This article was downloaded by: [Wojskowa Akademia Techniczna] On: 12 January 2012, At: 02:48 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Liquid Crystals Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/tlct20 Influence of the bias field on dielectric properties of the SmC A * in the vicinity of the SmC*–SmC A * phase transition P. Perkowski a , K. Ogrodnik a , W. Piecek a , M. Żurowska b , Z. Raszewski a , R. Dąbrowski b & L. Jaroszewicz a a Institute of Applied Physics, Military University of Technology, Warsaw, Poland b Institute of Chemistry, Military University of Technology, Warsaw, Poland Available online: 09 Sep 2011 To cite this article: P. Perkowski, K. Ogrodnik, W. Piecek, M. Żurowska, Z. Raszewski, R. Dąbrowski & L. Jaroszewicz (2011): Influence of the bias field on dielectric properties of the SmC A * in the vicinity of the SmC*–SmC A * phase transition, Liquid Crystals, 38:9, 1159-1167 To link to this article: http://dx.doi.org/10.1080/02678292.2011.600836 PLEASE SCROLL DOWN FOR ARTICLE Full terms and conditions of use: http://www.tandfonline.com/page/terms-and-conditions This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.
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This article was downloaded by: [Wojskowa Akademia Techniczna]On: 12 January 2012, At: 02:48Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House,37-41 Mortimer Street, London W1T 3JH, UK
Liquid CrystalsPublication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/tlct20
Influence of the bias field on dielectric properties ofthe SmCA* in the vicinity of the SmC*–SmCA* phasetransitionP. Perkowski a , K. Ogrodnik a , W. Piecek a , M. Żurowska b , Z. Raszewski a , R. Dąbrowski b
& L. Jaroszewicz aa Institute of Applied Physics, Military University of Technology, Warsaw, Polandb Institute of Chemistry, Military University of Technology, Warsaw, Poland
Available online: 09 Sep 2011
To cite this article: P. Perkowski, K. Ogrodnik, W. Piecek, M. Żurowska, Z. Raszewski, R. Dąbrowski & L. Jaroszewicz (2011):Influence of the bias field on dielectric properties of the SmCA* in the vicinity of the SmC*–SmCA* phase transition, LiquidCrystals, 38:9, 1159-1167
To link to this article: http://dx.doi.org/10.1080/02678292.2011.600836
PLEASE SCROLL DOWN FOR ARTICLE
Full terms and conditions of use: http://www.tandfonline.com/page/terms-and-conditions
This article may be used for research, teaching, and private study purposes. Any substantial or systematicreproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form toanyone is expressly forbidden.
The publisher does not give any warranty express or implied or make any representation that the contentswill be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses shouldbe independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims,proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly inconnection with or arising out of the use of this material.
Liquid Crystals,Vol. 38, No. 9, September 2011, 1159–1167
Influence of the bias field on dielectric properties of the SmCA∗ in the vicinity of the
SmC∗−SmCA∗ phase transition
P. Perkowskia*, K. Ogrodnika, W. Pieceka, M. Zurowskab, Z. Raszewskia , R. Dabrowskib and L. Jaroszewicza
aInstitute of Applied Physics, Military University of Technology, Warsaw, Poland; bInstitute of Chemistry, Military University ofTechnology, Warsaw, Poland
(Received 9 April 2011; final version received 23 June 2011)
In a large class of smectic mixtures prepared at our University, the phase transition between chiral ferroelectricsmectic C (SmC∗) and chiral antiferroelectric smectic C (SmCA
∗) phases can be observed on cooling. Under biasfield the temperature of the phase transition SmC∗−SmCA
∗ decreases (ca. 100◦C in the investigated mixture). Thetransition is called: unwound SmC∗−twisted SmCA
∗ phase transition. The Goldstone mode in SmC∗ phase isreduced by a direct current field while two modes (PH and PL) in the SmCA
∗ phase are amplified. The amplitudeof the fast X mode observed in the SmCA
∗ phase is reduced. The aim of this paper is to show how parameters ofthe modes in SmCA
∗ phase (calculated from Cole–Cole model) change with bias voltage—when twisted structurein SmCA
∗ phase is gradually unwound. The character of the modes observed in SmCA∗ is discussed. A new effect
is shown: a high value of dielectric loss is detected in the unwound SmC∗ phase, which is very close to SmCA∗.
