A ferroelectric smectic phase formed by achiral straight core mesogens .... 4. Data for different films thicknesses (between 0.64 µm and 1.36 µm) coincide, thus ...
A ferroelectric smectic phase formed by achiral straight core mesogens Ralf Stannarius1 , Jianjun Li1 and Wolfgang Weissflog2 1 University
of Leipzig, Institute of Experimental Physics I,
Linn´estrasse 5, D-04103 Leipzig; 2 University of Halle, Institute of Physical Chemistry, M¨uhlpforte 1, D-06108 Halle, GERMANY
Abstract We report electro-optic experiments in liquid crystalline free standing films of achiral hockey stick shaped mesogens with a straight aromatic core. The material forms two smectic mesophases. In the higher temperature phase, a spontaneous polarization exists in the smectic layer plane and the films show polar switching in electric fields. It is the first example of a ferroelectric phase formed by nearly rodlike achiral mesogens. Mirror symmetry of the phase is spontaneously broken. We propose a molecular configuration similar to a synclinic ferroelectric (CS PF ) high temperature phase and an anticlinic, probably antiferroelectric (C A PA ) low temperature phase, but do not exclude that the symmetry may be even lower than that of known B 2 subphases of bent-core (banana-shaped) mesogens. PACS numbers: 61.30.-v (liquid crystals), 77.80.-e (ferroelectricity and antiferroelectricity), 68.15.+e (liquid thin films) 87.64.Rr (optical microscopy)
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Common achiral calamitic (rodlike) smectogens are known to form untilted smectic A type (symmetry D∞h ) as well as tilted smectic C type (symmetry C2h ) mesophases. Due to the existence of the mirror plane and a twofold rotation axis normal to that plane, neither of these phases can develop spontaneous polarization. Ferroelectricity has been found almost exclusively in mesophases formed by chiral molecules, which lack the mirror symmetry plane [1], and a spontaneous polarization can exist along the C2 axis. Exceptions are liquid crystalline phases of bent-core (banana shaped) molecules which are in the focus of scientific interest particularly because of their unusal symmetry properties [2–7]. So far, the search for materials that spontaneously develop polar inplane molecular order in the mesophase was only successful for mesogens with strongly bent rigid molecular core (with at least 5 aromatic rings). There are first hints by Hird et al. [8] that straightcore three-ring compounds, containing a 1,5-disubstituted 2,3,4-trifluorophenyl unit, can exhibit reduced symmetry regions in the smectic C phase. The question how large the deviations from the conventional straight core mesogen geometry (i.e. unbranched alkyl chains at para-substituted benzene rings with nearly parallel para axes in the core) must be in order to generate a spontaneous polar order and ferroelectric behaviour of non-chiral mesogens, remained unanswered so far. This study investigates a mesogen with a straight three ring core and two alkyl chains, one in para position and the opposite chain in meta position. Its chemical structure is shown in Fig. 1. The phase sequence in the bulk is crystalline 65 C (smectic C2 59 C) smectic C1 66.5 C isotropic, transition temperatures having been determined in DSC measurements [9]. The low temperature C2 phase is monotropic, it can easily be supercooled down to about 45 C. In very thin freely suspended films, the transition temperatures are slightly shifted: the clearing temperature raises above 70 C in films of a few layers thickness. In the films observed here, the transitions are at the bulk transition temperatures. A proposed classification of the two smectic phases will be given at the end of this paper. Previous X-ray structure analysis has revealed that both phases have similar smectic layer thickness [9]. Proton decoupled
13 C
NMR experiments suggest that
the molecules organize to a synclinic structure in the C1 phase (same tilt azimuth in subsequent layers) and to an anticlinic structure in C2 (opposite molecular tilt in subsequent layers) [9]. Our electro-optic experiments with freely suspended films support this model. We will show that the high temperature phase of this non-chiral, straight-core mesogen is polar and switchable in electric fields. The relative strength of the spontaneous polarization and its direction with respect to the tilt plane is determined. The low temperature phase does not exhibit a measurable spontaneous polarization but is dielectrically switchable. 2
Basic preparation and observation techniques of the samples are the same as in electro-optic experiments of conventional freely suspended smectic films [10–16]. The sample holder consists of a glass sheet with copper electrodes on opposite sides of a circular hole in the glass (Fig. 2). The hole diameter as well as the electrode separation are 0.96 mm. The freely suspended films are prepared at 65 C in the C1 phase, by drawing the material with a metal or teflon edge across the
0 2 K by a custom made heating
hole. Particular care has been taken to avoid any possible contamination with chiral impurities. The temperature of the films is controlled with an accuracy of
stage. The driving voltage is synthesized with an HP 33120A function generator, a linear amplifier providing
