OPTO-ELECTRONICS REVIEW 16(3), 262–266
DOI: 10.2478/s11772-008-0017-0
Dielectric relaxation behaviour of liquid crystals with opposite orientation
of –COO ester group in molecular core
J. RUTKOWSKA*, P. PERKOWSKI, W. PIECEK, Z. RASZEWSKI, and J. KÊDZIERSKI
Institute of Applied Physics, Military University of Technology,
2 Kaliskiego Str., 00-908 Warsaw, Poland
Dielectric measurements were performed for two smectogens, being structurally analogous with the opposite space orientation of the –COO ester group in the molecular core, using a HP4192A impedance analyser. Gold coated electrode cells of
different thicknesses were used. Temperature dependences of the relaxation frequency fR and the inverse of the dielectric
strength De ^
¢ -1 obtained by fitting experimental values of perpendicular components, i.e., the real e ^
¢ and the imaginary e ^
¢¢
parts of the complex dielectric permittivity to the Cole-Cole equation as well as the investigation of modification of relaxation processes under bias were determined for the SmC*, SmA*, and N* phases of studied compounds. One can conclude,
on the basis of the above results, that dielectric relaxation processes observed by us in the studied compounds are similar to
those of the soft and Goldstone mode typically observed by others in the SmC*, SmA*, and N* phases. It is concluded from a
comparison of their properties with other related compounds that the link between the biphenyl moiety and –COO ester
group is closely related to the stability of smectic phases.
Keywords: ferroelectrics liquid crystals, dielectric relaxation, Goldstone mode, soft mode
1. Introduction
The following two compounds were studied to elucidate
the effects of orientation of the –COO ester groups in a molecular core:
4’ octyloxy-biphenyl-4-carboxylic acid 4-(1-methyl-heptyloxy)-phenyl
ference between these compounds is a molecular tilt in the
SmC* phase, for 2-OC compound it is 45° and for 2-CO
compound it is only 20°. The spontaneous polarization for
both compounds is almost the same [1,2]. From experimental point of view, the main aim of this work is to compare
dielectric properties of these compounds.
2. Experimental
and 4-(1-methyl-heptyloxy)-benzioc acid 4’-octyloxy-biphenyl-5-yl-ester
The opposite orientation of the ester group, located in
the same place as a molecular rigid core, leads to different
phase sequences Cr 339 K SmH* 356.7 K SmC* 381 K
SmA* 426.1 K* Iso for 2-CO and Cr 351.2 K SmC* 372.4
K N* 393.7 K Iso for 2-OC. The other most important dif*e-mail:
262
[email protected]
For both studied compounds, the measurements of the tilt angle, spontaneous polarization, smectic layer thicknesses, and
dielectric spectra were performed. Some of these results,
among other the preliminary measurements of the complex
dielectric permittivity in ITO-coated cells of a planar alignment (commercially available EHC cells) were presented by
us earlier in Ref. 2. The ITO cells were not suitable for high
frequency measurements, because the high frequency dielectric measurements are affected by many parameters and the
high resistance of the ITO layer is one of them. To avoid this
problem, gold coated electrode cells of different thicknesses
have been prepared in our laboratory and used in measurements. It is known that on the gold plated surfaces, the liquid
crystal molecules can take planar orientation with a molecular
axis parallel to the electrode surface. In order to achieve the
better planar orientation, these surfaces were coated with the
film of suitable polyimide. To obtain a planar wound geometry in the SmC* phase, the cell thicknesses of 12 µm and
20 µm were chosen to be much higher than the pitch of the
studied compounds.
Opto-Electron. Rev., 16, no. 3, 2008
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Dielectric measurements were performed in the frequency range from 50 Hz to 10 MHz with HP4192A impedance analyser. The measuring AC voltage of 0.1 V was
applied perpendicularly to the helical axis so, the perpendicular components of the real e ^
¢¢ parts
¢ and imaginary e ^
of the complex dielectric permittivity were studied. The
measurements were made in two steps, without superimposition of a DC bias to the measurement electric field and
with superimposition of DC bias to unwind the helical
structure in the SmC* phase. During all measurements, the
temperature was controlled by the Linkam TMS91 controller with an accuracy of 0.1 K. The dielectric strength De ^
¢,
the relaxation frequency fR, and the dispersion parameter b
were determined by fitting the dielectric data to the wellknown Cole-Cole distribution.
De ^
¢
.
e *^ = e ^
¢ - ie ^
¢¢ = e ^¥ +
(1 + if f R ) b
fect and they are enhanced by the relatively high value of
the bias field. In Figs. 5(A) and 5(B), the relaxation frequency fR and the inverse of the dielectric strength De ^
¢ -1
for 2-CO compound are shown as a function of the temperature on both sides of the SmA*®SmC* phase transitions.
