Abnormal switching behavior of nanoparticle composite systems

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Abnormal switching behavior ofnanoparticle composite systemsPankaj Kr. Tripathi a , Abhishek Kr. Misra a , Kamal Kr. Pandey a ,Satya P. Yadav a & Rajiv Manohar aa Liquid Crystal Research Laboratory, Physics Department ,University of Lucknow , Lucknow , IndiaPublished online: 01 Feb 2013.

To cite this article: Pankaj Kr. Tripathi , Abhishek Kr. Misra , Kamal Kr. Pandey , Satya P. Yadav& Rajiv Manohar (2013) Abnormal switching behavior of nanoparticle composite systems, PhaseTransitions: A Multinational Journal, 86:12, 1241-1255, DOI: 10.1080/01411594.2012.761698

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Abnormal switching behavior of nanoparticle composite systems

Pankaj Kr. Tripathi, Abhishek Kr. Misra, Kamal Kr. Pandey, Satya P. Yadav and

Rajiv Manohar*

Liquid Crystal Research Laboratory, Physics Department, University of Lucknow, Lucknow, India

(Received 24 September 2012; final version received 19 December 2012)

We have investigated the properties of liquid crystals (LCs) doped with ZnO (8% Cudoped) nanoparticles. The electro-optic properties of LCs have changed with varyingconcentration of ZnO nanoparticles. The dielectric anisotropy obtained from thevalues of dielectric permittivity at 5 kHz in the nematic and smectic phases was foundto increase with increasing concentration of nanoparticles in LCs. It has beenestablished that the effect of nanoparticles on the dielectric anisotropy depends on thephysical properties of LCs; the nanoparticle disturbs the orientation ordering of LCmolecules. The nanoparticle also influences the switching behavior, splay elasticconstant, rotational viscosity and threshold voltage of pure LCs. A small quantity ofnanoparticles causes slight reduction of the splay elastic constant and rotationalviscosity of LC cells.

Keywords: nanoparticle; liquid crystal; dielectric anisotropy; switching; splay elasticconstant

1. Introduction

Liquid crystals (LCs) are a mesostate between solids and liquids. These share the aniso-

tropic properties of optical (uniaxial and biaxial) crystals and the fluid properties of iso-

tropic liquids [1,2]. These materials are extremely sensitive to the small external factors

(electric and magnetic fields, surface effects, temperature, etc.) and possess order and mo-

bility at microscopic and macroscopic levels [3]. The thermotropic LCs are technological-

ly most important among all the LC mesophases, and the nematic mesophase is one of

them which have broad applications in many engineering devices. Another important ap-

plication of nematic LCs is their utilization in holographically formed polymer-dispersed

LCs. These switchable diffraction gratings have broad engineering applications: video

displays, switchable focus lenses, and photonic time-delay generators for optically

assisted phased-array radars [3–6]. The remarkable advances in LC technology have led

to the appearance of LC-based spatial light modulators (SLMs) and display applications

[7]. The correct performance of all the above-mentioned devices requires LC materials

that are stable over a long period of time, have high thermal stability and thermal range,

high dielectric and optical anisotropy, and low switching voltage and switching times.

These various requirements are achieved by using chemical synthesis and carefully

designed mixtures of different LC materials such as dye, polymer, and nanoparticle [8,9].

It is important to note that in optimizing one property usually results in changes in other

properties, mostly in an undesirable direction. Therefore, designing right materials for

commercial applications is a challenging task.

*Corresponding author. Email: [email protected]

� 2013 Taylor & Francis

Phase Transitions, 2013

Vol. 86, No. 12, 1241–1255, http://dx.doi.org/10.1080/01411594.2012.761698

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mailto:[email protected]

http://dx.doi.org/10.1080/01411594.2012.761698

During the past four decades, the doping of nanomaterials in LCs has been extensively

studied [9] and this area of research is now completely mature and can be used for device

fabrication. The interpretation of measured properties of LCs and proper understanding

of LC devices depends on the knowledge of the geometry of LC systems and anchoring

energy. The doping of different nanoparticles such as BaTiO3 nanoparticles, silica nano-

particles, and cadmium telluride quantum dots has been used in recent times for high-

quality performance of the devices [10–13]. Most of the groups have presented results

of doping in ferroelectric LCs (FLCs) especially for display applications [14,15]. They

observed enhancement of the E–O properties is attributed to the variation of the order

parameter and dielectric studies of BaTiO3 nanoparticles dispersed in a FLC matrix. [14]

Gold nanoparticles change the elastic parameter and rotational viscosity of the FLCs.

