Measurement of the birefringence induced in liquids by ultrasonic waves : application to the study of the isotropic phase of PAA near the transition point

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Measurement of the birefringence induced in liquids by ultrasonic waves : application to the study of the isotropic phase of PAA near the transition point

P. Martinoty, M. Bader

To cite this version:

P. Martinoty, M. Bader. Measurement of the birefringence induced in liquids by ultrasonic waves :

application to the study of the isotropic phase of PAA near the transition point. Journal de Physique,

1981, 42 (8), pp.1097-1102. �10.1051/jphys:019810042080109700�. �jpa-00209095�

Measurement of the birefringence ^{induced in} liquids by ultrasonic waves :

application ^{to the} study ^{of the} isotropic phase ^{of PAA}

near the transition point

P. Martinoty ^{and M. Bader}

Laboratoire d’Acoustique Moléculaire (*), Université Louis-Pasteur, 4, ^rue Blaise-Pascal, ⁶⁷⁰⁷⁰ Strasbourg Cedex, ^France (Reçu ^{le 9} janvier 1981, accepté ^{le 30 mars} 1981)

Résumé.

On a développé ^une technique permettant ^{de mesurer la} biréfringence induite par les ultrasons dans les liquides : ^{les mesures} effectuées dans la phase isotrope ^{du PAA montrent} qu’il ^est possible d’obtenir des résultats fiables d’une façon simple ^et rapide grâce à des améliorations sensibles de la technique traditionnelle. En plus ^{de la} biréfringence ^{induite ce} dispositif ^mesure également le coefficient d’absorption de l’onde ultrasonore. La cellule de mesure utilise un faible volume de liquide ^{et est} particulièrement ^bien adaptée ^aux études des liquides ^rares et/ou ^des liquides très absorbants. Les résultats dans le PAA montrent que la quantité 0394n/~P, ^{où 0394n est la biré-}

fringence ^{induite et P} l’intensité acoustique, diverge ^{selon une loi en} puissance. ^Au voisinage ^de Tc ^le système

passe du régime ^{03C903C4 ~ 1 au} régime 03C903C4 ~ 1. Ces résultats qui ^{ont été} interprétés ^sur la base du modèle de de Gennes permettent de déduire le temps de relaxation orientationnel.

Abstract.

A technique ^{has been} developed for ultrasound-induced birefringence experiments. Measurements made in the isotropic phase ^{of PAA} (p-azoxyanisole) show that it is possible ^to obtain reliable results quickly

and in a very simple ^way through straightforward improvements of the traditional technique. In addition to the induced birefringence measurements our technique ^also provides measurements of the absorption ^coeffi-

cient of the ultrasonic wave. The cell has a low sample volume and is particularly ^{suited to studies on rare} liquids and/or highly attenuating liquids. The results on PAA show that the quantity 0394n/~P, where 0394n is the induced birefringence ^{and P the acoustic} intensity, diverges according ^{to a} power law. As ^one approaches Tc ^the

system crosses over from the 03C903C4 ~ 1 regime ^{to the} 03C903C4 ~ 1 regime. The results are interpreted ^on the basis of the de Gennes model. The orientation relaxation time is deduced from these measurements.

Classification

Physics ^Abstracts

61.30

78.20H - 64.70E

1. Introduction. - Some liquids ^{and solutions}

which are isotropic ^{at rest become} birefringent ^{in the}

presence of a sound wave and behave as a uniaxial

crystal ^{with its} optic ^axis lying along the direction of propagation ^{of the wave. This effect,} first observed

by ^Lucas [1] ^{over 40} years ago, depends strongly ^on

the acoustic intensity ^{and on} the related ultrasonic

absorption ^{in the} sample.

A number of theories for the effect have been

developed [2-5]. Although these theories clearly ^indi-

cate the potential value of acoustic birefringence studies, ^few experimental results have been reported

from which properties ^{of the} liquids ^can be deduced.

This situation _appears to be a result of the experi-

(*) ^{E.R.A. au C.N.R.S.}

mental difficulties involved in the measurement.

These difficulties arise from :

-

(1) ^the necessity ^to simultaneously ^{measure the}

induced birefringence and the acoustic intensity ^at

the place ^{where the induced} birefringence ^is observed ;

-

and (2) the small value of’the induced birefrin- gence which can be masked by ^different parasitic effects, namely, ^acoustic streaming ^which depends ^on

the absorption coefficient of the liquid

the increase in temperature ^{of the} liquid produced by ^the absorp-

tion of the sound wave

cavitation, which is the formation of small _gas bubbles that scatter and absorb the sound wave - the _presence of standing

waves.

