Structural defects in smectic c* liquid crystals...smectic liquid crystalline solids [4-6] well crystalline solids. However, if long range distortions are induced, as in the case of

HAL Id: jpa-00247637https://hal.archives-ouvertes.fr/jpa-00247637

Submitted on 1 Jan 1992

HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, estdestinée au dépôt et à la diffusion de documentsscientifiques de niveau recherche, publiés ou non,émanant des établissements d’enseignement et derecherche français ou étrangers, des laboratoirespublics ou privés.

Structural defects in smectic c* liquid crystalsI. Voigt-Martin, R. Garbella, S. Vallerien

To cite this version:I. Voigt-Martin, R. Garbella, S. Vallerien. Structural defects in smectic c* liquid crystals. Journal dePhysique II, EDP Sciences, 1992, 2 (3), pp.345-357. �10.1051/jp2:1992138�. �jpa-00247637�

https://hal.archives-ouvertes.fr/jpa-00247637https://hal.archives-ouvertes.fr

J. Phys. II France 2 (1992) 345-357 MARCH 1992, PAGE 345

Classificafion

Physics Abstracts61.14 61.30 77.80

Structural defects in smectic c* liquid crystals

1. G. Voigt-Martin I'), R. W. Garbella I') and S. U. Vallerien (~)

(1) Institut f%r physikalische Chemie, Universitkt Mainz, Germany(2) Max-Planck-Institut fur Polymerforschung, Mainz, Germany

(Received J6 January J99J, revised J9 September I99J, accepted 5 December J99I)

Abstract. In this paper the structure of a smectic c* liquid crystalline material which can beswitched in an electric field is investigated by electron microscopic techniques. Using this method

the director field is revealed and typical disclinations observed. Analysis of these features enablesthe elastic anisotropy of the material to be calculated.

Sample description.

For our structure investigations a liquid crystalline material (4-(3-(s)-methyl-2-(s)-chloro-pentanoyloxy)-4'-octyloxy-biphenyl) with two chiral centres was synthesised using known

procedures [I]. This material has been investigated by broadband dielectric spectroscopy, thesoft- and Goldstone modes were analysed [2a] as well as the high frequency rotation of the

molecules around their long axis [2b]. The structural formula is :

* *C~HS-~H-CH-C-)-~(CH~)7-~H3I

CH~ Cl O

c322KSi 328KSt338Ki

The transition temperatures as determined by D.S.C. measurement and dielectric spectros-3U K

~3~8 K 338 K

copy are crystalline - S~ phase, Sf -SA phase and St - isotropic.

Sample preparation.

The sample was pressed between two glass plates coated with polyimide and separated by10 ~m (ITO cells supplied by E.H.C.CO., LTD. of Japan). It was heated into tile isotropicregion in order to erase the structures due to the previous tllennal and mechanical history andthen cooled into the Sf phase.

Subsequently a d.c. electric field was applied perpendicular to the glass plates. It wasestablished by polarising light microscopy that switching the d.c. field caused bright-dark

reversal (Figs. lc, 16).

346 JOURNAL DE PHYSIQUE II N° 3

a) b) c)

Fig. I. Light micrographs showing effect of electric field on sample (a) E = 0, (b) E up, (c) E down.

The sample was not unifornlly oriented and contained many defects. On cooling to roomtemperature, dark stripes with a pitch of about 10 ~m appeared within the domains which

were of focal conic nature (Fig. lc). The domain size was in the millimetre region.Electron microscopy was chosen as the method of investigation because it offers the unique

advantage of revealing details about the microstructure. In order to obtain information aboutthe smectic phase, the cell was quenched very rapidly from 325 K to room temperature andopened, leaving material on both glass plates. The liquid crystalline sample had solidified, andthe intemal structure was revealed by a special ion etching technique. The freshly exposedsurface was tllen shadowed and a direct replica produced.

Experimental results.

