154 CHAPTER VI EFFECT OF ZINC OXIDE NANOPARTICLES ON THE TRANSITION TEMPERATURE AND DIELECTRIC PROPERTIES OF ELECTROCLINIC LIQUID CRYSTALS In this chapter, the effect of zinc oxide nanoparticles (ZnO NPs) on the dielectric relaxation behavior of electroclinic liquid crystal (ELC) materials has been described. The addition of ZnO NPs into ELCs, caused a remarkable shift in ferro to paraelectric (Sm C* to Sm A*) phase transition temperature which was investigated by the dielectric and electro-optical measurements. The different behavior of ZnO NPs doped ELC from pure ELC has been explained by determining the dielectric strength, distribution parameter and the corresponding relaxation frequency, etc. and these results have been compared with the data calculated by using theoretical model. Effect of ZnO NPs addition on physical parameters such as spontaneous polarization (P s ) and rotational viscosity (η) has also been discussed in this chapter. 6.1 INTRODUCTION Nanoscience and nanotechnology is one of the vital frontiers in scientific research. A broad area of research topics from fundamental physical, biological and chemical phenomenon to material science has been addressing by the scientific society at the nanoscale [1-3]. Nanoparticles (NPs) doping technology provides a more convenient and flexible approach for the modification of liquid crystal (LC) materials and designing new and improved devices based upon LCs. As discussed in previous chapter, by adding copper oxide (CuO) decorated multi-walled carbon nanotubes (MWCNTs) into ferroelectric liquid crystals (FLCs), one can improve the response of the device (Chapter V). LC is itself a flexible material whose properties can be customized by mixing different chemicals mutually. A small addition of NPs into LC
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154
CHAPTER VI
EFFECT OF ZINC OXIDE NANOPARTICLES ON
THE TRANSITION TEMPERATURE AND
DIELECTRIC PROPERTIES OF
ELECTROCLINIC LIQUID CRYSTALS
In this chapter, the effect of zinc oxide nanoparticles (ZnO NPs) on the dielectric
relaxation behavior of electroclinic liquid crystal (ELC) materials has been described.
The addition of ZnO NPs into ELCs, caused a remarkable shift in ferro to paraelectric
(Sm C* to Sm A*) phase transition temperature which was investigated by the dielectric
and electro-optical measurements. The different behavior of ZnO NPs doped ELC from
pure ELC has been explained by determining the dielectric strength, distribution
parameter and the corresponding relaxation frequency, etc. and these results have been
compared with the data calculated by using theoretical model. Effect of ZnO NPs
addition on physical parameters such as spontaneous polarization (Ps) and rotational
viscosity (η) has also been discussed in this chapter.
6.1 INTRODUCTION
Nanoscience and nanotechnology is one of the vital frontiers in scientific research. A
broad area of research topics from fundamental physical, biological and chemical
phenomenon to material science has been addressing by the scientific society at the
nanoscale [1-3]. Nanoparticles (NPs) doping technology provides a more convenient
and flexible approach for the modification of liquid crystal (LC) materials and
designing new and improved devices based upon LCs. As discussed in previous
chapter, by adding copper oxide (CuO) decorated multi-walled carbon nanotubes
(MWCNTs) into ferroelectric liquid crystals (FLCs), one can improve the response of
the device (Chapter V). LC is itself a flexible material whose properties can be
customized by mixing different chemicals mutually. A small addition of NPs into LC
155
materials has improved many special characteristics in the form of frequency
modulation response, non-volatile memory effect, fast electro-optic response and low
driving voltage [4-7]. Among all the fascinating materials emerging from the field of
nanotechnology, the metal NPs such as silver(Ag), gold(Au), palladium(Pd),
platinum(Pt) or their alloys doped liquid crystal displays (LCDs) exhibited the faster
response time than that of the LCDs with conventional driving methods [8-12] and
continue to attract immense research interests. However, still a lot of efforts needs to
put in the improvement of nanomaterials research, particularly, the agglomeration or
the aggregation tendency of NPs over time due to which the alignment and
performance of the LCD device get affected [13].
