On the rectangular-hexagonal columnar phase transition in disc-like liquid crystals

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On the rectangular-hexagonal columnar phase transition in disc-like liquid crystals

C. Destrade, Nguyen Huu Tinh, J. Malthête, A.M. Levelut

To cite this version:

C. Destrade, Nguyen Huu Tinh, J. Malthête, A.M. Levelut. On the rectangular-hexagonal colum- nar phase transition in disc-like liquid crystals. Journal de Physique, 1983, 44 (5), pp.597-602.

�10.1051/jphys:01983004405059700�. �jpa-00209636�

On the rectangular-hexagonal ^columnar phase ^transition

in disc-like liquid crystals

C. Destrade, Nguyen ^{Huu Tinh}

Centre de Recherche Paul-Pascal, ^Domaine Universitaire, 33405 Talence Cedex, ^France

J. Malthête

Laboratoire de Chimie des Interactions Moléculaires, Collège ^de France, 11, place Marcelin-Berthelot, 75231 Paris Cedex 05, ^France

and A. M. Levelut

Laboratoire de Physique ^{des Solides} (*), ^Bât. 510, ⁹¹⁴⁰⁵ Orsay, ^France

(Reçu le 11 octobre 1982, accepté ^le 28 janvier 1983)

Résumé. 2014 Le diagramme binaire isobare pour deux mésogènes discoïdes, l’hexa-n-octyloxytriphénylène ^et l’hexa-n-octanoyloxytriphénylène, ^est étudié par l’examen des ^textures optiques, l’analyse enthalpique ^différen-

tielle et la diffraction des rayons X. Ces trois techniques confirment l’existence d’une transition directe entre méso-

phase ^{en colonnes} hexagonale ^{ordonnée et} mésophase ^{en colonnes} rectangle désordonnée ; ^ce type de transition est également décrit dans un corps pur discoïde : l’hexa-n-décanoate de truxène. Par ailleurs ^on révèle, ^{dans le} diagramme binaire, ^un comportement ^{fortement non-idéal avec la} présence d’un fuseau à maximum à la transi- tion colonne-isotrope. ^{Le domaine} d’existence de la phase ^{en colonnes} hexagonale ^{ordonnée dans un espace con-} centration-température ^{est discuté d’un} point ^{de vue} structural.

Abstract.

We report the isobaric binary phase diagram ^{for two disc-like} mesogens, hexa-n-octyloxytripheny- lene and hexa-n-octanoyloxytriphenylene, ^{which was studied} by ^{means of} optical ^texture observations, ^diffe-

rential scanning calorimetry ^and X-ray diffraction measurements. They all confirm the presence of ^a direct tran- sition between an hexagonal ordered columnar phase ^{and a} rectangular disordered columnar phase; ^{this kind}

of transition is also described in a pure disc-like mesogen : hexa-n-decanoate of ^truxene. Furthermore we show,

within the binary phase diagram, ^a strongly ^non-ideal behaviour with a marked maximum of the spindle ^bet-

ween the isotropic ^{and the} mesomorphic phase. The existence domain of the hexagonal ^ordered phase ^versus temperature and concentration is discussed from a structural point ^{of view.}

Classification

Physics ^Abstracts

61.30E - 64.70M

1. Introducrion.

We recently reported ^{on several} examples ^of colminar _phases of binary ^{mixtures with a} strongly non-ideal behaviour [1, 2] : ^the spindle

between the isotropic and the columnar phase ^exhibits

a marked maximum. This behaviour, revealed ⁱⁿ the case of rod-like liquid crystals [3], ^is demonstrated

to exist in the case of disc-like mesogens. In fact the total miscibility ^method [4], extensively ^{studied to} identify mesophases ^of elongated molecules, ^{has been} recently ^{extended to} the identification of the meso-

phases ^of disc-shaped ^molecules [1, 2, 5-9]. ^These

studies ^concern the isomorphism ^{of the} mesophases

encountered in the different series of benzene [6], triphenylene [1, 2, 5, 9], ^{or truxene} [2, 8], hexa-substi- tuted mesogens. But ^more recently, examples ^{of total} miscibility ^of mesophases belonging ^{to two members of}

two different chemical series have been demonstrated

[7,11]. ^{In this} paper ^we report ^the study of the isobaric

phase diagram ^{for the} hexa-n-octyloxytriphenylene (C,HET) ^{and the} hexa-n-octanoyloxytriphenylene (C7HAT). ^This study ^{was carried out} by ^{mean of}

texture observations, differential scanning calorimetry

and X-ray diffraction.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01983004405059700

