

where

a =

K2 5'

;

one neglects the Fisher's exponent

y.

(a,u/ac),.,. behaves as

E~ ;

so we have written

:

(when

^E =

1 , (3

^{p,T =}

_($1 2 ^.

All parameters are known, except ( a ~ / a c ) , . ~ which we must compute. If we suppose that the internal field which acts on the fluctuations can be described by a Lorentz-Lorenz field (there is some evidence that the problem is much more complicated

:

see references [6]

and [7]), one finds

:

=

0.472 and (g) - 200 .T/cm3 .

0

(2) The turbidity (2) is the rate of decrease of the incoming beam (Io) per unit length. If I is the transmitted light through a cell of length ( I ) , one can write : I = I 0 e-fa. s may be deduced by integrating the first scattering [4, 51.

C1-228 D. BEYSENS, A. BOURG iOU AND G. ZALCZER

If one assumes the mixture to be ideal, one can compare this result with calculations performed by Berg6 and Dubois 181

:

The ratio between (apldc), and (d,~/dc)~, is about 1.

Let us now consider the depolarized contributions

:

4. The reorientation spectrum [9].

-

In 1973, Atakhodzaev et al. [lo] reported spectral measurements of the depolarized light scattered in a binary mixture of nitrobenzene and n-hexane. They explained the narrowing of the depolarized Rayleigh linewidth (T) as resulting from a new xnexpected critical effect, and described the total spectrum as the sum of 2 Lorent- zian lines with characteristic relaxation time

^7,

and

^{7 ,}

(T,,, =

l l n r ,

,,

following the authors notations [lo])

:

where o, - ^o2 - 0.6, close to the critical exponent

v.

Moreover, zJpg < 10-lo

^{S, 7:} =

5.9 x 10-'I s, zYg

=

3 x 10-12s and

7: =

4.6 x 10-l3 s.

4.1 LINEWIDTH.

-

Following the authors nota- tions [lo], the depolarized spectrum at T

-

Tc

⁼

10 OC would consist of 2 Lorentzian lines of half-width

r1

⁼

1 / 7 ~ 7 ~

=

0.47 GHz and T,

=

1 / 7 ~ 7 ~

=

44 GHz, and therefore should be easily apparent in the 60 GHz free spectral range of our spectrometer.

In fact it was impossible to show the existence of two lines. All the spectra fit very well with one single lorentzian line plus a Dirac function (elastic scattering) convoluted with the apparatus function. This Dirac function is related to the non ideal polarization geo- metry, and near Tc to the multiple scattered light which drastically increases when approaching the critical point (3). As Aref'ev [ l l ] has pointed out, such a phenomenon can explain the two lines found in reference [lo] and also their temperature dependence.

Moreover, the method employed by Atakhodzhaev et al. to find the linewidths (plot of I-' versus the square of the frequency) is often of poor accuracy when there is an important amount of elastic light.

Figure 6 shows the variations of the half-width r

versus 1 000/T (semi-log. plot). T is the absolute temperature. Unfortunately, no valid measurements could be performed very close to Tc ( T

-

Tc < 1 OC), owing to the increase of the multiple scattering (see Fig. 2

:

at T

-

T,

=

0.610 OC, no spectrum could be seen). In figure 6 one can see also the reference [lo]

data concerning only the broader spectrum (7,) which is undoubtedly the less altered by the multiple scat- tering. We had to divide these latter values by an arbi-

(3) This multiple scattered light, as we are going to show, is obviously still visible when one observes outside of the exciting beam.

70- Atakhodzhaev I*VL)

8:

Our rneosurernents

7 - A A l m s l e x t ~ o p o l a t e d l 7

6

FIG. 6. - Comparison between our linewidth measurements and light-scattering or viscosity data. The upper points (m 0 A) concern light-scattering experiments (left scale), the lower points

(+ X ) relate to viscosity measurements (right scale).

trary constant factor

(=

4) in order to make these data consistent with ours at large T

-

Tc. In fact this discrepancy is certainly due to the method employed in reference [lo] to measure the half-widths. Never- theless, near the critical point, these data are lower than ours.

As in other binary mixture [12], the variation of I' versus 1 000/T (Fig. 6) shows that the temperature variation of the critical mixture of nitrobenzene and n-hexane is governed by an Arrhenius' law

:

where

E

is an activation energy, k the Boltzmann constant and T the absolute temperature.

