High resolution study of the compression modulus B in the vicinity of the nematic-smectic A transition in 60CB/80CB mixtures

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High resolution study of the compression modulus B in the vicinity of the nematic-smectic A transition in

60CB/80CB mixtures

H.-J. Fromm

To cite this version:

H.-J. Fromm. High resolution study of the compression modulus B in the vicinity of the nematic- smectic A transition in 60CB/80CB mixtures. Journal de Physique, 1987, 48 (4), pp.647-650.

�10.1051/jphys:01987004804064700�. �jpa-00210481�

High resolution study ^{of the} compression ^{modulus B}

in the vicinity of 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.

(Requ le 21 août 1986, accepte le 18 dgcembre 1986)

Résumé.

On emploie

technique ^de diffusion de lumière à haute résolution pour étudier la dépendance

en

température du module de compression ^B des couches moléculaires de la phase smectique ^A

voisinage

de la transition nématique-smectique ^{A. En} utilisant des mélanges des cristaux liquides ^{60CB et} 80CB,

trouvons que B suit

loi de puissance de la forme B

B0(Tc-T)~. ^La grandeur ^{du saut} de B à la transition est plusieurs ordres de grandeur plus faible que les valeurs données par Fisch et al. Le préfacteur B0 ^semble

pas dépendre de la composition ^des mélanges.

Abstract.

The temperature dependence ^{of the} compression modulus B of the molecular layers ^{in the}

smectic A phase ^{has been studied in the} vicinity of the nematic to smectic A transition by high-resolution light- scattering ^studies. Using mixtures of the liquid crystals 60CB and 80CB it is shown that B obeys

simple

power law of the form B

B0(Tc-T)~. ^The magnitude ^of

discontinuity jump ^{of B at} the transition temperature compared with values of Fisch et al. is found to be smaller by ^{orders. The} prefactor B0 appears ^to be independent ^{of the} concentration of the mixtures.

Classification

Physics ^Abstracts

61.30

64.70M

The transition from the nematic phase ^{to the}

smectic A phase is characterized by ^{the onset of a} layered structure at Tc. ^In contrast to smectic C

phases the thickness of the layers ^is only ^determined by ^the length of the molecules or the molecular aggregates [1]. ^For many applications ^the layered

structure can therefore be regarded ^as incompres-

sible. Detailed analysis of the transition however shows that the compression modulus is expected ^to

increase continuously in the smectic phase obeying

power law of the form B

Bo(Tc-T)’P [2].

Moreover B should be proportional ^to the inverse of the longitudinal correlation length 61 which shows a

critical behaviour according ^{to a critical} exponent

vi (therefore vi

p). Although experimental

studies do not yield ^the expected ^critical exponent

most of them confirm [3-8] ^the reported power law

dependence. However, Fisch et al. [9] who investi-

gated ^the temperature dependence of B in mixtures of 80CB (octyloxycyanobiphenyl) ^{and 60CB} (hexyloxycyanobiphenyl) found the simple power law to be applicable only ^{in the case} of pure 80CB.

Increasing the molecular ratio _y (60CB/80CB) they

had to add a concentration dependent ^constant BI(y) which increases with increasing ^{y. Such a}

discontinuity ^{in B at} T,, has also been discussed by Halsey and Nelson [10] ^who investigated ^the N-SA

transition in order to identify ^{it with}

^{well defined} universality ^{class. As}

result of their investigations they found that the possible critical behaviour ac-

cording ^{to the} relation vi

2 v 1. implies ^a jump discontinuity ^{of B at} Tc. vp and _{v 1.} are the critical exponents ^{of the} longitudinal and transversal corre-

lation length respectively.

It was the aim of the work reported ^{here to check}

the behaviour of B and from this to deduce some

information about the nature of the transition. The

particularity ^{of the} phase diagram ^{of 60CB/8QCB}

mixtures which is shown in figure 1, especially ^the disappearing SA phase ^at Ymax, increases the interest in this work.

The measurements were carried out utilizing light- scattering experiments. Although ^the compression

modulus B cannot be measured directly ^{with this}

method it has the advantage that the studies can be done on well-defined oriented samples without dis-

turbing ^{the texture. In} particular ^{this is} important ^if

smectic phases ^{are to be} investigated.