Gold nanoparticle doping creates a strong intrinsic field inside the sample generating high

tilt and a reproducible observation of memory effect [16]. Each type of these nanopar-

ticles has its own effect on alternation of the LC material properties. It has been estab-

lished that the impurity ions in LC systems strongly impact the device performance,

reducing the LC display quality particularly at higher temperature.

Therefore, in the present paper, we have observed the change in the nature of dielectric

anisotropy with changing the electro-optical parameters. We have used ZnO nanoparticles,

which provided best alignment of LC molecules in our cells. The switching behavior of

LC molecules has been affected due to the presence of nanoparticles in pure LCs. The di-

electric and electro-optical parameters have been evaluated for pure and nanoparticle-doped

LCs. The temperature dependence of the different dielectric and electro-optical parameters,

such as dielectric anisotropy, threshold voltage, splay elastic constant and rotational viscosi-

ty, has also been discussed with the help of different theories of LCs.

2. Experimental details

2.1. Materials

The investigated LC used in the present study is p-butoxybenzylidene, p-heptylaniline

(BBHA). The phase sequence of BBHA is smectic � 20�C ! nematic �55�C ! isotropic

�83�C. The chemical structure of BBHA is shown in Figure 1. The use of nematic LCs for

photonic applications is still of great interest, and so it can be electrically modulated within

this wide working temperature range.

The Cu2þ-doped ZnO nanoparticles have been used in the present study; ZnO (wide

band gap) is one of the most important materials for blue and ultraviolet (UV) optical

device applications. The structure of ZnO can be simply described as a number of

alternating planes composed of tetrahedrally coordinated O2� and Zn2þ ions, heaped

alternatively along the c-axis. The tetrahedral coordination in ZnO leads to a non-central

symmetric structure, which is one of the most important structural characteristics of

wurtzite nanostructured materials. ZnO shows strong electromechanical coupling due to

its unique structure, which results in strong piezoelectric and pyroelectric properties. The

other important structural characteristic of ZnO is its polar surfaces. ZnO nanoparticles

have a normal dipole moment and spontaneous polarization along the c-axis [17]. The

synthesis of these copper-doped ZnO nanoparticles has been given by our synthesis group

Sharma et al. [17].

Figure 2 shows the X-ray diffraction pattern for the 8W nanoparticle used for doping

in LCs. The spectra show broad peaks at the positions of 31.63�, 34.50�, 36.25�, 47.50�,56.60�, 62.80�, 66.36�, 67.92� and 68.91�, as shown in Figure 2. The values are in good

1242 P.Kr. Tripathi et al.

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agreement with the standard JCPDS file for ZnO (JCPDS number 36-1451, a ¼ b ¼ 3.249

A, c ¼ 5.206 A) and can be indexed as the hexagonal wurtzite structure of ZnO having

space group P63mc [17]. The average particle size of a ZnO:Cu2þ nanoparticle is �13 nm,

estimated by the Debye–Scherer equation [17,18]. The uniform nano rod-shaped particles

having diameter 12�15 nm and length 40�80 nm were observed from Scanning Electron

Microscopic (SEM) images, shown in Figure 3 [17].

2.2. Preparation for sample cells

The planar as well as homeotropic sample cells have been used in the present study. The

sandwiched-type (capacitor) cells were made by using two optically plane glass substrates

Figure 2. X-ray diffraction spectra of ZnO for 8% doping of Cu2þ.

Figure 1. Molecular structure of LC BBHA.