It is well known [13] that r has the same tempera- ture dependence as the inverse of the viscosity, and in figure 6 one can see the data for

^{i j - l}

obtained by Drapier [14] and Szafronska [IS]

;

their results were extrapolated to the exact concentration we used. It is clear on figure 6 that the data of light scattering and viscosity are in good agreement. They both lead to the following value of the activation energy

:

E - ^{1.75 x} 10-l3 e r g .

The corresponding value for pure nitrobenzene is

:

2.4 x 10-l3 erg according to viscosity and light scattering data from references [16, 17, 181 and 1.2 x 10-13 erg for pure n-hexane from viscosity data of references [14], [18].

On the other hand, it is well known [19, 201 that the width of the reorientation spectrum of nitrobenzene significantly increases in solution, and it is somewhat surprising to find in [lo] a strong decrease

:

at 30 OC,

r2

^N

44 GHz and corresponds to the Rayleigh wing

(- 1 000 GHz [20] in pure nitrobenzene), and

r, - 0.47 GHz corresponds to the dzfluse line (- 5.50 [16], [19, 201

(4)

GHz in pure nitrobenzene).-One has therefore to compare our values with those expected in a binary mixture far from its critical point. This

(4) And our measurements.

comparison is possible because the study [20] of the 5.1 OXTOBY-GELBART'S

THEORY

[23]. - In 1974 reorientation time of the difSise line of nitrobenzene Oxtoby and Ge1ba1-t ~ r e d c t e d the temperature depen- in weak polar and weak anisotropic solvents shows a dence of the multiple scattered light assuming the roughly linear dependence of (2 nT)-l versus concen- following points

:

tration and viscosity (y) of the mixture

:

i) the 4-body correlation function can b.e expressed

1 as the product of two pair-correlation functions

;

- =

2 n r

^CY

+

^To

ii) triple or higher order-scattering is negligible.

where

c =

6.0 x 10-l2 cp-I and does not depend on The first assumption is all the more justified when the solvents. z0 is no longer dependant on solvents and is a illuminated and observed volumes are separated by a function of the concentration of nitrobenzene. At the macroscopic distance (i. e. a distance greater than the exact concentration used in the critical mixture, one correlation length). Moreover, these assumptions can finds

z, =

7.5 x 10-l2 s. From the viscosity data be checked by comparing measurements inside and

one infers

:

outside the exciting beam.

The result of the calculation is expressed by the

r - 14 GHz (at 24 OC) .

This result is in agrement with our data : T - ^{10 GHz}

at the same temperature. The critical mixture linewidth has therefore a value which can be deduced from general data in other binary mixture far from their critical point.

4.2 INTENSITY.

-

The integrated intensity of the reorientation spectrum can be compared with the corresponding value in pure nitrobenzene (we recorded some spectra of pure nitrobenzene in the same condi- tions as for the critical mixture)

:

IVH - 0.18 (at 24 OC) .

IVH (NBz)

The depolarized intensity measurements performed in many different solutions of nitrobenzene far from their critical point (but at the same concentration of nitrobenzene we used) lead to the same result, the measurements being of a spectral [20] or not spectral nature [21]

:

IVH - 0.22 (at 24 OC) .

IVH (NBz)

One can therefore conclude that there is no critical behaviour of the linewidth in this binary mixture, except perhaps a weak decrease due to the critical anomaly of the viscosity. Such a conclusion was put forward in 1974 by Aref'ev for the critical mixture of nitroethane-isooctane [Ill. This mixture is in fact well known for its very weak opalescence even close to the critical point. The multiple scattering is therefore negligible and cannot lead to errors.

Let us now study this multiple scattered light

:

5. Spatial and thermal dependence of the multiple scattering [22].

-

The peak which is superimposed on the spectrum (Fig. 3) is still observed when looking outside the exciting beam. This is consistent with the fact that this peak measures the multiple scattering intensity.

What are the predictions for the multiple scattered light behaviour near T,

?

following equation, where IDS is the double scattering intensity

:

s

I s

² ILL

^{dV1 S@O - kl)}

^x

The indexes

⁽⁽

OBS

))

and

⁽⁽

ILL

⁾⁾

denote respectively the observed and illuminated volumes

;

is related to the Fourier Transform of the pair corre- lation function.

ko is the incident wavevector of light in the medium, k, is the first scattering wavevector, k2 is the second scattering wavevector. F is a factor which accounts for the polarization effects.

