Dielectric spectroscopy of the SmQ* phase

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Dielectric spectroscopy of the SmQ*phaseP. Perkowski a , A. Bubnov b , W. Piecek a , K. Ogrodnik a , V.Hamplová b & M. Kašpar ba Institute of Applied Physics, Military University of Technology,Warsaw 00-908, Polandb Institute of Physics, Academy of Sciences of the Czech Republic,Na Slovance 2, Prague 18221, Czech Republic

Available online: 27 Jun 2011

To cite this article: P. Perkowski, A. Bubnov, W. Piecek, K. Ogrodnik, V. Hamplová & M. Kašpar(2011): Dielectric spectroscopy of the SmQ* phase, Phase Transitions, 84:11-12, 1098-1107

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Phase TransitionsVol. 84, Nos. 11–12, November–December 2011, 1098–1107

Dielectric spectroscopy of the SmQ* phase

P. Perkowskia*, A. Bubnovb, W. Pieceka, K. Ogrodnika,V. Hamplovab and M. Kasparb

aInstitute of Applied Physics, Military University of Technology, Warsaw 00-908, Poland;bInstitute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2,

Prague 18221, Czech Republic

(Received 12 February 2011; final version received 9 April 2011)

Liquid crystal possessing two biphenyl moieties in the molecular core and lateralchlorine substitution far from the chiral chain has been studied by dielectricspectroscopy. On cooling from the isotropic phase, the material possesses thefrustrated smectic Q* (SmQ*) and SmCA* phases. It has been confirmed bydielectric spectroscopy that the SmQ* phase can be related to the SmCA* anti-ferroelectric phase. However, only one relaxation process has been observed inthe SmQ* phase, while in the SmCA*, two relaxations are clearly detectable.It seems that the mode found in the SmQ* can be connected with high-frequencyanti-phase mode observed in the SmCA* phase. Its relaxation frequency is similarto PH relaxation frequency, but is weaker. The same relaxation has been observedeven a few degrees above the SmQ*–Iso phase transition. Another explanation forthe mode detected in SmQ* and isotropic phases can be molecular motionsaround short molecular axis.

Keywords: chiral liquid crystal; dielectric spectroscopy; antiferroelectric phase;smectic Q* phase; relaxation mode

1. Introduction

It has been found that materials with three phenyl rings in the molecular core and thechiral part based on the lactate units possess a broad temperature range ferroelectric SmC*phase [1–5] and those possessing two lactate units show a tendency to form the anti-ferroelectric SmCA* [2,3,5,6]. Several frustrated liquid crystalline phases like the re-entrantferroelectric SmC* phase, twist grain boundary TGBA and TGBC phases, ferroelectrichexatic and the SmQ* phases have also been found for the materials possessing lactategroups in the chiral part [1,5,7].

For the first time, the frustrated SmQ* phase existing between the antiferroelectricSmCA* and isotropic phases has been reported by Levelut et al. [8] and so far it has beenobserved rather rarely [7–12]. The SmQ* phase has been intensively studied by X-ray,which enables us to identify four different structure types – all belonging to the class ofdefect crystals [8,13]. Two of them can be described as an array of twist boundaries in anti-ferroelectric smectics [12]. One of these four structures concurs with I4122 symmetry [8,13].Two different models designated as I and II have been proposed [13] to interpret the

*Corresponding author. Email: [email protected]

ISSN 0141–1594 print/ISSN 1029–0338 online

� 2011 Taylor & Francis

http://dx.doi.org/10.1080/01411594.2011.580432

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architecture of the SmQ* phase with I4122 symmetry. Both model structures are built fromelementary blocks composed of pieces of SmCA* double layers with different orientationof molecules. Several recent works are devoted to the study of rather complicatedtetragonal supramolecular, chirality-induced 3D structures [10,14,15].