If we restrict our attention to scattering geometries

in which the detected stray-light ^is only ^caused by

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01987004804064700

648

Fig. 1. - Phase diagram of 60CB/80CB. Form of diag-

ram

is taken from reference [13] using ^the optimal density

model [14].

splay deformations of the director, ^the intensity ^of

the scattered light ^can be described by

For small deviations from this geometry (mode 1)

one has to replace equation (1) by

qj and ql ^{are the} projections ^{of the}

^vector q in

respect ^{to the} director n. K1 ^and K3

^{the elastic}

constants for splay ^{and bend mode} fluctuations

respectively. Using typical values for K3 ^{and B it can}

be calculated that K3 q2 ^{can be} neglected ^outside

temperature interval of some mK at the transition

point. Within this interval B is small

even

vanishes and K3 q2 ^{may be taken into account. In}

this case K3 ^{is an} offset value in respect ^to

B (T)lq 2 and should be detected by high ^resolution temperature dependent measurements. Keeping ⁱⁿ

mind that the width r of the Rayleigh-peak ^obtained by dynamic light-scattering is related to the intensity

I and the splay viscosity." s by ^{r =} (ns I )-1 [11] ^and that, q, ^{as well as} K1 ^{are not affected} by ^the phase

transition one can obtain the temperature depen-

dence of B either by measurements of I or r. Using ^a sophisticated heterodyne spectrometer including ^a scaled-clipping autocorrelator we are able to measure the relaxation time

and herewith r of

splay-mode fluctuations independent ^{of static} stray-

light which may eventually ^{occur. The} problem ^of

excess stray-light which disturbes intensity ^measure-

ments arises especially in the smectic phase. ^There-

fore

decided to measure r.

The sample is mounted in a two stage ^{oven whose} temperature is controlled by ^a micro-computer. ^It

can be set and stabilized with an accuracy of

± 0.3 mK, ^{so that} measurements in the vicinity ^of

the transition point ^{can be carried out.} Using ^this procedure the existence of

offset of the quantity BIKl ^at Tc ^{should be} detectable.

In the smectic phase the scattered light strongly depends ^{on the} scattering geometry ^{as can be seen in}

equation (2). Therefore the geometry ^{has to be} adjusted precisely. ^As

^basic requirement ^the liquid crystal samples ^{must have a} perfectly ^uniform (homogeneous) alignment. ^The geometry ^{in which} only pure splay-mode fluctuations can be detected is calculated for each sample ^as

function of the temperature. ^{The laser} light ^is polarized ^{normal to}

the scattering plane ^and parallel ^{to n ; the} analyser

lies in the scattering plane. ^The geometry is op- timized in the experiment by maximizing ^{the inten-} sity ^of stray-light in the smectic phase. Starting ^with

this geometry the relaxation time of the dynamically

scattered light is measured as a function of q . ^It is varied by rotating the cell about small angles ^{0 on}

axis orthogonal ^to the LC cell. Choosing ^a geometry in which the wave vector kf of the scattered light ^is

orthogonal ^{to the} liquid crystal ^{cell, a rotation on the}

axis kf only affects qi. ^A representative result of such

a

measurement is shown in figure ^{2. The} plotted

curve

is obtained by

least square fit according ^to equation (2). The minimum of the parabola is pro-

portional ^to Kl while its curvature directly yields BIKI. ^{For each} sample ^these measurements have been carried out at various temperatures ^{in order to} attain some information about the existence of an

offset in B or BIK, respectively. ^While Kl ^{is almost}

constant in a temperature ^interval Tc - 1 ^K

T Tc ^{+ 1 K the} quantity B/Kl ^{shows the} expected temperature dependence (Fig. 3). ^{It has to be stres-}

sed that the large number of individual measure-

Fig. ^2.

Line width r

function of the angle 0

between q and the smectic layers (Nr°-SA transition).

Fig. ^3.

^Double logarithmic plot ^of B/Kl

^function

of the reduced temperature t

(Tc-T)/Tc.

ments necessary for obtaining ^a plot ^{such as is shown}

in figure ² requires very stable and uniform samples especially for y :5 ^{Ymax’ where even small} gradients ⁱⁿ

the concentration ^cause

large diffusion induced

temporal drift of the transition temperature ^which

can hardly be corrected.

Measurements on samples ^with y > 0.4046 which would seem to be _very interesting ^{cannot be carried}

out with the required degree ^of accuracy. The temperature range under investigation ^{cannot be}

extended significantly ^over three orders of mag- nitude in the temperature. ^{In the} vicinity ^of 7c the studies are restricted by ^time dependent ^shifts

of Tc ^{and at lower} temperatures by ^{the onset of}

textural changes ^{which can} easily be detected by comparing ^the results for quasi-homodyne ^and heterodyne measurements. The inevitable drift of

7c with time was between 2mK/h and 2 mKlday depending ^{on the} quality and concentration of the

sample. ^{It was} calculated by carrying ^{out the meas-}

urements several times. By ^{this the} temperature ^of the individual data points could be corrected within

± 0.4 mK.

