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Undulation instability of a planar S*c liquid crystal in the presence of dilation strains
A. Jákli, R. Bartolino, N. Scaramuzza
To cite this version:
A. Jákli, R. Bartolino, N. Scaramuzza. Undulation instability of a planar S*c liquid crys- tal in the presence of dilation strains. Journal de Physique, 1989, 50 (11), pp.1313-1321.
�10.1051/jphys:0198900500110131300�. �jpa-00210997�
Undulation instability of a planar S*c liquid crystal in the
presence of dilation strains
A. Jákli (*), R. Bartolino (**) and N. Scaramuzza (**)
Unical Liquid Crystal Group, Dipartimento di Fisica, Universita della Calabria, 87036 Arcavacata di Rende - Cosenza, Italy
(Reçu le 30 septembre 1988, révisé le 9 janvier 1989, accepté le 16 février 1989)
Résumé. 2014 A cause des dilatations au-dessus d’une valeur seuil, on observe une instabilité d’ondulation dans un cristal liquide CE3 en phase S*c. Contrairement à ce qui se produit pour
SA, on ne retrouve pas d’instabilité dans l’alignement homéotrope dans la phase Sc*. On présente quelques résultats expérimentaux préliminaires mais détaillés ainsi qu’une simple explication phénoménologique.
Abstract. 2014 Due to sample dilations above a threshold value an undulation instability was found
in a planar S*c of the commercially available thermochromic liquid crystal CE3. Contrary to the SA practice no instability was found in the homeotropic alignment of the S*c phase. Preliminary
but detailed experimental results and a simple phenomelogical explanation are presented.
Classification
Physics Abstracts
61.30 - 46.30L
Introduction.
During the last decade chiral smectic C (Sc*) liquid crystals have found a growth of interest because of their unique macroscopic properties. They exhibit spontaneous polarization [1],
which is linearly coupled to the electric field thereby resulting in delicate electrooptical [2-4]
and electromechanical [5-7] effects. Due to these interesting electrical behaviours most of the
investigations regard on these effects and only little attention has been paid to the investigation of the pure mechanical behaviour of this phase [8-9].
In the case of SA materials the mechanical behaviour of the homeotropically aligned SA phase was investigated very intensively (see e.g. Refs. [10-13]). It was found that above a
critical dilation 5th of a homeotropic sample (the smectic layers are parallel to the bounding plates) the layers undulate in order to compensate the increase of the sample thickness.
Similar results have been found [14] in Sc: in this case a dilative strain reorientates the
molecules, then a transition to SA is induced ; finally an undulation is produced. Its threshold
(*) Permanent address : Central Research Institute for Physics, H-1525 Budapest, P.O.B. 49, Hungary.
(**) G.N.S.M. (C.N.R.) - C.I.S.M. (M.P.I.), I.N.F.M., Unità di Cosenza.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198900500110131300
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is larger than in the previous case and depends quadratically on the initial tilt angle. Similar
« buckling » instability has been shown in planar cholesteric phase [15]. In this case the
« pseudolayers » of the cholesteric are also parallel to the bounding plates.
In this paper we first report on the behaviour of homeotropic and planar aligned samples being in the Si phase of a commercially available thermochromic liquid crystal.
Contrary to the homeotropic SA phase we have not found any undulation instability in the homeotropic Si samples, however we have found a special undulation instability in planar samples.
Experimental.
For the experiments we used a commercially available material CE3 which was made by the
BDH [16]. Its phase sequence is the following :
In the CLC and Si phase CE3 has a helical structure with a pitch being in the light wavelength regime [16]. For our investigations we made sandwich cells bounded by 3 mm thick glasses.
The bounding glass plates were mounted in a Fabry-Perot like holder with no spacer. The
glass plates were coated by transparent Sn02 conductive layers. The appropriate sample temperature was ensured by the dissipated heat of the current flowing on the electrodes. The temperature was controlled better than ± 0.2 °C. For dilations and compressions we used a piled sequence of 40 pieces of P4-68 type piezoelectric ceramics joined together mechanically
in series and electrically in parallel. In the case of the large sample thickness which we used
(d = 100 ± 5 J..Lm ) the elastic réaction of the sample can be supposed to be negligible thus the applied displacement was equal to the free-space displacement of the ceramics [10]. In this
geometry, from the characteristics of the ceramics determined by the producer (Quartz &
Silice in France), we can deduce that at the temperatures where the measurements were done
(70 °C - T -- 85 °C) by applying ± 100 V on the ceramics the variation of + 2.2 ilm was
created. We worked in the 0-250 V range, that is 5.5 )JLm was the largest sample thickness
dilation. The applied strain corresponded to a square-wave signal with the frequency of
0.5 Hz (this was low enough to ensure the complete relaxation of the internal mechanical stresses as observed during the experiment itself).