ELECTRON MICROSCOPY. In order to obtain samples suitable for electron microscopy twodifferent routes are possible ; (a) high resolution phase contrast techniques and (b) surface

replication methods. In method (a) tile smectic planes or individual molecules are imageddirectly. We have described this method in several publications [3-6]. Method (b) has tiledisadvantage of lower resolution and therefore not revealing individual molecules. However,

the light microscopic results indicated that the defects are rather large scale, therefore method(b) seemed more appropriate. The sample was cooled from the isotropic into the smectic c*phase and rapidly quenched. In order to reveal tile structure beneath the surface of the bulksample, the surface was etched by a special ion etching technique using oxygen ions andsubsequently coated in a perpendicular direction with carbon and at an appropriate oblique

angle with pt/C. The replica was then prepared for electron microscopy using standardmethods [7].

Using this technique a number of specific disdination structures were revealed, as indicatedin figures 2-6.

It is well established that the disclination structure can be used to calculate the elastic

constants of liquid crystals [8, 9]. In order to understand the principles which make it possible

to understand these electron micrographs, it is necessary to analyse these defects and to recall

some basic concepts about ferroelectric liquid crystals. This is done in the followingdiscussion.

N° 3 STRUCTURAL DEFECTS IN SMECTIC c* LIQUID CRYSTALS 347

~['

60165

Copy of transparent overlay

~i

10 pm lo pm

Fig. 2. -Surface replica, obtained from ferroelectric liquid crystal 4-[3-(s)-methyl-2-(s)-chloropen-tanoyloxy]-4'-octyloxy-biphenyl (monomer).

-

~

60~70

Copy of

_- --

5 pmFig. 3.


