**5.1 Morphological analysis**

HPDLC films are free of light scattering. These films have faster response time and require higher switching voltages. In PDLC and HPDLC films, no surface alignment

Polymer-stabilized liquid crystal is a thin composite film prepared from the homogenous mixture of LC and monomer. Typically, the monomer concentration in PSLC is less than 10% of the total weight. The small amount of monomer is used to stabilize/lock the oriented LC structure at different optical states and to reduce the switching time and operating voltage [73]. The homogenous mixture of LC and polymer is prepared and filled into the prefabricated cells made of transparent ITOcoated electrodes for photopolymerization using PIPS technique [51]. For improved display performance, LCs should be homogenously and uniformly aligned inside the cell. To control the orientation of LC, the inner face of electrodes is coated with a transparent polymeric material (generally PI) followed by baking and rubbing [53]. A thin layer of PI is known for its excellent strong and outstanding heat, mechanical, and chemical resistivity [53]. The mechanical treatment such as unidirectional rubbing modifies surface topography by breaking the symmetry and creating linear microgrooves on the polymer surface [48, 54, 56]. The rubbing

direction on one ITO plate is 0° or 90° with respect to the other depending upon the parallel/antiparallel or twisted mode, respectively [55, 74]. This induced anisotropic surface diffuses monomer molecules preferentially along the rubbing direction. Due to strong interaction and anchoring between LC and monomer, the polymer network formed during/after polymerization keeps the LC director in a definite direction [75]. Along with the surface alignment layer, the configuration and orientation of LC can also be controlled by application of external field and/or temperature during photopolymerization. Even low electric field is sufficient to align the LC director along the field by fixing torque on it. After establishing the proper combination of surface treatment and applied field, the sample is irradiated by ultraviolet (UV) light to induce photopolymerization to obtain the desired texture. Since the

monomer concentration is very small, a continuous LC texture along with

after polymerization [61, 76–78] as shown in **Figure 20**.

time, and dielectric properties of PSLC films [79].

**Figure 20.**

**32**

*Polymer stabilized liquid crystal.*

interconnected, interpenetrating and mitigated polymer network can be obtained

Because of application of electric field during photopolymerization, oriented LC domains are formed. Also, this controlled alignment of the LC molecules between polymer networks has significant effect on the transmittance, absorbance, response

layer is needed [72].

**5. Polymer-stabilized liquid crystal**

*Liquid Crystals and Display Technology*

**Figure 21** shows POM images of PSLC films which are prepared using LC BL036 and prepolymer NOA-65 in 95/5 wt/wt% ratio under different rubbing directions and in the absence and presence of electric field [80].

**Figure 21** shows the POM image of four types of PSLC films named as "A" (antiparallel rubbing; electric field absent), "B" (antiparallel rubbing; electric field present), "C" (twisted rubbing; electric field absent) and "D" (twisted rubbing; electric field present). On the acute observation of these images in all the four samples, complex geometrical structures of LC and polymer network were found. Samples A and C which were prepared without applying any electric field during polymerization showed rectilinear alignment. Since polymer network has a strong aligning effect on the LC, therefore it tends to keep LC in the aligned state [81]. In these films, polymer chains move throughout the sample parallel to the rubbing direction; therefore shorter chains with smaller domains entrapped between them were observed. In the case of samples B and D, which were prepared by applying electric field during polymerization, bigger LC domains were formed. Upon application of electric field during sample preparation, LC material orients and often indefinitely retains the alignment imposed by an electric field [82]. Because of the adsorption of LC droplets at the polymer wall, polymer network grows in the direction of field. Due to which cross linked, thicker and topologically defective polymeric walls were formed. Also, diffraction of light was observed from polymer nodules.

The effect of electric field on the orientation and confirmation of the LC material between the boundaries of polymer network gives deep insight in understanding PSLC film behaviour.