Comparing with other metallic NPs, ZnO NPs have attracted increasing attention
owing to wide application in nano-generators, gas sensors, highly efficient solar cells,
field-emission transistors, ultraviolet photo detectors and in biomedical systems such
as cancer detecting biosensors and ultra sensitive DNA sequence detectors [14-18].
Due to its large dipole moment (> 100 D), ZnO NPs are very much appropriate for LC
material as ZnO NPs generates a powerful field inducing dipolar interaction resulting
into the enhancement of anchoring of LC molecules which may give rise to the well
ordered molecular structure [19]. Numerous research groups have explored that the
addition of ZnO NPs into FLCs reduced the threshold voltage and improved the
optical contrast of the devices based on LCs [20, 21]. In the starting of 2008, Huang et
al. explored that the doping of ZnO NPs into surface stabilized ferroelectric liquid
crystals (SSFLCs), can improved the alignment and field induced reorientation
processes of FLCs [22]. In 2009, Li et al. proposed a physical model, which shows an
interaction of ZnO NPs with surrounding FLC molecules [23]. Till now, researchers
mainly emphasis on the addition of ZnO NPs into FLCs to improve the material
parameters. The effect of ZnO NPs on the phase transition temperature and dielectric
relaxation processes of FLC materials has not been reported.
The frequency domain dielectric spectroscopy (FDDS) is a promising tool to detect
several collective/non-collective dielectric relaxations in FLCs in chiral smectic C
(Sm C*) to chiral smectic A (Sm A*) phase transitions [24-27]. The dielectric
relaxation behaviour of FLCs provides important information regarding its dipolar
response to external stimulus. Various dielectric modes have been found to exist in
156
Sm C* phase of the FLC materials owing to either collective dielectric processes or
the molecular reorientation processes connected with the polarization of the
molecules. To investigate the dielectric relaxation behaviors of FLCs in Sm C* phase,
one can give details of two modes, Goldstone and soft modes, which have been
discussed in previous chapter of the thesis (Chapter II). Moreover, there may be
some additional dynamic modes produced by the dynamics of the molecules or by the
molecular interaction between the molecules of the FLCs and some dopant materials
[28-32].
In the present study, noticeable investigations have been carried out extensively in
order to understand the shift in phase transition from ferro (Sm C*) to paraelectric (Sm
A*) phase of electroclinic liquid crystal (ELC), which is a special type of FLC. In
ELCs, the Sm A* mesophases are capable to show the induced polarization (PS)
similar to Sm C* mesophases. ELC materials have been discussed in detail in the first
chapter of the thesis (Chapter I). The effect of ZnO NPs on the transition temperature
of ELCs has been demonstrated by using FDDS. After analyzing the dielectric
relaxation behavior of ZnO NPs doped ELC, a low frequency peak along with the
Goldstone mode in the Sm C* phase has also been observed near the transition
temperature. Further, it has been observed that this low frequency peak depends
strongly on temperature and electric field. The results have also been compared with
the data calculated by using theoretical model (Cole-Cole model). The effect of
doping of ZnO NPs, on the physical characteristics of materials such as spontaneous
polarization (Ps) and rotational viscosity (η) has also been discussed.
6.2 EXPERIMENTAL DETAILS
The LC sample cells for the thermal and dielectric studies of ELC materials were
prepared by using by photolithographic technique and the rubbed polyimide technique
was used to obtain the homogeneous (HMG) alignment. The detail procedure of
sample cell fabrication has given in the previous chapters. The commercially available
ELC materials used in our present study are BDH 764E and Felix-20 and the phase
sequences of the materials are as follows:
157
Cryst. →← °− C7Sm C* →← Cº28
Sm A* →← Cº73N →← C92º-89
Iso. (BDH 764E)
Cryst. →← °− C8 Sm C* →← − Cº1815
Sm A* →← Cº75N →← C92º
Iso. (Felix-20)
A small amount (1 wt%) of ZnO NPs was doped into ELC materials and then ZnO
doped ELC materials were introduced into the cells by means of capillary action at
elevated temperature (~95°C) to ensure that filling takes place in isotropic phase of
the ELC materials.