/

~

~~~~60~63


10~m~ ~

10~m

Fig. 4. Surface replica, obtained from ferroelectric liquid crystal 4-[3-(s)-methyl-2-(s)-chloropen-tanoyloxy]-4'-octyloxy-biphenyl (monomer).


60~59

spm spm



_~

~ll~~

~

60~60


~ ~1° pm 10 pm


Discussion of results.

THE FERROELECTRIC EFFECT. The shape of the molecule is an essential factor govemingthe formation of liquid crystalline phases [10]. This becomes particularly relevant in tile caseof ferroelectric liquid crystals. In order for a substance to become ferroelectric, the electricpolarisation must be invariant under symmetry operations. Therefore the polar axis must bealong a unique rotation axis to which no perpendicular plane of reflection symmetry belongs[10-12]. The high symmetry of most liquid crystal phases tllerefore prohibits the developmentof ferroelectricity. However, certain tilted phases may satisfy the required symmetry

conditions and exhibit ferroelectricity. The structural parameters of 7 known tilted smecticphases that may exhibit ferroelectric properties are given in table I, which is taken from

reference [14]. Both electron diffraction and the appearance of a Goldstone mode in dielectric

spectroscopy established the existence of an Sf phase.By quenching the material from the Sf phase, remnants of the defects typical of that phase

were clearly frozen in. In order to understand the micrographs, a further aspect offerroelectricity has to be discussed the polarisation vector P is always locally perpendicular

to the director and in order for the material to have ferroelectric properties, it must remaininvariant by all symmetry operations that leave the medium invariant. The molecules musttherefore be tilted with respect to tile smectic layers. However, even a smectic C phase with a

point group C~~ cannot have spontaneous electric polarisation. The symmetry elements of

our molecule was therefore reduced still further to C~~, «~~, C~~ giving a macroscopicpolarisation along the C~ axis. Symmetry arguments show that P is perpendicular to the planecontaining the layer normal z and the director n. The sign convention is that if z, n and P make

a right-handed system P is positive, for a left-handed system it is negative.


Table I (from Ref. [14]).

Tilt m-plane Layer Bond Layer Helical Rotationalgrouping orienta- correla- packing orienta- correla- tilt distribu-

tion tion order tional tion orienta- tionlength order length tion

C* tilted none tree

iquid I* tilt to short (2) long rangeapex range

F* tilt to short (~) long rangeside r,rage

J * (G' * tilt to long range b-fold

apex (~) de generate

G* to long mngerally range (~)

Disordered H* lilted (~) long )ong range 2_fold

range oscillation

K*(H'* ) jilted (~) long range 2-fojdoscillation

(~) The tilt direction is either to the short or long edge of the packing matrix, however, it has not been experimentallydetermined by combined miscibility and structural studies which phase is H and which is K.(2) The bond orientational order has to have the helical structuring taken into account for the direction perpendicular to

the layers.(3) Hexagonal packing in the plane normal to the tilt direction, and the phase is effectively (4) centered monoclinic.(4) The packing is of a distorted hexagonal type in the plane normal to the tilt direction.

So far, only the local symmetry (onelayer) of the helicoidal structures C*, F*, I* has beenconsidered. In figure 7a a typical helical C* structure is indicated, showing that the director n

spirals on a cone when moving in tile z-direction so that a helicoidal structure w1tll acharacteristic pitch Z is formed. This motion on a cone with a helical superstructure is

responsible for the Goldstone mode. It is clear that macroscopically the polarisation averagesto zero. Such a structure is optically active but not ferroelectric.

Thus in order to obtain a macroscopic polarisation P, all the dipoles should be oriented inthe same direction, creating a structure with a unifornl director n. This can be achieved byapplying an electric field in very thin ITO cells (~ 2 ~m) thus creating the structure figure 7b,referred to as a non-helicoidal C* structure. These features have been discussed in detail by

Clark and Lagerwall [12, 13].

STRUCTURAL DEFECTS REVEALED BY ELECTRON MICROSCOPY. It i~ well known that liquidcrystals have characteristic defects which give rise to characteristic texbures in the lightmicroscope [14, 15]. These textures are caused by defects, which give rise to translational or

orientational distortions of the material. Those which do not cause extensive distortion of the

material such as dislocations, occur in smectic liquid crystalline solids [4-6] as well as incrystalline solids. However, if long range distortions are induced, as in the case of the

disclinations shown in figures 2 to 6, the defects can occur only in liquid crystals. The specificdefects in smectic c and smectic c* structures based on light microscopic observations havebeen studied in considerable detail [16-18]. The distortions give rise to a rotation of the


~,,

rrrrrrrril

rrrrrrrr

Pil ((((I(it

Z.

~fffffffrf

if ~~iiii~~

ril

rrrrrrrr

Helicoidal smectic cX structure Schmectic c* structure

Macroscopie polarisafion P=0 helix suppressed Macros-copie polarisation P=P2

