Molecular structure and elastic behaviour of SA liquid crystals

365

Molecular structure and elastic behaviour of SA liquid crystals

R. Bartolino

Laboratoire de Physique ^des Solides, Université de Paris-Sud, ⁹¹⁴⁰⁵ Orsay, ^and Dpt. ^{Fisica, Univ.} Calabria, Cosenza, Italia J. Malthete

Laboratoire de Chimie des Hormones, Collège ^de France, ^Paris Cedex, ^France

and O. Barra

Dpt. Fisica, ^Univ. Calabria, Cosenza, Italia

(Reçu ^{le 19 octobre} 1979, ^{révisé le} 6 décembre 1979, accepté ^{le 17 décembre} 1979)

Résumé.

On présente ^un essai de corrélation entre l’élasticité des cristaux liquides smectiques ^{A et leurs} structures

moléculaires. En utilisant un appareillage déjà décrit, ^{on a} mesuré le module de compressibilité isotherme B du comportement déformation-contrainte. On a examiné des dérivés du benzoate de phényle ^avec différentes longueurs

et symétries. ^Les premiers résultats montrent _{que la} rigidité ^{de la} phase SA augmente ^{avec la} symétrie moléculaire ;

on discute nos résultats en relation avec les modèles moléculaires de strate SA-

Abstract.

A tentative correlation of the elasticity of smectic A liquid crystals ^{with molecular structure} is pre- sented. The isothermal compressibility ^{modulus B was} measured via the stress-strain relation by ^{means of a} previously ^described apparatus. ^{A number} of benzoate derivatives of different lengths ^and symmetries ^{were exa-}

mined. Preliminary ^results showing ^{that the stiffness of the} SA phase apparently increases with molecular symmetry,

are discussed in relation to molecular models of the SA layers.

J. Physique ⁴¹ (1980) ^{365-368 AVRIL} 1980, :

Classification Physics ^Abstracts

61.30

1. Introduction.

Much expérimental ^evidence

tends to support ^the existence of a close relationship

between the molecular structure of liquid crystals

and their elasticity. ^Different homologous ^series

of organic compounds displaying nematic order have been studied [1, 2, 3]. ^The type ^of experiments per- formed on smectic A phases ^have proved ^{to be} unsuccessful ^{so far} [4]. However, several authors noticed some connections between the length ^{and the}

symmetry of molecules with the appearance of smectic C phases [5, 6, 7]. ^{This allows two limit}

models describing ^the arrangement ^{of the molecules} in thermotropic ^{smectic A} layers ^{to be} envisaged [8].

In the first, ^{the molecules are} disposed ^at random, either head to head or head to tail (Fig. 5a), whereas, in the second, ^the rigid polar parts ^{and the} paraffinic

chains _are, like in _soaps, in two distinct juxtaposed regions (Fig. 5b). ^Our purpose ^{was to} undertake a

systematic study ^{of the elastic} properties of smectics

changing ^{some molecular} parameters, ^{with the aim} in mind, ^of gaining ^some insight ^{into the} type ^of

order present ⁱⁿ the smectic layers. Here, ^{we measure}

the elastic _response in the smectic A phase, ^{of a}

number of mesogenic derivatives with different mole- cular lengths ^and symmetries.

We prepared eight p-n-alkoxybenzoates ^of p-n-

alkoxyphenyl previously ^described by ^{H. Schubert}

et al. [9]. ^The transition temperatures ^{of these} compounds ^were determined with a differential

scanning calorimeter ; they ^are given ^{in table I. The} mesophases ^have been identified by examining ^their

textures under a polarizing microscope ^{with a} heating

stage.

2. Expérimental ^work.

2.1 PREPARATION.

The

synthesis ^{of these benzoates was carried out} by reacting ^a p-n-alkoxybenzoylchlorid ^{with the corres-} ponding p-n-alkoxyphenol ⁱⁿ dry pyridine ^{at room}

temperature (24 h.). ^After addition of water the

precipitates ^are filtered, washed with dilute hydro-

chloric acid, ^{then with} by water, and finally ^with

a NaHC03 ⁵ % ^{solution. The esters are} recrystallized

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01980004104036500

366

Table 1.