#### **Figure 21.**

*POM images of homogenously aligned PSLC films: (A) antiparallel rubbing cured without any voltage, (B) antiparallel rubbing cured by applying 10 V, (C) 90° twist rubbing cured without any voltage and (D) 90° twist rubbing cured by applying 10 V, observed using 5 objective.*

**Figure 22** shows effect of electric field on sample A, prepared with antiparallel rubbing direction and in the absence of field. Upon application of low electric field of �10 V, change in color was observed, which indicates change in refractive index. The change in refractive index is basically due to orientation of LC molecules in the domains. Also �10 V vivid polymeric boundaries were made visible due to adsorption of LC molecules on frozen polymer network. On the application of high electric field of �40 V and above, dark homeotropic state with the LC directors aligned

*An Overview of Polymer-Dispersed Liquid Crystal Composite Films and Their Applications*

The voltage-transmittance curve (**Figure 23**) of PSLC film indicates that it follows an opposite trend to that of the PDLC films. It is clear from the graph that PSLC film has maximum transmittance (*T*OFF) when no voltage is applied. Upon application of electric field, the LC orientation changes from planar to homeotropic

At a particular voltage, transmittance of PSLC decreases by additional 10% of the OFF-state transmittance; this voltage is termed as threshold voltage (*V*TH). With the further increase in voltage, the polarization state of light is perpendicular to the analyser which gives dark state or minimum transmittance (*T*ON) state. A definite value of voltage at which PSLC film achieve *T*OFF state is termed as ON-

The ratio of maximum to minimum transmittance gives contrast ratio (CR) of the film, and difference between maximum and minimum transmittance gives

CR <sup>¼</sup> *<sup>T</sup>*OFFð Þ %

**Table 2** gives voltage-transmittance data of PSLC film prepared using monomer

*<sup>T</sup>*ONð Þ % (11)

*ΔT*ð Þ¼ % *T*OFFð Þ� % *T*ONð Þ % (12)

state of alignment, and the transmission decreases rapidly for PSLC film.

perpendicular to the substrate surface was observed [83].

*DOI: http://dx.doi.org/10.5772/intechopen.91889*

state voltage (*V*ON) condition.

transmittance difference (Δ*T*). Mathematically

NOA-65 and LC BL036 in 95/5 wt/wt%.

**Figure 23.**

**35**

*Transmittance vs. voltage curve of PSLC film.*

**5.2 Voltage dependence of transmittance at fixed frequency**

**Figure 22.**

*Effect of voltage on homogenously aligned PSLC film sample A (anti-parallel rubbing; electric field absent during polymerization) observed at (a) 0 V, (b) 2 V, (c) 6 V, (d) 10 V, (e) 20 V (f) 40 V, (g) 60 V and (h) 80 V using 5 objective lens.*

*An Overview of Polymer-Dispersed Liquid Crystal Composite Films and Their Applications DOI: http://dx.doi.org/10.5772/intechopen.91889*

**Figure 22** shows effect of electric field on sample A, prepared with antiparallel rubbing direction and in the absence of field. Upon application of low electric field of �10 V, change in color was observed, which indicates change in refractive index. The change in refractive index is basically due to orientation of LC molecules in the domains. Also �10 V vivid polymeric boundaries were made visible due to adsorption of LC molecules on frozen polymer network. On the application of high electric field of �40 V and above, dark homeotropic state with the LC directors aligned perpendicular to the substrate surface was observed [83].

#### **5.2 Voltage dependence of transmittance at fixed frequency**

The voltage-transmittance curve (**Figure 23**) of PSLC film indicates that it follows an opposite trend to that of the PDLC films. It is clear from the graph that PSLC film has maximum transmittance (*T*OFF) when no voltage is applied. Upon application of electric field, the LC orientation changes from planar to homeotropic state of alignment, and the transmission decreases rapidly for PSLC film.

At a particular voltage, transmittance of PSLC decreases by additional 10% of the OFF-state transmittance; this voltage is termed as threshold voltage (*V*TH). With the further increase in voltage, the polarization state of light is perpendicular to the analyser which gives dark state or minimum transmittance (*T*ON) state. A definite value of voltage at which PSLC film achieve *T*OFF state is termed as ONstate voltage (*V*ON) condition.