Keywords: phase transition; dielectric modes; ferroelectrics and antiferroelectrics; Cole–Cole model; bias field
1. Introduction
A smectogenic mixtuxe W1000 exhibiting the broad-est antiferroelectric phase ever known was preparedat our University recently [1–3]. On the basis of previ-ous experiments at formulating smectogenic mixtureswith broad antiferroelectric phases [4, 5], a seriesof derivative mixtures were prepared. In this paper,results of a dielectric study of the derivative mixtureW1000-B are presented.
Besides two collective modes called PL and PH
modes [6], observed at the smectic antiferroelectricphase, the evidence of the existence of a third modewas reported in our previous papers [1, 4]. Thisvery fast, temperature dependent mode, was calledby our group, the X mode. Results of the dielec-tric spectroscopy studies of smectogenic mixtures atthe antiferroelectric phase have been discussed pre-viously [2, 7] on the basis of the theory presentedin [8]. In our previous report [2] it was suggestedthat a forth mode (the last collective mode at chi-ral antiferroelectric smectic C (SmCA
∗) phase amongthose predicted in [8]) can be indicated, while thestrongly non-symmetrical shape of the X mode peakis registered.
The bias electric field affects the observations ofthe dielectric modes of the SmCA
∗ phase [4, 9, 10, 11].It was shown that the application of a direct cur-rent (DC) field makes the PH and PL modes stronger,while the X mode becomes weak. This effect supportsthe theory, that the PH and PL modes have different
origins to the X mode. We suggest [2] that PH and PL
are phase modes while the X mode is an amplitudemode. Without bias voltage the X mode is strongerthan the PH and PL modes. The application of a DCfield causes the PH and PL modes, which are called‘non-cancelled’ modes [7], to become as strong as theX mode.
At the vicinity of the DC field, the helical struc-ture of SmC∗ is suppressed and the Goldstonemode disappears [12]. A strong DC field causes thisunwound structure to persist in the lower tempera-ture region, proper for a twisted SmCA
∗ structure. Insuch an unwound structure, it is impossible to detectmodes typical for SmCA
∗ phase.
2. Mixture under study
The W1000-B mixture (Figure 1) was composedon the basis of an equimolar binary mixture W-1000 [1–3]. Two fluorinated isomers (S) constitutingthe W1000 mixture were doped in an eutectic pro-portion with structurally analogous dopant; it wasa racemate (R, S) possessing non-fluorinated rigidmolecular core.
The temperatures of the phase transitionsobserved by means of differential scanning calorime-try (DSC) were as follows (Cr = crystal; Iso =Isotropic; SmA∗ = smectic A):
Figure 1. Three compounds constituting the W1000-B mixture at 0.39679, 0.38849 and 0.21472 molar fractions, respectively.
They are very similar to those found for theW1000 mixture [5]. All the temperatures of the phasetransitions observed using dielectric spectroscopydiffer from the temperatures observed using DSC.
3. Experimental setup
Experiments were achieved using a HP 4192Aimpedance analyser wired to custom-made cells.Custom-made measuring cells with gold electrodeswere used. Gold electrodes were used to avoid thehigh frequency losses related to finite conductivityof indium tin oxide electrodes [13, 14, 15]. The lowresistivity wires were soldered into the cell, withan ultrasonic USS-9200 unit. A cell thickness ofaround 5 μm was used to get good alignment and toavoid creating the untwisted structure. The cell wasfilled using capillary action in the Iso phase, closeto the temperature of the Iso–SmA∗ phase transi-tion (110◦C). Measurements were conducted at low(0.1 V) measuring voltage (AC) to avoid non-lineardielectric response, while the bias voltage varied from0 to 30 V. Measuring frequencies varied from 100 Hzup to 10 MHz.
The temperature was controlled using acomputer-driven Linkam TMS 92 unit and hotstage Linkam TMSH 600 with an accuracy of 0.1◦C.All measurements were taken every 0.5◦C for thewhole temperature range. Between measurements,the cells were slowly cooled at a rate of 0.1◦C min−1.
4. Results and discussion
The first measurement of the W1000-B mixture takenin the temperature range of 21−115◦C confirmed thesequence of the mesogenic phases (SmA∗, SmC∗ andSmCA
∗) observed for the parent mixture W1000 [1].