The main objective of this study is to use the dielectric spectroscopy as a powerful toolfor characterization of the SmQ* phase in order to gain knowledge on the existingrelaxation processes. Dielectric behaviour of the SmQ* phase is compared with that of theantiferroelectric SmCA* phase to evaluate the model of the SmQ* phase as composed ofblocks with the SmCA* structure. Generally, in the SmCA* phase (in the frequency range500Hz–5MHz), one can detect the anti-phase mode (PH), the in-phase (Goldstone like)mode (PL), non-compensated in the antiferroelectric phase due to the existence of helicalstructure [16] or the rotation of molecules around their short axes, the last being a non-collective mode [17].

2. Liquid crystal material under the study

Recently, a series of chlorine substituted rod-like liquid crystalline compounds containinga different number of lactate units in the chiral chain have been synthesized andcharacterized [7]. For this study, we selected 40-((1-(1-(2-methylbutoxy)-1-oxopropan-2-yloxy)-1-oxopropan-2-yloxy)carbonyl)biphenyl-4-yl 30-chloro-40-(undecyloxy)biphenyl-4-carboxylate liquid crystal (LC) material possessing two biphenyl moieties in the molecularcore and lateral chlorine substitution far from the chiral chain and two chiral lactategroups. The chemical formula of the LC material is shown in Figure 1.

Molecular structures of the material had been checked by 1H-NMR (200MHz, CDCl3,Varian Gemini 2000). Chemical purity of the material was determined by high-performance liquid chromatography (HPLC), which was carried out with an EcomHPLC chromatograph using a silica gel column (Separon 7 mm, 3� 150, Tessek) with amixture of 99.8% toluene and 0.2% methanol as an eluent. The chemical purity was foundto be better than 99.8% under these conditions.

1H-NMR of 40-((1-(1-(2-methylbutoxy)-1-oxopropan-2-yloxy)-1-oxopropan-2-yloxy)carbonyl)biphenyl-4-yl 30-chloro-40-(undecyloxy)biphenyl-4-carboxylate (CDCl3, 300MHz):8.28d (2H, ortho to –COOAr); 8.18d (2H, ortho to –COOC*); 7.70m (7H, ortho to –Ar);7.52dd (1H, para to –Cl); 7.38d (2H ortho to –OCOAr); 7.02d (1H, meta to –Cl); 5.40q (1H,ArCOOCH*); 5.22q (1H, C*COOCH*); 4.00–4.10m (4H, CH2OAr and COOCH2); 1.60and 1.78dþd (6H, CH3, CH*COO); 1.20–1.90m (21H, CHþCH2); and 0.90t (6H, CH3).

The sequence of mesophases and the phase-transition temperatures were determinedfrom characteristic textures and their changes observed on the planar cells in a polarizingmicroscope (NIKON ECLIPSE E600POL). A Linkam LTS E350 heating stage with TMS93 temperature programmer was used for the temperature control, which enabled thetemperature stabilization within �0.1K. The phase-transition temperatures were checked

*

CH3

COO(CHCOO)2CH2CHC2H5COO

CH3Cl

*C11H21O

Figure 1. Chemical formula of 40-((1-(1-(2-methylbutoxy)-1-oxopropan-2-yloxy)-1-oxopropan-2-yloxy)carbonyl)biphenyl-4-yl 30-chloro-40-(undecyloxy)biphenyl-4-carboxylate.

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by a differential scanning calorimetry (DSC; Pyris Diamond Perkin Elmer 7) on coolingand heating runs (5Kmin�1). The sequence of phases and phase-transition temperaturesdetermined by DSC and found from dielectric spectroscopy data are slightly different(discussed later) and are shown in Table 1. From these results, one can observe that theSmQ* phase is stabilized up to higher temperatures when the compound is placed in a thincell with respect to the bulk sample used for the DSC. On the other hand, the SmCA*phase becomes monotropic in a thin planar sample, while in the bulk sample it isenantiotropic in character.

Textures of the observed mesophases have been studied by polarizing opticalmicroscopy. Taken on cooling cycle, the typical microphotograph of mosaic texture ofthe SmQ* phase is shown in Figure 2. A very similar texture for the SmQ* has beenpresented in [13].