The ratio of maximum to minimum transmittance gives contrast ratio (CR) of the film, and difference between maximum and minimum transmittance gives transmittance difference (Δ*T*). Mathematically

$$\text{CR} = \frac{T\_{\text{OFF}}(\text{@})}{T\_{\text{ON}}(\text{@})} \tag{11}$$

$$
\Delta T(\text{@}) = T\_{\text{OFF}}(\text{@}) - T\_{\text{ON}}(\text{@}) \tag{12}
$$

**Table 2** gives voltage-transmittance data of PSLC film prepared using monomer NOA-65 and LC BL036 in 95/5 wt/wt%.

**Figure 23.** *Transmittance vs. voltage curve of PSLC film.*

**Figure 22.**

**34**

*(h) 80 V using 5 objective lens.*

*Liquid Crystals and Display Technology*

*Effect of voltage on homogenously aligned PSLC film sample A (anti-parallel rubbing; electric field absent during polymerization) observed at (a) 0 V, (b) 2 V, (c) 6 V, (d) 10 V, (e) 20 V (f) 40 V, (g) 60 V and*


**Table 2.**

*Voltage-transmittance data of PSLC film prepared using monomer NOA-65 and LC BL036 in 95/5 wt/wt% ratio.*

### **5.3 Hysteresis effect**

In a scan up cycle, as voltage increases from 0 V to *V*max, transmittance of PSLC films decreases from *T*OFF to *T*ON, whereas in scan down cycle as voltage decreases from *V*ON to 0 V, transmittance increases from *T*ON to *T*OFF, but it does not follow the same path. The above observed phenomenon is termed as hysteresis and should be minimized for better electro-optic properties. It was observed that at a given voltage, transmittance for scan up cycle was higher than the transmittance for scan down cycle. A measure of hysteresis is given by the voltage width at half of maximum transmittance (Δ*V*50). The hysteresis behaviour of a PSLC composite film is shown in **Figure 24**. Also, hysteresis effect was not observed at high fields because at higher voltages of scan down cycle, LC domains remain in the same state of orientation. However, when the applied field is reduced further, reorientation of LC domains begins, giving rise to hysteresis effect.

**5.5 Dielectric properties of polymer-LC composite films**

*Rise and decay time vs. voltage curve of PSLC film.*

*DOI: http://dx.doi.org/10.5772/intechopen.91889*

Polymer-LC composite films are complex heterogeneous system, holding intrin-

sic anisotropy of LC and polymer. In order to gather the information about the structure, alignment, phase transitions and intermolecular interactions of composite films, knowledge of their dielectric properties is essential [85, 86]. For this purpose dielectric relaxation spectroscopy (DRS) is one of the best methods to measure the dielectric constant and associated parameters with high accuracy and sensitivity in polymer-LC composites. It is based on a concept of "energy storage" and resulting "relaxation" per release of this energy by the system's individual components. By developing analogy between polymer-LC composites and passive electrical circuit, polymer-LC composite films can be conveniently illustrated as a parallel plate capacitor. Here, two ITO-coated glass plates act as a parallel electrode with plate separation *d* and plate area *A*, and polymer-LC material acts as a dielectric material as shown in **Figure 26(a)**. The effective circuit of polymer-LC cell is shown below (**Figure 26(b)**), where *R*<sup>o</sup> is the resistance of electrodes and *R*LP and

*An Overview of Polymer-Dispersed Liquid Crystal Composite Films and Their Applications*

*C*LP are resistance and capacitance of polymer-LC layer, respectively.

from the formula given below:

**Figure 25.**

orientational and interfacial [87].

**37**

electric field is removed [88, 89].

The capacitance is measured, and the relative permittivity *ε<sup>r</sup>* can be calculated

*Cp* <sup>¼</sup> <sup>ε</sup>0ε*rA*

tivity *ε<sup>r</sup>* is complex quantity, also known as dielectric constant; it depends on parameters like temperature, pressure and frequency. To elucidate the frequency dependence of *εr*, we must understand the different polarization mechanisms that contribute to the dielectric constant (permittivity). In response to an applied electric field, various types of polarisations may arise, such as electronic, ionic,

a. Electronic/atomic polarization: Electronic polarization occurs when the electric field displaces the centre of a negatively charged electron cloud relative to the positive nucleus of the atom and induces a dipole moment. It has been found to be independent of frequency and vanishes as soon as the

where *<sup>ε</sup>*<sup>0</sup> <sup>¼</sup> <sup>8</sup>*:*<sup>854</sup> � <sup>10</sup>�<sup>12</sup> F/m is the permittivity of free space. Relative permit-

*<sup>d</sup>* (13)

**Figure 24.** *Hysteresis curve of PSLC film.*

#### **5.4 Response time**

Response time is the sum of rise time (*τ*r) and decay time (*τ*d). Upon application of electric field, LC molecules align along the field, and transmittance of film decreases in PSLC. The time in which transmittance of film reaches from 90–10% is termed as rise time. On the removal of field, these LC molecules relax back to their initial position. The time in which transmittance reaches from 10–90% is termed as decay time. Variation in rise and decay time of PSLC films with respect to applied voltage is shown in **Figure 25**. However, with the increase in voltage rise time shortens, but the trade-off is longer decay time [83, 84].

