Effect of lateral fluorination in antiferroelectric and ferroelectric mesophases: synchrotron X-ray diffraction, dielectric spectroscopy and electro-optic study

Journal of Physics and Chemistry of Solids 88 (2016) 14–23

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Effect of lateral fluorination in antiferroelectric and ferroelectric mesophases: synchrotron X-ray diffraction, dielectric spectroscopy and electro-optic study Kartick Ch. Dey a, Pradip Kr. Mandal b,n, Roman Dabrowski c a

Acharya Prafulla Chandra Roy Govt. College, Siliguri-734010, India Department of Physics, University of North Bengal, Siliguri-734013, India c Institute of Chemistry, Military University of Technology, Warsaw–00208, Poland b

art ic l e i nf o

a b s t r a c t

Article history: Received 9 May 2015 Received in revised form 14 August 2015 Accepted 24 August 2015 Available online 5 September 2015

Effect of lateral fluorination in the rigid core on several macroscopic and microscopic properties of a terphenyl based mesogenic chiral ester has been studied by synchrotron X-ray, dielectric and electrooptic techniques. Correlation lengths across the smectic planes, in para-, ferro- and antiferroelectric phases, are found to be significantly less in the fluorinated compound. Para to ferroelectric transition is found to be tricritical in nature in both the compounds. Fluorination resulted in slower response under a square pulse. Collective mode relaxation behaviour, with and without bias field, in all the phases are also found to be different in the fluorinated compound. & 2015 Elsevier Ltd. All rights reserved.

Keywords: A. Organic compounds C. X-ray diffraction D. Ferroelectricity D. Phase transitions D. Dielectric properties.

1. Introduction: Mesogenic behaviour of a compound is strongly influenced by the structure of the rigid molecular core as well as by the lateral substitutions. Because of the small size of a fluorosubstituent and high strength of the C–F bond, liquid crystals with fluorosubstituents show low birefringence, viscosity and conductivity; and high chemical and thermal stability. As a result many liquid crystal compounds with fluorosubstituents both in the cores and alkoxy chains were designed and synthesized in achiral as well as in chiral systems [1–7]. Liquid crystals with fluorinated chains are also very promising as antiferroelectric materials especially as the threshold less ones [7–10]. Phase behaviour and physical and electro-optical properties of fluorinated derivatives in many aspects are quite different from their protonated analogues which create new possibilities for their applications [9]. Effect of fluorination has been reviewed recently in detail for both achiral and chiral systems [1]. For example, a terphenyl based ester compound with CH3COO group at the achiral end exhibits SmC* and SmA* phases while the analogous compound with CF3COO group shows SmCA* phase in addition, but stronger polar end group (CNCOO) shows only SmA* phase [11]. Induction or enhancement of SmCA* phase due to fluorination has also been reported in reference [12]. Effects of fluorination on the relaxation and switching behavior n

Corresponding author. E-mail address: [email protected] (P.Kr. Mandal).

http://dx.doi.org/10.1016/j.jpcs.2015.08.016 0022-3697/& 2015 Elsevier Ltd. All rights reserved.

of para, ferro and antiferroelectric liquid crystals have been discussed by many authors [9,10,13–17]. Rigidity of the core structure, nature of chirality and extent of fluorination of the constituent molecules are found to have pronounced effect on the collective mode relaxation behaviour in room temperature FLC mixtures [15]. We present in this communication, effect of lateral fluorination in the rigid core of terphenyl based ester compounds on the macroscopic and microscopic properties as revealed by optical polarizing microscopy, small and wide angle synchrotron X-ray diffraction, frequency dependent dielectric spectroscopy and electro-optic measurements. The two compounds, (S)-(þ )-4/-(1-methylheptyloxycarbonyl)biphenyl-4-yl 4-[6-(4,4,4,3,3,2,2-heptafluorobutoxy)hex-1-oxy] benzoate and (S)(þ )-4/-(1-methylheptyloxycarbonyl)biphenyl-4-yl 4- [6-(4,4,4,3,3,2,2heptafluorobutoxy)hex-1-oxy]-2,3- difluorobenzoate (DM0 and DM3 in short) under investigation were synthesized in Military University of Technology [18]. Molecules contain an asymmetric carbon atom in the methylheptyloxy moiety rendering chirality while the carbonyl (–C¼O) functional group provides a transverse permanent electric dipole moment. Molecular structures of the compounds are shown in Fig.1, they differ only in lateral fluorination in the rigid core.