By using pulsed waves, instead of continuous waves

which are generally employed, ^{the mean} power of the

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:019810042080109700

1098

acoustic intensity ^{is reduced} by ^a large ^{factor and}

the above difficulties are virtually eliminated. Further- more, by adjusting the duration of the ultrasonic pulse ^{to a} value less than the transit time through ^the liquid, ^{it is} possible ^{to avoid} any reflected sound

during ^the measurement of the induced birefringence.

In the first part ^{of the} paper ^we describe a technique

based _upon the pulse transmission method. This method not only ^reduced parasitic effects, but it also enabled us to measure the relative variations of the acoustic intensity. ^{In the} past the acoustic intensity

has always been evaluated from optical diffraction effects by employing Raman-Nath theory. However, the validity ^{of these} measurements are limited to the range where the Raman-Nath conditions relating ^to

sound wavelength, beam width and optical ^wave- length ^are applicable. This limitation is overcome by

the electrical measurements which are used here. This method offers, ⁱⁿ addition, the substantial advantages

of being ^more convenient, ^{more accurate and of also} measuring ^the ultrasonic absorption ^{in the} sample.

In order to reduce the acoustical path length ^and thereby the volume of the cell, ^the technique ^uses

two transducers, ^{one for} transmitting ^{and one for} receiving.

In the second part ^{of the} paper ^we present ^a study

of the birefringence ^induced by ultrasound in the

isotropic phase ^{of the} liquid crystal ^PAA (p-azoxyani- sole) ^{near its} isotropic-to-nematic ^transition ( Tc ’" ^135.4 OC).

The isotropic phase ^of liquid crystals ^{shows some}

remarkable short _range order effects which have been discussed theoretically by de Gennes in terms of a Landau model [6]. ^{The short} range order gives

rise to an induced birefringence larger than that in conventional liquids, but it also gives ^{rise to a} strong increase in the ultrasonic absorption and therefore in the heating ^and streaming effects. Since these last two effects are reduced to a minimum by ^{the use of} pulsed ^{waves, our} apparatus ^{is thus} particularly

suited to this study; ^these measurements give ^the

first conclusive results on the critical behaviour of the birefringence ^induced by ultrasound in the iso-

tropic phase ^{of a} liquid crystal.

Fig. ^1.

Experimental set-up ^{for the} measurement of the bire-

fringence ^induced by ultrasonic waves.

The work in the field of acoustically induced bire-

fringence performed prior ^to 1964 has been reviewed

by ^Jerrard [7] ^and Hilyard ^{and Jerrard} [8]. Only

two papers [9, 10] ^{on the} subject ^{have been} published

since then. Recently ^we have shown the possibility

of making ^a light shutter based on the birefringence

induced by pulsed ^{acoustic waves in the} isotropic phase ^{of a} liquid crystal [11].

2. Experimental.

^{A schematic} diagram ^{of the} experimental set-up ^{is shown in} figure ^{1. In} considering

the apparatus ⁱⁿ detail, ^the optical system including

the principles ^of measurement, ^the cell, ^{and the elec-} tronic system will be described separately.

2. 1 PRINCIPLES OF MEASUREMENT AND OPTICS.

In an acoustic birefringence experiment the direction of propagation of the incident light ^{beam is} perpen- dicular ^to that of the acoustic wave in the sample

and the light ^is linearly polarized ^{at an} angle ^{of 450}

from the vertical by ^{use of a} polarizer. ^In the absence of ultrasonic waves an analyser is crossed with the

polarizer ^so that there is no optical transmission. If,

on the application of the ultrasonic _waves, the liquid

becomes birefringent, ^the light polarization ^{vector is}

rotated through ^an angle ^{b and} light is transmitted

through ^the analyser. ^The intensity ^{7 of the trans-}

mitted light ^is given by

where I0 is ^the intensity ^{measured in} the absence of the sound wave when the polarizer ^and analyser ^are parallel.