3. Dielectric measurements – experimental

Dielectric spectroscopy studies have been performed using an HP 4192A impedanceanalyzer. Cells 5 mm thick, with golden electrodes covered by polyimide layers in order toassure planar alignment of the director within the cell, have been used for the study.

Figure 2. Microphotograph of typical mosaic texture obtained in the SmQ* on cooling. Width ofthe picture is about 300 mm.

Table 1. Sequence of phases and phase transition temperatures Tc (�C) on heating and coolingdetermined by DSC (5Kmin�1) and by dielectric spectroscopy (DIEL).

Tc (�C) Tc (

�C) Tc (�C)

DSC heating Cr 91 SmCA* 114 SmQ* 126 IsoDSC cooling Cr 65 SmCA* 108 SmQ* 113 Iso

DIEL heating Cr 94 Cr1 113 SmQ* 127 IsoDIEL cooling Cr 93 SmCA* 107 SmQ* 126 Iso

Notes: Phase denoted as Cr1 stands for the crystalline phase with structure different from the usualcrystal (Cr) phase.

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Golden electrodes were applied to avoid high-frequency absorption peaks related to finiteresistance of indium tin oxide (ITO) electrodes [18]. Low resistance wires were soldered tothe cell electrodes using ultrasonic USS-9200 unit.

For temperature control, the Linkam THMSE 600 hot stage driven by the LinkamTMS 92 controller was used with a heating/cooling rate of 0.2Kmin�1 stabilized with anaccuracy of 0.1K. In order to study the effect of the applied electric field on the relaxationprocesses in the SmQ* phase, bias electric field (UB¼ 0, 5 and 10V) has been applied to thesample during specific measurements. The experimental setup was controlled by home-made measuring programme designed under Agilent Vee software.

4. Results and discussion

In Figure 3, the imaginary part "00 of complex permittivity as a function of the temperature(T ) and frequency ( f ) is presented on the cooling cycle. A sharp phase transition (�92�C)occurs between the crystalline and SmCA* phases. The coexistence of antiferroelectricSmCA* and SmQ* phases is clearly observed at about 8�C broad temperature region.Above 108�C, the pure SmQ* phase is observed up to the clearing temperature. Thedetected relaxation processes can be easily seen in Figure 3. For the SmCA* phase, twowell-known PH and PL [19,20] modes are detectable. In the phase coexistence region(within 104–108�C), the PL mode disappears, while PH mode (gradually modified) stillexists. In the isotropic phase, a few degrees above the clearing point, one can still observe arelaxation process with relaxation frequency slightly lower than that at the SmQ* phase.It means that in the isotropic phase, some aggregates which exhibit a structure similar tothe SmQ*, can already exist.

The application of the bias electric field does not affect the phase sequence; however,the amplitudes of PH and PL modes are higher under the bias field (Figure 4).

Figure 3. Imaginary part "00 of complex permittivity vs. temperature and frequency on coolingwithout bias field. Arrows on the temperature axis indicate the phase transition temperatures; redarrows show the anti-phase (PH) and the in-phase (PL) modes.

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Recently, a similar effect observed in the SmCA* has been reported [21]. But such a bias

field does not influence the relaxation processes in the SmQ*.The imaginary part "00 of complex permittivity versus temperature and frequency

obtained on the heating cycle are shown in Figure 5. At the temperature 94�C the phase

Figure 4. Imaginary part "00 of complex permittivity vs. temperature and frequency on cooling (10Vbias field). Arrows on the temperature axis indicate the phase transition temperatures; red arrowsshow the anti-phase (PH) and the in-phase (PL) modes. The amplitudes of PH and PL modes arehigher than those in Figure 3.

Figure 5. Imaginary part "00 of complex permittivity vs. temperature and frequency on heating cycle(without bias field). Arrows on the temperature axis indicate the phase transition temperatures.