Here, however, the phase transition temperatureswere lower than those obtained from the DSC study.
In Figure 2, the dielectric losses (ε′′) versus tem-perature T for several frequencies of the alternat-ing measured electric field are presented. The plotsdemonstrate the measurements without (a) and with(b) the bias field. As one can see, some peaks gethigher with the bias field while some become lower.This means that relaxation is responsible for theinduction of the various peaks that are of differentorigin.
Moreover, one can observe that the SmCA∗–
SmC∗ phase transition temperature is reduced whileUBIAS is applied. Such an effect was observed previ-ously [9]. To confirm such behaviour we decided toconduct measurements in the presence of the biaselectric field exceeding the former one. The nextexperiment done at the bias voltage reaching 30 Vwas performed upon cooling from 100◦C to 24◦C.
In Figures 3−5, plots of ε′′ versus temperatureT and frequency f obtained for bias fields equal to10, 20 and 30 V, respectively, are presented. One cansee that the bias voltage unwinds the helical struc-ture of the SmC∗ phase and suppresses the Goldstonemode. The DC field induces the unwound structurefor the temperature region, where without bias, theantiferroelectric SmCA
∗ phase normally exists.At 10 V, the bias field does not shift the phase
transition. It simply suppresses the Goldstone modein SmC∗ by creating the unwound structure. Whenthe bias is higher (20 V) the temperature of the tran-sition between the unwound structure SmC∗ and thetwisted SmCA
∗ (TC−CA) becomes lower and reaches86◦C. When UBIAS = 30 V, the transition occursaround 60◦C.
Using an Agilent 4294A impedance analyser weconfirmed that if the bias voltage is increasing upto 40 V the temperature of the transition between
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Liquid Crystals 1161
1.2(a)
0.5 kHz 1 kHz10 kHz100 kHz1 MHz
5 kHz50 kHz500 kHz5 MHz0.8
0.6ε′
0.4
0.2
020 40 60 80 100
T (°C)
1
(b)1.2
0.5 kHz 1 kHz10 kHz100 kHz1 MHz
5 kHz50 kHz500 kHz5 MHz
0.8
0.6ε″
0.4
0.2
020 40 60 80 100
T (°C)
1
Figure 2. Imaginary part ε′ ′ of the electric permittivity ε versus temperature T for chosen frequencies of measuring alternatingfield obtained (a) without bias voltage and (b) with the bias field at UBIAS = 15 V.
PL
PH
X
ε″
0.11
10100
ƒ (kHz) 100010000
2535
4555
6575
8595
1.2
1.4
0.8
0.6
0.40.2
0
1
T (°C
)
Figure 3. Imaginary part ε′ ′ of electric permittivity ε ver-sus frequency f and temperature T at the bias field UBIAS =10 V. The Goldstone mode is suppressed at SmC∗. Theunwinding of the helical structure at the SmCA
∗ phase isobserved at 97◦C.
the unwound SmC∗ structure and the twisted SmCA∗
phase is lower than 10◦C. In Figure 6 the tempera-ture versus bias field is presented. For small DC fields,the temperature of transition: unwound structure–SmCA
∗, is constant. At around 10 V it starts todecrease and finally reaches a few centigrade atUBIAS = 40 V. The SmCA
∗ phase can be detected fortemperatures below zero so if we could apply a DCvoltage higher than 40 V the SmCA
∗ would probablybe created at lower temperatures.
In Figure 5 another new and interesting effect isvisible. This effect seems to have been created by a
PL
PH
X
ε″
0.11
10100
ƒ (kHz) 100010000
2535
4555
6575
8595
1.2
1.4
0.80.60.40.2
0
1
T (°C
)
Figure 4. Imaginary part ε′ ′ of electric permittivity ε ver-sus frequency f and temperature T at the bias field UBIAS =20 V. The transition between the unwound structure ofSmC∗ and the twisted SmCA
∗ is around 86◦C.
strong bias field. At temperatures a bit higher thanthe temperature of transition between the unwoundSmC∗ and the twisted SmCA
∗ phase, there is a hugeincrease of dielectric losses ε′′ for high frequencies(>2 MHz). This effect is also well visible in Figure 9b.It seems that this effect can be related to the X modein SmCA
∗. To interpret these results and to be surethat the increasing of ε′′ in unwound SmC∗ is relatedto the X mode, dielectric spectroscopy of a widerrange (at least up to 100 MHz) should be performedand a method of avoiding problems with inductance(L) of the connecting wires should be developed.
