High-resolution light-scattering study at the nematic-smectic A transition in 60CB/80CB mixtures

HAL Id: jpa-00210480

https://hal.archives-ouvertes.fr/jpa-00210480

Submitted on 1 Jan 1987

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.

High-resolution light-scattering study at the

nematic-smectic A transition in 60CB/80CB mixtures

H.-J. Fromm

To cite this version:

H.-J. Fromm. High-resolution light-scattering study at the nematic-smectic A tran- sition in 60CB/80CB mixtures. Journal de Physique, 1987, 48 (4), pp.641-645.

�10.1051/jphys:01987004804064100�. �jpa-00210480�

High-resolution light-scattering study ^at the nematic-smectic A transition in 60CB/80CB mixtures

H.-J. Fromm

Physikalisches Institut der Universität Münster, Domagkstr. 75, ^D-4400 Münster, ^{F. R. G.}

(Reçu le 21 août 1986, accepté le 18 décembre 1986)

Résumé.

On présente ^les premières ^{mesures du} mode de torsion dans la region critique de la transition N-

SA ; ^la technique ^{est la} spectroscopie hétérodyne de corrélation de photons. ^En appliquant la théorie de Jähnig

et Brochard, ^{on montre} que la dépendance ^en température ^de K2 et de K3 peut ^être décrite par la même formule. L’exposant critique qui ^en résulte pour 03BEI, ainsi que les préfacteurs 03BE|0 ^et 03BE~0 ^{sont en} très bon accord

avec les valeurs fournies par les rayons X. Les ^{mesures montrent} que la théorie de Jähnig ^{et Brochard} peut ^être appliquée ^{à la} dépendance ^en température ^de K2 ^{si on} suppose ^un passage de 03BE| ^et 03BE~ à ^un régime critique isotrope.

Abstract.

First twist mode measurements in the critical region ^{of the} N-SA transition using heterodyne photon-correlation spectroscopy ^are reported. Application ^{of the} theory ^of Jähnig ^and Brochard indicates that the temperature dependence ^of K2 ^and K3 may be ^described by ^{the same} formula. The resulting ^critical exponents of 03BEl ^{as well as the} prefactors 03BE|0 ^and 03BE~0 ^are in very good agreement ^with X-ray values. The measurements show that the theory ^of Jähnig and Brochard concerning ^the temperature dependence ^of K2 ^is applicable, ^{if one assumes a crossover to an} isotropic critical behaviour of 03BE| ^and 03BE~.

Physics ^Abstracts

61.30

64.70M

Among the various phase transitions observed in

liquid crystals the transition between the nematic and smectic A phase ^{is of} special interest. On the

one hand the melting of the one-dimensional solid- like smectic A phase into the three-dimensional

liquid-like ^nematic phase appears ^to be one of the

simplest transitions in the field of liquid crystals. ^On

the other hand it is attractive because of the

analogies ^to systems ^{such as} superconductors ^and superfluids ^{as discussed first} by ^{de Gennes} [1]. ^The particular dimensionality ^and symmetry ^{of the smec-}

tic phase ^have caused intensive theoretical studies aimed at identifying ^{the critical} point ^{with a well}

defined universality ^class [2-4]. ^{In order to describe}

the transition properly ^a large ^{number of} exper- imental studies have also been carried out [5-18].

unfortunately ^{there are} still fundamental discrepan-

cies between experimental and theoretical results

[14]. ^{The main reason for this arises} because of the lack of true long-range ^{order in the smectic} phase

and the anisotropy ^{in the} longitudinal ^and transversal correlation lengths §j and j_ characterizing ^the

smectic order parameter.

The experimental situation is also not confirmed.

Concerning measurements of K3 and 61 respectively

there is usually ^a disagreement ^{between the results}

of light-scattering ^and X-ray investigations. ^{It was}

only very recently ^that agreement could be achieved

[19]. Moreover the temperature dependence ^of K2 ^and y 1 has ^not been investigated ^{in the critical} regime ^and measurements of the compression ^mod-

ulus B have led to inconsistent results for some

liquid crystals ^mixtures [17]. ^To clarify ^this situation, high-resolution measurements in the critical regime

have been carried out. In this paper ^the critical behaviour of K2 ^and K3 ^is reported. ^{Results concern-} ing y 1 and B will be published ⁱⁿ forth-coming

papers.