Transition temperatures of

from ethanol (yield ^{about 70} %). ^{All these} compounds

gave satisfactory ^elemental analysis.

The compounds ^{1, 2, 3 and 4 form an isometric}

series (n ^{+ m = 1 = 13 carbon} atoms) ^{and 5 and 6}

another series with longer ^chains (1 ⁼ 18). Finally,

the compounds ^{7 and 8 have a central core with short} (7) ^or long (8) ^chains.

2.2 MEASUREMENTS OF ELASTIC RESPONSE.

We measured the elastic _response of the smectic A phases

of the previous ^described compounds.

The experimental apparatus ^has already ^been

described in detail [10]. ^{It is based on the} following principle : ⁱⁿ the presence of an electric field, ^a piezo-

electric ceramic produces ^{a strain e. With a} sample

of thickness d (typically d ^{= 175} g.m), ^{if the defor-}

mation is _p (dilation ^or compression), ^the correspond- ing expression ^{reads : 8 =} p/d.

This strain induces a pressure J, which is partially

transmitted by ^{the smectic, and in turn} generates

an electric field in a second piezoelectric ceramic ; from measurements of this field, the value of J can

be determined. Plotting 6 ^{versus 8} enables the value of

B, ^the elastic isothermal compression modulus of the system, ^{to be found via}

Since our system ^{is not} infinitely stiff, ^{there will be}

a difference between the measured value of B and the true elastic modulus, ^{due to the elastic}

response of the system. ^We will ^{therefore have}

to take this effect into account. B has been defined by

de Gennes [11] ^{for a zero} frequency ; ^{as is} known,

however, ^{it is} frequency dependent ; besides in the smectic phase ^we expect ^{that because of} defects,

the material should flow at low frequency. ^{For this}

reason we look at the instantaneous _response of the system ; ^{i.e. at} high frequencies, having ⁱⁿ mind, of course, that the low frequency response could be different. We can estimate that our excitation reaches its full level in less than 1 ms, so our response is the response ^at about 1 kHz.

3. Results.

We measured the relation between

stress and strain at various temperatures. Figure ¹

shows a typical ^{curve for this} relationship, ^which

Fig. ^1.

Typical stress-strain curve in the linear region.

remains linear for small strains of the order of

e - 10-4. We present ^our first experimental ^results.

To obtain the true value of B, ^{we must} incorporate

a correction. For this _purpose, we test the rigidity

of the system by putting ^a solid into the holder.

The value we find for the elasticity of the solid gives

us the correction term for equation (1). ^{This term}

is of the order of 105 CGS. Measurements ^were _per- formed on fresh samples ; ^a systematic decrease in the

rigidity ^{of the material was} found in all samples ^as they grew older [10, 12]. ^The temperature ^was controlled to within 0.1 °C by ^{an electric oven. All} samples ^were homeotropically ^oriented by coating

flat optical glasses ^{with a silane solution.} SA ^mono-

domains formation is favoured by ^the presence of

an N phase which defines an orientation : we intro- duce an isotropic liquid sample ^{into the cell, cool it,}

thus observing ^{N and} finally SA phases. ^This greatly

restricts the choice of suitable isomeric series all the more, since we cannot resort to an orienting magnetic ^{field. We also have to use} material dis-

playing ^an SA phase ^{at less than about 100 OC in order}

not to deteriorate our ceramics. The parallelism ^of

367

the sample ^was regulated ^to better than 10 - 3 to

prevent ^{any variation} in the elastic response due ^to defects.

_

Typical results of BA ^versus temperature ^{are shown} in figure 2 ; they ^{concem the} isometric ^{series cha-}

racterized by 1 = 13. The value of BA ^{we have} adopted

is the one it assumes in the middle of the temperature range of the smectic A phase : this ^{is possible if this}

range is wide enough ^so that B remains practically

constant over at least ^{a few degrees ; close to the}

phase transitions, B ^varies very rapidly because of

pretransitional ^{effects ;} if the range is ^too narrow,

the value of BA ^is extrapolated (see Fig. 2). ^{The values} of B decreases from about 10’ CGS to 10’ CGS, ^at

the transition ; figure ^{3 shows the values} of BA ^{versus 1} (the ^chain length).

Fig. ^2.