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transition between crystalline phases probably occurred. It can be supposed that within94–113�C, a new molecular crystal with a structure different than the ordinary crystallinephase exists, because no relaxation modes are detected in this temperature range. At113�C, the crystal–SmQ* phase transition takes place. On further heating at 127�C, thephase transition to the isotropic phase is seen. The relaxation process observed in theSmQ* phase is similar in both cooling and heating cycles. This relaxation still exists in theisotropic phase, a few degrees above the clearing point.

At high frequencies, rather high values of "00 are seen for both, heating and coolingcycles (Figures 3 and 5, respectively). In Ref. [18], it was shown that such an effectobserved in the measuring cell with electrodes made of ITO is related to the electrodesfinite resistance. As cells with golden electrodes have been used in this study, the resistanceof electrodes is very low in comparison with any electrodes made of ITO. So, the observedeffect could be related to the inductance (L) of connecting wires. Inductivity of connectingwires plays an important role at high-frequency measurements ( f4 2–3MHz).Unexpectedly, such behaviour is not observed in the crystalline phase (below 95�C).Therefore, one can conclude that this effect might be related to high-frequency collectivemotions peculiar for the SmCA* and called X-mode [21] or molecular non-collectivemotions around short molecular axis. Such processes are definitely faster than the high-frequency limit of our measurements (5MHz).

X-mode could be visible well in the SmCA* when the temperature range of this phasewas quite broad (more than 100�C) [22] because its relaxation frequency decreases withtemperature decreasing. In the investigated compound, temperature range of anti-ferroelectric phase is only 20�C and we cannot characterize this mode because we can seejust the beginning (high-frequency side) of this mode. Beyond all doubts, this relaxation isdetectable in the SmCA*, the SmQ* on cooling as well as in the Cr1 and SmQ*phases onheating.

5. Fitting of the experimental data

In order to analyse the complex permittivity and extract the parameters of the relaxationprocesses, the Cole–Cole model of the dielectric relaxation has been applied. Relaxationfrequency (fR), dielectric strength of mode (D"), high-frequency permittivity limit ("1) anddistribution parameter of the relaxation times (�) are found to fit experimental results withCole–Cole equation [23,24]:

"� ¼ "1 þD"

1þ ð jf=fRÞ1��

, ð1Þ

where j is an imaginary unit, f stands for frequency of the measuring electric field, fR therelaxation frequency of investigated mode and � the distribution parameter of the relax-ation times. We used Cole–Cole model for one relaxation (1) as the observed relaxationsare well separated in a frequency domain. In Figure 6(a), the relaxation frequency fRvalues of higher (PH) and lower (PL) frequency modes in the SmCA* and a mode existing inthe SmQ* (Q mode) on cooling and heating are presented. Both relaxation frequencies riseup with the increase in temperature. Such an effect has been already observed in manyantiferroelectric materials [21]. The relaxation frequency fR of the mode detected for theSmQ* phase is similar to the relaxation frequency of the PH mode. In Figure 6(b), thetemperature dependences of the dielectric strength of investigated modes are presented.The dielectric strength of the PL mode is slightly higher than that of the PH mode and both

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are nearly constant within the temperature range of the SmCA* phase. Within the SmCA*–SmQ* phase co-existence region, the dielectric strength of the PL mode decreases.Dielectric strength D"Q of the relaxation mode detected in the SmQ* phase is lower thanthe dielectric strengths D"PH of mode PH in the SmCA*. The relaxation frequencies fR anddielectric strengths D" of the mode detected in the SmQ* and isotropic phases on heatingcycle are very similar to those obtained on cooling cycle. It means that the structure of theSmQ* phase appearing on cooling and heating cycles does not depend on the thermalhistory of the sample and does not exhibit temperature hysteresis.