The molecular and collective dielectric studies were carried out by dielectric
spectroscopy using Wayne Kerr 6540A impedance analyzer in the frequency range of
20 Hz to 1 MHz. The dielectric set up was fully computer controlled and automated.
The sample temperature was controlled within the accuracy of ± 0.01oC using
temperature controller JULABO F-25 HE. Optical tilt angle measurements were taken
with the sample cell mounted on a rotatable stage of the polarizing optical microscope
(Axioskop-40) interfaced with a canon digital camera. Automatic liquid crystal tester
(ALCT-P), which works on the principle of current measurement with time on the
application of triangular pulse [33], was used for measuring spontaneous polarization
(Ps) and rotational viscosity (η). The sample holder was kept thermally isolated from
the external sources.
6.3 RESULTS AND DISCUSSION
The ZnO NPs used in the present study, were synthesized in alcoholic medium at
room temperature by using zinc acetate and lithium hydroxide. The characteristic size
of synthesized ZnO NPs estimated by XRD pattern was found to be around ~ 7 nm
which is calculated using Debye–Scherrer formula [34]. The XRD pattern of ZnO-
NPs is shown in Fig. 6.1.
158
Figure 6.1: XRD pattern of zinc oxide nanoparticles.
For the comparative studies, we prepared and used the sample cells containing ZnO
NPs doped ELC materials and pure ELC materials. Addition of ZnO NPs into pure
ELC materials results in the redistribution of intermolecular interaction energies
which can affect almost all the physical parameters of pure materials.
Dielectric relaxation spectroscopy is one of the important tool to study the molecular
relaxation and dielectric properties of the materials. Temperature dependence of
dielectric relaxation can be described by Debye theory but if collective dielectric
processes exhibits a continuous distribution of relaxation time for LCs then it can be
described by Cole-Cole equation as given by:
11,2...
( )*( )
1 ( ) i
i i
o
i iiα
ε εε ω ε
ωτ∞
∞ −=
−= +
+∑ (6.1)
where, ε0, ε∞ and τ stand for the static dielectric permittivity, frequency independent
permittivity at high frequency and relaxation time, respectively. ‘i’ represent the
number of relaxation processes and ‘α’ stands for the distribution parameter. α is a
measure of the width of the relaxation distribution and if the value of α is very small
or equal to zero then the above Cole-Cole equation will obey the Debye process.
The real and imaginary part of permittivity can be separated out easily from the
complex function by the relation:
159
ε*(ω) = ε' (ω) - iε "(ω) (6.2)
where, ε' denotes the real part of the complex dielectric permittivity, ε" is the
imaginary part of the permittivity and ω is the angular frequency of applied electric
field.
Figure 6.2 shows the real part of dielectric permittivity (ε') as a function of frequency
for a large temperature range of ELC material (BDH 764E) doped with 1 wt % ZnO
NPs, while the dielectric permittivity (ε') of pure ELC material is shown in the inset of
Fig. 6.2 and the solid lines represents the best theoretically fit data by using Cole–
Cole model. As seen from the inset, the dielectric permittivity (ε') of pure ELC
material continuously decreases in Sm C* phase near the transition temperature of Sm
C* to Sm A* (~28°C). The value of dielectric permittivity (ε') in ELC is very high at
lower frequencies and almost constant at higher frequencies in both Sm C* and Sm
A* phases. The ELC material (BDH 764E) doped with ZnO NPs shows a drastic
change in the dielectric relaxation processes as shown in Fig. 6.2.
Figure 6.2: Dispersion curves of dielectric permittivity (εεεε′′′′ vs frequency) at
different temperatures for ZnO NPs doped BDH 764E and in inset, for pure
BDH 764E sample cells, under no bias. Here, solid lines represent the
theoretically calculated data.