2. Experimental Phase behaviour and transition temperatures of the compounds have been investigated by studying their optical textures

K.Ch. Dey et al. / Journal of Physics and Chemistry of Solids 88 (2016) 14–23

O

O DM0 : C3F7CH2OC6H12O

O

C

15

O

C

* CH

C6H (S) 13

CH3

Cr (26) 61 SmCA* (83) 94 SmC*(122.2)123 SmA* (124.4) 125 Iso O

O DM3 : C3F7CH2OC6H12O

C F

O

C

O

* CH

C6H (S) 13

CH3

F

Cr (32.5) 63.2 SmCA* (82.2) 85.2 SmC*(109.1) 109.3 SmA* (111.5) 111.6 Iso Fig. 1. Molecular structures and transition temperatures (°C) of the compounds during heating. Figures in the parentheses represent transition temperatures during cooling.

under Olympus BX41 polarizing microscope equipped with CCD camera, temperature regulation was made within 70.1 °C using a Mettler FP82 central processor and FP84 hot stage. Mesophase structures were investigated using synchrotron radiation facility (PETRA III beam line at P07 Physics Hutch station) at Deutsches Elektronen Synchrotron, Hamburg. The samples were taken in Lindeman glass capillary of diameter 1.0 mm and very slowly cooled down from isotropic phase to the desired temperature to get an aligned sample. A Perkin Elmer 2D detector of pixel size 200  200 mm2 and total size 400  400 mm2 was used for image grabbing which was placed at 3.3 m away from the sample. 50 images of exposure time 0.2 s were grabbed and averaged to get one diffraction image and two such images were collected at a particular temperature. All the physical parameters were averaged over these two image data. QXRD program for PE Area Detector (G.Jennings, version 9.8, 64 bit) was used for data acquisition and also for analyzing the image. Images were integrated using a step size of 0.002 to get the intensity versus scattering wave vector (Q) distribution [19]. Smectic layer spacings (d) and average intermolecular distances (D) were determined following procedures described earlier [20]. Under rigid rod approximation, tilt of the molecules in smectic planes, often referred to as primary order parameter of an FLC phase, was determined d using the formula θ = cos−1( d ), where dA is the layer spacing in A

SmA* phase. Dielectric and electro-optical studies were performed using Indium–Tin oxide (ITO) (sheet resistances about 20 Ω/□) coated homogeneous (HG) cells of 10 mm thickness. Dielectric measurements were made using HIOKI 3532-50 impedance analyzer (40 Hz–5 MHz), cell temperature was controlled within 70.1 °C placing the cell inside the Mettler FP84 hot stage. An automatic data acquisition arrangement was made using RS 232 interface with a PC. To find the dielectric increment and relaxation frequency of a particular mode, dielectric absorption spectra were fitted to the following complex dielectric permittivity expression proposed by Cole and Cole [21,22], which was modified to take into account the low and high frequency parasitic effects:

ε* = ε′ − iε″ = ε∞ +

∑ k

Δεk 1 + (iωτk )1 − αk

σ −i ωϵ0

(1)

where Δεk ¼ ε0  ε1 is dielectric increment (ε0 and ε1 being the real part of the low and high frequency limit permittivities), τk is relaxation time (inverse of critical angular frequency) and αk is asymmetry parameter signifying deviation from Debye type behaviour of kth mode relaxation process, s is the conductivity of the cell that arises due to charge impurities which contributes mainly in low frequency region and ε0 (¼8.85 pF/m) is the permittivity of

the free space. While fitting the data, ITO mode was also included in the second term to take care of its contribution in the high frequency region. The polarization reversal current method [23] was used to measure spontaneous polarization (Ps). A triangular wave pulse of suitable frequency (10 Hz) and of varying amplitude from Agilent 33220A LXI function generator was amplified 20 times (F20A amplifier, FLC, Sweden) and applied across the series combination of parallel plate capacitor cell filled with the material and a standard resistor (R¼ 100 kΩ). The applied voltage and the voltage across R were fed to a digital storage oscilloscope (Tektronics TDS 2012 B model) in separate channels. Total current through C–R combination composed of three components, namely, the capacidV V tive term (iC ¼ C dt ), the resistive term (iR ¼ / , R/  108 Ω, the efR

fective resistance of the cell), and the polarization current (iP ¼

dP ). dt

The first two terms exist at all the voltages but iP appears as hump only when the applied voltage is high enough to unwind the helix and lead the polarization reversal in the sample. The spontaneous polarization was evaluated from the polarization peak area using the relation