By measuring ^{the ratio} III, ^{it is} possible ^{to deduce ô}

and consequently ^{the induced} birefringence ^{which is}

related to b by

where 1 is the optical path length in the medium and 03BB the optical wavelength ^{in vacuum.}

In our experiment ^{we used an He-Ne} laser with a

beam of ^{5 mW} power and a diameter ^{0.8 mm.}

The analyser ^and polarizer ^{were two} identical Glan- laser prisms ^{with an} extinction of 10-6. ^To improve

the sensitivity of the detection a quarter-wave plate,

with the fast axis parallel ^{to the incident} polarization direction, ^was placed between the sample ^{and the} analyser. The transmitted light ^{was detected} by ^a photomultiplier and recorded on one trace of a dual- trace storage oscilloscope, ^{the other trace} being ^used

to observe the acoustic pulse (see below). ^{The lens}

focussed the diffracted beams onto the photomulti- plier. ^{In order to take account of the} temperature-

dependent transmission of the beam, the value Io

was measured for each temperature.

2.2 Tue CELL.

The cell (Fig. 2) ^was composed ^of

the liquid ^bounded by ^two transducers which were

Fig. ^2.

^Schematic diagram ^{of the} acousto-optic cell. The follow-

ing parts ^are labelled : a) Thermostated jacket ; the heater is not

indicated; b) Optical chamber ; c) ^Window tube; d ) ^Transducer mounting; e) BNC connector ; f ) ^Teflon 0-ring ^for parallelism adjustment ; g) Optical window ; h) Transducer.

mounted in a brass ring. The transducers were adjusted parallel with three screws acting against ^{two Teflon} encapsulated 0-Rings. ^Two optical ^windows placed centrally, in between the transducers allowed the light

to pass through ^the liquid perpendicular ^{to the direc-}

tion of propagation of the acoustic wave. The optical

windows were thin cover glasses cemented with a

soft silicone adhesive to minimize strain birefringence.

The cell was enclosed between two identical heating jackets. ^Two types ^of jackets ^were constructed, ^one using electrical heating ^{and the} other, ^{water from a} temperature-regulated ^{bath. Because of the} high

temperature range where PAA is isotropic ^{we used}

the jackets with electrical heating ^{in this} experiment.

The temperature of the cell was controlled automa-

tically ^{to within} 0.01 OC. A calibrated platinum probe, positioned inside the sample ^{volume was used}

to read the temperature. ^The optical path ^{1 submitted}

to ultrasound was 10 mm. The strain birefringence

was estimated to be below 10-10. This cell which has a sample volume of N 0.5 cm’ and an acoustical

path ^{d of 1.37} mm, is suited to studies on rare liquids

and highly attenuating samples.

2.3 ELECTRONICS. - A tunable sine wave gene- rator, gated by ^DC pulses ^to produce ^RF pulses, ^and

a power amplifier ^{were used to} drive the emitting

transducer and to generate ^acoustic pulses. ^After propagating through the medium the acoustic pulses

were reconverted into RF pulses by ^the receiving

transducer. These pulses ^were amplified ^{and dis-} played ^{on the} oscilloscope. ^A calibrated attenuator

was used to cbntrol the amplitude of the acoustic

pulses.

As mentioned above the acoustic intensity ^{P within}

the liquid ^{must be known in an induced} birefringence experiment. ^{In the} present study ^{we have not deter-}

mined the absolute value of P, ^but only its relative variation as a function of the temperature, by keeping

the amplitude ^{of the} received acoustic pulse constant,

using ^the attenuator. Under these conditions, ^the

relative variation of P in the middle of the acoustical

path ^{where the induced} birefringence ^is measured, ^is given by

where L1 (dB) represents the number of decibels needed to maintain the acoustic receiving ^{level at a}

fixed value when the temperature is varied from Ti

to T2. ^L1 (dB) ^is directly ^{read on the} attenuator and its value also provides ^measure of the relative varia- tion of the absorption coefficient a which is given by

where d is the acoustical path length and the factor 0.115 converts a from decibels to nepers.

Absolute values of P can be obtained, ^if necessary,

by comparison ^{with a reference} liquid and absolute values of a can be obtained by measuring ^{An at}

several places along the acoustical path ^or by using

the cell as an acoustic resonator [12-13]. ^{This last}

method also allows measurements of the velocity ^of

the wave.

In the present experiment ^a frequency ^{of 7.98 MHz}

was used. The ultrasonics were pulsed ^{at a} frequency

of about 10 Hz. The duration of the acoustic pulses

was 1 ils, which is comparable ^{to the} time of travel

through ^the cell, ^{and the} top ^{of the} pulses ^{was flat.}

2.4 REMARKS.

In the determination of the bire-

fringence ^{An one must} take into account the fact that An varies sinusoidally (1) ^and decays ^{in the}

direction of propagation ^as

Ano being the maximum birefringence, ^{and a, v and ce} respectively ^the absorption coefficient, ^the velocity

and the frequency ^{of the wave.}

Thus :

1) Since the induced birefringence ^is oscillating ^it

is the r.m.s. value An of An which is measured.