598

2. Materials.

The two pure disc-like substances

belong ^{to the} general ^{formula :}

These substances were reported ⁱⁿ references [1]

and [2]. ^The corresponding thermodynamic ^{data are :}

(K ^{= solid, I =} isotropic, Dh. ⁼ columnar phase with

an hexagonal lattice and ordered molecules in the columns [2, 12], Drd ^{= columnar} phase ^{with a rectan-} gular ^lattice and disordered discs in the columns [2,13]).

Transition temperatures ^{are in} degrees Celsius, ^molar enthalpies (between brackets) ^{in kcal.}

3. Diagram. - ^{The isobaric} phase diagram ^{is repre-}

sented in figure ^{1. This} diagram ^{was built up} by studying ^{several mixtures} of 1 and 2 : the transition temperatures ^were determined through ^a polarizing microscope equipped ^{with a} heating stage (Mettler FP5); ^the molar transition enthalpies ^{were measured} using ^a DUPONT calorimeter.

Fig. ^1.

^Phase diagram of mixture of 1 ^{(C,HET) on the} right ^{with 2} (C7 HAT) ^{on the left.}

The identification of the phases ^{was first} performed by ^texture observations. Figures 2a ^{and 2b} represent the optical ^{textures of the} pure C8HET derivative. Just below the clearing point (Fig. ^{2a, 83} °C) ^{one can}

observe several homeotropic finger-like germs typical

of an hexagonal ordered columnar phase Dho [1, 5, 14].

On cooling ^the germs coalesce and form a mosaic of

domains (Fig. 2b, ⁶⁹ °C) ; ^{most of them} correspond ^to

Fig. ^2.

Optical ^{textures of the} compounds 1 ^(C8HET),

2 (C7HAT), and of the mixtures 50/50 ^{and 79} % ^{of 2 :}

a) Dho phase of 1 ^at 83 °C; b) Dho phase ^of 1 ^{at 69} °C;

c) Drd phase of 2 ^at 121 °C ; d) Dho phase of ^the 50/50

mixture at 117 °C ; e) Dho phase ^{of the} 79 % ^{mixture of}

2 at 80 °C; fl Drd phase ^{of the 79} % mixture of 2 at 57 OC.

normally ^{oriented areas but some} birefringent ^defects

are observed with rectilinear axes. Figure ^{2c shows the} typical fan-shaped ^{texture of the pure} C7HAT ^meso- phase ^which corresponds ^{to a} rectangular ^disordered

columnar phase Drd [2,13]. Figure ^{2d shows the texture}

of a 50/50 mixture of 1 and 2 near the clearing point ( 117°) ^between half-crossed -polarizers : ^{the corres-} ponding mesophase ^can be, ^{on the} basis of the evidence,

attributed to a Dbo ^one (compare Figs. ^{2a and 2d).}

Figures ^{2e and} 2 f correspond ^{to a mixture of 79} % ^of

2 and show the presence of ^a Dbo ^columnar phase ^at

«high temperature ^» (Fig. ^{2e at 80} OC) ^{and of a} Dra

columnar phase ^{at « low} temperature ^» (Fig. 2 f ^at

57 °C).

This diagram exhibits three main features :

-

It is evident that the two columnar phases ^are

not miscible. This result is consistent with previous optical ^texture observations [1, 2] ^and X-ray ^measure-

ments [12, 13].