A third hypothesis was assumed by Oxtoby and Gelbart

:

the light source was punctual at the center of a spherical sample. This ideal experimental arran- gement leads to the following form for the double scattered light intensity (scattering angle

8 =

900)

:

where a

=

k2 t2

⁼

2 k? t2 and Rs is the radius of the sample.

J(a) is an integral which is a function of the geometry (spherical here)

:

a

CI

(I +

^--

sin

8

cos

@ )

(I -

-

+ a sin

8

cos

@

l + a )

J(a) is a relatively smooth function of a.

In the temperature range T - T, > 0.3O, J(a) is almost a constant, and we find the physically expected result

:

rDs - ( z , , ) ~

E - ~ Y .

Our preliminary results [24] recently showed this

C1-230 D. BEYSENS, A. BOURGOU AND G . ZALCZER

2

y

dependence. Nevertheless, it is clear that the geo-

metry used in the Oxtoby-Gelbart calculation is rather ideal

;

furthermore, the turbidity is not taken into account

:

this is consistent with the fact that the third scattering is found to be negligible. But near the critical point, we have seen that the turbidity increases dras- tically, making this latter assumption uncertain.

So we performed a new calculation to describe the multiple scattering behaviour with more realistic assumptions

:

5.2 A

MORE REALISTIC CALCULATION. -

The first two assumptions of Oxtoby and Gelbart are kept.

Nevertheless we consider the real experimental geo- metry (Fig. 7)

:

a cylindrical sample (radius R, length L) with the laser beam along the axis. We can select a thin cylindrical volume in the sample by moving the collect- ing lens (Fig. 2) along the Z-axis. This proof volume has a diameter determined by the pin-hole (i. e.

:

0.01 cm in the air) and a length which is almost cons- tant and equal to 2 R if one neglects terms such as Z2/R2.

We can therefore calculate the double scattering in the parallelepiped 2 R x 2 R x L if we take into account the influence of the refraction on the scattered field polarization (angle Z/R (1 - l l n ) ) and if Z/R remains small.

FIG. 7. - Experimental scattering geometry. n is the refractive index of the mixture. L/2 = R = I cm.

Furthermore, we neglect the sections of the incident beam and of the proof volume

:

both are assumed to be ideal lines. This last assumption leads to neglecting some geometrical convolutions for very small Z.

These simplifications give the foilowing results, when the calculation is started from (1)

:

where

P2 =

x2 + ^{y 2} + z2 ^{and R}

⁼

L - . ₂

The two brackets in the numerator correspond respectively to the Y and

Z

polarizations of the scat- tered light (I,,,,, intensity).

In order to take the turdibity into account near the critical point, we multiply the contribution of each path in the integral by exp(- TI)

:

I

=

L + p + ^Y - X and

z

is the turbidity early determined. This turbidity effect has here the following meaning (Fig. 8)

:

i) Loss of intensity along the incident beam by 1st scattering (path L/2 + Y).

ii) Loss of intensity along the first scattering path by 2nd scattering (path p).

iii) Loss of intensity along the 2nd scattering path

^{FIG. 8.}

-

Path of the light in the medium : i) the incoming beam, from (0, - L/2,O) to (0, Y, 0) ; ii) the first scattered light,

by 3rd scattering (path L/2 - X ) .

_{from (0, Y, 0)} to (X, 0 , Z ) ; iii) the second scattered light, from

On the other hand, it is obvious that all the light

(X, 0, Z ) to (R/2,0,Z).

lost by turbidity contributes to the increase of the

scattering intensity

^{( 5 ) .}

In order to clear up this point, we performed the integration of (3) either with the turbidity

(z #

0) or without the turbidity

(z =

0). The

( 5 ) In reference [25] a calculation is carried out which shows

that in a very particular geometry the turbidity acting on the

calculation (due to M. Tourharie) was performed

1st scattering can exactly cancel the increase of intensity due to

on a computer.

the 2nd scattering.

Let us point out that the critical Fisher exponent q

was assumed to be zero. Owing to its smallness (q - 0.08) [5] this assumption is justified and leads to much simpler calculations.