The next interesting phenomenon is visible whenboth antiferroelectic phasons (PH and PL) are
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1162 P. Perkowski et al.
PL
PH
X
ε″
0.11
10100
ƒ (kHz) 100010000
2535
4555
6575
8595
1.2
1.4
0.8
0.6
0.40.2
0
1
T (°C
)Figure 5. Imaginary part ε′ ′ of electric permittivity ε ver-sus frequency f and temperature T at the bias field UBIAS =30 V. The transition between the unwound structure ofSmC∗ and the twisted SmCA
∗ is around 60◦C (colourversion online).
100
90
80
70
60
50
TC–C
A (
°C)
40
30
20
10
00 10 20
Bias (V)30 40
Figure 6. Temperature (TC−CA) of transition between theunwound structure of the SmC∗ phase and the twistedstructure of the SmCA
∗ phase versus applied DC field(colour version online).
observed at cooling when the twisted SmCA∗ phase
appears at different bias fields. When the DC fieldis weak (10 V) one can see a clear increase betweenthe unwound SmC∗ structure and the SmCA
∗ twistedstructure. At such conditions, the SmCA
∗ phase aswell as both modes are created rapidly at cooling(Figure 3). For higher DC field (30 V) one can see,in Figure 5, that the PH and PL modes are cre-ated gradually (without any clear increase). It seemsthat the antiferroelectric environment has difficultieswith annihilation of effects related to high bias influ-ence on structure. Finally, the annihilation of the
unwound structure can be only reached continuouslyat UBIAS = 30 V.
Additionally, from Figures 3−5 one can deducethat the bias voltage induces the increase of PH
and PL strengths (�ε) while decreasing the X modestrength. To observe this in detail, Figures 7−10were prepared. In these figures, the imaginary ε′′ andreal ε′ parts of the electric permittivity at 25, 50,65 and 85◦C, measured at several bias voltages, arepresented.
One can see that at 25◦C (low temperatureSmCA
∗ phase) two relaxations are observed: ultra-high frequency relaxation (X) and high frequencyrelaxation (PH). At this temperature both relaxationsare not very fast but we know from previous work[1, 2, 4, 5, 10] that for higher temperatures in SmCA
∗these modes are really fast. When the DC field ishigher for this temperature, the PH mode is strongerand the X mode is weaker. It seems that the PH modeis amplified at the cost of the X mode.
The relaxation frequency for the PH mode is con-stant with bias and equals around 15 kHz, while therelaxation frequency of the X mode is around 1.5MHz and 2.2 MHz without bias and with 30 V DCfield, respectively. Additionally, the unsymmetricalshape of the X mode peak may suggest that it is cre-ated by more than one relaxation [2]. In our opinionthe best model applied for the X mode description isthe Havriliak–Negami model of relaxation [16]. Theexplanation for such an asymmetric shape of the Xmode peak was presented in [2]. The reason can bemore than one relaxation creating this peak (in [2] atleast three peaks were considered).
In Figure 8, the SmCA∗ phase is presented again
but at a higher temperature (50◦C). The relaxationfrequency of PH is higher than at 25◦C and equals120−140 kHz. For low frequencies one can see thebeginning of the PL mode while for high frequenciesthe end of the X mode. One can estimate the relax-ation frequency of PL is less than 100 Hz while for theX mode it is more than 10 MHz. It is just estimation,due to of measuring range of the applied impedanceanalyser. The PL mode, as well as PH mode, is bias-dependent: when the DC field increases the strengthof PL is higher. Still, one can see the opposite effectfor the X mode.