-

In a narrow domain (around ⁷⁹ % ^of 2) ^{of the} diagram ^{there is a direct} Drd-Dbo phase transition.

That is the first example ^{of such a kind} of columnar- columnar transition [15].

-

The Dho ^columnar phase of the HET derivative is strongly stabilized by ^a large ^amount (up ^{to 75} %)

of alkanoyloxytriphenylene. ^The largest mesomorphic

range is observed for a 50/50 ^{mixture :} furthermore the

enthalpy ^{of the} columnar-isotropic phase transition is enhanced : 1.5 kcal , mole-’ in the 50/50 ^mixture.

4. X-ray diffraction data.

In order to see if there is a significant difference in the stacking of the mole- cules in a column between the two columnar phases,

we have performed X-ray diffraction experiments.

Let us recall that one column formed of regularly spaced ^{molecules will} give ^a diffraction pattern, ^the intensity ^{of which is localized on} parallel regularly spaced planes ^{in the} reciprocal spaced ^{These sheets are} perpendicular ^to the axis of the column : the distance between two planes ^is Qo ⁼ 2 n/do ^where do ^{is the} period along the column. The intensity dependence ⁱⁿ

the plane ^is given by ^{the form factor of} the column in a

plane perpendicular ^to its axis. If the molecules are not

strictly regularly ^stacked the diffracted intensity ^{is not}

so sharply localized and the diffuse plane ^becomes

broader. Therefore the width of the maxima of inten-

sity ^{in a direction} parallel ^to the axis of the column is

proportional ^{to the} inverse of the correlation length

which characterizes the order inside the column. The diffraction pattern ^{of a} periodic two-dimensional _array of such columns is similar to the pattern ^{of one column} except ^for the equatorial plane which becomes discon- tinuous and forms Bragg spots ^which characterize the

plane ^lattice.

In fact the actual pattern ^{is not as} simple ^as expected,

since we have some difficulty ⁱⁿ obtaining single

domains of these mesophases. ^{As a matter of} fact, ^an

intense quasi-rectilinear stripe characteristic of a one-

dimensional periodicity ^{has been seen} only ^for single

domains of the hexa-n-pentyloxytriphenylene, C5HET [ 12]. ^{In this case} the correlation length ^is greater ^{than a} few hundred angstroms. ^{Beside this diffuse} stripe ^we

see also diffuse spots coming ^{from the} interference between aliphatic ^chains lying ^at Q ^{= 1.6 A-1} Generally ^the direction of the column axis fluc- tuates inside the sample. ^{In this case the} stripe ^becomes

a portion ^{of a} circle and the width of the circle depends

on the order parameter ^{and on the} correlation length.

At the same time the paraffinic ^{chains are more disor-}

dered both because of the fluctuations of the director and because of the length of each chain and these two factors are probably ^not independent (Figs. ^{3b and 3c).}

For an oriented sample containing disordered columns the ring corresponding ^to the interference between

cores takes place ^at larger angles. ^{The two features are}

not well separated ^{but the} angular extension of the spot is smaller in its outside part (cores) than in its inside one (chains) (Fig. 3d).

In our experiment ^we compare the patterns ^obtained

600

Fig. ^3.

X-ray pattern (A ^{= 1.54} A) ^{of oriented} samples

of columnar phases : a) CSHET (80 °C) (flat ^{film at 40 mm}

from the sample); b) mixture of 50 % ^of 1 ^{(C8HET), 50 %}

of 2 (C, HAT) ^{at 79 °C} (cylindrical film); c) C9 HATX (90 °C) (cylindrical film) ; d) C9 HATX (140 °C) (cylindrical film).

with partially ^oriented samples ^{held in a Lindemann} glass ^tube (0 ^{= 1.5} mm), aligned ^{with a 1.7 T hori-}

zontal magnetic ^field perpendicular ^{to the} glass ^tube

axis. Therefore the axis of the columns can be aligned

in _any direction perpendicular ^{to the} magnetic ^field.