*An Overview of Polymer-Dispersed Liquid Crystal Composite Films and Their Applications DOI: http://dx.doi.org/10.5772/intechopen.91889*

**Figure 25.** *Rise and decay time vs. voltage curve of PSLC film.*

**5.3 Hysteresis effect**

*Liquid Crystals and Display Technology*

**Table 2.**

*ratio.*

**5.4 Response time**

*Hysteresis curve of PSLC film.*

**Figure 24.**

**36**

In a scan up cycle, as voltage increases from 0 V to *V*max, transmittance of PSLC films decreases from *T*OFF to *T*ON, whereas in scan down cycle as voltage decreases from *V*ON to 0 V, transmittance increases from *T*ON to *T*OFF, but it does not follow the same path. The above observed phenomenon is termed as hysteresis and should be minimized for better electro-optic properties. It was observed that at a given voltage, transmittance for scan up cycle was higher than the transmittance for scan down cycle. A measure of hysteresis is given by the voltage width at half of maximum transmittance (Δ*V*50). The hysteresis behaviour of a PSLC composite film is shown in **Figure 24**. Also, hysteresis effect was not observed at high fields because at higher voltages of scan down cycle, LC domains remain in the same state of orientation. However, when the applied field is reduced further, reorientation of LC domains begins, giving rise to hysteresis effect.

**Sample** *T***OFF (%)** *T***ON (%) Δ***T* **(%) CR** *V***TH (V)** *V***ON (V)** N36 83.6 0.20 83.4 418 2 25

*Voltage-transmittance data of PSLC film prepared using monomer NOA-65 and LC BL036 in 95/5 wt/wt%*

Response time is the sum of rise time (*τ*r) and decay time (*τ*d). Upon application

of electric field, LC molecules align along the field, and transmittance of film decreases in PSLC. The time in which transmittance of film reaches from 90–10% is termed as rise time. On the removal of field, these LC molecules relax back to their initial position. The time in which transmittance reaches from 10–90% is termed as decay time. Variation in rise and decay time of PSLC films with respect to applied voltage is shown in **Figure 25**. However, with the increase in voltage rise time

shortens, but the trade-off is longer decay time [83, 84].

#### **5.5 Dielectric properties of polymer-LC composite films**

Polymer-LC composite films are complex heterogeneous system, holding intrinsic anisotropy of LC and polymer. In order to gather the information about the structure, alignment, phase transitions and intermolecular interactions of composite films, knowledge of their dielectric properties is essential [85, 86]. For this purpose dielectric relaxation spectroscopy (DRS) is one of the best methods to measure the dielectric constant and associated parameters with high accuracy and sensitivity in polymer-LC composites. It is based on a concept of "energy storage" and resulting "relaxation" per release of this energy by the system's individual components. By developing analogy between polymer-LC composites and passive electrical circuit, polymer-LC composite films can be conveniently illustrated as a parallel plate capacitor. Here, two ITO-coated glass plates act as a parallel electrode with plate separation *d* and plate area *A*, and polymer-LC material acts as a dielectric material as shown in **Figure 26(a)**. The effective circuit of polymer-LC cell is shown below (**Figure 26(b)**), where *R*<sup>o</sup> is the resistance of electrodes and *R*LP and *C*LP are resistance and capacitance of polymer-LC layer, respectively.

The capacitance is measured, and the relative permittivity *ε<sup>r</sup>* can be calculated from the formula given below:

$$\mathbf{C}\_p = \frac{\mathbf{e}\_0 \mathbf{e}\_r \mathbf{A}}{d} \tag{13}$$

where *<sup>ε</sup>*<sup>0</sup> <sup>¼</sup> <sup>8</sup>*:*<sup>854</sup> � <sup>10</sup>�<sup>12</sup> F/m is the permittivity of free space. Relative permittivity *ε<sup>r</sup>* is complex quantity, also known as dielectric constant; it depends on parameters like temperature, pressure and frequency. To elucidate the frequency dependence of *εr*, we must understand the different polarization mechanisms that contribute to the dielectric constant (permittivity). In response to an applied electric field, various types of polarisations may arise, such as electronic, ionic, orientational and interfacial [87].

a. Electronic/atomic polarization: Electronic polarization occurs when the electric field displaces the centre of a negatively charged electron cloud relative to the positive nucleus of the atom and induces a dipole moment. It has been found to be independent of frequency and vanishes as soon as the electric field is removed [88, 89].