5.3 THE Z-DEPENDENCE.

-

Figure 9 shows the

I Z 1-dependence

⁽⁶⁾

of the depolarized intensity (I,,,,,) at various T - T, (log-log plot). Solid lines

FIG. 9. - Spatial variation of the multiple scattering (HH

+

^HV)

at various T- Tc (log-log plot).

are the calculated variations (the difference between z

=

0 or

z #

0 is negligible). One can see 2 different behaviours

:

i) large T - Tc

:

theoretical variations and experi- mental values are in good agreement if we add to the calculated double scattering some amount of 1st scattering which has the experimental shape of the beam. This is the same spurious amount which had to be substracted in reference [24] and is due to the extinction ratio of the polarization geometry ;

ii) small T

-

Tc

:

the single scattering becomes negli- gible, but the experimental curve is too flat. We can interpretate this phenomenon in terms of scattering of higher orders

:

3rd, 4th ..., etc ... which are the only phenomena able to increase the scattering light so far away from the beam.

5.4 THE

TEMPERATURE DEPENDENCE.

- The solid lines plotted in figure 10 shows the temperature depen- dence of the double-scattered light. The curves for the different geometries have been scaled in order to fit to each other at large T

-

T,. One distinguishes two calculations for two different I Z I, with turbidity (z

#

0) or without

(z =

O), and the Oxtoby-Gelbart result (where z

=

0).

The experimental points correspond to measure- ments performed outside the beam (I

Z [ =

0.1 cm) or inside ( 1 Z I

=

0.01 cm)

;

for the latter values, the

( 6 ) The symmetry of the data is always verified.

FIG. 10. - Temperature dependence of the multiple scattering (HH

+

HV) at various

I

^Z

I.

Solid lines are the calculated varia- tions with the turbidity taken into account (z # 0) or not (z = 0). Curves are scaled to fit to each other at large T- Tc.

FIG. 11.

-

Thermal dependence of the multiple scattered light (HH

+

HV) for 8 different geometries. 11 sets of experiments are shown. In order to give an absolute scale, these measurements are compared with the corresponding values obtained with well

known scatterers (see text).

lo-z 10.' 1 10 T-Tc

I ' " " ' " I '

lo5

_

^_

.

$ OW7srn z = o l c m + 6 0 0 0 7 Z=OOl

0 boo18 z = o

T - . $ 0 0 3 5 Z=O

IMS(unlt . $ O O 3 5 r n e o s ) ^o 4 0 0 7 0 2-01

r o

.

/007O ^{l o l o} 2 - 0 ^{z = o}

r 6 OlL 2 x 0 -

. .

^{- Z = 01cm}

i

t ^8?,

^dJp

lo5

10'

C1-232 D. BEYSENS. A. BOURGOU AND G. ZALCZER

single scattering amount had to be substracted for large T

-

T, (as in ref. [24]). The Z-flattening close to T, that we have noticed above is not visible, and all points lie on a single curve, which seems to be in good agreement with our calculation which takes into account turbidity.

One can notice also (Fig. 10) that the geometry has a weak influence on the temperature dependence of the multiple scattering

:

i. e. the 0.1 cm and 0.01 cm curves are relatively close to one another.

So we have plotted (in Fig. 11) 11 sets of experi- mental data corresponding to 8 different scattering geometries. All points could be matched to a single curve, the proportionality constant being related to the geometrical dimensions of the scattering volume and to the I Z I-variations of the intensity. Units correspond to measurements performed at Z

=

0 with a scattering diameter of 0.035 cm (in the medium). The deviations at very small T - T, can be attributed to third scatter- ing, fourth scattering, etc ... which compensate the effect of the turbidity.

In this figure are also shown intensity measurements performed in the same conditions on the reorientation spectrum of pure nitrobenzene, on the Rayleigh

-

Brillouin spectrum of pure benzene, and on the reorien- tation spectrum of the critical mixture. All measure- ments are spectral type and intensities are measured by the integral of the spectra. The values so obtained are in close agreement with those of other authors (see chap. 4) and give an absolute scale for the multiple scattering intensity in this particular geometry.

6. Conclusion. -

We have reviewed here the main phenomena responsible for the scattered light depo-

larization near the critical point of a binary mix- ture.

We have shown that all available data on the nitro- benzene and n-hexane mixture confirms, as for the nitroethane-isooctane mixture, that there is no signi- ficant change in the linewidth of the depolarization spectrum when approaching the critical point. The critical mixture linewidth exhibits the same tempera- ture dependence as ordinary mixtures do, except perhaps a weak anomaly due to the increase of visco- sity near the critical point.

In a wide range of temperature, multiple scattering is seen to be a double scattering, and its temperature and spatial dependence is well explained by an Oxtoby- Gelbart calculation

-

if however the turbidity is taken into account.