PS =

1 2AR

∫ v(t )dt

(2)

where v(t ) is the voltage across the standard resistance R, A is the effective area of the cell, the factor 2 in the denominator arises since one complete peak corresponds to 2 Ps. Switching time was measured by monitoring the electrical response, in the storage oscilloscope, to a square wave pulse (Vpp ¼2.5 V, 10 Hz) applied to the same liquid crystal cell used for polarization measurement. Polarization bump occurs on the time scale away from the square pulse edge of the applied voltage. Time delay of occurrence of the polarization bump in time axis from the applied square pulse edge directly gives switching ( τ ) time of the sample as shown in Fig. 2.

3. Results and discussions 3.1. Optical polarizing microscopy From texture study under polarizing microscope, transition temperatures were determined and the phases were identified. Transition temperatures were also determined from DSC study, which differ slightly from those obtained from texture study. Phase sequence and the transition temperatures of the compounds, as obtained from texture study, are shown in Fig. 1. Although no change in phase sequence is observed due to

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SmC* phase [Fig. 3]. 3.2. Optimized geometry

Fig. 2. Figure showing input square pulse, developed polarization bump and the switching time ( τ ).

fluorination, the melting point is found to increase by 2°, clearing point decreases by 13°,thermal stability of SmCA* decreases by 11° and that of SmC* by 5°. Large super cooling effect is observed in both the compounds in texture study as well as in dielectric and electro-optic measurements. Textures were observed under planar anchoring condition for both the compounds. Typical fan shape texture was observed in SmA* phase which was broken in SmC* and SmCA* phases, existence of helicoidal structure is visible in the form of parallel equidistant lines more in SmCA* phase than in

In order to explore the conformational structures of the compounds, their molecular geometries were optimized using PM3 molecular mechanics method in Hyperchem software package [24]. While optimizing the geometry the bond, angle and torsional interactions were considered in the force field along with the van der Waals and electrostatic interactions. Total energy, most extended molecular length, moments of inertia and dipole moment of the two compounds are compared in Table 1. Most extended length of the two molecules, as expected, is the same and their total energy is also almost the same. Moments of inertia in DM3 are slightly more than those of DM0. However, dipole moment of DM3 is found to be substantially higher than DM0 because of the introduction of the two lateral fluorine atoms. Major increase of dipole moment is in the y-component, which is transverse to the molecular long axis. 3.3. X-ray study The synchrotron X-ray diffraction photographs were recorded throughout the mesophases. Transition temperatures seen from X-ray study are found to be shifted to higher side by about 3° than those observed from optical microscopy which might be the result of using two different temperature baths. The temperature dependence of average intermolecular distance (D) and layer spacing (d) are shown in the Fig. 4. The average intermolecular distance (D)

Fig. 3. Characteristic textures of SmCA*, SmC* and SmA* phases of DM0 taken during cooling. (a) SmCA* (60 °C) (b) SmC*(98 °C) (c) SmA* (123.7 °C).

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Table 1 Selected parameters of the molecules in optimized geometry. Sample

Most Extended Molecular Length (Å)

Energy (kCal/ mol)

Moment of Inertia in 10-46 kgm2 About x-axis

DM0 DM3

38.37 38.39

9788.7 9802.3

2235 2447

About y-axis

103770 104336

Dipole Moment (Debye) About z-axis

104698 105453

Components

Total

x

y

z

 1.55  1.15

 3.68  5.98

 2.53  3.11

4.73 6.84

Fig. 4. Temperature dependence of (a) intermolecular distance and (b) smectic layer spacing.