120 V maximum amplitude. The films are observed in a reflection microscope (NU2,
Carl-Zeiss Jena). Reflection images and video sequences are recorded with a CCD camera, stored and processed digitally. In thin films (up to a few dozen layers), a strong electroconvection flow is excited when the films are exposed to DC electric fields. Therefore, switching experiments have been performed with thick films (well above 100 layers), where the convection threshold is not reached [17]. In both mesophases, the films are in-plane optically anisotropic. At normal incidence, their optical appearance is rather similar. Unoriented films exhibit characteristic Schlieren textures indicating local variations of the alignment axis, often with defects of integer strength. C1 appears nearly uniaxial with the optic axis tilted respective to the layer normal, C2 is strongly biaxial with the two optic axes tilted in opposite directions, symmetrically to the layer normal. At the phase transition (during heating and cooling), one observes arrays of ’waves’ with sharp fronts crossing the film plane, with propagation speeds of a few hundred µm/s. We interpret this as synclinic to anticlinic transitions of individual smectic layers or stacks of layers. These findings confirm the structure model [9] derived from NMR and X-ray scattering. In sufficiently strong electric fields, the films align to uniform orientation, but often, domain walls persist and separate aligned domains. We will primarily focus on these objects. When the films are exposed to in-plane DC electric fields, dielectric anisotropy as well as a possible spontaneous polarization in the layer plane both contribute to electro-optic switching, whereas in AC fields of sufficiently high frequency, only the dielectric term is effective. The torque balance includes viscous, polar, dielectric and elastic terms in the simplest, flow-free dynamics γϕ˙
ϕ
PE sin ϕ
p
εa ε0 E 2 sin ϕ cos ϕ
K∇2 ϕ
(1)
where γ is a rotational viscosity, P is an in-plane spontaneous polarization, ϕ is the angle between 3
c-director (projection of the tilt azimuth on the layer plane) and electric field E, and ε a
ε ε
is the dielectric anisotropy in the film plane. K represents a mean elastic constant for variations of the c-director in the layer plane (one-constant approximation). With the angle ϕ p , we allow for different possible orientations of P with respect to the c-director (in C1 ). We introduce the coherence lengths ξ p
K PE , ξ K ε ε E , and the ’crossover’ field E P ε ε . a 0
d
2
c
a 0
Since a small spontaneous polarization P is difficult to measure directly, we compare the torque on P in electric fields with the elastic torques on the c-director. For that purpose, we concentrate on particular stationary solutions of Eq. 1 that are spatially inhomogeneous in one dimension. In absence of the polar term (E
Ec ), a π inversion wall of the c-director: tan
ϕ 2
exp
ξx
(2)
d
represents such a solution, and in the limit of a dominating polar term (E stationary 2π wall tan
ϕ
ϕp 4
exp
E c ) one obtains a
ξx
(3)
p
At normal incidence and with crossed polarizers, the local reflectivity of the films is given by R
R0 sin2 2φ
(4)
where φ is the angle between the polarizer and the local c-director, and R 0 is a function of the phase difference of the two polarization components, in the tilt plane and perpendicular to the tilt plane, resp. When the polarizer is in electric field direction, one can set φ
ϕ.
Fig. 3a shows the reflection image of a C1 film in a 100 Hz square wave AC electric field of 104 kV/m, taken with crossed polarizers parallel and perpendicular, resp., to E. At frequencies above
30 Hz, the wall shape is stationary and frequency independent, which means that possible
polar interactions are averaged out. The aligned domains are black and the π walls appear in the form of two parallel bright stripes in the image. The insert shows an optical profile calculated with Eqs. 2,4. From the fit of the optical profiles using these two equations, one obtains the dielectric coherence length, ξd . Figure 4 shows its field strength dependence (bullets) together with the fitted linear slope ξd E
1 8 V.
When the electric field is suddenly switched to DC, the π walls start to move and neighbouring pairs combine to 2π walls. A pair of such 2π walls is shown in Fig. 3b together with the calculated profile (using Eqs. 3,4). Since the polar term at low fields is clearly dominating, it is sufficient to use Eq. 3 for the determination of ξ p . We have confirmed this by comparing the wall profiles 4
with numerical solutions of Eq. 1, using ξd from the fit of the AC structures. The electric field dependence of ξ p together with the fit ξ p E 1
2 3 10 2
3
V1 2 m 1
2
is given in Fig. 4. Data for
different films thicknesses (between 0.64 µm and 1.36 µm) coincide, thus we can exclude that the polarization is merely produced by surface layers. The transition from AC to DC excitation reveals the azimuthal orientation of P in the film plane. Fig. 5a gives a space-time plot of the reflection intensity profile. The cross section is taken nearly perpendicular to an array of walls. Initially, four π walls are visible. After switching from
AC to DC, two 2π walls remain. The favoured regions in the DC field differ by roughly π 2 and
π 2, resp., from those in the AC field, i.e.
the azimuth of the spontaneous polarization
π 2.