102
103
104
105
106
0
50
100
150
200
102
103
104
105
106
0
20
40
60
80
100
120
140
160
180
Pure BDH 764E
εε εε'
Frequency (Hz)
20oC
20oC
22oC
22oC
24oC
24oC
25oC
25oC
26oC
26oC
28oC
28oC
29oC
29oC
31oC
31oC
32oC
32oC
εε εε'
Frequency (Hz)
20 o
C
20 o
C
24 o
C
24 o
C
26 o
C
26 o
C
28 o
C
28 o
C
30 o
C
30 o
C
32 o
C
32 o
C
34 o
C
34 o
C
35 o
C
35 o
C
36 o
C
36 o
C
37 o
C
37 o
C
38 o
C
38 o
C
40 o
C
40 o
C
160
The high dielectric permittivity (ε׳) which is due to phason mode in Sm C* phase
appears up to 36°C. This shows the shifting in transition temperature (around 8°C) of
Sm C* to Sm A* phase of BDH 764E material by doping ZnO NPs in it.
Figure 6.3 shows the behavior of dielectric loss factor (tan δ) versus frequency of
ELC material (BDH 764E) doped with 1 wt % ZnO NPs, at different temperatures
while the inset of this figure shows the behavior of loss factor (tan δ) versus frequency
of pure BDH 764E material at same parameters.
Figure 6.3: Behavior of dielectric loss factor (tan δ) with frequency at different
temperatures for ZnO NPs doped BDH 764E and in inset, for pure BDH 764E
sample cells, under no bias.
From these graphs, one can confirm the change in phase transition temperature. As
seen from the inset of Fig. 6.3, there is an abrupt increment in the value of relaxation
frequency near 29oC while for ZnO NPs doped BDH 764E, the increment in
relaxation frequency is about 36ºC. In Sm C* phase, there are two or more than two
relaxation peaks present in ZnO NPs doped BDH 764E, which was totally absent in
pure BDH 764E material.
The phase transition (Sm C* to Sm A*) can be varied depending upon the
concentration (C) of ZnO NPs in BDH 764E material. In our study, we have found
102
103
104
105
106
0.0
0.5
1.0
1.5
2.0
2.5
3.0
102
103
104
105
106
0.0
0.5
1.0
1.5
2.0
2.5
3.0
26 C
27 C
28 C
29 C
30 C
31 C 32 C
(Pure BDH 764E)
tan δδ δδ
Frequency (Hz)tan
δδ δδ
Frequency (Hz)
26o
C
27o
C
28o
C
29o
C
30o
C
32o
C
34o
C
35o
C
36o
C
37o
C
38o
C
161
that when the value of C of ZnO NPs is around 1 wt%, then the shift in transition
temperature is maximum. The above graphs shows the behavior of dielectric
permittivity (ε') and loss factor (tan δ) with frequency, for BDH 764E material doped
with 1 wt % ZnO NPs [Figs. 6.2 & 6.3]. Figure 6.4 shows the behavior of dielectric
permittivity (ε') and loss factor (tan δ) with frequency for different values of C (< 1
wt %, i.e., 0.5 wt % and >1 wt %, i.e., 2 wt %).
Figure 6.4: Frequency dependences of (a) dielectric permittivity (εεεε') and (b)
dielectric loss factor (tan δ) for 0.5 wt % ZnO NPs doped BDH 764E, while (c)
dielectric permittivity (εεεε') and (d) dielectric loss factor (tan δ) for 2 wt % ZnO
NPs doped BDH 764E sample cells, at different temperatures and under no bias.