is found to decrease slowly with decreasing temperature without showing any significant change at transitions in both the compounds. Due to fluorine substitution in the core, average increase in D-value is about 0. 2Å. It decreases from 5.47 Å (SmA*) to 5.24 Å (SmCA*) in DM0 while in DM3 from 5.60 Å (SmA*) to 5.49 Å (SmCA*). On the other hand, smectic layer spacing of both the compounds decrease rapidly on cooling from SmA*–SmC* transition point (Tc), the rate of fall reduces gradually as the temperature goes deeper into the SmC* phase. Anomalous changes are observed at para- to ferro–electric transition (Tc) and ferro- to antiferroelectric transition (TAF) in both the compounds as shown in Fig. 4(b), anomalies in the later is clearly visible in the inset. Such behavior was also reported in a fluorinated terphenyl compound [25]. In SmC* phase maximum value of ‘d’ is found to be almost the same in both the compounds, 34.9 Å in DM0 and in DM3 it is 34.8 Å, which are substantially less than the most extended molecular lengths as a result of tilt of the molecules. In both the compounds, on cooling, tilt increases rapidly near Tc, rate of increment is slow as moved away from Tc, it remains essentially constant in antiferroelectric phase and small discontinuity is observed at ferro- to antiferroelectric transition. Maximum tilt is 24.8° and 24.2° in DM0 and DM3 respectively. Thus due to F-substitution no significant change is observed in layer spacing and tilt angle. It is further noted that temperature dependence of layer spacing in SmC* phase is parabolic in nature. Under rigid rod approximation of the mesogenic molecules and for a second order transition approaching the tricritical point in generalized meanfield theory, it can be shown that dC/dA ≈ 1-a |T–Tc|½ [26] which is consistent with our observation as shown in Fig. 4(b). Observed data fitted to the above equation nicely implying that the second order SmA*–SmC* transition is nearly tricritical in nature in both the systems.

Fig. 5. Intensity profile of the low and high angle scattering wave vector diffraction features.

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Fig. 6. Correlation lengths (a) across the smectic layers [ξ|| ] and (b) within the layer [ξ⊥] in different phases as a function of temperature. Tm represents crystal–antiferroelectric transition temperature.

To probe the extent of correlation of the molecules across and within the smectic layers correlation lengths (ξ), defined as ξ ¼2π/ FWHM where FWHM is the full width at half maxima in the scattering vector (Q) of the relevant Bragg peak, have been calculated from the intensity profile of the low and high angle diffraction features shown in Fig. 5. In SmCA* of DM0 maximum correlation length is found to be 986 Å across the smectic layers (ξ||) which is equivalent to about 25 molecular lengths and 24.5 Å within the layers (ξ⊥) which means correlation up to about 5 molecular diameters. Corresponding values are respectively 894 Å and 23 Å in DM3, as shown in Fig. 6. In SmC* phase maximum values of ξ|| are 969 Å and 748 Å and those of ξ⊥ are 23 Å and 21 Å in DM0 and DM3 respectively. Similar correlation lengths have been reported recently in the ferroelectric SmC* phase of a terphenyl based compound [19]. Thus correlation length across the plane is significantly less in DM3 compared to DM0 in both the ferro and antiferroelectric phases. As expected with decreasing temperature both the correlation lengths increase in both the compounds, however, it increases faster within the plane than across the plane. Moreover, a substantial jump is observed in ξ|| at SmC*–SmCA* transition in fluorinated DM3, also in SmCA* phase the rate of increase of ξ⊥ is much faster in DM3 compared to DM0. It is not clear why ξ|| decreases slightly from the middle of SmCA* till crystallization in DM3.

3.4. Spontaneous polarization (Ps) measurement The samples were heated to isotropic phase and then cooled at slow rate of 0.2 °C/min. well within SmC* phase while spontaneous polarization was measured as a function of ac field (E). It is observed that Ps increases rapidly with increasing field and reaches a maximum at a certain value of the field called the critical field (Ec),Fig. 7 (a). As the electric field increases from zero, interaction of the polarization vectors with the field causes gradual unwinding of the helix as well as polarization reversal. At the critical field Ec, helix is completely unwound, bulk domains are formed where all the dipoles are oriented in the direction of the field and the field causes only polarization reversal. In other words, critical field is the minimum field required for the operation of an FLC based display device. In protonated DM0 the Ec is found to be 2.03 V/mm at 95 °C [Tc-28], which increases to 3.69 V/mm at 80 °C [Tc-28] in laterally fluorinated DM3. Due to fluorine substitution in DM3, the transverse component of dipole moment increases and hence more driving force and stronger electric field is required to unwind the helix. The temperature dependence of Ps has been shown in the Fig. 7 (b). With decrease of temperature Ps increases rapidly near Tc and slowly away from Tc, reaching a maximum of 210.8 nC/cm2 in DM0 at 69 °C and 191.7 nC/cm2 in DM3 at 70 °C. In SmCA* it falls very rapidly to zero. Ps does not show any discontinuity at SmC*–SmCA*

Fig. 7. (a) Field dependence of spontaneous polarization (Ps) at Tc-28oC and (b) temperature dependence of Ps at saturation field.