Phase Transitions 1243

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coated with conducting indium tin oxide (ITO) layers. Planar alignment has been

achieved by conducting layers with an adhesion promoter and coating with polymer nylon

(6/6). After drying the polymer layers, both the substrates were rubbed unidirectionally

by velvet cloth [18–22]. The substrates were then placed one over another to form a

capacitor. The cell thickness was fixed by placing a Mylar spacer (2.5 mm in our case) in

between the two substrates and then it was sealed by a UV sealant. Similarly, for homeo-

tropic alignment, the glass substrates were coated with a dilute solution of lecithin (cetyl

trimethyl ammonium bromide). The substrates were dried at 220�C for 10 hours before

assembling the cell. Sample cells were calibrated using analytical reagent grade carbon

tetrachloride (CCl4) and benzene (C6H6) as standard references for dielectric studies.

We prepared two mixtures of different concentrations of 8W, i.e., 0.5% and 1.0%

wt/wt, in LCs. The nanoparticles were dispersed in pure LCs physically. Each mixture was

heated at room temperature from the smectic to isotropic phase and cooled back to room

temperature. Then the heating–cooling cycle was repeated. The mixture was viewed under

a polarizing microscope to assure homogeneous distribution of the nanoparticles. The

assembled cells were filled with the suspension and the pure nematic liquid crystal (NLC)

at a temperature higher than the isotropic temperature of NLCs by the capillary method

[20–22]. Nanoparticle composite systems are prepared by dispersion of 8% copper-doped

zinc oxide nanoparticles (8W) in pure BBHA LCs. These samples are hereafter denoted as

mixture 1 and mixture 2.

2.3. Dielectric measurement

The dielectric measurements have been carried out by using a computer-controlled

impedance/gain phase analyzer (HP4194A) in the frequency range 100 Hz to 10 MHz.

The measurements in the high frequency range have been limited to 10 MHz because of

the dominating effect of the finite sheet resistance of ITO coating on the glass plates and

the lead inductance [21–23]. The temperature has been maintained by using a computer-

controlled hot plate (Instec Corporation, USA). Experiments were performed by ramping

Figure 3. SEM images of ZnO:Cu2þ (8% Cu2þdoped ZnO) nanoparticles.


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the temperature at a very slow heating rate of 0.5�C min�1 and temperature stability was

better than �0.1�C [23].

2.4. Electro-optical measurement for the rise and fall time

An arbitrary AC signal voltage (20Vpp and 1 Hz) was applied to the cells using a function

generator. He–Ne laser beam with a wavelength 632 nm as the input signal is detected by

a new focus photodetector (Instec-PD02LI) connected directly to a digital storage oscillo-

scope (Tektronix TDS-2024C). From the detected shapes of the waveform in Figure 4,

we calculated the rise time (ton) and fall time (toff) for pure LCs and nanoparticle-doped

LCs. Here, ton is the time required for the transmittance to rise from 10% to 90% and toffis the time required for the transmittance to fall from 90% to 10% [7,23]. The cell is set at

angle 45� crossed polarizer and analyzer for ensuring maximum optical transmittance.

Thus, the cell works as a phase retarder, thereby altering the polarization of light. When

voltage is applied, the LC molecules are aligned in the applied field direction. Again

when the voltage is switched off, the LC molecules relax and return to their initial state.

3. Results and discussion

Dielectric anisotropy has been calculated by using dielectric data of planar as well as

homeotropic alignments. The value of dielectric permittivity for both the alignments has

been corrected due to sheet inductances and lead inductances of the cell [20–22]. By

least-squares fitting, we have evaluated the corrected dielectric permittivity for both

alignments and then the dielectric anisotropy was calculated by [7] using De ¼ e║� e?,where e║ and e? represent the dielectric permittivity for the applied electric field E

parallel and perpendicular to the macroscopic molecular orientation n, respectively.