In Figure 9 (65◦C) the electric properties of boththe SmCA
∗ phase and the unwound SmC∗ structureare presented. Both the PH and PL modes are welldefined and amplified by the DC field as it was for25 and 50◦C. When the bias reaches 24 V, the PL
and PH modes rapidly diminish. The SmCA∗ phase
for this temperature and for such bias starts to beunwound, and the untwisted SmC∗ phase is created.For the X mode one can see the opposite effect:
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Liquid Crystals 1163
8.5
7.5
8
6.5
5.5
4.50.5 5 50
X
PH
500
ƒ (kHz)
5000 50000
5
7
6
(a)
0 V
12 V
24 V
4 V
16 V
28 V
8 V
20 V
30 V
ε′
0
0.2
0.4
0.6
0.8
1
1.2
1.4
XPH
0.5 5 50 500
ƒ (kHz)
5000 50000
0 V
12 V
24 V
4 V
16 V
28 V
8 V
20 V
30 V
(b)
ε″
Figure 7. (a) Real ε′ and (b) imaginary ε′ ′ parts of the electric permittivity ε versus frequency f of the measuring signal atchosen DC fields (0, 4, 8, 12, 16, 20, 24, 28 and 30 V) obtained for the SmCA
∗ phase (25◦C).
8
7.5
6.5
5.5
0.5 5 50
X
PH
PL
500
ƒ (kHz)
5000 500005
7
6
(a)
0 V
12 V
24 V
4 V
16 V
28 V
8 V
20 V
30 V
ε′
0
0.2
0.4
0.6
0.8
1
1.2
X
PHPL
0.5 5 50 500
ƒ (kHz)
5000 50000
0 V12 V24 V
4 V16 V28 V
8 V20 V30 V
(b)
ε″
Figure 8. (a) Real ε′ and (b) imaginary ε′ ′ parts of the electric permittivity ε versus frequency f of the measuring signal forchosen DC fields (0, 4, 8, 12, 16, 20, 24, 28 and 30 V) obtained for the SmCA
∗ phase (50◦C).
for bias lower than 24 V this mode is weaker whilefor bias higher than 24 V it starts to be stronger.The same effect is noticeable in Figure 5. The relax-ation frequency of PL equals around 900 Hz whilethe relaxation frequency of the PH mode is around300 kHz. It is worth noting that the extinction of thePH and PL modes leads a value of ε′ of 7.1. Suchvalue of ε′ is exactly in the middle of ε′ betweenthe PL and PH modes. This effect is better seen inFigure 11. Points for the 30 V curve start betweenCole–Cole arcs for PL and PH (plotted for lower biasvalues).
In Figure 10 (85◦C) the same effects are seen as inFigure 9 but the bias field necessary for the unwind-ing of the SmCA
∗ phase is lower (22 V) than at 65◦C(30 V). This means that the structure of SmCA
∗ ismore stable at 65◦C and a higher field is necessary
to change the anticlinic structure into the unwoundsynclinic one. In Figure 9 the PH and PL modes areeliminated by the bias field and ε′ reaches a value of6.75, exactly in the middle between the PL and PH
modes.The X mode at 85◦C is difficult to detect and its
relaxation parameters cannot be determined. Whencells with gold electrodes are used, the main reasonfor distortion of the measured results at high frequen-cies (>5 MHz) can be due to the inductivity of theconnecting wires.
Such behaviour of antiferroelectric materials waspresented in our previous works [4, 9] but in theW-1000B mixture the scale of these effects is muchlarger.
For the SmCA∗ phase we calculated the relaxation
parameters of PH, PL and X modes for measurements
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1164 P. Perkowski et al.
8.5
8
7.5
6.5
5.5
PH
PL
ƒ (kHz)
0.5 5 50 500 5000 50000
7
6
(a)
0 V
12 V
24 V
4 V
16 V
28 V
8 V
20 V
30 V
ε′
0
0.2
0.4
0.6
0.8
1
1.2
1.4
PHPL
0.5 5 50 500
ƒ (kHz)
5000 50000
0 V
12 V
24 V
4 V
16 V
28 V
8 V
20 V
30 V
(b)
ε″
Figure 9. (a) Real ε′ and (b) imaginary ε′ ′ parts of the electric permittivity ε versus frequency f of the measuring signal forchosen DC fields (0, 4, 8, 12, 16, 20, 24, 28 and 30 V) obtained for the SmCA
∗ and unwound SmC∗ phases (65◦C) (colour versiononline).