K.Ch. Dey et al. / Journal of Physics and Chemistry of Solids 88 (2016) 14–23

19

transition, such behaviour was reported before [25,27–28]. Ps was fitted to the mean field equation [29]

PS = Po(1−T /TC ) β

(3)

and fitted Tc values are found to match exactly with the observed critical temperatures in both the compounds. However, order parameter critical exponent β is found to be 0.27 and 0.25 in DM0 and DM3 respectively, such values have been reported before [22,30]. For a pure second order transition, Ps, the secondary order parameter of the phase, should continuously reach to zero with critical exponent β ¼0.5 whereas a β value of 0.25 is expected in the case of second order transition approaching the tricritical point [31,32]. Thus the paraelectric to ferroelectric transition is tricritical in nature revealed from both X-ray and polarization study. 3.5. Switching time ( τ ) and Rotational Viscosity (γ) Both the compounds show sub-millisecond switching time, however, slower switching is observed in laterally fluorinated DM3 ( τmax  500 ms) compared to non-fluorinated DM0 ( τmax  340 ms). In a phenyl based non-fluorinated compound switching time was reported at around 10.5 ms [33] which was increased to around 88 ms [22] in the terminally fluorinated compound, supporting the present observation that fluorination causes slower response. Further, τ increases with decreasing temperature and clear anomalies are observed at the onset of antiferroelectric phase [Fig. 8(a)]. The torsional viscosity (γ ) of the materials has been determined using the relation [34]

γ = τ ·Ps ·E

(4)

where E is the applied field. Due to fluorination γ was found to increase as shown in Fig. 8(b). Assuming the temperature dependence of γ is Arrhenius type, activation energy (Ea), which is the energy barrier for the dipole relaxation, was calculated and found respectively to be 38.19 kJ/mole and 44.34 kJ/mole in DM0 and DM3. 3.6. Dielectric study Dielectric absorption spectrum were fitted to modified to Cole– Cole function as mentioned in Section 2 and an exemplary fitted

Fig. 9. Fitted absorption spectra in SmCAn phase of DM0 at 33 °C showing clearly the PL and PH modes.

spectrum only in SmCA* phase is shown in Fig. 9. Both the compounds possess very large dielectric increments in the ferroelectric SmC* phase as shown in Fig. 10, fluorinated DM3 depicting higher value than the protonated DM0. This is consistent with the fact that DM3 possesses higher dipole moment. Several relaxation modes are observed in different phases which are discussed in the next section. 3.6.1. SmCA* phase In the antiferroelectric phase two collective relaxation processes are usually observed in kHz and 100 kHz ranges which respectively are connected with in-phase (PL) and anti-phase (PH) reorientations of the molecules in adjacent smectic layers. In DM0, PL is observed only at temperatures far below TAF (transition takes place at 83 °C but PL starts at 45 °C), whereas in fluorinated DM3 although PL is observed throughout the SmCA* phase but at much lower frequency (Fig. 11) and observed mode is very weak compared to DM0 which might be due to large ionic contribution in permittivity. That indeed the case in DM3 is confirmed by the fact that PL peaks become clear, although slightly shifted, when a DC bias field is applied which reduces the ionic contribution (Fig.12).

Fig. 8. (a) Comparison of (a) switching time [τ] and (b) viscosity [ γ ] of DM0 and DM3.

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K.Ch. Dey et al. / Journal of Physics and Chemistry of Solids 88 (2016) 14–23

Fig. 13. Temperature dependence of critical frequency (fPH) of PH mode. Fig. 10. Temperature dependence of dielectric increment ( ∆ε ).

Fig. 11. Temperature dependence of critical frequency (fPL) of PL mode.

Fig. 12. Clear evidence of PL in DM3 on application of bias (6 V) voltage.