Fig. 7.- Schematic diagram indicating that macroscopic polarisation can only occur when helixformation is suppressed (flom Ref. [13]).

~j jfi jW [ @

s=1/2 s=-1/2 s=-Ij ~~j ~)( @s=I,c=0 s=I,c=~/~ s=I,c=~/2

C

~j

~s=3/2 s=2

fly 16$~( if~ ~s=-3/2 s=-2~

s=5/2

Fig. 8. -General schematic showing dependence of defect structures on parameters s and c (fromRef. [15]).


director, which is defined as the direction of the molecular axis. The director field can then be

obtained from the free energy density of a deformed specimen, by an expression involving theelastic constants. For nematics this equation and its solution is well known [19], and thedirector fields normally generated are shown in figure 8 for different values of the director

strength s, which is defined such tllat s x 2 ar yields the angle by which the director tums on aclosed curve round the centre. None of these cases describes the features observed in the

micrographs. The reason is that smectic C* layered structures represent a much morecomplicated situation because specific interactions between layers are involved and thegeneralised Landau equation is required to calculate the free energy density [20]. In order toanalyse the observed defects it was therefore necessary to make the simplifying assumptionthat the three elastic constants are equal.

In the one-constant approximation, the elastic energy density of the distortions in ~fi may bewritten as [8]

aj ~ aj ~ aj ~~2llGl ~l~l ~lG~l1'~~~

Where the c-director (which is the projection of tile preferred molecular orientation in eachlayer on the xy plane) spirals around the z-axis, such that

~P= qz

where q=

2 ar/p, p is the pitch of the helix and ~fi the angle which the local C-director makeswith the x-axis.

Minimisation of (I) yields

V~4=

0 (2)

and the defects which can occur are wedge dislocations along the z-axis with

~b = s tan~' ~

+ qz (3)x

and twist dislocations along the y-axis with

4 =s.tan~'( ~ +qz. (4)x

This expression was calculated analytically giving the director fields shown in figure 9. For

s=

± I, the main features observed in the replicas of figures 2, 4, 6 are described rattler well.The director field loses tile 4-fold symmetry associated with tile line s = I disclinations for

nematics. This was also found experimentally. Furtherrnore, the s = + I disclination is closelyassociated with the s = I disclination, as is required.

However, the analytic results shown in figures 10a, b for s=

±1/2 disclinations are veryreminiscent of the experimental director fields observed in figures 3, 5.In view of this discussion, how can the structures observed in the replicas be interpreted ?

Clearly, the replicas do not give the same resolution as that which we obtained in the highresolution work [4,6]. This means that it will not be possible under these circumstances to seeindividual smectic planes. Moreover, tile treatment which was given to the samples in order to

obtain the replicas must be taken into consideration. The bulk material was ion etched. Thistreatment leads to a preferential depletion in those regions where the sample is distinguished

physically from the remaining regions. In this case preferential etching will occur at tile«edges» of the planes marking chain ends. There is consequently a complementary


a) b)

Fig. 9. Calculated director field for s = ± I. a) s = I, q = 0.I ; b) s = I, q = 0.1.

.,

a) b)

Fig. 10. Calculated director field for s = ± 1/2. a) s = 0.5, q = 0.I b) s = 0.5, q = 0.1.

relationship betwwen tile director field and the«

lines»

observed in the micrographs. This issketched schematically in figure I I. Therefore the micrographs show disclinations of strength

s=

± 1/2 and s=

± 1.

Orientation of molecular axis vith respect to the layers.

Although the samples was quenched rapidly from the smectic phase, it is impossible to avoidcrystallisation. In fact, this behaviour is advantageous, because it

«decorates

»the director

field of the original sample when it is subsequently etched. Another advantageous feature isthat the crystal edges

«mark

»the molecular direction. This becomes clear when a highly

magnified region is analysed (Fig. 12). The enornlous curvature which was a typical feature ofthe liquid crystal clearly cannot be supported by the crystal. Therefore crystal lamellaedevelop which incorporate the molecules as long as the tilt does not deviate too much from


j--<1

-~ ~

I'

~II

J

j~ ~~ ~~~~~~

llj 11~~/~

mu

-- @) b)10Vm

~-=-'

~

~~

"-

~~

,

/~~~~

'

~~

6X~

'@) b)

~10pm

,/)~

~-~~ ~/ $~ ~~/

/ ,

$

~/~,[~ ~

~

'fi I ', ~

~~

/ '6A~ ' I' ~) b)

~'~

Fig. ii- Schematic diagram showing complementary relationship between director field (- -) andstructure observed in replicas.


a

5.5 pm

~S,j

_ j

b1 c

~j

'~

j j

~Fig. 12. -Micrograph and schematic showing relationship between crystals and smectic planes. a)

Surface replica from ferroelectric liquid crystal showing disclination core. b) Copy of transparentoverlay from crystallised sample depicting individual crystals. c) Transparent overlay showing sameregion in liquid crystal phase.

II fi)' / /y

j~

- j

~ /~ ~lla) 16)

Fig. 13. Schematic diagram showing orientation of molecules within smectic planes (a) and lamellae(b) after crystallisation.