The X-ray ^beam (which is monochromatic CuKa) ^is perpendicular ^{to the} magnetic ^{field and to the tube}

axis and thus we can detect the ordering ^{inside a}

column along the vertical axis of the film.

With this geometry ^a determination of the corre-

lation length along ^{a column is} possible ^{but would}

need a complete analysis ^based upon the knowledge

of the director disorientations in planes parallel ^and perpendicular ^{to the} magnetic ^field Nevertheless a

simple comparison of the diffraction patterns espe-

cially along ^a vertical axis going through ^{the incident}

beam impact ^would give ^{a useful} insight ^{into the} dependence of the linear order in a column on tempera-

ture and concentration.

We have obtained X-ray patterns for various concen-

trations of the mixture C8HET/C7HAT. ^{All the} samples ^are partially ^{oriented in the} magnetic ^field.

In a direction perpendicular ^{to the} magnetic ^{field an}

outer ring lying ^at Q ^{= 1.8} Å - 1 is visible for samples containing less than 75 mole percent of the HAT derivative. For a sample containing ^{79 mole} percent HAT, ^{the outer} ring is visible at 85 OC but disappears ^at

low temperature (T ⁼ 70°C). Going ^{from 79 to}

50 mole percent of HAT the width of the outer ring

decreases while the intensity ^at the maxima increases.

The 50 10 sample ^{is the best oriented one and it seems}

that the correlation length of the one-dimensional order inside a column and the degree of orientation of the sample ^increase simultaneously. ^{For this} sample

we have also seen a second diffraction ring ^at Q ⁼

0.9 Å - 1, corresponding ^to the second order of inter-

Fig. ^4.

Evolution of the scattered intensity ⁱⁿ arbitrary

units versus the scattering angle for the different concen-

trations of the 1 and 2 mixtures.

ference, ^{but it is} very weak compared ^{to the} first order.

Except ^{for 79 mole} percent ^of HAT, ^the X-ray pattern does not change ^{with the} temperature in the whole range of stability of the columnar phase. Figure ⁴ gives the evolution of the scattered intensity ^with

concentration at 85 OC. This intensity ^{was measured} by ^a microdensitometer trace in the direction _per-

pendicular ^{to the} magnetic ^{field. It} is clear from this

comparison that the correlation length for the linear order in a column varies with the concentration and is maximum for a 50 jo mixture. Nevertheless an

abrupt change ^occurs probably between the hexago-

nal and the rectangular phases ^{since the outer} ring disappears completely ^{at T = 71 OC for a 79} jo ^HAT

mixture. The corresponding ^curve is similar to the pure C7HAT derivative.

The same sequence has been found in a pure sub- stance : hexa-n-decanoate of truxene (CGHATX)

which exhibits the following ^{« inverse} sequence » [8] :

Figure ⁵ gives ^the intensity dependence ^{for the rectan-} gular (T ^{= 90} OC) and for the hexagonal mesophases (T ^{= 145} oC). ^{There is no} evolution of the curve inside the stability range of the ^two mesophases. ^Moreover

in a direction perpendicular ^{to the} magnetic ^{field the}

curve is similar for the nematic (T ^{= 78} OC) ^{and the} rectangular phase. ^{We have also to} notice that it is difficult to see any change ^{in the} first ^diffuse ring (Q ^{= 1.6} Å - 1) ^{versus either} temperature ^or composi-

tion. The outer ring characteristic of a periodic stacking

inside a column _appears at the transition from the

rectangular ^{into the} hexagonal lattice. The width of this ring is similar to that of a 79 % ^{mixture at} high temperature. ^{In other words we can} confirm that the

rectangular ^columnar phase ^{of the} C9HATX ^{is a} Drd,

and that the hexagonal ^{one is a} Dho phase [ 16]. ^Further-

more this substance exhibits the first example ^{of a} Dra-Dho sequence in a pure disc-like _mesogen.

Fig. ^5.

Evolution of the scattered intensity ⁱⁿ arbitrary

units versus the scattering angle ⁱⁿ C9HATX.