Temperature dependence of critical frequencies (fPL) is also found to be different, in DM0 it decreases with decreasing temperature from 195 kHz to 30 kHz while in DM3 it increases from about 6.5 kHz to 13.5 kHz (this observation is in bias field as mentioned above). On the other hand, high frequency anti-phase antiferroelectric mode has been observed throughout the SmCA* phase in both the compounds, critical frequencies (fPH) being much higher in DM0 compared to DM3 as observed in PL. However, fPH increases with decreasing temperature in both the compounds, in DM0 from 580 kHz to 925 kHz and in DM3 from 22.5 kHz to 125 kHz (Fig. 13). From the fitted data, αPL and αPH values are found to be 0.003 and 0.038 respectively, signifying that both the processes are Debye type. Diverse reports on range and temperature dependence of critical frequencies of both the modes are found in the literature and no report on the effect of lateral fluorination on relaxation behaviour is found. For example, Panarin et al. [35] reported PL process at  2.5 kHz and PH from 10 kHz to 70 kHz in a laterally fluorinated biphenyl carboxylate compound. The range of the PL and PH processes obtained by Fafara et al. [36] are 10– 20 kHz and 900 kHz–2 MHz respectively in a different nonfluorinated biphenyl carboxylate compound and both processes were temperature independent. Buividas et al. [37] reported PL mode at about 400 Hz–20 kHz and PH around 200 kHz to 2 MHz in a non-fluorinated biphenyl compound with different chain type and both the modes were found to be sharply temperature dependent. Both the relaxation processes (PL, PH) in DM0 and DM3 are observed to be influenced by the DC bias field. Strength of dielectric absorption of PL decreases gradually with bias and finally suppressed at the critical field of 1.95 V/μm and 1.37 V/μm in DM0 and DM3 respectively, Fig. 14(a). The critical frequency fPL initially decreases with bias and finally remains constant in DM0 while in DM3 it increases slowly to a constant value. However, the constant value of fPL is 1100 Hz in both the compounds, Fig. 14(b). On the other hand, strength of dielectric absorption and critical frequency of the PH mode in both the compounds remain almost constant with bias except considerable discontinuous increase near the critical fields where PL was suppressed. No appreciably change was reported by Buividas et al. [37] in both the PL and PH critical frequencies but PH was found to vanish at sufficient bias field, whereas Perkowski et al. observed increased strength of both the modes with bias [38]. Molecular conformation as well as strength and orientation of transverse dipole moments may be the cause of such conflicting dynamical response, more systematic study is required for a proper explanation of such behavior.

K.Ch. Dey et al. / Journal of Physics and Chemistry of Solids 88 (2016) 14–23

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// Fig. 14. Bias field dependence of (a) absorption maxima ( εPL ) and (b) critical frequency ( fPL ).

Fig. 15. Variation of critical frequency of Goldstone (fGM) and Soft mode (fSM) of (a) DM0 and (b) DM3.

3.6.2. SmC* and SmA* phase Characteristic Goldstone mode (GM) was observed in the ferroelectric smectic phase of both the compounds. GM critical frequency (fGM) in DM0 increases with temperature from 1400 Hz to 3800 Hz and that in DM3 from 450 Hz to 1800 Hz, anomalous behavior is observed in fluorinated DM3 while approaching SmCA* transition (Fig. 15). Soft mode (SM) is found in both the compounds, however, in DM0 the mode is observed only in SmA* phase while in DM3 it is also found to penetrate nearly 1.5 °C inside the SmC* phase and produces a V shape at TC as expected from mean field theory [39]. The SM critical frequency (fSM) is also found to be greater in DM0 (220–810 kHz) than in DM3 (110– 425 kHz). It is further seen from the figures that fGM decreases slowly with decreasing temperature but the fSM decreases sharply. This is in accordance with the generalized Landau model of Carlson et al. [40]. So due to fluorination critical frequencies of both the GM and SM decrease significantly. That the Goldstone mode of SmC* phase is a result of phase fluctuation of the molecules is evident from the fact that it diminishes gradually by the application of DC electric field in addition to the measuring AC field and suppresses completely at a certain value of DC field, called critical field, which corresponds to complete unwinding of the helix. DC field required to suppress the GM in DM0 is 0.93 V/ μm . For DM3 it is 0.68 V/ μm as shown in

Fig. 16(a). However under strong bias field a residual mode, with dielectric spectrum different from GM, is observed, this mode is known as domain mode (DM) [28,41,42]. Critical frequency (fDM) of this mode increases non-linearly with increasing bias field and finally remains constant at 14 kHz in DM0 and 37.5 kHz in DM3 as depicted in Fig. 16(b). Thus DM relaxation frequency is roughly 4 and 20 times in DM0 and DM3 respectively compared to GM frequency, 2 and 10 fold increase was reported by Czerwiec et al. in two non-fluorinated compounds [28]. A selected list of parameters of DM0 and DM3 along with literature values of related compounds has been given in Table 2 for comparison.