The extracted dielectric anisotropy for pure LCs and nanoparticle composite systems

is plotted as a function of temperature in Figure 5. The value of dielectric anisotropy is

enhanced for nanoparticle composite systems. The dielectric anisotropy is generally con-

stant for one phase (smectic) and suddenly decreases for other phase (nematic) for pure

LCs [24,25]. Figure 5 shows the little change in magnitude of dielectric anisotropy after

doping of nanoparticles in the pure LC. It can be seen that the value of dielectric anisotro-

py increases with the increase in the temperature for pure LCs in negative order, while its

value is in positive order for nanoparticle composite systems. We consider that the pure

LC molecule exhibits a continuous symmetry breaking phase transition on varying a

Figure 4. (a) Applied arbitrary wave and (b) detected shapes of the waveform in the oscilloscope.


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control parameter. The dielectric anisotropy was found to increase with increasing con-

centration of nanoparticles in pure LCs. The dielectric anisotropy (De) increases signifi-cantly for pure LCs in negative order, but ultimately changes its sign for nanoparticle

composite systems. The dielectric anisotropy (De) of LCs mainly depends upon the

change of effective dipole moment of LC molecules [26]. The change in the molecular

polarizability of nanoparticle composite systems will also change the dielectric anisotro-

py according to the equation

De ¼ e‘ � e?¼ NhF

e0Daþ m2F

2KBTð3cos2b� 1Þ

� �S: ð1Þ

Here N is the number density, h and F are the internal field factors, e0 is the permittivity

of vacuum, De is the dielectric anisotropy and Da is the anisotropy of the polarizability, S

is the orientational order parameter, KBT is the thermal energy, and b is the angle between

the molecular net permanent dipole moment and the long molecular axis of the molecule.

The resultant dipole moment of the LC molecule attained a new orientation with respect

to the long molecular axis. Therefore, it can be concluded that the 8W nanoparticle signifi-

cantly influenced the geometrical orientation of the used BBHA molecule in suspension.

The contribution of the electronic polarizability to dielectric permittivity is greater in

the direction along the molecular long axis than perpendicular to it. Consequently, De ispositive, as there are additional contributions from dipolar relaxation because the ZnO

nanoparticle with diameter 12 nm possesses dipole moment > 100 D which is much larger

than that of an LC molecule. This large value of dipole moment on ZnO nanoparticles

Figure 5. Dielectric anisotropy of pure LC and ZnO nanoparticle doped composite systems atdifferent temperatures.


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interacts strongly with dipolar species present in the LC mixtures. This dipolar interaction

enhances the anchoring and hence the ordering of LC molecules which surround the ZnO

nanoparticles. For composite systems, the dipole moment of ZnO nanoparticles, which

contributes slightly more in the parallel case than in the perpendicular component? For

nanoparticle composite systems, a reversal in the sign of the dielectric anisotropy has

been seen both in the nematic and in the smectic A (SmA) phases [24]. The change in

sign is caused by a decrease in the value of e?with increase in the concentration of nano-

particles in LCs on entering the smectic and nematic phases, whereas e║ increases anoma-

lously. The decrease of e? in nanoparticle systems results from the smaller distance

between the nanoparticle and LC molecules, leading to an increased antiparallel correla-

tion between the components of the dipole moments along the molecular long axis. Con-

sequently, the effective dipole moment in this direction is reduced, causing a decrease in

e?. The absolute value of the static dielectric permittivity for LCs with a weak dipole mo-

ment is much smaller than for ZnO nanoparticles with a strong dipole moment.

The electro-optical properties have been studied on planar alignment for pure LCs and

nanoparticle composite systems. The alignment layer greatly affects the electro-optical

properties of the LCs [27]. The more confined and uniform alignment quality leads to a

better LC device performance. It is known that at an applied external field, the electro-

optical response of LCs is related to the surface anchoring energy which depends on the

boundary surface energy [7,27]. The alignment of the LC molecule director is determined

by the competition among the surface interactions, bulk interactions, visco-elastic proper-

ties and the externally applied electric field. As the surface anchoring strength decreases,

the LC response time also decreases, and the electro-optical switching becomes faster [7].