8.5
7.5
6.5
5.50.5 5 50
XPH
PL
PL
500
ƒ (kHz)
5000 50000
7
6
(a)
0 V
12 V
22 V
4 V
16 V
26 V
8 V
20 V
30 V
ε′
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
PH
0.5 5 50 500
ƒ (kHz)
5000 50000
0 V
12 V
22 V
4 V
16 V
26 V
8 V
20 V
30 V
(b)ε″
Figure 10. (a) Real ε′ and (b) imaginary ε′ ′ parts of the electric permittivity ε versus frequency f of the measuring signal forchosen DC fields (0, 4, 8, 12, 16, 20, 22, 26 and 30 V) obtained for the SmCA
∗ and unwound SmC∗ phases (85◦C) (colour versiononline).
2
1.5
0.5
5.5 6 7 86.5
ε′7.5 8.5
1
0
PH
0V
20V
8V
24V
12V
28V
16V
30V
PL
ε″
Figure 11. Cole–Cole arcs (ε′ ′ versus ε′) for chosen bias fields (0, 8, 12, 16, 20, 24, 28 and 30 V) for the data shown in Figure10 (colour version online).
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Liquid Crystals 1165
100000
(a)
10000
1000
XPHPL
ƒ R (
kHz)
100
10
1
0.120 40 60 80
T (°C)
100
(b)
XPHPL
Δε
1
10
0.120 40 60 80
T (°C)
100
(c)
XPHPL
α
0.1
1
0.0120 40 60 80
T (°C)
100
Figure 12. Cole–Cole model parameters: relaxation frequency (f R), dielectric strength (�ε) and distribution parameter (α) ofevery mode (X, PH and PL) detected in SmCA
∗ versus temperature. UBIAS = 0 V (colour version online).
100000
(a)
10000
1000
XPHPL
ƒ R (
kHz)
100
10
1
0.120 40 60 80
T (°C)
100
(b)
XPHPL
Δε 1
10
0.120 40 60 80
T (°C)
100
(c)
XPHPL
α
1
0.1
0.01
0.00120 40 60 80
T (°C)
100
Figure 13. Cole–Cole model parameters: relaxation frequency (f R), dielectric strength (�ε) and distribution parameter (α) ofevery mode (X, PH and PL) detected in SmCA
∗ versus temperature. UBIAS = 10 V (colour version online).
100000
(a)
10000
1000
XPHPL
ƒ R (
kHz)
100
10
1
0.120 40 60 80
T (°C)
100
(b)
XPHPL
Δε
1
10
20 40 60 80
T (°C)
100
(c)
XPHPL
α
0.1
1
0.01
0.00120 40 60 80
T (°C)
100
Figure 14. Cole–Cole model parameters: relaxation frequency (f R), dielectric strength (�ε) and distribution parameter (α) ofevery mode (X, PH and PL) detected in SmCA
∗ versus temperature. UBIAS = 20 V (colour version online).
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1166 P. Perkowski et al.
(c)
XPHPL
α 0.1
1
0.0125 35 45 55
T (°C)
65
(b)
XPHPL
Δε 1
10
0.125 35 45 55
T (°C)
65
100000
(a)
10000
1000
XPHPL
ƒ R (
kHz) 100
10
1
0.1
0.0125 35 45 55
T (°C)
65
Figure 15. Cole–Cole model parameters: relaxation frequency (f R), dielectric strength (�ε) and distribution parameter (α) ofevery mode (X, PH and PL) detected in SmCA
∗ versus temperature. UBIAS = 30 V (colour version online).
without and with bias (0, 10, 20 and 30V) using aone-mode Cole–Cole model [17] [Equation (1)]:
ε = ε′ − jε′′ = ε∞ + �ε
1 −(
j ffR
)1−α, (1)
where j is the imaginary unit, f is the frequency andε∞ is the high frequency limit of electric permittivity.
The relaxation frequency (f R), dielectric strength(�ε) and distribution parameter (α) for every modewas calculated and the results are shown in Figures12−15 for bias fields: 0, 10, 20 and 30 V, respectively.Due to good separation of all modes in the frequencydomain, it was possible to treat every mode sepa-rately and analyse only the top of every Cole−Colearc. In the case of the X mode arc (due to its asymme-try) results from the Cole−Cole model should differfrom the Havriliak−Negami model. Here, we consis-tently used one model for all calculations. In Figures12(a)−14(a) one can see that the relaxation frequen-cies are really well separated in the frequency domain(around two decades). The relaxation frequenciesdecrease with decreasing temperature.