4. Conclusion On the basis of the X-ray, dielectric and electro-optic studies effect of lateral fluorination in the core may be summarized as follows: 1. No change in phase sequence is observed, however, due to fluorination the melting point is found to increase by 2°, clearing point decreases by 13°; thermal stability of SmCA*

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K.Ch. Dey et al. / Journal of Physics and Chemistry of Solids 88 (2016) 14–23

Fig. 16. Bias field dependence of (a) dielectric increment ( ∆ε ) of Goldstone mode and (b) critical frequency (fD) of domain mode.

Table 2 Selected list of parameters of DM0, DM3 and related compounds. Parameters

Ranges or values

Δε fGM(Hz) fSM(kHz) fPL(kHz) fPH(kHz) D(Å) d (Å) ξ|| (Å) ξ⊥ (Å) Ps (nC/cm2) τ (ms) γ (Pa.s) Β Ea (kJ mol  1)

350 (DM0) 1400–3800 (DM0) 220–810 (DM0) 30–195 (DM0) 580–925 (DM0) 5.46 (DM0) 34.9 (DM0) 986 (DM0) 24.5 (DM0) 210 (DM0) 340 (DM0) 1.37 (DM0) 0.27 (DM0) 38.19 (DM0)

400 (DM3) 450–1800 (DM3) 110–425 (DM3) 6.5–13.5 (DM3) 22.5–125 (DM3) 5.59 (DM3) 34.8 (DM3) 894 (DM3) 23 (DM3) 191.7 (DM3) 500 (DM3) 1.49 (DM3) 0.25 (DM3) 44.34 (DM3)

decreases by 11°, that of SmC* by 5°. 2. Dipole moment of the fluorinated DM3 is considerably higher than the protonated DM0. 3. Only marginal increase of average intermolecular distance is observed in DM3. Layer spacing of DM3 in the SmC* phase is slightly less compared to DM0, behaviour is opposite in the SmCA* phase; similar trend is observed in the tilt angles, maximum value of which is around 25°. With decreasing temperature correlation length increases faster within the smectic plane than across the plane. Correlation across the plane, in all the phases, is significantly less in DM3 compared to DM0 although at ferro- to antiferroelectric transition a substantial jump is observed in DM3. Also correlation within the plane increases much faster in DM3 compared to DM0. 4. Significantly higher field is required for saturation of the spontaneous polarization in DM3 than in DM0. However, in both the compounds PS is almost the same until 40 °C below Tc although the fluorinated compound has much stronger dipole moment. X-ray and polarization studies indicate that the second order SmA*–SmC* transition is nearly tricritical in nature in both the systems. 5. Fluorination results in slower response under a square pulse. 6. Both the compounds exhibit very large dielectric increment in SmC* phase, fluorinated one possesses slightly higher value. Critical frequencies of all the relaxation modes (PL, PH, GM and SM) are found to decrease due to fluorination. Similarly less amount of critical field is required to suppress both the PL and GM. Moreover, PL critical frequency decreases with temperature

92 [22] 400–4700 [22] 2–70 [25] 0–2 [35] 10–50 [35] 6.00 [22] 34.3 [25] 1180 [19] 30 [19] 120 [25] 88 [22] 0.37 [22] 0.45 [25] 97.09 [22]

25.8 [25] 400–900 [25]

400 [36]

10–20 [36] 900–2000 [36] 29.2 [33]

195 [33] 10.5 [33] 2.0 [25] 0.32 [33] 48.14 [25]

300 [36] 0.42 [33]

while opposite behavior is observed in DM0. Under strong bias field although domain mode is observed in both the compounds, however, saturated critical frequency of DM3 was almost two and half times of that of DM0. Thus, in fine, lateral fluorination in the core substantially changes the dynamics of the ferro and antiferroelectric phases as well as several other macroscopic and microscopic properties.

Acknowledgement Financial support under BRNS (DAE), India project 2010/37P/ 44/BRNS/1441 is thankfully acknowledged. Authors are also grateful to Department of Science and Technology, Govt. of India, for providing financial assistance under Project No. I-20110546 to perform experiment at DESY, Hamburg, Germany.

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