(respective to the largest component of ε in the film plane) is ϕ p
When the DC field
polarity is reversed, the previously anti-aligned, energetically unfavourable regions ( 0 5π 1 5π)
grow, while previously aligned domains (0 5π 2 5π) shrink. The initial 2π walls rearrange to new 2π walls (Fig. 5b). The quasi uniform 180 reorientation of the c-director far from domain walls is reflected in characteristic brightness changes, crossing two maxima, along the vertical axis in Fig. 5b. If the DC field is switched back to AC at the same effective field, the 2π walls split to π wall pairs again. The azimuth of dielectric alignment (i.e. the sign of εa and the c-director orientation respective to the AC electric field) is determined in a transmission microscope. Since C1 is only weakly biaxial, it can be considered in rough approximation as uniaxial, with the optic axis along the molecular tilt. When the film in the C1 phase is tilted slightly (
7 ) into the direction of the AC field, the
effective birefringence of one of the aligned domains next to a π wall increases and that of the opposite domain decreases (the film tilt increases the optic axis tilt in one domain, while it reduces it in the other domain). On the other hand, a tilt of the film perpendicular to the field direction leads to equal birefringence changes in both aligned domains. This demonstrates that the film aligns dielectrically with the c-director parallel or antiparallel to E (εa
0), and consequently, P
is perpendicular to the tilt plane formed by c-director and layer normal (see discussion of Fig. 5a). In the low temperature C2 phase, the birefringence change in dielectrically aligned domains separated by π walls is always symmetric, irrespective of whether the film is tilted parallel or perpendicular to the alignment axis. From comparison of the width of π walls in C2 and C1 we conclude
that ξd (and thus the ratio K εa ) is of comparable magnitude in both phases. When the C2 films are exposed to DC fields, the wall shapes and widths are the same as in AC fields. At field reversal, the only observable effect is a lateral shift of the walls, because surface charges on the film may 5
initiate some transient flow. No polar interaction of the sample orientation with the electric field is measurable. We conclude that the investigated non-chiral mesogen forms a tilted ferroelectric smectic phase C1 with a small but well measurable spontaneous polarization, which is film thickness independent in the thickness range studied (up to 1.36 µm). Its component in the layer plane is, within experimental accuracy, perpendicular to the c-director. Therefore the C1 phase is chiral, i. e. the mirror symmetry of the mesogens is spontaneously broken. In the nomenclature of B 2 subphases of banana shaped molecules, C1 behaves equivalent to the CS PF (synclinic ferroelectric) configuration. Since the hockey stick molecule lacks the twofold rotation axis of common ’banana shaped’ mesogens, however, the symmetry could be even lower. The low temperature phase of the material is strongly biaxial and shows no polar response in the electric field. Its electro-optical, NMR and x-ray properties are consistent with a CA PA (anticlinic antiferroelectric, also chiral) structure model. The experimental parameter EC
ξ ξ E 0 61 MV/m indicates the field where the dielectric d
p
2
term in Eq. 1 overtakes the polar one. In thin sandwich cells, where the applied electric fields are of the order of several MV/m, the polar term is probably masked to a large extend by the dielectric torque. The order of magnitude of the spontaneous polarization in C1 can be assessed from EC . If we assume εa
1 (which may be slightly overestimated), P amounts to only 0.5 nC/cm 2 .
Although this value is extremely low compared to commercial ferroelectric smectics, it is unambiguously identified in our experiment, so that this sample represents the first almost rodlike non-chiral mesogen that exhibits a ferroelectric smectic phase. This might stimulate the search for ferroelectric behaviour in a large class of similar materials. Since in the comparably high electric fields applied in sandwich cells, small ferroelectric interactions masked by the dielectric term may have been overlooked, some earlier electro-optical experiments might have to be reconsidered. The authors acknowledge G. Pelzl and S. Grande for making their experimental results available prior to publication. This study was supported by the Deutsche Forschungsgemeinschaft within SFB 294.
[1] R. B. Meyer, L. Liebert, L.Strzelecki, P. Keller; J.Physique Lett. 36 L69 (1975). R. B. Meyer; Ferroelectrics 28 319 (1980).
