Anisotropy of X-ray critical scattering in EEBAC

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Anisotropy of X-ray critical scattering in EEBAC

A. Rajewska, B. Pura, J. Przedmojski

To cite this version:

A. Rajewska, B. Pura, J. Przedmojski. Anisotropy of X-ray critical scattering in EEBAC. Journal de

Physique, 1982, 43 (11), pp.1669-1672. �10.1051/jphys:0198200430110166900�. �jpa-00209548�

Anisotropy ^of X-ray ^critical scattering ^{in EEBAC}

A. Rajewska (*), ^{B. Pura and J.} Przedmojski

Institute of Physics, ^{Warsaw Technical} University, Koszykowa 75,00-662 Warsaw, ^Poland

(*) Institute of Physics, Warsaw Technical University, ^{Branch in P0142ock,} Lukasiewicza 17,09-400 P0142ock, ^Poland (Reçu le 20 avril 1982, accepte ^le 23 juillet 1982)

Résumé. 2014 On

étudié expérimentalement la diffusion des rayons X par EEBAC (C20H21NO3)

voisinage

de la transition smectique A-nématique. ^Les valeurs des exposants critiques estimées à partir des résultats obtenus sont : 03B3

1,23 ± 0,06, _03BD~

0,71 ± 0,04, 03BD

0,45 ± 0,05. ^Le rapport ^{de la} longueur de corrélation parallele 03BE~ à ^{la longueur} de corrélation perpendiculaire 03BE : 03BE ~ /03BE augmente graduellement quand ^la température ^réduite t=(T - Tc)/Tc diminue. Sa valeur change ^{d’un facteur} 2,3 dans le domaine de température ^réduite 10-4 ~t~10-2.

Abstract.

X-ray ^critical scattering ^{from EEBAC} (C20H21NO3)

the smectic A-nematic phase ^transition

were

investigated. The critical exponents y

1.23 ± 0.06, _03BD~ ^{= 0.71} ± 0.04, 03BD

0.45 ± ^{0.05 were extracted} from

data. The ratio of the longitudinal ^to transverse correlation lengths 03BE~/03BE, ^increases gradually ^with decreasing ^reduced temperature t

(T - Tc)/Tc, changing by

factor of 2.3

the reduced temperature range

10-4 ~t~ 10-2.

Physics ^Abstracts

64 . 70E

1. Introduction.

The transition between nematic and smectic A phases ^of liquid crystals ^{has been the} subject ^{of much recent} experimental and theoretical

study. ^As pointed ^out by ^McMillan [1] ^and Kobaya-

shi [2], this transition _may be either first order ^or second order depending ^on the details of the molecular interactions. The _way to understanding second order

or weakly first order nematic-smectic A transitions

was paved by ^{de Gennes} [3], ^who proposed ^{a model}

in which the free energy corresponds ^to that of the

Ginzburg-Landau ^{model of} superconductivity. ^In

this _paper we report the results of high resolution X- ray critical scattering ^from (EEBAC) ethyl p-(4-ethoxy- beniylidene amino-) ^{cinnamate near} the smectic A- nematic phase transition. The most interesting ^feature

of the correlation function near the smectic A-nematic

phase transition is the anisotropy usually expressed

in terms of the correlation length ratio ç II/Ç.i. ^More-

over, it has been found that this anisotropy ^increases

as the transition point ^is approached.

2. Experiments.

^The experiments ^{were carried}

out on DRON-3 X-ray spectrometer ^{with use of} CUK0152 radiation. X-ray primary ^beam (20 mA, ⁴⁰ kV)

was monochromated by ^{a flat} germanium single crystal. ^{A second} germanium monochromator ^was

placed in front of the scintillation counter. Our spec- trometer was analogous ^{to that described} by ^Als-

Nielsen [4]. ^This provides ^{a basis to} express the

instrumental spatial resolution ^{as :} half-width at a

maximum of 8 ^x 10-4 A-1 in the longitudinal ^direc- tion, ^{10 - 4} Å -1 in the transverse direction and of 2 x 10 - 2 Å - 1 in the direction perpendicular ^to

the scattering plane. ^The liquid crystal ^was placed

in a copper container in the form of a box of dimen- sions 4 x 15 x 1 mm. X-rays penetrated ^the liquid crystal through berylium windows and illuminated

an area of the liquid crystal of dimensions 0.1 x 5 mm.