The measurements of the elastic constants K2 ^and K3 ^{were carried out} using dynamic light-scattering [20]. Choosing ^an appropriate scattering geometry

the intensity of the scattered light only depends ^on

one of the elastic constants Ki, K2 ^and K3. ^{In the}

presence of a nematic to smectic A transition the situation is described by equations (1a) ^and (lb) [10,

2f] ^whose applicability ^{is selected} by geometry

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01987004804064100

642

Here B and D are the coefficients for layer ^dilation

and director tilt respectively ^{which are} defined in the smectic phase. qll and ql ^{are the} components ^{of the} scattering ^{vector q with reference to} the director n.

In the case of pure bend (mode 2 ; q

qll) ^{and twist} (mode 2 ; q

ql) fluctuations we have to consider the critical behaviour of K2 ^and K3 which has been calculated by Jahnig and Brochard [4]. ^{If one} sepa- rates the critical parts ^of K2 ^{and K3 so that}

K2

K20 ⁺ k2 ^and K3

K30 ^{+ K3 one finds :}

In these equations t ^{is the reduced} temperature

defined by t

(T - Tc)/Tc. ^The temperature depen-

dence of II , C_L ^{and D can be} expressed by

and

Equations (2a) ^and (2b) ^{include the crossover from a} hydrodynamic ^{to a critical} regime. ^While equation (2b) ^{describes the} temperature dependence

of K3 very well ^even in the critical regime [12] ^the validity ^of equation (2a) ^{has not been checked for} K2. ^If equation (2a) ^{is correct for the case of} K2 ^{as well, one should} expect ^{a crossover from}

anisotropic ^to isotropic increase of the correlation

lengths (vj

v_L) ^{or a behaviour} expressed by

vll

2 vl [2]. ^{Otherwise one should observe an}

increase of the intensity of scattered light ^{in the} vicinity ^of Tc although l, _L ^and K2 increase when

approaching Tc. ^This behaviour appears unphysical.

Intensity measurements of twist mode fluctuations in the critical regime appear ^to be suitable methods in

order ^to clarify this situation. The results are com-

pared ^with equivalent measurements of K3.

The reported studies have been carried out on

various mixtures of the liquid crystals ^80CB

(octyloxycyanobiophenyl) ^{and 60CB (hexyloxy-} cyanobiphenyl). ^The phase diagram ^is plotted ⁱⁿ figure ¹ using the molecular ratio y (60CB/80CB)

as a parameter. ^{In this} system the transitions N-

SA ^{have been} proved ^{to be of almost second order} [22]. Furthermore the appearance of ^reentrant- nematic phases ^{at lower} temperatures ^{allows the} determination of the background ^terms K20 ^and K30 ^by interpolation between both nematic phases.

The method will be described below. In excess it is

Fig. 1. - Phase diagram of 60CB/80CB mixtures.

possible ^to investigate samples ^{with different values}

of Ki/Ki by changing ^the concentration of the mixtures.

The mixtures were sandwiched between glass- plates prepared ^for homogeneous (lyend) ^{or homeot-}

ropic alignment (twist). Cell thicknesses of 13 _um and 130 _um were used to examine the influence on

critical behaviour. In the reported experiments ^no

difference occurred between both sample ^thicknes-

ses. Great care has to be taken to guarantee scattering geometries ^{in which} only ,pure bend ^or pure twist director fluctuations can be detected. The geometry ^is calculated in dependence of the refrac- tive indices which are measured absolutely ^{for each} sample ^{as a} function of temperature ^{with an} accuracy of 0.2 %. For measurements in the bend and twist mode the laser-beam is polarized orthogonal ^{to the} scattering plane. ^{The direction of} the detected light

as well as the director n lie in the scattering plane. ⁿ

is orthogonal ^to q in the ^case of twist-mode measure- ments and parallel ^to q for bend-mode measurements. To maximize the critical temperature interval in the twist mode a large scattering angle (q ^{= 1.33 x 1W} m-1) ^{was used for all} samples. ^In

order ^to achieve sufficient 5tray-light intensity ^the scattering ^vector q ^was restricted to q