The experiment was performed both in the cholesteric and in the Si phase with both homeotropic and planar alignments. The homeotropic alignment was obtained by conven-
tional surface treatment (the bounding plates were coated by homeotropic « SURFINE »
polymer), while the planar one was ensured by high enough sample thickness vibration induced by the ceramics in the cholesteric and at the CLC-Sà phase transition temperature
(see the details in Ref. [17]). We could investigated both alignments on the same samples :
- heating up the material until the isotropic phase and then cooling down the homeotropic sample created without any external influences ;
- cooling down the sample from the isotropic phase maintaining appropriate sample
thickness vibration induced by the ceramics in the cholesteric and during the CLC-Sà phase transition ; planar samples were obtained with monodomain areas being typically 0.5-1 CM2.
On the basis of optical birefringence the quality and type of the alignment were checked by
a polarising microscope. From selective refrective measurements (by a photospectrometer)
we know that the pitch length is about 0.24 itm at the temperatures where the mesurements
were carried out. Due to this small pitch the visible light cannot resolve the helix (the
dechiralization lines are not observable by light). Thus, optically the sample behaves as an SA material. In the case of homeotropic alignment the sample is dark placing anyhow between
crossed polarizers. However in the case of planar alignment the passed light intensity depends
on the direction of the smectic layer normal relative to the direction of polarizers. The
observed light intensity oscillates turning around the sample between crossed polarizers. The
observation of this oscillation does not mean that the smectic layers are perpendicular to the bounding plates, but does mean that the alignment is not homeotropic. Anyway, from the depth of the observed light intensity oscillation we guess that the angle between the smectic
layer normal and the bounding plate is small.
For observing the instabilities we used the following methods.
1) Direct microscopical observation by means of a « Seitz Wetzlar Orthoplan » polarizing microscope.
2) Observing the intensity of the direct transmitted beam of a He-Ne laser (À = 6 328 Â ).
3) Light scattering observation. A polarized laser (He-Ne, À = 6 328 À) beam was
directed into the sample at an angle about 10°. The scattering intensities at different scattering angles were measured by a photodiode. We turned an analyser to get the minimum transmission when the sample was at rest. Then we measured the scattered light intensity
versus the applied dilation 6. Displacing the photodiode to different places we could
determine the minimum value of the threshold dilation dth as the function of the scattering angles, which made possible for us to determine the wave vector qc of the instability.
Expérimental results.
1. DIRECT MICROSCOPICAL INVESTIGATIONS.
1.1 Homeotropic alignment of Si . - Due to the aligning effect of the sample thickness
vibration [17] far from the centre of the homeotropic sample, a planar texture was created if
the vibration amplitude was larger than about 0.5 itm. Avoiding this effect we investigated
the centre of the sample. Up to the sample thickness variation 0=5 J..Lm we could not find any structure (by microscope the smallest observable distance was about 1 )JLm).
1.2 Planar alignment of S c *. - Applying alternatively dilations and compressions (by means
of square wave voltage on the ceramics) we have observed that in some parts of the sample parallel stripes appeared perpendicular to the smectic layers. The average distance between the stripes was found to be approximately 3 J..Lm. The observable threshold was found to be about 6 = 0.6-0.7 )ubm. If the sample thickness were kept constant the created stripes were
annealed in about 0.1 s after the sudden dilation (the rise speed of the signal was about
100 jjLs/jjbm). At the compression only the flow (in reversed direction) was found without the creation of any stripes.
1.3 Planar cholesteric phase. - We observed the so-called buckling instability which has been
described earlier also in other cholesteric materials [15].
2. OBSERVATION OF THE DIRECT BEAM OF THE TRANSMITTED He-Ne LASER LIGHT.
2.1 Homeotropic S! sample. - Far from the centre (where flow was present) we observed a large light intensity decrease (DIII - 50 9à ) following both the compressive and dilative
edges of the sample thickness variation.
At the centre of the sample (where there was no flow) we observed a different behaviour.