^Typical results obtained for the elastic response constant B versus temperature ^{for the} isometric series with 1 ⁼ 13.

Fig. ^3.

^Values of BA ^{versus the chain} length (for ^{1 =} 12 ; 1 ⁼ 13 ; 1 = 18 and 1 = 19).

_ It ^is possible ^{to detect a decrease in the value of} B when ^{the chain length} increases. ^{For 1 = 13 (n = 11)}

B = 3.5 ^x 107 CGS, whereas BA = ^{2 x} 10’ CGS for 1 ⁼ 19. Typical ^errors in B are of the order of 106 CGS.

Fig. ^4.

^{Values of} BA ^{versus molecular} asymmetry b, dotted lines connect results for the isometric series.

Fig. ^5.

Models for the smectic A phase : a) ^random model ; b) soap-like ^model.

In figure ^{5 we} plot BA ^{versus the} asymmetry para-

meter l5( = n - m). ^{The lines} correspond ^{to values}

obtained for samples ^{of different} symmetry ^but

having ^{the same} length. ^{Here also we notice a decrease}

in the elastic _response modulus when the position

of the core in the molecule becomes more and more

asymmetric. ^The variations are of the same order in figures ^{3 and} 4, ^{and to a first} approximation ^we

have linearly decreasing functions. Some apparent anomalies in such a behaviour could be easily ^explain-

ed by ^{the criterion we chose to estimate} BA ; .in ^fact

the greatest anomaly ^{is for} sample 1, ^{with 1 =} 13,

ô ⁼ 3, ^which corresponds ^{to the smallest} temperature

range, inducing ^a greater incertitude in the esti-

mation.

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4. Discussion.

The principal ^{result of our} expe- riment is that the elasticity ^of S, phases depends

upon molecular structure : when the length ^{of at least}

one of the paraffinic ^chains increases, the smectic A becomes softer. ^{Our results can be} easily explained

within the framework of both molecular models

proposed ^{for the} SA phase. ^{In fact, in the model}

where the steric interactions of the core are most

significant (Fig. ^{5b), the} intermolecular potential ^is unchanged ^{when the chains} change, but also in this case, the elastic _response of the system ^{can be} depicted

in the following way.

The elastic _response of such a molecule would

correspond ^{to that of 2} springs ^{in series connected} by ^a rigid ^{mass. The total} response is governed by

the softer spring, this does explain ^{our results, but}

cannot tell us which of the two models applies ^best

for the molecular dispositions (Figs. 5a-5b).

NMR studies of the ordering of the chains [13,14,15]

support ^this type ^of comparison : indeed, ^{it was}

shown that, ^{on the} whole, chains remained stretched out, retaining ^same mobility ^{about the} major ^axis

of the molecule. Besides the mobility ^{of the links}

increases as one moves away from the rigid ^aromatic part. This could explain ^the increasing softness ^with increasing ^chain length : ^{only the} end of chain controls the variation of B ; finally ^{the same} spring ^model

accounts for the decreasing rigidity ^{of the} SA ^with

increasing ^molecular asymmetry, both chains having

on average the ^same mobility. Asymmetry ^means transferring ^{the terminal} link from one end to the

other, yields ^{to an increase} in the average mobility

of the longer ^chain.

5. Conclusion.

We have measured the high ^fre-

quency (1 kHz) response of a smectic A. The results indicate a decreasing ^{in the} rigidity ^{of the smectic A} phases ^{when the molecular} length ^{increases or when}

the molecule becomes more asymmetric. Our results

are in qualitative agreement ^{with two molecular} models of the SA phase. ^A great difficulty ^{in our} experiment, ^{was in the} requirements limiting ^the

choice of the samples (temperature, presence of a

nematic phase). ^{Further data on a} greater variety

of samples ^are required ^to gain ^{a better} understanding

of the mechanism of molecular interactions. A sta-

tistical calculation of the elasticity ^{due to the} possible configurations ^{of a flexible} chain is also needed ;

we hope ^{it will then be} possible ^to quantitatively ^fit

our results.

Acknowledgments.

The authors are very grateful

to G. Durand and J. Jacques ^{who have allowed}

this collaborations, ^{and for} many useful discussions.

They would also like to thank Miss J. Gabard for

synthesis ^work.

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