2) ^{Because of the} decay ^of An, the distance x

d/2

where the birefringence ^{is observed must be known}

with _accuracy. This is particularly important ^for highly attenuating liquids ^{such as} liquid crystals.

3) Since the optical ^{beam has a} certain width

(labelled by ² e) and since An varies exponentially

with the distance, ^the quantity which is measured is in fact a mean birefringence given by

(1) Except ^for large rigid particles in solution where the orienta-

tion is supposedly ^caused by radiation pressure and ^not by ^the

oscillating gradients of the local velocity.

1100

If the product ^{as is small, An can} be written as :

where An(df2) represents ^{the r.m.s. value of the} birefringence ^{at the} middle of the acoustic path.

In this experiment ² E > 0.8 mm and the maximum value of a was less than 5 _nepers. cm-1. Therefore the correction term in equation (6) ^was negligible ^and

the measured birefringence ^was An(d/2). Experimen- tally ^{we did not observe} variations of the birefringence by reducing ^{the width of the} optical beam, ^{even near} Tc,

so this confirms the above conclusion.

4) ^{In the} derivation of the formula giving ^the

induced birefringence (Eq. (7) below) it has been assumed that a « w This condition was fulfilled in

v

the experiment.

3. Theoretical background ^{and results.}

For pure

liquids, ^the reorientation of the molecules is due to the velocity gradient ^G set-up ^{in the} liquid by ^the

passage of the acoustic wave [7, 8]. ^This gradient

acts in much the same way ^{as a} flow gradient giving

flow birefringence, ^{so that} birefringence ^induced by

ultrasound is closely related ^{to flow} birefringence.

Hence, ^{the r.m.s.} value An of the alternating ^bire- fringence may be written as :

where ônIG ^{is the} quantity ^{measured in a flow bire-} fringence experiment. ^P is the acoustic intensity,

v the velocity ^{and m the} frequency ^{of the wave. The}

relaxation term comes from the fact that the bire-

fringence ^{does not} disappear ^{with the wave but exists}

for a time -c which is the orientation relaxation time.

According ^{to the Landau-de Gennes model of the} pretransitional behaviour in the isotropic phase ^{of a} liquid crystal, T ^and bn/G ^are given by [6, 14] :

In these expressions the coefficient A(T) ^{is taken to}

be A (T ) ⁼ â(T - Tc*) where â is a constant and T/

the theoretical second order transition temperature which is slightly ^{below the} clearing temperature T,.

Ae is the maximum anisotropy ^{for a} perfectly ^orien-

tated liquid crystal ^{and n the mean} refractive index.

,u and v are weakly temperature dependent viscosity

coefficients.

Substituting ^{the value of} bn/G ^into equation (7)

one finds :

In the low frequency ^limit (cor « 1) :

and for _{mi » 1 :}

assuming that y, As and n do not vary significantly

with T.

_

Equation (7) shows that en is proportional ^{to the}

square ^root of the acoustic intensity P, ^{or to the vol-} tage V ^{at the} receiving transducer. Thus a graph ^of An against V should be linear and our results in figure ³

show that this is the case.

Fig. ^3.

Variation of the r.m.s. birefringence ^{An with the} voltage V

at the receiving transducer for various temperatures. ^{The linear} variation shows that An is proportional ^to the square ^root of the acoustic intensity.

In figure ^{4 we} present ^{our measured values of An} and L1 (dB) ^{as a} function of temperature. ^As expected

~n exhibits a strong critical increase when approaching

the transition. As mentioned above, ^{to obtain a} quantitative interpretation of the data it is _necessary to take into account the temperature dependence ^of

the acoustic intensity. This has been done in ^{figure 5}

where the temperature dependence of ~P/~n ~pv3 ^is

plotted ^{relative to} its value at an arbitrary tempera-

ture To (To

^155.06 OC).,IP- ^{has been} calculated by

formula (3) using the values of L1 (dB) reported ⁱⁿ figure ^{4. The} temperature dependence ^{of v was taken}

from reference [13]. ^{We have} ignored ^the slight ^tem- perature dependence ^{of fi and} 03BC.

Fig. ^4.