To be sure that the relaxation mode detected in the SmQ* phase (Q mode) can berelated to PH mode observed in SmCA* phase, Figure 7 was plotted. PH mode becomesfaster when temperature approaches the phase transition. For low temperatures, Q modein the SmQ* is slower than PH relaxation but on heating Q mode frequency increases. Thatconfirms the results shown in Figure 6. It is worth underlining that the slope of "0( f ) plotfor high frequencies ( f4 800 kHz) is the same for both SmCA* and SmQ* phases. It seemsthat for high-frequency range, the same mode or the same behaviour for the SmCA* andSmQ* phases are seen. It is worth underlining that the plot slope ("0 vs. f ) for PH and PL

modes is higher than that for Q mode. It can suggest that Q mode has got a differentmechanism.

6. Summary of results and conclusions

The presence of the SmQ* phase in material under study has been earlier confirmed in Ref.[7] and by texture observations. The article confirms that the SmQ* borders with SmCA*phase. In the SmQ*, only one relaxation is observed (in the measuring range), while in theSmCA* phase, two relaxation processes have been detected. It seems that the relaxationmode detected in the SmQ* (Q mode) can be explained in two different ways.

It can be related to the anti-phase PH mode observed in the SmCA* phase. Relaxationin the SmQ* phase is weaker (ca 3�) than the PH mode. Relaxation frequency of Q modeis close to relaxation frequency of PH mode. These explanations can support the results of

Figure 6. Temperature dependencies of (a) relaxation frequency ( fR) and, (b) dielectric strength (D")obtained using Cole–Cole model for all detected relaxation modes in the SmCA*, SmQ* andisotropic phases on cooling cycle: ‘þ’ (crosses) – PH mode, ‘ ’ (triangles) – PL mode in the SmCA*,‘�’ (empty circles) – mode in the SmQ* and isotropic phases and on heating cycle ‘ ’(full circles) –mode in the SmQ* and isotropic phases.

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dielectric spectroscopy for TGBA presented in [25]. The dielectric strength of Q modeshould be reduced in comparison with PH mode due to elastic strain, which is related to theanchoring at the grain boundaries of the cubic structure of the SmQ* phase. It is worthunderlining that the same relaxation process (as in the SmQ* phase) has been observed inthe isotropic phase, a few degrees above the SmQ*–Iso phase transition. It indicates thatsome microregions with the SmQ* molecular structure exist in this temperature range.To confirm this conclusion, X-ray diffraction studies will be carried out and presentedelsewhere. The dielectric behaviour of the SmQ* phase on heating and cooling is verysimilar. However, the liquid crystalline alignment is usually better on cooling thanon heating, which seems not to be the case of the SmQ* phase due to cubic structure in theSmQ* phase.

The second possible explanation is that Q mode consists of simple molecular motionsaround short molecular axis. This explanation can be supported by different functionslopes "0 versus frequency for PH and Q modes, presented in Figure 7(a) and by theexistence of this mode also in isotropic phase.

The last problem is the existence of high-frequency relaxation (much faster than PH inthe SmCA* and Q mode in SmQ*). Unfortunately, such relaxation screens weak relaxationin the SmQ* phase (for PH mode it is not so important). This relaxation can be measuredbetter by an impedance analyzer with a broader frequency range. It seems that the resultsof measurements with frequency up to 100MHz would be necessary to answer thequestions related to the mechanism of the high-frequency mode seen in the investigatedphases.

Acknowledgements

This study was supported by the MUT grant no. PBS 23 827/2010/WAT and project MEB 050828from Ministry of Education, Youth and Sports of the Czech Republic. The authors are grateful to

Figure 7. Real ("0) and imaginary ("00) parts of complex permittivity vs. frequency, close to theSmCA*–SmQ* phase transition at indicated temperatures. Open symbols stand for the SmCA* whilefull (red) ones are for the SmQ* phase.

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DrMilada Glogarova (Prague) for a very fruitful discussion. This study was also partly supported byprojects: GA ASCR IAA100100911, CSF 202/09/0047, CSF P204/11/0723 and RFASI02.740.11.5166.

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