that required by the crystal structure. This is shown schematically in figure13. For this

reason, the crystallites are laterally much shorter in the centre of the distortions where thecurvature has a maximum value.

At the edges a tilt angle of about 32° with respect to tile lamella (layer) normal is typicallyobtained. Investigations are in progress in order to deternline the crystal structure of thesematerials in the crystalline phase and how this angle is related to the molecular tilt.

Conclusion.

In this work, the features observed in a quenched smectic c* liquid crystalline material aredescribed and analysed. These include :

I) Dark, parallel lines which disappear when tile field is switched on. These aredisclination, or unwinding lines related to the helicoidal nature of the smectic c* phase [21].Orientation in tile electric field orients the dipoles, thus unwinding the helix and causing the

lines to disappear. This is the non-helicoidal smectic c* structure. The effect has beenextensively discussed in the literature [12, 13].

2) A broken fan-shaped texture is observed [15]. The oriented regions within the domains

are several millimeters in diameter. Without the application of special alignment techniquesthe bulk material is not homogeneously aligned. At the present time, homogeniously alignedcells have also been prepared by pre-aligning the molecules in the cell using capillary forcesand subsequently improving the alignment in a low frequency field (5 Hz). Analysis of theresulting defects is in progress.

3) On a submicroscopic scale revealed by special electron microscopic techniques, defectlines are observed which are related to the director field. The disturbance in the director field

is several microns. The observed features can be analysed on the basis of a simplified Landauequation. The director field for various disclination configurations is calculated.

4) The calculated director fields correspond to disclinations of strength s=±1/2,

s = ±1.

5) Half integer disclination lines are not allowed in smectic c or smectic c* liquid crystals [8,22]. This is because + c and c are not equivalent configurations (c is the vector along the

molecular direction). Therefore such disclinations may be remnants of the smectic A phasewhich appears just below tile isotropic transition.

6) The integer disclinations are expected to occur both in smectic c* and smectic c systemsbut s = I no longer has four fold symmetry. The features observed in figures 2, 4, 6 are

therefore probably related to the tilted phase.

The results indicate that the electron microscopic techniques described can give ratherdetailed infornlation about defects in liquid crystals and their dimensions even in this lowresolution range. At the same time it will also be necessary to produce homogeneouslyoriented samples in order to facilitate a unique interpretation.

Acknowledgement.

The authors gratefully acknowledge some very helpful comments by Prof. M.K16manregarding some specific points in the manuscript. We are also indebted to the Deutsche

Forschungsgemeinschaft for supporting this work within the framework of tile SFB 262. Wewish to acknowledge tile technical assistance of R. Wiirfel who helped to develop theexperimental methods which made these images possible.


References

[1] YosHlNo K., OzAKI M., KRISHIO S., SAHURAI T., MIKAMI N., MIGUCHI R., HOMME M., Mol.

Cryst. Liq. Cryst. 144 (1987) 87.[2] a) VALLERIEN S. U., KREMER F., KAPITzA H., ZENTEL R., FRANK W., Phys. Lett. A 138 (1989)

219.

b) KREMER F., VALLERIEN S. U., KAP«zA H., ZENTEL R., FISCHER E. W., Phys. Rev. A42(1990) 3667.

[3] VOIGT-MARTIN I. G., DURST H., Liq. Cryst. 2 (1987) 585.[4] VOIGT-MARTIN I. G., DURST H., Macromolecules 22 (1989) 168.

[5] VOIGT-MARTIN I. G., KRUG H., Macromolecules 22 (1989) 595.[6] VOIGT-MARTIN I. G., KRUG H., VAN DYCK D., J. Phys. France 51 (1990) 2347.

[7] REIMER L., Elektronenmikrospische Untersuchungs-und Prhparationsmethoden (Springer Verlag,1967).

[8] CHANDRASEKHAR S., RANGANATH G. S., Adv. Phys. 35 (1986) 507.[9] THOMAS E., WooD E. L., Faraday Disc. Chem. Sac. 79 (1985) 229.

[10] LAGERWALL S. T., DAHL I., Mol. Cryst. Liq. Cryst. l14 (1984) lsl.[ll] MEYER R. B., Mol. Cryst. Liq. Cryst. 40 (1977) 33.[12] LAGERWALL S., OTTERHOLM B., SKARP K., Mol. Cryst. Liq. Cryst, 152 (1987) 503.[13] CLARK N., LAGERWALL S., Recent Development in condensed matter Physics, J. Devreese,

L. Lemmens, V. van Doren, J. Royen Eds. (Plenum Publishing Corporation, 1981).

[14] GOODBY J. W., LESUE T. M., Mol. Cryst. Liq. Cryst. l10 (1984) 175.[15] DEMUS D., RICHTER L., Textures of Liquid Crystals (Verlag Chemie, 1978).[16] KLtMAN M., Points, Lignes et Parois (Les Editions de Physique, 1977).[17] BOULIGANAD Y., KLtMAN M., J. Phys. France 40 (1979) 79.[18] RAPINI A., J. Phys. France 33 (1972) 237.[19] FRANK F. C., Philos. Mag. 42 (1951) 809.[20] CARLSSON T., ZEKS B., FILIPIC C., LEVSTIK A., Phys. Rev. A 42 (1990) 877.[21] GLOGAROVA M., J. Phys. France 45 (1984) 142.[22] BOURDON L., SOMMEIRA J., KLtMAN M., J. Phys. France 43 (1982) 77.

JOURNAL DE PHYSIQUE II -T 2, N'3, MARCH 1992

Documents

Structural defects in smectic c* liquid crystals...smectic liquid crystalline solids [4-6] well crystalline solids. However, if long range distortions are induced, as in the case of