102
103
104
105
106
0.0
0.5
1.0
1.5
2.0
2.5
3.00.5 wt % ZnO NPs doped BDH 764E
tan
δδ δδ
Frequency (Hz)
24oC
26oC
28oC
29oC
30oC
32oC
34oC
35oC
36oC
38oC
40oC
(b)
102
103
104
105
1060
40
80
120
160
0.5 wt % ZnO NPs doped BDH 764E
εε εε'
Frequency (Hz)
24oC
26oC
28oC
29oC
30oC
33oC
35oC
36oC
38oC
40oC
(a)
102
103
104
105
106
0
40
80
120
160
200
ε ε ε ε '
2 wt % ZnO NPs doped BDH 764E
Frequency (Hz)
24oC
25oC
26oC
27oC
28oC
30oC
32oC
34oC
35oC
(C)
102
103
104
105
106
0.0
0.5
1.0
1.5
2.0
2.5
3.0
(d) 2 wt % ZnO NPs doped BDH 764E
24oC
26oC
27oC
28oC
29oC
30oC
31oC
32oC
34oC
35oC
tan
δδ δδ
Frequency (Hz)
162
From the figures one can see that as the value of C increases, the shift of the transition
temperature decreases. At C ~ 2 wt %, there is no shift in transition temperature with
the pure BDH 764E sample as shown in Figs 6.4 (c) and (d). However, at C ~ 0.5
wt %, there is a notable shift in transition temperature (from 28oC to 35oC) as shown
in Figs 6.4 (a) and (b).
The behavior of dielectric loss factor (tan δ) of 0.5 wt % ZnO NPS doped BDH 764E
with frequency, is almost similar as in case of 1 wt %, however, the shift in transition
temperature is little less (around 1 to 2oC). The comparable enhancement in transition
temperature with ZnO NPs addition has also been checked in another ELC material,
Felix-20. Figure 6.5 (a) shows the behaviour of dielectric permittivity (ε') as a
function of frequency for a large temperature range of Felix-20 material doped with
ZnO NPs having
Figure 6.5: Frequency dependences of (a) dielectric permittivity (εεεε') and (b)
dielectric loss factor (tan δ) of 1 Wt % ZnO NPs doped ELC (Felix-20) material
and in inset, for pure Felix-20 sample, at different temperatures and under no
bias.
C ~ 1 wt%, while the dielectric permittivity (ε') of pure Felix-20 has shown in the
inset of Fig. 6.5 (a). As seen from the inset, the dielectric permittivity (ε') of pure
Felix-20 continuously decreases in Sm C* phase near the transition temperature of Sm
102
103
104
105
106
0
40
80
120
160
200
240
100
101
102
103
104
0
20
40
60
80
11o C
13o C
15o C
17o C
19o C
21o C
23o C
ε ε ε ε '
Frequency (Hz)
Pure Felix-20
εε εε '
Frequency (Hz)
15o C
18o
C
22o C
24o
C
25o
C
26o
C
27o
C
28o
C
30o
C
ZnO NPs doped Felix-20 (a)
102
103
104
105
106
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Frequency (Hz)
ZnO NPs doped Felix-20
15o C
18o C
20 oC
22o C
24o C
25o C
26o C
28o C
30o C
tan
δδ δδ
(b)
163
C* to Sm A* (18°C). The value of dielectric permittivity (ε') in Felix-20 is very high
at lower frequencies in Sm C* phase. The ELC material (Felix-20) doped with ZnO
NPs shows a drastic change in the dielectric relaxation processes as shown in Fig.
6.5(a). The high dielectric permittivity (ε׳) in Sm C* phase appears up to 26°C. This
shows the shifting in transition temperature of Sm C* to Sm A* phase (from 18°C to
about 26°C) of Felix-20 material by doping ZnO NPs in it. Figure 6.5 (b) shows the
behavior of dielectric loss factor (tan δ) versus frequency of Felix-20 material doped
with ZnO NPs, at different temperatures. From this graph, one can confirm the change
in phase transition temperature. There is an abrupt increment in the value of relaxation
frequency of ZnO NPs doped Felix-20 material up to the temperature about 26ºC, In
Sm C* phase, there are two or more than two relaxation peaks present in ZnO NPs
doped Felix-20 material as in case of another ELC material (BDH 764E) doped with
ZnO NPs. The edge of the high frequency dielectric loss above 100 KHz in Figs. 6.3
and 6.5 (b), occurs due to the finite resistance of the ITO coating on the glass
substrate of the sample cell. This ITO effect on dielectric measurements has also been
reported elsewhere [35].