For each set of experimental ^{data we} performed ^a least-square ^{fit over} three orders of magnitude ^{in the} temperature according ^{to the formulas B}

Bo . t "

and B

Bl ⁺ Ba t ’P’. Tc ^is gained ^{as a} freely adjusted parameter. B1 is the maximum offset which can be

brought into line with the experimental ^{data. The}

results concerning ^the N-SA transition are shown in

table I. For comparison ^the corresponding ^{values of} Bi ^obtained by Fisch et al. (interpolated) ^{are com-} pared ^{with our values of} Bl. The transition tempera-

ture obtained by ^both fitting ^{functions are almost the}

same. The difference is ² mK, ^0.5 mK, ^{and 0 mK for}

y

0, 0.3327 and 0.4046 respectively. ^This implies

that both fits are applicable. ^{If one} compares the

experimental ^{data of} independent measurements the values of Bo/ Kl ^and Bó/ Kl ^appear reproducable

within 10 %. The values of cp and (p’ ^{have an} absolute error of ± 0.02. A comparison ^of Bo/Ki

and Bi /Ki ^{as well as cp and cp’} shows that the results of the fits are even rather insensitive to the introduc- tion of an offset Bl. ^{Because of the} uncertainty ^{in the}

absolute values of Kl the absolute values of

B1 (y) ^{is well}

^{those of} Bí/ B1 ^{can only be}

estimated within

relative error of 50 %. The

quality ^{of the} measurement is sufficient to fix the order of the maximum tolerable offset in B. It is clear from the results that a possible ^{offset must be}

very small and can be neglected ⁱⁿ general. ^This implies ^that possible influences of the K3 ^{term in} equation (2) ^{can also be} neglected. Confirmation by experiment ^{of the non} existence of an offset is not

possible. ^{A course for the} decreasing upper limit of

Bl ^with increasing y ^{is due to} the fact that with

increasing y the value of B/Kl decreases and the

intensity (at ^fixed angle 0) ^{increases as can be seen in} equation (2). Therefore the experimental ^studies

can be extended over a larger ^{interval å8 which}

increases the degree ^of accuracy of the measurements. A limit is set by ^the increasing sensitivity ^to concentration changes.

Proceeding ^{from the} assumption ^that Kl ^{does not} sighificantly depend ^{on the molecular} ratio y ^{one can}

estimate Bo(y) using extrapolated values of Kl (80CB) [12] using ^the temperature dependence ^of Kl (y) determined in our experiments. The results indicate that the dependence ^of Bo ^{on the concen-}

tration of the mixture must be _very weak. As stated above measurements on samples with Y -5 ymax, which were desirable, ^make extremely high ^demands

on the stability ^{of the} samples ^{and could not be}

carried out in the frame of this work.

Evaluating ^{the curvature of the} parabolas ^accord- ing ^to figure ^{2 and} equation (2) ^{we found}

^unex- pected behaviour when crossing the transition tem-

Table I.

Comparison of ^the offset ^values B1( y) ^{of the} compression ^{modulus B obtained} by

fitting procedure

to the experimental ^{data with the according values} of ^{Fisch et al.}

c=

10-18 m2; c’

1011 N-1; c"

10-7 m2fN.

650

perature. ^If

define the curvature as positive ^{in the}

smectic phase it decreases to zero when approaching Tc. Above the smectic-nematic transition (in ^the

nematic phase) it becomes slightly negative ⁱⁿ

temperature range of about 10-2 ^K and vanishes

again ^for higher temperatures. The maximum nega- tive amplitude corresponds ^to B/Ki = ²

^{1016 m- 2}

in the smectic phase. ^A quantitative analysis ^{of this}

behaviour is the subject of further investigations. Up

to now we cannot explain this effect taking ^{all the}

known influences on the measurements in account.

We have shown that the temperature dependence

of the compression ^{modulus B can be described} by

simple power law without any restrictions. ^As the

experimental ^{data of} Fisch et al. ^as well as ours can

be fitted by

power law leading ^to comparable

critical exponents ^we believe that the difference in the estimated offset value of B does not arise

because of the _usage of different measurement

techniques. ^{On the} contrary it may be explained by

different temperature ranges used, especially ^at large values of _{y. A} comparison of the critical exponent of B with values of other authors [3-8]

indicates that _cp either does not depend ^or depends only very weakly

^{the nature of the} liquid crystal.

Unfortunately the value cp = 0.30 cannot be

plained by any known theory. ^{Moreover we have}

shown that in the mixtures of 80CB and 60CB the

prefactor Bo ^{does not} depend ^on the molecular ratio _y.

Acknowledgments.

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

Fischer for his support ^and stimulating interest in this work.

References

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