The _copper container was electrically heated and the temperature ^{of the} sample ^was stabilized and controlled automatically ^within ± 0.01 °. The sample

was ordered with the help ^{of a} magnetic ^{field of} intensity ⁵ kG. The field was turned off during ^the

measurements of critical scattering. ^The powder ^of ethyl p-(4-ethoxybenzylidene-amino-) ^cinnamate (EEBAC) ^{used for} X-ray investigations ^was produced by ^{E. Merck} (FRG). ^The phase diagram ^{for this} liquid crystal ^{is :} solid - 78 °C - SB - ^{110 °C -} SA -

154 °C - N - 158 °C - I. X-ray investigations ^of

this substance in the solid state are described in [5]

and in the liquid ^{state in} [6].

3. Results.

Measurements of Bragg scattering

in the smectic A and smectic B give ^the peak position

in the reciprocal space with qo = 0.277 ^{A -1} (qo = 2 nld,

d

22.6 A). From the cross-section given by ^Als-

Nielsen et al. [7] which is of the form :

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198200430110166900

1670

we have calculated the correlation lengths ç II and ç.i

for q II and qj_ ^direction respectively, ^{where the cons-}

tant 6o corresponds ^to qo

(0, 0, qo). Dependence

on temperature ^{of the} intensity ^{of the} Bragg ^reflection

in smectic B and smectic A is shown in figure ^{1. The}

Fig. ^1.

Bragg scattering intensity

temperature.

smectic A-nematic phase transition occurs at 156.03 OC.

The transition temperature T c ^{was taken as the tem-} perature ^at which the transverse scan showed the minimum linewidth. Because there was neither a

jump in the order parameter nor’was the singularity temperature different from the transition tempera-

ture Tc, ^we have assumed that the phase ^transition

is a continuous one. We have carried out longitudinal

scans (ql

0, q 11

-

varied) ^and transverse scans (q 11 = qo, ql -varied) ^{for a fixed} temperature. The results of these measurements for T

T c ^{+ 0.4 K are} pre- sented in figure 2. The results of the fit of equation (1)

to the experimental ^{data are} given ⁱⁿ figures ^{3 and 4.}

From these data we have obtained the temperature behaviour of the correlation lengths and of the sus-

Fig. ^2.

Anisotropy ^{of critical} scattering ^for longitudinal

and transverse scans for T

T C ^{+ 0.4 K.}

Fig. ^{3. - The} longitudinal (ç II) ^and transverse (ç.1) ^corre-

lation lengths in units of qo

the reduced tempera-

ture.

Fig. ^4.

^The susceptibility (0’)

function of reduced temperature t ⁱⁿ arbitrary ^units.

ceptibility. Assuming ^a single power law over the

complete temperature range 10 - 4 t 10 - 2,

t

(T - Tc)/Tc, ^we find from the least-squares

analysis :

I

Fig. ^5.

Equi-intensity ^{contours of} X-ray ^diffuse scattering ^{observed at T}

7B ^{+ 3.6 K} (counts ^for 500).

I

Fig. ^6.

Equi-intensity ^{contours of} X-ray ^diffuse scattering ^{observed at T}

T e ⁺ 0.4 K. The numbers by ^the

give

counts for 300

The error bars represent standard-deviation stati- stical errors. In figure ^{4 we} also show the ratio ç II/Ç.i

which changes ^{from 3} ± ^{1 at t}

10 - 2 to 7 ± ^{1 at}

t

10 - 4. At the temperature corresponding ^to

t

10-4 the correlation lengths are ç II

630 A, ç.i 90 A and for t

10-2theyareequaltoçll=60Á,

ç.i ^{= 20 A. The} equi-intensity ^contour maps observed in the (qli, q_L)-plane ^{at T}

^{Tc + 3.6 K and}

T

Tc ^{+ 0.4 K are} given ⁱⁿ figures ^{5 and} 6, respec-

tively. The theoretical curves in these figures ^are

similar to the experimental ^{ones. The data were} analysed ^{in the terms} of the cross-section (1) ^convo-

luted with the instrumental resolution function. We notice that the anisotropy of critical scattering ^decrea-

ses when the temperature ^increases.