Figure 6.6 shows the Cole-Cole plots at four different temperatures, three in Sm C*
Figure 6.6: The Cole-Cole plots for ZnO NPs doped BDH 764E sample in Sm C*
(25ºC, 30ºC and 34ºC) and Sm A*(38ºC) phases, under no bias field.
0 50 100 150 200 2500
50
100
150
200
34 o
C
30 o
C
25o
C
0 10 20 30 40 50 60 700
10
20
30
40
50
60
αααα2=0.139
αααα=0.3
αααα1=0.025
εε εε''
εεεε'
38oC
34oC
αααα1=0.011
αααα=0.028
αααα2=0.139
αααα2=0.056
αααα=0.3
αααα1=0.025
εε εε''
εεεε'
38 o
C
ZnO NPs doped BDH 764E
164
phase (25oC, 30
oC and 34
oC) and one in Sm A* phase (2
o above transition
temperature) for ZnO NPs added BDH 764E material while inset of the figure shows
the magnifying Cole–Cole plots for ZnO NPs doped ELC at 2o below (34oC) and 2o
above (38oC) the transition temperature (38oC), respectively. From Fig. 6.6, one can
see that in deep Sm C* phase (i.e., 25oC) by fitting the expression of equation (1),
only one relaxation behavior is present which is attributed to Goldstone mode while
further increase in temperature or near transition temperature (i.e., 30oC and 34
oC),
one can observe that the Cole-Cole diagrams are the superposition of two semicircles,
i.e., at this temperature range, two modes are contributing to the dielectric response.
At higher temperature or in Sm A* phase (38ºC), only one relaxation behavior is
present which is attributed to soft mode in case of ZnO doped ELC material.
Figure 6.7 shows the Cole-Cole plots at three different temperatures, two plots in Sm
C* phase (20ºC and 26ºC) and one in Sm A* phase (31ºC) for pure ELC (BDH 764E)
Figure 6.7: The Cole-Cole plots for pure BDH 764E sample in Sm C* (20ºC and
26ºC) and Sm A* (31ºC) phases, under no bias field.
material. From all above Cole-Cole plots for pure ELC material, one can observe that
there is only single relaxation behavior in complete temperature range.
0 30 60 90 120 150 1800
30
60
90
120
150
26o
C
31o
C
20o
C
αααα=0.011
αααα=0.11
αααα=0.028εε εε''
εεεε'
Pure BDH 764E
165
The behavior of relaxation frequency (νR,ε'') in Sm C* and Sm A* phases has been
shown in Fig. 6.8, calculated by the formula , " ,tanR R oε δν ν ε ε∞= [36]. Figure 6.8(a)
shows the relaxation frequency versus temperature for ZnO NPs doped ELC and inset
shows the same for pure ELC material, without any bias application. The solid line
represents the best theoretically calculated data by using Cole-Cole model through the
experimental points. As seen from the inset of Fig. 6.8(a), the relaxation frequency is
found to be independent of temperature in deep Sm C* phase and at transition from
Sm C* to Sm A* phase there is a continuous increment in the value of relaxation
frequency for pure ELC material. In case of ZnO NPs doped ELC material, two
relaxation peaks present which we have been discussed earlier in Fig. 6.3. In Fig.
6.8(a) the behavior of both relaxation peaks have been shown with respect to
temperature.
