HAL Id: jpa-00247637
https://hal.archives-ouvertes.fr/jpa-00247637
Submitted on 1 Jan 1992
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Structural defects in smectic c* liquid crystals
I. 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 de Physique II, EDP Sciences, 1992, 2 (3), pp.345-357. �10.1051/jp2:1992138�. �jpa-00247637�
Classificafion
Physics Abstracts
61.14 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 be switched 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 enables the 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, the soft- 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-~H3
I
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 by
10 ~m (ITO cells supplied by E.H.C.CO., LTD. of Japan). It was heated into tile isotropic region in order to erase the structures due to the previous tllennal and mechanical history and
then cooled into the Sf phase.
Subsequently a d.c. electric field was applied perpendicular to the glass plates. It was established by polarising light microscopy that switching the d.c. field caused bright-dark
reversal (Figs. lc, 16).
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 room temperature, 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 about the smectic phase, the cell was quenched very rapidly from 325 K to room temperature and opened, leaving material on both glass plates. The liquid crystalline sample had solidified, and the intemal structure was revealed by a special ion etching technique. The freshly exposed
surface was tllen shadowed and a direct replica produced.
Experimental results.
ELECTRON MICROSCOPY. In order to obtain samples suitable for electron microscopy two
different routes are possible ; (a) high resolution phase contrast techniques and (b) surface
replication methods. In method (a) tile smectic planes or individual molecules are imaged directly. We have described this method in several publications [3-6]. Method (b) has tile
disadvantage 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 bulk
sample, the surface was etched by a special ion etching technique using oxygen ions and
subsequently 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 standard
methods [7].
Using this technique a number of specific disdination structures were revealed, as indicated in 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 following
discussion.
~[
'
60165
Copy of transparent overlay
~ i
10pm 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 pm
Fig. 3.
/
~~
~~~60~63
Copy of transparent overlay
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).
Copy of transparent overlay 60~59
spm spm
Fig. 5. Surface replica, obtained from ferroelectric liquid crystal 4-[3-(s)-methyl-2-(s)-chloropen- tanoyloxy]-4'-octyloxy-biphenyl (monomer).
_~
~ll
~~
~
60~60
Copy of transparent overlay
~ ~
1° pm 10 pm
Fig. 6. Surface replica, obtained from ferroelectric liquid crystal 4-[3-(s)-methyl-2-(s)-chloropen- tanoyloxy]-4'-octyloxy-biphenyl (monomer).
Discussion of results.
THE FERROELECTRIC EFFECT. The shape of the molecule is an essential factor goveming
the formation of liquid crystalline phases [10]. This becomes particularly relevant in tile case of ferroelectric liquid crystals. In order for a substance to become ferroelectric, the electric
polarisation must be invariant under symmetry operations. Therefore the polar axis must be
along 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 development
of ferroelectricity. However, certain tilted phases may satisfy the required symmetry
conditions and exhibit ferroelectricity. The structural parameters of 7 known tilted smectic phases 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 of ferroelectricity 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 remain invariant by all symmetry operations that leave the medium invariant. The molecules must therefore 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 macroscopic
polarisation along the C~ axis. Symmetry arguments show that P is perpendicular to the plane containing 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 Rotational
grouping orienta- correla- packing orienta- correla- tilt distribu-
tion tion order tional tion orienta- tion
length order length tion
C* tilted none tree
iquid I* tilt to short (2) long range
apex range
F* tilt to short (~) long range
side r,rage
J*(G' * tilt to long range b-fold
apex (~) de generate
G* to long mnge
rally range (~)
Disordered H* lilted (~) long )ong range 2_fold
range oscillation
K*(H'* ) jilted (~) long range 2-fojd
oscillation
(~) The tilt direction is either to the short or long edge of the packing matrix, however, it has not been experimentally
determined 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 been considered. 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 a characteristic 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 averages
to 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 in the same direction, creating a structure with a unifornl director n. This can be achieved by applying 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 liquid
crystals have characteristic defects which give rise to characteristic texbures in the light microscope [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 in
crystalline 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 specific
defects in smectic c and smectic c* structures based on light microscopic observations have been studied in considerable detail [16-18]. The distortions give rise to a rotation of the
rrrrrrrr il
rrrrrrrr
P il ((((I(it
Z.
~f ffffffrf
if ~~iiii~~
r il
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 helix formation is suppressed (flom Ref. [13]).
~j jfi j
W [ @
s=1/2 s=-1/2 s=-I
j ~~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 (from Ref. [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 the elastic constants. For nematics this equation and its solution is well known [19], and the director 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 a closed 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 more
complicated situation because specific interactions between layers are involved and the
generalised Landau equation is required to calculate the free energy density [20]. In order to
analyse the observed defects it was therefore necessary to make the simplifying assumption
that the three elastic constants are equal.
In the one-constant approximation, the elastic energy density of the distortions in ~fi may be written as [8]
aj ~ aj ~ aj ~
~2llGl ~l~l ~lG~l1'
~~~
Where the c-director (which is the projection of tile preferred molecular orientation in each layer 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 makes with 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 closely
associated with the s
=
I disclination, as is required.
However, the analytic results shown in figures 10a, b for s
=
±1/2 disclinations are very reminiscent 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 high
resolution work [4,6]. This means that it will not be possible under these circumstances to see individual 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. This treatment 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 is sketched 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 avoid
crystallisation. In fact, this behaviour is advantageous, because it « decorates » the director field of the original sample when it is subsequently etched. Another advantageous feature is that 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 of the liquid crystal clearly cannot be supported by the crystal. Therefore crystal lamellae
develop 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 (- -) and structure observed in replicas.
a
5.5 pm
~S
j,
_ j
b 1 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 transparent overlay from crystallised sample depicting individual crystals. c) Transparent overlay showing same region in liquid crystal phase.
II fi)
' / /y
j
~
- j
~ /~ ~l
la) 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 the
curvature has a maximum value.
At the edges a tilt angle of about 32° with respect to tile lamella (layer) normal is typically
obtained. Investigations are in progress in order to deternline the crystal structure of these materials 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 are described and analysed. These include :
I) Dark, parallel lines which disappear when tile field is switched on. These are disclination, 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 been
extensively 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 techniques
the bulk material is not homogeneously aligned. At the present time, homogeniously aligned
cells have also been prepared by pre-aligning the molecules in the cell using capillary forces and subsequently improving the alignment in a low frequency field (5 Hz). Analysis of the
resulting defects is in progress.
3) On a submicroscopic scale revealed by special electron microscopic techniques, defect lines 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 Landau
equation. 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 phase
which appears just below tile isotropic transition.
6) The integer disclinations are expected to occur both in smectic c* and smectic c systems but 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 rather detailed infornlation about defects in liquid crystals and their dimensions even in this low
resolution range. At the same time it will also be necessary to produce homogeneously
oriented samples in order to facilitate a unique interpretation.
Acknowledgement.
The authors gratefully acknowledge some very helpful comments by Prof. M.K16man
regarding 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. We wish to acknowledge tile technical assistance of R. Wiirfel who helped to develop the
experimental 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