From Figures 12(c)−15(c) one can conclude thatthe PH mode can be treated as a Debye-like mode,due to the smallest value of α. The X mode, due tothe highest value of α, can be considered as a super-position of many sub-modes. The shape of the Xmode arc can support this statement. It is worth not-ing that the bias voltage makes the X mode morecomplicated (the α parameter is higher for resultsobtained with bias than without).
It is clearly seen in Figures 12(b)−15(b) that thebias field makes the dielectric strengths of the PH andPL modes higher while making the X mode dielectricstrength lower. For low temperatures and without
bias voltage dielectric strength, �ε for the X mode is3 times higher than �ε for the PH mode, while calcu-lations prepared with bias voltage (30 V) show thatboth modes have similar dielectric strengths at lowtemperatures.
It seems that one cannot be sure about the resultsrelated to the PL and X modes close to the mea-suring limits of the equipment used. It seems thatthe parameters of PL for high bias and for low tem-peratures and parameters of the X mode for hightemperatures can be considered as an approximationshowing the general behaviour.
For PL and X modes when their relaxationfrequencies approach the measuring limits of theimpedance analyser, the parameters are calculatedwith high scattering. It is possible that the results forthe dielectric strength of the X mode at higher tem-peratures are calculated with a high error level, due toeffects related with connecting wires inductivity. Theresults calculated for the PH mode are determined tobe the best.
5. Conclusions
The bias field influences the dielectric spectroscopyof SmC∗ and SmCA
∗ phases. For lower DC fieldvalues, the PH and PL modes (initially weak) areamplified. This supports the suggestion that bothmodes are slightly ‘non-cancelled’ phasons [2]. Foran ideal bi-layer structure in SmCA
∗ they could notbe detected. The DC field disturbs the equilibrium inthe SmCA
∗ phase between neighbouring layers andthe ‘non-cancelled’ effect becomes stronger. The biasfield reduces the X mode. It is worth noting that thebias voltage influences the relaxation frequencies ofthe three mentioned modes slightly. It is observedthat, if the detected modes are well separated in
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frequency domain, one can use the Cole–Cole modelto calculate the relaxation parameters. If the biasvoltage is low, the modes are modified in the frame-work of the SmCA
∗ phase. At higher DC voltagesthe twisted SmCA
∗ phase switches into the unwoundSmC∗ phase. The PH and PL modes annihilate in sucha structure. In [11] it was suggested that the bias fieldcan gradually transform SmCA
∗ into SmC∗ acrossferrielectric phases, which seems not be the case forW1000-B mixture.
The experiments confirm that the bias field canlower the temperature of the transition: twistedSmCA
∗−unwound SmC∗ by around 100◦C.In the near future, measurements at higher fre-
quencies (using Agilent 4294A impedance analyser)will be performed to observe the X mode behaviourunder a bias field and to investigate if there are anycorrelations between high dielectric losses ε′′ in theunwound SmC∗ (Figures 5 and 9(b)) and the X modein SmCA
∗ phases. In an opinion presented in [2,9],the X mode is an amplitude mode related to a tiltangle fluctuation—similar to the soft mode in SmC∗.Maybe under strong bias the X mode can be pro-longed in the unwound SmC∗ phase. This can beproposed due to the high value of ε′′ observed athigh frequencies in the unwound SmC∗ phase at theSmC∗−SmCA
∗ phase transition (Figures 5 and 9(b)).To investigate high frequency modes in liquid
crystals a new model explaining how to find liquidcrystal properties from measurements performed ingold cells is needed. It is most likely an analytical orcalibration problem. At the time of developing theabove-mentioned model many questions relating tothe X mode and another fast modes (measured instandard measuring cells) will be answered.
Acknowledgements
This work was conducted in 2011 under financial sup-port from the Polish Ministry of Sciences and HigherEducation, Key Project POIG.01.03.01−14−016/08 ‘Newphotonic materials and their advanced application’.
References
[1] Perkowski, P.; Ogrodnik, K.; Piecek, W.; Raszewski,Z.; Zurowska, M.; Dabrowski, R. Mol. Cryst. Liq.Cryst. 2010, 525, 64–70.
[2] Perkowski, P.; Piecek, W.; Raszewski, Z.; Ogrodnik,K.; Zurowska, M.; Dabrowski, R.; Kedzierski, J. Mol.Cryst. Liq. Cryst. 2011, 541, 191–200.