^{0.26 x} 107 m-1 ¹ for bend-mode measurements. The values

of q only slightly depend ^{on the} temperature ^{and the} concentration of the sample ^{so that} it is almost constant within a few percent. ^{The exact values are}

determined for each measurement. The samples ^are

mounted in a two stage ^{oven with} computer ^control- led temperature regulation, ^{so that a} long ^time stability up ^{to ±} 0.3 mK is ensured. Sample heating

which might ^occur by ^the irradiation of He-Ne laser

light ^{can be estimated to} be smaller than the detection limit of 2 mK. It is kept ^constant using ^a

fixed laser-power output.

The light scattering experiments ^were performed

the reference-beam optic which allows individual

settings ^of polarization ^and intensity ^{of the local}

oscillator. The geometry ^{can be} changed ^continu- ously ^{without the need of delicate} adjustment. ^The set-up is similar to that of Sasaki and Mandel which

was published recently [23]. ^The heterodyne ^detec-

tion technique ^{was chosen} because the intensity ^of stray-light ^{due to defects} may eventually ^{affect the}

detection of dynamic ^scattered light [24]. ^In particu-

lar this influence has to be considered at the phase

transition and in the smectic phase. ^{If one} compares the calculated relaxation times r obtained by quasi- homodyne ^and heterodyne measurements one is able to estimate to what extent the measurements are disturbed by the uncontrollable scattering ^of

defects. By ^careful preparation ^{of the} samples ^and

accurate adjustment ^{of the} scattering geometry ^{it is}

possible ^to provide heterodyne ^{as well as reliable} homodyne conditions for temperatures T > Tc - 1 (nematic) ^{and T} Tc ^{+ 1} (reentrant nematic) ^re- spectively. By ^detailed homodyne ^and heterodyne

studies we were even able to establish the existence of a maximum of the relaxation time T near

Tc ^{which was} subject ^{to detailed} investigations

carried out by ^M. Delaye ^{et al.} [5, 6]. ^{The measure-}

ments described here are all performed ^{in the} heterodyne ^{as well as} homodyne ^{mode. The} quotient

of the resulting relaxation times was found to be greater ^{than 1.95} (ideal 2) ^{for the} measurements

reported here. The almost ideal relation between

homodyne ^and heterodyne ^values allows the direct determination of the stray light intensity using ^the photo-current ^{in the} homodyne ^{mode. The relax-}

ation time obtained in the heterodyne ^{mode is used}

to describe the dynamical behaviour of the LC.

To check the quality ^{of the} apparatus ^{and to} confirm the correctness of the interpretation ^of experimental results, measurements on diluted sam-

ples ^{of latex} spheres ^{were carried out. In excess} investigations ^{of bend} fluctuations have been per- formed for different molecular ratios y. Evaluation of the results according ^{to the} theory ^of Jahnig ^and

Brochard leads to an excellent agreement ^with results obtained by X-ray investigations. ^{In table I}

Figure ^{2 shows the} temperature dependence ^{of the} stray-light intensity ^{for the} probes ^{under inves-} tigation. ^{The curves are} normalized to the data at the phase transition. One can see that the transition,

described by ^the stray-light intensity, ^{loses its} sharp-

ness continuously ^{if one increases} the concentration

to y ~ ymax. Similar ^{results can be} obtained in the twist mode.

Fig. ^2.

Temperature dependence ^{of the} stray-light ^in- tensity (bend) ^at various nematic to smectic A transitions.

To discuss the critical behaviour of K2, high

resolution measurements in the vicinity of the transi- tion have been performed. Figure ^{3 shows the result}

of such a study ^{at a smectic A} reentrant-nematic transition (here ^{the nematic} phase ^is at ^{the lower} temperature side). ^{It is} surprising ^that qualitatively

one finds the same behaviour as for comparable

measurements in the bend mode in disagreement

with theoretical predictions (see Eq. (2)). ^Calcula-

tions show that within the accuracy of the measure- ments a masking influence of competitive ^bend

mode fluctuations can be ruled out. Because of the

similarity ^{of the} plots ^{a fit to the} measured data has Table I.

literature

it holds :

644

Fig. ^3.