The threshold voltage Vth of the LC is given by the following equation [7,28]:

Vth ¼ p

ffiffiffiffiffiffiffiffiffiffiK11

e0De

r: ð2Þ

Here K11 is the splay elastic constant. The response time from the OFF state to ON state,

ton, and that from the ON state to OFF state, toff, are, respectively, given by the following

equations [7,28]:

ton ¼ gd2

e0DeðV 2 � V 2thÞ

ð3Þ

and

toff ¼ gd2

p2K11

: ð4Þ

Here d is the cell thickness and g is the rotational viscosity. All these parameter are

proportional to the order parameter of LCs. From this equation, the rise time depends on

both applied voltage and threshold voltage. However, the threshold voltage depends on

the LC dielectric anisotropy, which is dependent on the applied frequency. Thus, the rise

time depends on the applied frequency as well. Therefore, for a cell of fixed thickness

and a specific LC, the rise time (or the switch on time) depends mainly on the driving

frequency and applied field strengths.

Figure 6 shows the variation of the rise time with temperature in the nematic phase for

the pure LC and nanoparticle composite systems. The figure indicates that from 60�C to

71�C the rise time is constant for pure LCs, however, the rise time for mixture 1 and


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mixture 2 decreases in this temperature range. The rise time decreases from 72�C to 83�Ctemperature for all systems. It is also clear that the rise time basically depends upon the

viscosity and order parameter. The viscosity and order parameter always decreases with

increase in temperature. The rise time is greater for nanoparticle composite systems com-

pared to pure LCs. The rise time of mixture 2 is less than mixture 1, but its value is higher

as compared to the pure LC. The reason is that the nanoparticle produces the maximum

viscosity and interaction on the surface boundary. So the rise time increases with increase

in the concentration of nanoparticles in LCs. The other reason is that the interaction be-

tween nanoparticles and LC molecules is weak, but the interaction between LC molecules

and the surface electrode is strong. So the anchoring strength is strong for mixture 1,

while .the interaction between nanoparticles and LC molecules is strong as compared to

the interaction between LC molecules and the surface electrode for mixture 2 Therefore,

the anchoring strength of mixture 2 is weak as compared to mixture 1. The response time

of LC molecules depends upon the anchoring strength of the sample cell, which in turn

means the response of LC molecules depends upon the surface anchoring of the alignment

layer. However, nanoparticles also increase the response time. Therefore, the doping of

such nanoparticles in this LC is not a perfect requirement in the application of display

technology. If anyhow we can develop a process to decrease the rise time of the LC sam-

ple, then this process should be useful for display devices.

Figure 7 shows the temperature variation of fall time in the nematic phase for the pure

LC and nanoparticle composite systems. Generally, the fall time does not depend upon

the applied field, but it depends upon the elastic constant and rotational viscosity. If the

rise time decreases, then the fall time increases with variation of temperature [7]. The fall

time of mixture 1 and mixture 2 is longer as compared to the pure LC, because the nano-

particle opposes the LC molecules to reach their initial position. Therefore, the LC

Figure 6. Variation of the rise time with temperature for pure LC and nanoparticle compositesystems.


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molecule could not easily attain its original position. The rise time, fall time, rotational

viscosity, splay elastic coefficient, saturated voltage, threshold voltage and dielectric an-

isotropy have been evaluated experimentally, as given in Table 1, at 72�C temperature.

Threshold voltage increases for mixture 1 and it decreases for mixture 2. Theoretically,

the threshold voltage depends upon the magnitude of dielectric anisotropy as shown in

Equation (1).

The rise time and fall time also have been measured as a function of the applied

voltage. Figure 8(a) and (b) show the applied field strength effects for the pure LC cells

and nanoparticle-doped cells at a frequency of 1 Hz. The field strength increased from

5 volts to 10 volts. The rise time strongly depends on the applied voltage according to

Equation (3). When the applied voltage is just above the threshold voltage for mixture 1,

mixture 2 and pure LCs, the rise time is comparatively higher. However, the rise time is

reduced effectively just by increasing the applied voltage. The decrement in the rise time

found in this study is 33.76 ms, 14.00 ms, and 10.6 ms for mixture 1, mixture 2, and pure

LC, respectively, as shown by the dotted line in the figure. At below 7 volts, the rise time

is very large for mixture 2 in comparison to the pure LC and mixture 1. The threshold

voltage is minimum for mixture 2 as compared to mixture 1 and the pure LC. In this sys-

tem, the maximum rise time achieved due to presence of nanoparticles, and some LC

molecules respond at this voltage. But a higher concentration of nanoparticles disrupts

the alignment of LC molecules. Other reason is the surface anchoring of the alignment

layer produced due to the interaction of nanoparticles between the substrates.