The inverse of dielectric strength and the relaxation frequency linearly depend on the temperature (T–TC). Such
3. Discussion of experimental results
3.1. Dielectric measurements for 2-CO compound
The results of dielectric measurements of 2-CO compound
are presented in Figs. 1 and 2. The second order phase transition from the SmA* to the SmC* phase is characterized
by the strong maximum for low frequency and minimum
for high frequency dielectric responses. Thus, at 381 K one
can see a phase transition to the SmC* phase. Below 10
MHz frequency, for 2-CO compound, the dielectric spectra
in the SmC* phase display one relaxation mechanism with
high dielectric permittivity decreasing near TC (TC is the
phase transition temperature from SmC* to SmA* phase)
and the relaxation frequency is almost temperature independent. This relaxation process corresponds to phase fluctuations in the azimuthal orientation of the director (the
Goldstone mode). Because of the high Goldstone mode
contribution, it is difficult to observe other dielectric processes in the SmC* phase. However, when a DC bias field
of 1 V µm–1 was superimposed to the measuring AC voltage, it is critical field for the suppression of the Goldstone
mode and then the soft mode in the SmC* phase can be observed (see Fig. 3). In the SmA* phase, with the temperature growth to the value TC, De ^
¢ increases and fR decreases. This mechanism is attributed to the soft mode
which comes from fluctuations of the magnitude of the tilt
angle of the director. As it can be seen, the intensity of the
Goldstone mode in the SmC* phase is distinctly lower than
that of the soft mode at the SmA*®SmC* transition. Such
behaviour is characteristic for the de Vries transition [3]. In
the SmA* phase, when a bias field is applied, the dielectric
strength and the relaxation frequency are dependent on the
DC bias field near the phase transition temperature TC
(De ^
¢ decreases and fR is shifted to the higher frequencies),
but far from TC we have obtained the same value of De ^
¢
and fR as that obtained without a bias field (see Fig. 4).
These changes of De ^
¢ and fR are due to the electroclinic efOpto-Electron. Rev., 16, no. 3, 2008
Fig. 1. Temperature dependences of dielectric permittivity for two
frequencies (100 kHz and 200 kHz) obtained on a cooling cycle for
compound 2-CO (cell thickness 20 µm).
Fig. 2. Dielectric spectra of a soft mode in SmA* phase for
compound 2-CO (cell thickness 20 µm).
Fig. 3. Temperature dependence of relaxation frequencies of
relaxation processes observed in SmC* and SmA* phases of
compound 2-CO (cell thickness 20 µm).
263
J. Rutkowska
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Dielectric relaxation behaviour of liquid crystals with opposite orientation of –COO ester group in molecular core
behaviour agrees with the theoretical model which predicts
that De ^
¢ -1 and fR satisfy the Curie-Weiss law close to TC.
The calculated slope values for the relaxation frequency
72.1 kHz K–1 (SmC*) and 79.2 kHz K–1(SmA*) and the inverse of dielectric strength –0.154 K–1(SmC*) and 0.77 K–1
(SmA*) are in good agreement with the results obtained by
other authors for many materials [4,5].
3.2. Dielectric measurements for 2-OC
Fig. 4. Temperature dependence of relaxation frequency and
dielectric strength for a soft mode in SmA* phase of compound
2-CO observed without and with DC bias field of 1 Vµm–1 (cell
thickness 20 µm).
The results of dielectric measurements of 2-OC compound
are presented in Figs. 6 and 7. As shown in Fig. 7, one single relaxation process is very clearly seen up to 6 K above
the transition temperature in the N* phase. In the N* phase,
close to TC, the appearance of cybotactic groups is responsible for the observed fluctuations in the low frequency region. The dielectric parameters for this mode are obtained
by fitting a Cole-Cole function to the experimental points
and shown in Fig. 8. The relaxation frequency fR and the inverse of the dielectric strength De ^
¢ -1 of this mode in the
N* phase are strongly temperature dependent. As it can be
seen from Fig. 8, the inverse dielectric strength and the relaxation frequency for this process are also linear functions
Fig. 6. Temperature dependences of dielectric permittivity for two
frequencies (100 kHz and 200 kHz) obtained on a cooling cycle of
compound 2-OC (cell thickness 20 µm).
Fig. 5. Temperature dependences of relaxation frequency (a) and
inverse of dielectric strength (b) obtained by fitting to Cole-Cole
distribution in SmC* and SmA* phases of compound 2-CO (cell
thickness 20 µm).
264
Fig. 7. Dielectric absorption at some temperatures for N* phase of
compound 2-OC (cell thickness 20 µm).