This phenomenon still exists near the gas-liquid critical point of a pure fluid and was recently exten- sively studied by L. A. Reith and L. H. Swinney [26].

They found the same 2

y

intensity variation in a quite different geometry, but no data close to T, were pre- sented.

Among the Oxtoby-Gelbart hypotheses, only the assumption relative to third, fourth ... scattering was found uncertain. We did not notice any evidence of effects from genuine three or four-body correlations.

Low-frequency spectral analysis is presently under- way in our laboratory to try and confirm this last affirmation.

Acknowledgments.

- The authors wish to thank P. Berg6 and P. Calmettes for very stimulating discus- sions. Also they thank P. Bonville and J. Hodges for their comments on this manuscript.

References

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1 (1969) 64 ; [IS] Handbook of Chemistry and Physics (R. C. West. Ed. Cleve- OSTROWKY, N., Thesis (unpublished) Paris (1970) ; land) 1966.

LAI, C., CHEN, S. H., Phys. Lett. A 41 (1972) 259. [19] CHABRAT, J. P., ROUCH, J., VAUCAMPS, C., C . R. Hebd. Sci.

[2] TOURNARIE, M., J. Physique 30 (1969) 47. Acad. Sci. B 270 (1970) 1556.

[3] BEYSENS~ D.9 Revue P h ~ s - 8 (1973) 175 and to be [20] ALMS, G. R., BAUER, D., BRAUMAN, J., PECORA, R., J. Chem.

published in J. Chem. Phys. (March 15, 1976). Phys. 59 (1973) 5310.

[4] PUGLIELLI, v., FORD, N., ~ h y ~ . Rev. Lett. 25 (1970) 143. [21] CouMou, D. J. HIJMANS, J., and MACKOR, E.-L., Trans.

[5] CALMETTES, P., LAGUES, I., LAJ, C., Phys. Rev. Lett. 28 (1972) Faraday SOC. 60 (1964) 2244.

478. [22] A more complete discussion can be found in : BEYSENS, D.,

[6] BEYSENS, D., to be published in J. Chem. Phys. (March 15, ZALCZER, G., to be published.

1976).

[7] GIGLIO, M., VENDRAMINI, A., P h y ~ . Rev. Lett. 35 (1975) 168. [23] OXTOBY, D. W. and GELBART, W. M., J. Chem. Phys. 60 [8] DUBOIS, M., BERGE, P., Phys. Rev. Lett. 26 (1971) 121. (1974) 3359.

[91 A more complete discussion can be found in : BEYSENS, D., [241 BEYSENS, D., BOURGOU, A., CHARLIN, H., P ~ Y s . Lett. A 53 BOURGOU, A., ZALCZER, G., Opt. Commun. 15 (1975) 436. (1975) 236.

[lo] ATAKHODZAEV, A. K., KASHEEVA, L. H., SABIROV, L. H., [25] BRAY, A. ^{J . y} CHANG, R. F., Phys. Rev- A l2 2594.

STANUROV, V. S., UTAROVA, T. H., and FABELINSK~~, 1261 REITH, L. A., SWINNEY, H. L., ~ h y s . ~ e v . A. 12 (1975) I. L., J. E. T. P. Lett. 17 (1973) 65. 1094.

[I 11 AREF'EV, I. M., Opt. Coinmun. 10 (1974) 3. [27] This broad depolarized Rayleigh line is due to inter- [12] SHAPIRO, S. L., BROIDA, H., Phys. Rev. 154 (1967) 129. molecular interactions. See for instance :

[13] See for instance : FRENKEL, J., Kinetic Theory of Liquids MCTAGUE, J. P. et al., J. Physique Colloq. 33 (1972) C 1-241, (Doves Pub. N-Y) 1955 and FABELINSKII, I. L., Mole- and GELBART, W. H., Adv. Chem. Phys. 26 (1974) 1.

cular Scattering of light (Plenum Press N-Y) 1968. [28] This experiment is connected with the study of the multiple- [14] DRAPIER, P., Bull. C 1. Sci. Acad. R. Belg. (1911) 621. scattering low-frequency spectrum, the results of which [15] SZAFRONSKA, Bull. Acad. Pol. Sci., A (1935) 110. will be published elsewhere.

[16] ZAMIR, E., GERSHON, N., BEN-REUVEN, A., J. Chem. Phys. 55 [29] See for instance : BERGE, P. and DUBOIS, M., Phys. Rev. Lett.

(1971) 3397. 27 (1971) 1125.