The threshold voltage behavior exists when the pretilt angle is zero. However, in most

LC devices a non-zero pretilt angle is required in order to avoid domain formation during

molecular reorientation. In nanoparticle composite systems, some LC molecules also tilt

Figure 7. Variation of fall time with temperature for pure LC and nanoparticle composite systems.


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Table1.

Experim

entalvalueoftherise

time,falltime,rotationalviscosity,splayelasticcoefficient,saturatedvoltage,threshold

voltage,anddielectricanisotropy

forpure

LCandnanoparticlecompositesystem

sat72� C

temperature.

Sam

pleat

72� C

temperature

Dielectric

anisotropy

(De)

Thickness

(d)

Threshold

voltage

(Vth)(involts)

Saturation

voltage

(Vsat)(involts)

Risetime

(ton)

(inmilliseconds)

Falltime

(toff)

(inmilliseconds)

Splayelastic

coefficient(K

11)

inorder

ofmagnitude(�

10�11)

Rotational

viscosity

(g)(inpoise)

Pure

�2.9069

6mm

2.13

5.83

23.4

44.4

1.1838

1.428

Mixture

1þ0

.6537

6mm

4.10

5.10

45.4

144.5

0.9863

3.903

Mixture

2þ0

.5871

6mm

1.36

3.90

22.4

122.4

0.0974

0.032


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due to the presence of nanoparticles. In addition to this, the nanoparticles also generate a

multidomain in the bulk of LC cells. From 7 volts to 10 volts the rise time has small de-

pendence for mixture 1, mixture 2 and the pure LC. Above 7 volts, the nanoparticle aligns

in the direction of the electric field and does not easily reach its own position. Therefore,

the rise time is reduced for nanoparticle-doped systems.

Figure 8(b) shows the fall time with variation of the applied electric field (voltage) for

pure LCs and nanoparticle-doped systems. The fall time increases with the applied field

for mixture 1 increases suddenly from 6 volts to 8 volts while it changes little for pure

LCs. This suggests that the rise time remains minimum at 8 volts and 9 volts, which

means the LC molecules show very fast response at that condition and molecules do not

immediately attain their initial position. The fall time decreases with the rise in voltage

from 5 volts to 7 volts for mixture 2 and after that the fall time saturates with increasing

voltage from 7 volts to 10 volts. At this applied field, the nanoparticle opposes the re-

sponse of LC molecules. They do not attain their initial position. Above 8 volts, the fall

time of mixture 2 saturates with the applied field. In this condition, the nanoparticle is

fully aligned to the direction of the applied electric field and therefore only LC molecules

are responses to it.

The response of LC molecules is related to rotational viscosity. The connectivity of

the LC cavity network has some effects on the switching times (rise and fall time). In con-

ventional nanoparticle composite systems, fall times typically exceed rise times, since

relaxation is driven only by elastic energy, with no electric field. The fall time is propor-

tional to the characteristic size of nanoparticles and LC molecules. This model predicts

that isolated, spherical LC droplets should have anomalously long fall times [29–31].

Figure 8(a) and (b) provide a comparison of rise and fall times for various applied electric

fields for both the pure LC and the nanoparticle composite systems. For the nanoparticle

composite system, the shorter rise versus fall times agree with expectations.

In a continuum of this study, we have also determined the rotational viscosity and

splay elastic constant for pure LC and nanoparticle composite systems. The splay elastic

constant is obtained from Frederick’s threshold voltage with the help of Equation (1)

[32]. Figures 9 and 10 show the temperature behavior of rotational viscosity and splay

elastic constant for the pure LC and nanoparticle composite systems [33,34]. One can

conclude from the figures that they would have both changed in the similar way with re-

spect to the nanoparticle concentration and this similar change is proportional to the order

Figure 8. (a) Variation of rise time with applied voltage for pure LC and nanoparticle compositesystems. (b) Variation of fall time with applied voltage for pure LC and nanoparticle compositesystems.