Until about Ul = 150 V (,61 = 3 J..Lm) no effect was found. 51 increased with decreasing
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temperatures (at T = 79 °C 81 == 2.9 J..Lm was found). Even by increasing further the applied voltage on the ceramics, an intensity decrease of less than 10 % always occurred at both the
dilative and compressive edges.
2.2 Planar Sê sample. - As a consequence of our planar aligning method [17] the centre of
the sample was in homeotropic state. Therefore we should have investigated the areas far
from the centre, that is we could not avoid the effect of flow. Fortunately our investigations
showed that the flow in planar sample did not result in such a large light scattering as in the
case of homeotropic alignment. (The reason might be the same as the sample thickness
vibration had not disturbed the planar alignment, while in the homeotropic state it induced a
transition to the planar state [17].) In the compressive edge the relative intensity change in
every case was below 3 % (the measuring error was about 2 %), however in the dilation edge
the intensity change in dilations 5 > 1.2 )JLm was found to be systemaically larger than 3 %. A
typical light transmittance function observed at T = 79.5 °C can be seen in figure 1, and the applied dilation dependences are summarised in table 1.
Fig. 1. - A typical light transmittance as the function of time observing the direct beam of a He-Ne laser. (a) The dilation and compression applied on the sample. (b) Signal of photodiode. As the
influence of the dilation there is a large intensity decrease due to the light scattering.
Table 1. - Applied dilation dependences of planar S! phase of a.100 JJ..ffi sample o f CE3 at
T = 79.5 °C. SIII is the relative intensity change o f the transmitted He-Ne laser light due to the sample dilations. T means the life time of the observed instabilities.
3. INVESTIGATION OF THE SCATTERED BEAM.
3.1 Homeotropic S! phase. - Analysing the scattering pattern in the homeotropic Sà state we could not observe any particular light scattering for some special wave vector (which is usual for undulation instabilities).
3.2 Planar Si alignment. - Our planar S* sample can be regarded as a diffraction grating
with the size of the grating being equal to the pitch p. For the diffraction condition we obtain that a diffraction occurs only if p > A. (À = 6 328 À is the wavelength of the incoming light beam.) Because in our material p = 0.24 J.Lm without dilation we could not see any
diffraction, only the direct beam was seen. However applying a large sufficiently sudden
dilation (the rise speed was 100 f.Ls/J.Lm) a scattering pattern normal to the laser beam
appeared on the screen (see Fig. 2). This pattern showed that the scattered vector was
perpendicular to the helical axis (in accordance to our microscopical observation). Looking by
a photodiode for the maximum intensity of the scattered spot we got that the wave number of the light scattering was qc = (2.7 ± 0.3 ) x 106 m 1 at T = 78 °C. In the S c * temperature interval the variation of qc was less than the measuring error. Displaying on a scope the sign of
the photodiode when it was in the place corresponding to the q,, we could deduce that the
decay time of the undulation changed similarly to the case of the direct beam (see Tab. I).
The light intensity dependence is plotted in figure 3 (continous line). For the scattered light intensity it was found that after the threshold dilation (8th = 0.65 ± 0.3 f.Lm) the intensity
increased linearly until 8 = 1.8 J.Lm, but then the slope of the curve suddenly steepened until
about 6 -- 2.7 J.Lm when irreversible changes appeared in the sample (decreasing the applied voltages a strong hysteresis in the behaviour was present). For the sake of comparison we also
Fig. 2. - Set up for the examination of the scattered light pattern due to the dilation of sample thickness
of planar Sc! liquid crystal. The scatterring pattern indicates an undulation with a wave vector being perpendicular to the smectic layers.
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Fig. 3. - (a) The scattered light intensity at qc as the function of dilation (continous line). It can be seen
that 8 th = (0.65 ± 0.3 ) J-I-m. After 8 2.7 J-I-m irreversible changes appear in the sample. (b) The light intensity decrease at dilation in the direct beam (dotted line).
plotted in the same figure the strain dependence of the intensity decrease appeared in the
direct beam at the dilation edges (dotted line). The latter curve was normalised so that at ô = 2.5 f.Lm the two functions let be in coïncidence. The similarity of the two curves indicates
that a large enough part of the scattering was due to the undulation with the wave number qc.
Similar to the temperature dependence of qc the temperature dependence of 6,h was very small, however it was measurable (e.g. at T = 69 °C b th = 0.82 ± 0.3 f.Lm was found).