4. Discussion and conclusions.

The critical expo- nents extracted from our data are y

1.23 ± 0.06, v II

0.71 ± 0.04, vl

0.45 ± 0.05. The values for _y

and v II agree within the errors with the helium ana-

logue values, however the transverse correlation

length exponent vl corresponds ^to the Landau value but disagrees with the helium analogue value. This dif- ference in correlation length exponents _v II

-

vl

0.26

corresponds ^{to a} change ^{in the} ratio ç 11/ ç.i ^{by a factor}

of 2.3 over the reduced temperature range 10 - 4 to

10 - 2. The results for the ratio Çll/Ç.i indicate that the clusters of correlated molecules gradually ^become

more and more elongated ^{as the} temperature ^decre-

ases towards the critical value. This behaviour ^corres-

ponds ^{to the} nonspherical ^{clusters discussed} by ^Als-

Nielsen and Birgenau [7] ^for uniaxial-dipolar systems.

Similar values for critical exponents ^{have been} obtained in p-cyanobenzylidene-p-n-octyloxyaniline (CBOOA) [4], octylcyanobiphenyl (8 CB) [8]. ^{The same}

results have been observed in 4-nitrophenyl-4-n-octyl- oxybenzoate (NPOB) [9,10]. ^{In all these} liquid crystals

the smectic A-nematic phase transition was investigat-

ed. The ratio of the longitudinal ^{to the transverse}

correlation lengths jjj/ji ^{increases gradually with}

decreasing ^reduced temperature. The values of the

correlation lengths ^{are connected} with the dimensions

1672

of clusters of molecules which are in the smectic A

phase. ^The temperature dependence ^of the j ^{II and ç.i}

correlation lengths ^for _q II and _{q 1-} directions is given

in figure ^3.

Acknowledgments.

^{We wish to} thank Prof J.

Kocinski, ^{Dr. J. Milczarek and to Dr. K. Wentowska}

for inspiring ^and helpful discussions and to Mrs Z.

Petykiewicz ^{M. Sc. for} help ⁱⁿ numerical calculations.

References

[1] MCMILLAN, W., Phys. ^{Rev. A 4} (1971) ^1238.

[2] KOBAYASHI, K., Phys. Lett. A 31 (1970) 125 ; ^J. Phys.

Soc. Japan ²⁹ (1970) ^101.

[3] ^DE GENNES, ^P. G., Solid State Commun. 10 (1972) 753 ; ^The Physics of Liquid Crystals (Clarendon, Oxford) ^1974.

[4] ALS-NIELSEN, ^{J. et} al., Phys. Rev. Lett. 39 (1977) 352 ;

LITSTER, J. D. et al., ^J. Physique Colloq. ⁴⁰ (1979)

C3-339.

[5] PRZEDMOJSKI, ^{J. and} PURA, B., ^Sixth European Crystal-

lographic Meeting, Barcelona, Spain 1980, ^Abs-

tracts 3-C-18.

[6] HERRMAN, K., ^Z. Kristallogr. ⁹² (1936) ^49.

[7] ALS-NIELSEN, ^{J. and} BIRGENAU, ^R. J., ^{Am. J.} Phys.

45 (1977) ^554.

[8] ^{DAVIDOV, D. et} al., Phys. ^{Rev. B 19} (1979) ^1657.

[9] PURA, B., PRZEDMOJSKI, J., ^The Eight International

Liquid Crystal Conference, Kyoto, Japan ^1980.

[10] PURA, B., PRZEDMOJSKI, ^{J. and} NAZAREWICZ, W., ^Solid

State Commun. 41 (1982) ^111.