Variation of the r.m.s. birefringence An with the tempe- rature for a fixed value of the acoustic receiving ^{level. L1} (dB) repre- sents the quantity ^{needed to} compensate ^the temperature ^variation of the,, ultrasonic absorption. A(T) r>n 0.15 °C is a temperature region in which the nematic and isotropic phases ^coexist.

As shown in figure ^{5 the} temperature dependence

of J7/Anp is linear over a wide temperature range, in agreement ^with equation (10), ^{and the} extrapolation ^of the dashed line gives Tt = ^{134.2 °C.}

As one approaches Tc, ^a departure ^{from the} ( T - Tc*) - ¹

law is observed as a result of the crossover from the mi « 1 regime ^{to the} 03C903C4 ~ 1 regime. ^{We made a}

direct fit of the data using equation (9). The fit is shown as the solid line in figure ^{5 and the} resulting parameters ^are

where DT

T - Tc*.

The only previous study ^{on the} birefringence

induced by ultrasound in the isotropic phase ^of liquid crystals ^{was carried out over} 30 years ago by

Tsvetkov et al. [15] ^{in PAA. But} they ^{did not show}

that the induced birefringence ^varies according ^to

the square ^root of the acoustic intensity. ^{Nor did}

this study ^{reveal a} temperature dependence ^{for the}

relaxation time, presumably because of the difficulties mentioned in part ^{1 of this} paper.

Fig. ^5.

Temperature dependence of the ratic norma-

lized to T

155.06 OC.

4. Conclusion.

The present study of the bire-

fringence ^induced by ultrasound has provided ^the

first conclusive results on the critical behaviour of

%/Qi ^{in the isotropic phase of a} liquid crystal.

It has also been demonstrated that the _accuracy,

sensitivity ^{and ease of} operation of induced birefrin- gence measurements can be greatly ^increased through straightforward refinements of the traditional tech-

nique.

Birefringence ^{values as small as 10- 9 have} already

been detected with our apparatus ^{and the} possibility

of working with small sample volumes should be

emphasized ; this could be useful with ^{scarce biological}

products. ^{In addition to the} An/",/p measurements

our apparatus ^also provides measurements of the

absorption coefficient a An ^{data can then be used}

~P

in connection with sound absorption ^{results to check}

if the same relaxation time occurs in these two expe-

riments, ^as recently predicted by Lipeles ^{and Kivel-}

son for conventional liquids [5,10].

The method can be applied ^{to a wide variety of} problems. Among many examples, ^{one can cite the} thermotropic ^and lyotropic liquid crystalline systems (nematic polymers, lipid-water multilayers), ^colloidal suspensions ^and polymer ^solutions.

Acknowledgments.

^{We would like to thank}

J. Klein for the careful construction of the cell.

1102

References [1] LUCAS, R., ^C’.R. Hebd. Séan. Acad. Sci. 206 (1938) ^827.

[2] LUCAS, R., Rev. Acoust. 8 (1939) ^121.

[3] FRENKEL, J., ^Kinetic theory of liquids (Clarendon Press, Oxford) 1946, Chap. 5, p. 292.

[4] PETERLIN, A., ^J. Physique ^{Radium 11} (1950) ^45.

[5] LIPELES, R. and KIVELSON, D., ^{J. Chem.} Phys. ⁶⁷ (1977).

[6] ^{See for} example, ^DE GENNES, P. G., The Physics of Liquid Crystals (Oxford University, Oxford) ^1974.

[7] JERRARD, ^H. G., Ultrasonics 74 (1964).

[8] HILYARD, ^{N. C. and} JERRARD, ^H. G., ^J. Appl. Phys. ³³ (1962) 3470.

[9] RILEY, W. A. and KLEIN, W. R., J. Acoust. Soc. Am. 45 (1969)

578.

[10] LIPELES, ^{R. and} KIVELSON, D., ^{J. Chem.} Phys. 72 (1980) ^6199.

[11] MARTINOTY, ^P. and BADER, M., Appl. Phys. ^{Lett. 37} (1980) ^33.

[12] KIRY, ^{F. and} MARTINOTY, P., ^J. Physique ³⁹ (1978) ^1019.

[13] THIRIET, ^{Y. and} MARTINOTY, P., J. Physique ⁴⁰ (1979) ^789.

[14] MARTINOTY, P., KIRY, F., NAGAI, S., CANDAU, S. and DEBEAU- VAIS, F., ^J. Physique ^{Lett. 38} (1977) L-159.

[15] TSVETKOV, ^{V. N. and} KROZER, S. P., Dokl. Akad. Nauk SSSR

63 (1948) ^653.