Temperature dependence ^{of the} stray-light ^in- tensity (twist) ^{at a} transition Nce -8 A (- ^best fit).

been tried using equation (2b) (bend !). ^{As can be}

seen in figure ^{3 there is an excellent} agreement between the analytical description and the exper- imental results. In figure ^{4 a} high resolution study ^of

the transition is presented. Disregarding statistical

errors it is obvious that there is no systematic

deviation from the theoretical prediction.

The value of the transition temperature ^was obtained by ^a fitting procedure having respect ^{to the}

crossover behaviour which is induced by ^the peticular shape of the transition line [13]. ^{The fits were carried}

out using ^{the data} for the smectic and nematic phase separately ^where the transition temperature ^was kept ^{as an} independent ^{variable. In all} measurements the obtained transition temperatures ^differed by ^less

than 5 mK. The parameters ^{of the} single ^{fits were} adjusted by fitting ^{the whole set of data} points starting ^{with the} predetermined ^{values. The tem-} perature range used for ^the fits always ^exceeded

three orders of magnitude ^to keep ^{the error bars as}

small as possible. ^{As a} consequence the values of the

background ^terms K4 ^and K30 ^{cannot be kept as}

temperature independent parameters. Investigations

of samples ^with y

Ymax in the bend and twist mode show that the temperature dependence ^of K2 ^and

Fig. ^4.

Temperature dependence ^{of the} stray-light ^in- tensity (twist) ^{in the} vicinity ^of T, (- ^best fit).

K3 ^{can be described} very satisfactorily by ^a simple

power ^{law K}

K(T - T)a. ^{Here K, T and a are} freely adjustable parameters. Deviations from this power law ^occur in the vicinity ^of transitions to the

isotropic phase. ^For samples with y

ymax ^and Y Ymax the increase of K2 ^and K3 ^{near the smectic} phase ^{lead to} discrepancies ^too. Taking values of the reentrant-nematic phase ^{into account it is} possible

however to interpolate between both nematic branches resulting ^{in the same} kind of power ^law which was found for _pure nematic samples. ^{A result}

of such a background approximation ^{is shown in} figure ^{5. For all} samples ^the parameters K, ^{T and a}

were determined by measurements of the tempera-

ture dependence ^{of the} stray-light intensity excluding

Fig. ^5.

Temperature dependence ^{of the} stray-light ^in- tensity (e) (twist) ^and background approximation (-).

temperatures ^near phase transitions. In the fits

concerning the critical behaviour of Ki ^{we used the}

so obtained values to T and a but left the pref actor ^K

as a freely adjustable parameter. ^We believe that by

this method the error in the background ^{term can be}

reduced to a minimum. The results for several

samples ^of different concentrations are collected in table 2. Here the critical exponent ^of K2 is ^denoted

by 2 ^to express ^that the relation between’ 2 and § ^is

not clear (see below). ^It is remarkable that the calculated values of .1.0 ^{are in such} good agreement with results obtained by X-ray ^{studies. In contradic-}

tion to the excellent correspondence of the exper- imental data with equation ^2b (bend) ^the application

of equation (2a) (twist) ^{would lead to some} unphysi-

cal behaviour, ^{if one assumes} that the critical exponents of 61 and 6_L ^are independent ^of tempera-

ture. In this case the intensity data should show inversion of the behaviour within Ot 4 x 10- 2 K above Tc (20 % ^deviation limit). ^{Moreover the} intensity should reach the intrinsic nematic value ^at

Tc. Figures ^{3 and 4 show} that there is no tendency

for such a behaviour. The discrepancy may be

explained by ^the occurrence of a crossover to

isotropic ^{critical behaviour as is} predicted by ^the

literature with.

« inverted x-y model » [2] leading to VI = v.L and thus to a constant value of K2 at Tc. ^{In this case the}

difference between equation (2a) ^and (2b) ^confines

to a small interval in temperature ^where k2 -

6_LI61 ^{with V.L =1= vi. In table II the} calculated tem-

perature interval AT at which a crossover to the critical regime ^{should occur} is added. Accepting

these data figure ^{4 indicates} that the fit describes the

experimental data very well ^even in the critical limit and the crossover region ^as well, ^{so that} possible

deviations arising ^out of differences in the fitting

functions must be small. They ^are possibly respons- ible for the slight difference in the critical exponents

of D measured in the bend and twist mode respect-

ively.