Three striking ^{facts arise from our} X-ray experi-

ments :

i) ^an abrupt change ^{in the linear order of a column}

can occur and a rectangular-hexagonal transition in the packing ^of parallel ^columns accompanies ^this change;

ii) ^a periodic linear order can take place ^{inside a}

column without _any correlation between neighbouring columns, but the correlation length ^{inside t column is}

not infinite. From the height ^of the outside ring ^com- pared ^{to the} paraffinic ring ^{we can} estimate that the correlation length inside the hexagonal ^ordered phase

varies at least by ^a factor 4. We have observed a second order of diffraction for the linear order, this second

ring ^{is of} very weak intensity and appears ^to be as narrow as the first one. But this was only ^{for the best}

ordered sample ^{and it is} likely that both the first kind and the second kind of disorder takes place ^for

this linear order;

iii) ^{in the 1 + 2} mixture the best ordered sample

contained hafl proportion ^{of the two} components ^and corresponds ^{to a} maximum for the clearing point.

Moreover the presence of ^a maximum in the isotropic-

ordered hexagonal temperature of transition is general

for the 50 jo composition 1 ^{+ 2.} Finally ^{we have also}

to notice that the correlation length for the linear order varies with composition ^{or with} the ^{nature of}

the sample ^{but does not} vary with temperature. ^The

transition Dho-Drd ^occurs with the shortest correlation

length. ^Moreover this length ^has roughly ^{the same}

value for the two studied cases.

Note that in the Dh. phase ^{of the} 50/50 mixture the distance between the cores is 3.6 A while the diameter of a rigid paraffinic ^{chain is at least 4.2 A} [17]. ^The comparison ^{of these two values leads to} the conclusion that the next neighbours ^{in a column must} intercalate their chains and this probably gives ^{some stiffness}

to the first CH2 groups ^near the core. This is illustrated both by the helicoidal superstructure ^{and the} sharp-

ness of the ^« paraffinic ^chain spot » ^{for the} CS HET [12]

which has the shortest chain length in this series.

5. Conclusiom

The existence of a rectangular disordered-hexagonal ^ordered (Drd-Dno) phase ^transi-

tion in a mixture of an ester and an ether of triphe- nylene ^{and in a} pure disc-like substance (truxene derivative) ^{has been} clearly demonstrated by ^{means of} optical textures, calorimetry ^and X-ray measurements.

The binary phase diagram ^between C7HAT ^and C8HET is another example ^of strongly ^non-ideal

behaviour in disc-like _mesogens where the spindle

between the isotropic and columnar phase ^{exhibits a}

marked maximum. We must point ^{out that both} X-ray

and calorimetric measurements show that the maxi-

mum of stability range of the Dho phase is obtained for

a 50/50 molar mixture.

We must note that the Dh. phase ^takes form, ^{in the}

602

concentration domain ^{where it} exists (between ⁰ %

and 80 % ^of 2), ^to the detriment of the Drd phase. ^As regards ^the 50/50 ^{mixture, the most} likely ^molecular

arrangement ^should correspond ^{to a} regular ^alterna-

tion of ester and ether molecules. Another possibility

consists in an arrangement ^{of columns} of 1 ^{and co-}

lumns of 2 : nevertheless, ^this configuration ^{is incon-}

sistent with the similar intensity ^{of the outer} ring ^{in the} diagrams ^{of the} 50/50 ^mixture and for the pure sub- stance (Fig. 3). ^{The first} hypothesis is consistent with

an ordered arrangement ^of molecules in the columns :

as a matter of fact two ester molecules are always

separated by ^one ether molecule. This configuration

avoids the steric hindrance which is probably ^res- ponsible ^for the disorder observed in the Drd type columnar phases. Anyway it is difficult to understand

why this situation strongly stabilizes the Dho phase.

We hope that these results will stimulate some

calculations of conformational energy and packing.

Acknowledgments.

^{The authors are indebted to}

P. Foucher for his contribution in DSC measurements and to Dr F. Hardouin for his help ^{in the} X-ray ^work.

References

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