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[2] T. Niori, F. Sekine, J. Watanabe, T. Furukawa, H. Takezoe; J. Mater. Chem. 6 1231 (1996). T. Sekine, Y. Takanashi, J. Watanabe and H. Takezoe; Jpn. J. Appl. Phys. 36 L1201 (1997). [3] D. R. Link, G. Natale, R. Shao, J. E. Maclennan, N. A. Clark, E. K¨orblova and D. M. Walba; Science 278 1924 (1997) [4] D. M. Walba, E. K¨orblova, R. Shao, J. E. Maclennan, D. R. Link, M. A. Glaser, and N. A. Clark; Science 288 2181 (2000) [5] G. Pelzl, S. Diele, and W. Weissflog; Adv. Mater. 11 707 (1999). [6] W. Weissflog, H. Nadasi, U. Dunemann, G. Pelzl, S. Diele, A. Eremin, H. Kresse, J. Mater. Chem. 11 2748 (2001). [7] A. Jakli, D. Kruerke, H. Sawade, G. Heppke, Phys. Rev. Lett. 86, 5715 (2001). [8] M. Hird, J.W. Goodby, N. Gough, K.J. Toyne, J. Mater. Chem. 11 2732 (2001). [9] B. Das, S. Grande, A. Eremin, M. Schr¨oder, S. Diele, G. Pelzl, H. Kresse, W. Weissflog, Liq. Cryst. (in press). B. Das et al. (Poster presented at the 30. Arbeitstagung Fl¨ussige Kristalle, Freiburg 2002). [10] D. Link et al., Phys. Rev. Lett. 84 5772 (2000), and references therein. [11] P. E. Cladis, P. L. Finn, H. R. Brand; Phys. Rev. Lett. 75 1518 (1995). P.E. Cladis, H. R. Brand; Liq. Cryst. 14, 1327 (1993). [12] C. Escher, T. Geelhaar, and E. B¨ohm; Liq. Cryst. 3 469 (1988). [13] R. Stannarius, N. Kl¨opper, Th. Fischer, and F. Kremer. Phys. Rev. E, 58 6884, (1998). [14] C. Chevallard, J.-M. Gilli, T. Frisch, I.V. Chikina, and P. Pieranski; Mol. Cryst. Liq. Cryst. 328 595 (1999). [15] G. Hauck, H. D. Koswig, C. Selbmann; Liq. Cryst. 21 847 (1996). G. Hauck, H. D. Koswig; Ferroelectrics 122 253 (1995). [16] R. Najjar, Y. Galerne; Mol. Cryst. Liq. Cryst. 366 2273 (2001). [17] The convection threshold increases approximately linearly with film thickness, see e.g. S. W. Morris, J. R. de Bruyn, A. D. May; Phys. Rev. Lett. 65, 2378 (1990); Phys. Rev. A 44, 8146 (1991). O C12H25O
C O
CH N OC10H21
FIG. 1: Chemical composition of the investigated mesogen.
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microscope glass support
film
electrodes
FIG. 2: Sketch of the experimental geometry.
a)
b) FIG. 3: Reflection images of a film in the C1 phase at 60 C. Polarizers are crossed, parallel and perpendicular to the electric field direction which is along the vertical in the images. a) π inversion walls in an AC field of 104 kV/m, 100 Hz square wave, image size 348 image size 393
!
!
313 µm; b) 2π walls in a DC field of amplitude 28.6 kV/m,
294 µm. Inserts show corresponding simulated optical profiles from Eqs. 2,4 (a), and 3,4
(b).
8
x [mm]
30
xd (AC)
20
xp (DC)
10 0 0
20
40
60 80 -1 1/E [mm V ]
100
120
FIG. 4: Electric coherence lengths determined from domain wall widths: ξ p (solid squares) in the DC field and ξd (bullets) in a 100 Hz rectangular wave AC field, together with the corresponding linear and square root fit curves (see text). Solid symbols correspond to a film of approximately 1 µm thickness in the C 1 phase at 60 C. Open symbols give ξ p for films of 0.64 µm thickness (open circles) and 1.36µm (open squares), resp., in C1 at 65 C.
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"*-),.+ ( '
6354 % "
# "
"
#$" "
%-),+
%&" "
a)
% / µ 021
(*),+
'&" "
( (&" "
8 7
b)
µ
FIG. 5: Spatio-temporal cross section of a wall array in an electric field of 52 kV/m. The spatial extension is 450 µm, the time interval is 4 s, time runs from bottom to top. Polarizers are crossed along and perpendicular to the electric field axis. (a) switching from 1kHz AC (bottom) to DC (top) after 2.3 s, (b) change of the polarity of the DC field after 1.6 s. The wall width in these plots is not reproduced quantitatively exact since the walls move during switching and they do not remain exactly perpendicular to the cut. The tilt azimuth (in rad) in the aligned domains respective to the bottom left domain in (a) is indicated above and below the images.
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