3.3 Planar cholesteric phase. - We could observe the buckling instability described earlier in other cholesterics [15] and found that at T = 85 °C 5th = 0.33 )JLm and qc = (1.8 ± 0.2) x 106 m- 1. This value is about 5 times larger than it is usual in cholesterics. (We note that our
material is not made from cholesteryl ester but the required chirality in the molecules was
introduced through a branched, terminal alkyl chain which contains the asymmetric centre [16].)
Discussion.
Comparing our results to the earlier results obtained in SA samples we can say that our results
are unexpected in two respects. Contrary to the SA phase we could not see any undulation
instability in the homeotropic state, however we could see an undulation in the planar alignment.
A. First we try to explain why no undulation was observed in the case of homeotropic alignment.
In the case of homeotropic SA samples the tilt is not able to ensure the dilation (the average tilt angle is 90°). In this case the only possibility to ensure the dilation is the undulation of the
layers. This arises at threshold 8th = 2 7TÇ independently of the sample thickness [10]. (Here
e is the penetration length of the order of periodicity of the system. In SA ) = (KIB )112 and is
of the order of the layer thickness.
In the case of Si materials the dilation may be also ensured by a tilting of the molecules away from the equilibrium tilt angle 80 (director clinic). By energy considerations let us
estimate which is the strain interval where this director clinic is more favorable than the undulation. In our material 00 = 45° (see Ref. [18]).
Regarding the whole molecule to be rigid the free energy increase due to the director clinic at the angle y is written
Here B 1- is the elastic constant which describes how difficult it is to tilt the molecules away from the equilibrium tilt angle. From geometrical considerations it is easy to see that due to a
director clinic y the strain E (e = 5 Id) reads :
For the energy increase due to the layer thickness strain we have :
Here B is the isothermal normal compression modulus of the smectic layers (B = 106-107 Nm- 2).
Reading the expression for E of equation (2) into equation (3) and comparing it to equation (1) one can compute the upper limit of yu where the layer tilt is energetically
favourable compared to the undulation instability. For (Jo = 45° we got the results summarised in table II.
Table II. - Summary o f results o f numerical calculation o f the upper limit o f the director clinic yu in the case o f different BIB, parameters. When Y : Yu holds the layer tilt is energetically favourable compared to the undulation instability.
From these results we can see that if B / B.l is smaller than 4 a director clinic never appears.
However we can calculate from equation (2) that if B/Bl is larger than 6 and the strain is
smaller than 0.28 a director clinic occurs due to the dilation. Bl is expected to be comparable
to B or smaller ; generally [10]
Taking into consideration the molecular model of CE3 (see Ref. [17]) we can estimate that in
our material BIB, =-..c 6-8. In the case of our sample thickness, this means that we should have
applied a dilation larger than 28 J.Lffi which was impossible in our experiment. Our calculation
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shows that for this behaviour the large tilt angle is necessary. For example if dilations would
larger than 0.5 fJ.-m and 00 = 10° would be than the undulation instability were favourable.
We would arrive at a similar conclusion following this argument : in the vicinity of the
transition SC-SA, where the tilt angle is small, we can induce an SA by dilation. Let us recall
from reference [14] what the amplitude of this dilation is. The tilt equilibrium value is
where C is the third term of the classical Landau free energy for Sc
(e is the relative dilation strain e = 6 /d).
For small angles in reference [14] we found the strain to induce a « ferroelastic »
SC-SA transition, by minimizing the equation (5) with respect to &
introducing it into the definition equation (4) we have
In a Sc 0 0 is usually small (of the order of 10-1 rad) and the threshold is of the order of ECA ’ 10- 3. However in the actual case 0() is at least one order of magnitude larger, therefore
SCA = 10- 1. In our case it would imply 5CA = 10 J,Lm. The undulation threshold would be
5t >- 5CA + 2 7TÇ >- 10 J,Lm.
B. Why is there an undulation in planar sample and what is the meaning of our
measurements in planar states ?
We think that for the appearence of an undulation an elastical response of the sample is
necessary. A smectic layer can be regarded as a viscous liquid. Consequently, as an influence
Fig. 4. - Supposed structure change of the dechiralization lines due to dilation 6. (a) The sample at
rest : the dechiralization lines are parallel to each other and to the bounding plates. (b) The result of dilation 5 > 5 th: the dechiralization lines undulate.