Figure 6.8: (a) Behavior of relaxation frequency with respect to temperature for
ZnO NPs doped ELC (BDH 764E) under no bias and in inset, the same behavior
for pure ELC sample. The symbols show the experimental points where the filled
square shows first dielectric process and filled circles shows the second dielectric
process. Solid lines represents the theoretically calculated data for the first and
second dielectric processes by using Cole-Cole equation, while (b) shows the
experimental behavior of relaxation frequency with different bias (0 V, 5 V and
10 V) for ZnO doped BDH 764E.
20 25 30 35 40
0
10
20
30
40
50
60
(a)
20 22 24 26 28 30 32
0
2
4
6
8
10
12
14
νν ννR
, εε εε''(
KH
z)
Temperature(oC)
Temperature (oC)
νν ννR, εε εε
'' (
KH
z)
20 25 30 35 40
0
15
30
45
60
75(b)
νν ννR
, εε εε'' (
KH
z)
Temperature (oC)
0 V
5 V
10 V
166
The solid lines of theoretically calculated data and the experimental data are almost
matching with each-other. As seen in the Fig. 6.8(a), one is able to separate both the
dielectric realaxation peaks in ZnO NPs doped ELC material. The frequency
separation of both relaxation peaks increases with temperature and the peak along
with the low frequency side almost vanishes after transition temperature of ZnO NPs
doped ELC material. After transition temperature only the regular soft mode process
remains which shows the usual behavior of ELC materials. Such type of low
frequency relaxation peak has also been observed in water added and graphene oxide
(GO) added ELC samples [32, 37].
In Fig. 6.8 (b), the relaxation frequency has been plotted with respect to temperature
for ZnO NPs doped ELC material at different bias values (0 V, 5 V and 10 V). The
behavior of νR,ε'' at 0 V bias for pure and ZnO NPs doped ELC is same, as below
transition temperature (Sm C* to Sm A*) it is independent of the temperature and
above transition there is a continuous increment in the value of νR,ε''. Now by applying
different bias values (5 V and 10 V) in deep Sm C* phase, the relaxation frequency is
independent of the temperature which starts decreasing near the transition
temperature. After transition temperature there is a abrupt increase in the value of
νR,ε''. The behavior of νR,ε'' with bias in ZnO NPs doped ELC material is similar to pure
ELC and it does not obey the Curie- Weiss law in Sm C* phase due to high
electroclinic coefficient of such ELC materials. Thakur et al. have reported earlier that
pure ELC materials do not obey the Curie-Weiss law near the transition temperature
[38]. In Sm A* phase the relaxation frequency is temperature dependent like in other
FLC materials.
The parameters like dielectric strength (∆ε), distribution parameter (α) and the
corresponding relaxation frequency (νR,ε'') obtained experimentally in a wide
temperature range have been given in Table 6.1 and 6.2, for both pure and ZnO NPs
doped ELC material and these parameters compared with the data calculated from
Cole-Cole model. One can observe from both the tables that there is an increment in α
with respect to temperature. The small values of α for both pure and ZnO NPs doped
ELC suggest that dielectric process is very close to Debye type of relaxation. The
increase of α with temperature indicates that the both samples become less dispersive
167
at higher temperatures and must show more than one relaxation process at some
higher temperatures in Sm C* phase.
Table 6.1: Variation of dielectric strength (∆ε), distribution parameter (α) and
relaxation frequency (νR,ε'') with temperature for pure ELC material and
comparison with theoretically calculated data.
Temperature
(oC)
∆ε α
(Experimental)
α
(Theoretical)
υR,ε'' (KHz)
(Experimental)
υR,ε'' (KHz)
(Theoretical)
20 166.25 0.011 0.010 0.222 0.232
22 161.56 0.017 0.030 0.225 0.256
24 150.33 0.022 0.032 0.232 0.294
25 138.70 0.022 0.035 0.241 0.312
26 128.47 0.028 0.045 0.268 0.333
27 109.45 0.028 0.050 0.322 0.335
28 83.65 0.031 0.074 0.453 0.498
29 40.75 0.033 0.080 2.205 1.923
30 28.86 0.100 0.090 3.674 3.122
31 18.16 0.110 0.096 7.420 6.670
32 12.66 0.144 0.100 11.110 9.523
168
Table 6.2: Variation of dielectric strength (∆ε), distribution parameter (α) and
relaxation frequency (νR,ε'') with temperature for ZnO NPS doped ELC material
and comparison with theoretically calculated data.