Opto-Electron. Rev., 16, no. 3, 2008
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4. Conclusions
Fig. 8. Temperature dependences of relaxation frequency and
inverse of dielectric strength obtained by fitting to Cole-Cole
distribution in SmC* and N* phases of compound 2-OC (cell
thickness 20 µm).
of the temperature with the calculation values of the slope
0.181 K–1 and 60.1 kHzK–1, respectively. Due to the same
behaviour of this mode, as the soft mode in the SmA*
phase (linearly decreasing fR and De ^
¢ -1 vs. temperature)
this relaxation process in the N* phase can be attributed to
fluctuations of the amplitude of the order parameters. This
soft mode, in the first order phase transition ferroelectric
liquid crystals, having the N* to the SmC* phase sequence
(like 2-OC compound) has been scarcely studied [4–7].
The qualitative behaviour obtained by us for 2-OC is in a
very good agreement with this already observed and reported in Refs. 4, 5, and 6, but the values of the slope
fR(T–TC) and De ^
¢ -1 (T–TC) dependences are however 2–4
times lower than that determined for other materials. It is
worth to mention that in Ref. 7 any relaxation mechanism
was not observed in the N* phase in the frequency range
below 10 MHz.
In the molecules of both studied by us compounds 2-CO
and 2-OC, the biphenyl moiety is sandwiched by an alkoxy
oxygen atom and a carbonyl ester group but in a molecule
of 2-OC compound director of an ester group is reversed. It
is interesting that seemingly a subtle change of a chemical
structure that is just reversing the director ester group in the
same place of the molecular rigid core brings about such a
drastic change in mesogenic phases.
A phase sequence for 2-CO compound is Iso®SmA*®
SmC*®SmH*®Cr but for 2-OC compound the SmA*
phase does not exist at all and in the SmC* phase it exhibits
high optical tilt with almost thermal independent characteristics.
One can conclude, on the basis of our dielectric results,
that the dielectric relaxation processes observed by us in
the 2-CO compounds are similar to those of the Goldstone
mode and the soft mode classically observed in the SmC*
and SmA* phases by others [4]. Our precise experiments
do not confirm the existence of an additional relaxation
mechanism in the SmC* phase of 2-CO compound [2]. It
was probably connected with LCR behaviour of ITO cells
because we have found it for the SmA* phase, too.
For the 2-OC compound in the N* phase, one relaxation
process was recognized and its linear temperature dependence suggests that it is due to the same mechanism as the
soft mode in the SmA* phase fluctuations of the amplitude
of the order parameters [5–7].
Below, one can see a comparison of phase sequences
(Table 1), the values of the tilt angle and spontaneous polarization of compounds studied by as with other 1-CO and
1-OC having identical cores like 2-CO and 2-OC (see Table
2), but the terminal n-alkyl and chiral chains are exchanged.
Table 1. Temperature ranges of mesophases of 2-CO, 2-OC, 1-OC, and 1-CO compounds.
Temperature
340
2-CO
1-OC
360
SmH*
SmC*
Cr
Cr
370
380
SmC*
Cr
2-OC
1-CO
350
SmC*
SmC*
Opto-Electron. Rev., 16, no. 3, 2008
390
400
410
420 K
SmA*
N*
Iso
Iso
N*
N*
Iso
Iso
265
J. Rutkowska
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Dielectric relaxation behaviour of liquid crystals with opposite orientation of –COO ester group in molecular core
Table 2. Values of spontaneous polarization and tilt angle of
2-CO, 2-OC, 1-OC, and 1-CO compounds (After Refs. 1 and 2).
T–TC = –30 K
Ps/nCcm2
q/deg
2-CO
1-OC
100
40
2-OC
50
45
1-CO
48
34
T–TC = –20 K
Ps/nCcm2
q/deg
50
20
The compounds 2-CO and 1-OC have identical core,
but the terminal alkyl and chiral chains are exchanged. For
1-OC, a chiral chain is directly linked to the biphenyl moiety. This difference of molecular structure leads to disappearance of the SmA* phase and twofold increase in spontaneous polarization and tilt angle.
The compounds 2-OC and 1-CO have identical core,
but with the reversed direction of the ester group than the
compounds 2-CO and 1-OC. For these compounds, exchange of the terminal and chiral chains leads to not such a
spectacular increase in spontaneous polarization and tilt angle. They show identical phase sequence.
Taking these characteristics into account, it is concluded that the SmA* phase exists in 2-CO compound, in
which the normal alkoxy chain, not chiral, directly joins to
the biphenyl moiety, the biphenyl moiety adopt a planar
structure by the conjugation between the alkoxy oxygen
atom and the carbonyl group [7]. Probably this conjugation
through the biphenyl moiety is not possible when the chiral
group is linked directly to the biphenyl moiety and the direction of a carbonyl group is reversed. For confirming this
conclusion, the study of a molecular structure of the investigated compounds by using the molecular mechanics
266
method MM+ and semi-empirical method MNDO is in
progress.
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Opto-Electron. Rev., 16, no. 3, 2008
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