This work shows that by ^careful measurements it is possible ^{to attain an} accommodation between light

scattering experiments ^{and the} generally accepted X-ray ^{studies even} in the critical regime. ^{Moreover it}

is shown that the theory ^of Jahnig and Brochard is

applicable ^to describe the twist mode if one assumes a crossover to isotropic critical behaviour so that vl

(C2 ⁺ Cl )/2 == 0.7 results. On the other hand,

if one uses the same analytical description ^{for the}

bend and twist mode a good approximation ^{of the} experimental ^{data can be} obtained for twist mode

measurements if one replaces l by ’ - t ’2 ⁱⁿ

equation (2b).

Acknowledgments.

I would ^{like to} express my thanks to Prof. -Dr. F.

Fischer for his support ^{and his} stimulating ^interest

in this work.

References

[1] ^DE GENNES, ^P. G., Solid State. Commun. 10 (1972)

753.

[2] LUBENSKY, ^T. C., ^{J. Chim.} Phys. ¹ (1983) ^31.

[3] HALSEY, ^Th. C., NELSON, ^D. R., Phys. ^{Rev. A 26} (1982) ^2840.

[4] JÄHNIG, F., BROCHARD, F., ^J. Physique ³⁵ (1974)

301.

[5] DELAYE, M., RIBOTTA, R., DURAND, G., Phys.

Rev. Lett. 31 (1973) ^443.

[6] DELAYE, M., ^J. Physique Colloq. ³⁷ (1976) ^C3-99.

[7] LÉGER, L., MARTINET, A., ^J. Physique Colloq. ³⁷ (1976) ^C3-89.

[8] ^BIRECKI, H., et al., Proceedings of the Third Int.

Conference on Light Scattering ^{in Solids, edit.}

M. Balkanski, Flammarion Sciences, ^Paris (1975).

[9] BIRECKI, H., et al., Phys. Rev. Lett. 36 (1976) ^1376.

[10] LITSTER, ^J. D., et al., Proceedings of the Nato Advanced Study Institute, Geilo, Norway, ¹⁹⁷⁹

Plenum New York (1980).

[11] ^{LITSTER, J. D., et al., J.} Physique Colloq. ⁴⁰ (1979)

C3-99.

[12] ^VON KÄNEL, H., LITSTER, ^J. D., Phys. ^{Rev. A 23} (1981) ^3251.

[13] KORTAN, ^A. R., ^et al., Phys. Rev. Lett. 47 (1981)

1206.

[14] LITSTER, ^J. D., Philos. Trans. R. Soc. Lond. A 309

(1983) ^145.

[15] GARLAND, ^C. W., ^et al., Phys. ^{Rev. A 27} (1983)

3234.

[16] KORTAN, ^A. R., et al., ^J. Physique ⁴⁵ (1984) ^529.

[17] FISCH, ^M. R., SORENSEN, ^L. B., PERSHAN, ^P. S., Phys. Rev. Lett. 48 (1982) ^943.

[18] MAHMOOD, R., et al., Phys. Rev. Lett. 54 (1985)

1031.

[19] SPRUNT, S., SOLOMON, L., LITSTER, ^J. D., Phys.

Rev. Lett. 53 (1984) ^1923.

[20] CHU, B., ^Laser Light Scattering (Academic Press, New York San Francisco London), ^1974.

[21] Groupe d’Etude des Cristaux Liquides (Orsay), ^J.

Chem. Phys. ⁵¹ (1969) ^816.

[22] LUSHINGTON, ^K. J., KASTING, ^G. B., GARLAND, ^C.

W., Phys. ^{Rev. B 22} (1980) ^2569.

[23] SASAKI, S., MANDEL, M., ^J. Phys. ^{E 17} (1984) ^738.

[24] FROMM, H.-J., Diplomarbeit, Mfnster 1980.