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Figure 9. Temperature behavior of rotational viscosity for the pure LC and nanoparticle compositesystems.

Figure 10. Temperature behavior of splay elastic constant for the pure LC and nanoparticlecomposite systems.


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parameter. The splay elastic constant remains constant for all samples. The value of the

splay elastic constant of nanoparticle composite systems has been found to be less as

compared to the pure LC. The splay elastic constant basically depends upon threshold

voltage and dielectric anisotropy. The magnitude of dielectric anisotropy of pure LCs is

high as compared to the nanoparticle composite system. In addition to this, the value of

splay elastic constant of mixture 2 is less in comparison to mixture 1.

The rotational viscosity of the pure LC and nanoparticle composite systems has been

determined with the help of Equation (3). The rotational viscosity of aligned LCs repre-

sents an internal friction among LC directors during the rotation process. The magnitude

of rotational viscosity depends on the detailed molecular constituents, structures, intermo-

lecular associations and temperature. As temperature increases, rotational viscosity

decreases rapidly. Rotational viscosity is an important parameter for many electro-optical

applications employing LCs, because the response time of the LC is linearly proportional

to the rotational viscosity.

According to the molecular theory developed by Osipov and Terentjiv [7,34], the

rotational viscosity of mixture 1 is larger than the pure LC. It is also clear that the molecu-

lar association between nanoparticles and LC molecules is strong as compared to an

LC–LC molecule. But for mixture 2 the intermolecular association of nanoparticles is

very strong as compared to a nanoparticle–LC molecule. At a higher concentration, the

nanoparticle is more effective than an LC–LC molecule, so the interaction of nanoparticle–

nanoparticle is very strong for mixture 2. Therefore, LCs with weak intermolecular asso-

ciation reduce the rotational viscosity significantly. Another reason is that the relaxation

time is proportional to the viscosity size of nanoparticles and the splay elastic constant in

LC cells. The splay elastic constant decreases with the addition of nanoparticles in pure

LCs. The reason is that the number of nanoparticles increases in the LC system, decreas-

ing the splay elastic constant for nanoparticle composite systems. According to the mean

field theory [7,28], the splay elastic constant depends upon the number and size of the

molecules.

K11 ¼ C11S2

V7=3n

; ð5Þ

C11 ¼ 3A

2

� �L

mg21

� �13

; ð6Þ

where C11 is called the reduced splay elastic constant, Vn is the mole volume, L is the

length of a molecule, m is the number of molecules, A is constant and S is the order

parameter.

4. Conclusion

Nanoparticle-induced electro-optical parameters and dielectric anisotropy have been

demonstrated in LCs. The dielectric anisotropy has been found to be of positive order for

nanoparticle composite systems and of negative order for pure LCs. In addition to this,

the rise time and fall time have also been measured for both pure and nanoparticle com-

posite systems with variation of voltage and temperature. The rise time has increased for

nanoparticle LCs compared to pure LCs. The electro-optical performance of these doped

systems is not good from the application point of view. The threshold voltage and satura-

tion voltage have decreased for nanoparticle composite systems. The dielectric anisotropy


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increases with increase in the concentration of the nanoparticles doped in LCs, indicating

that the nanoparticle changes the order parameter of the rod-like LC molecule. The splay

elastic constant remains constant for mixture 2 with variation of temperature, whereas it

increases significantly for mixture 1 and pure LCs with increasing temperature, suggest-

ing the coupling of the LCs due to distortion of nanoparticles.

Acknowledgements

The authors are sincerely thankful to ISRO for providing assistance in the RESPOND program inthe form of the project entitled ‘Designing of SLMs based on nematic LCs doped with non-mesogenic molecules’. One of the authors (AKM) is thankful to UGC, New Delhi, for the third-year grant of Dr D.S. Kothari Post Doctoral Fellowship No. F.4.2/2006 (BSR)-13-234/2008(BSR).

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