**Figure 26.** *(a) Schematic of polymer-LC composite film and (b) polymer-LC composite films as RC-circuit.*

b. Ionic/displacement polarization: Ionic polarization also called as vibrational polarization occurs in ionic substances and is related to the displacement of atoms, causing the separation of charges [90, 91].

represented by a phase difference. For this reason, dielectric constant is often treated as a complex function of the angular frequency (ω) of the applied field

*An Overview of Polymer-Dispersed Liquid Crystal Composite Films and Their Applications*

The frequency-dependent permittivity characterizes amplitude and timescale (via the relaxation time) of the charge-density fluctuations within the sample. For the evaluation of relaxation time (time required for LC droplet reorientation), dielectric permittivity is expressed as a complex function of angular frequency

ð Þ *ω* and *ε*00ð Þ *ω* are real and imaginary parts of the complex dielectric

Relaxation processes are characterized by a step-like decrease of the real part *ε*<sup>0</sup> and a peak in the imaginary part *<sup>ε</sup>*00of the complex dielectric function *<sup>ε</sup>* <sup>∗</sup> ð Þ *<sup>ω</sup>* with increasing frequency. The real part is related to stored energy also called as dispersion, whereas imaginary part is related to loss of energy or dissipation called as absorption of the system. It is reasonable to introduce here a quantity "loss tangent", which is a measure of the energy dissipated due to oscillating field also

> *tan<sup>δ</sup>* <sup>¼</sup> *<sup>ε</sup>*00ð Þ *<sup>ω</sup> ε*0

For parallel plate capacitors with ideal dielectrics, the loss angle *δ* can be

ð Þ� *ω iε*00ð Þ *ω* (14)

ð Þ ω *and* ε00ð Þ ω *denote real and imaginary*

ð Þ *<sup>ω</sup>* (15)

*<sup>ε</sup>* <sup>∗</sup> ð Þ¼ *<sup>ω</sup> <sup>ε</sup>*<sup>0</sup>

[93, 94].

**Figure 27.**

*5.5.1 Complex dielectric constant*

*A Dielectric constant Spectrum over a wide range of frequencies.* ε<sup>0</sup>

*part of the dielectric constant (relative permittivity) respectively.*

*DOI: http://dx.doi.org/10.5772/intechopen.91889*

known by dissipation factor "D" [21, 92, 95]:

graphically expressed as shown in **Figure 28**.

(*ω*) of applied field:

where *ε*<sup>0</sup>

constant.

**39**


As frequency increases the contribution from each type of polarization successively decreases because polarization can no longer follow the variation in the field. As a result, there is a decrease in dielectric constant (relative permittivity) with the increasing frequency. The frequency dependence of dielectric constant reflects the fact that a material's polarization does not respond instantaneously to an applied field. The response must always arise after the applied field which can be

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#### **Figure 27.**

b. Ionic/displacement polarization: Ionic polarization also called as vibrational polarization occurs in ionic substances and is related to the displacement of

*(a) Schematic of polymer-LC composite film and (b) polymer-LC composite films as RC-circuit.*

c. Dipolar/orientational polarization: Dipolar polarization usually occurs in materials with permanent dipoles. Under normal conditions, these materials exhibit zero net dipole moment and polarization, as the dipoles in these materials are randomly distributed/oriented. Upon application of an external electric field, the dipoles tend to orient along the direction of applied field,

resulting a non-zero net dipole moment and polarization [90, 91].

frequency dependence of various types of polarisations [90–92].

field. The response must always arise after the applied field which can be

As frequency increases the contribution from each type of polarization successively decreases because polarization can no longer follow the variation in the field. As a result, there is a decrease in dielectric constant (relative permittivity) with the increasing frequency. The frequency dependence of dielectric constant reflects the fact that a material's polarization does not respond instantaneously to an applied

d. Interfacial/translational polarization: Interfacial polarization is associated with migrating charges, by electrons or ions, over macroscopic distances in an applied field. These charges get trapped and accumulate at physical barriers such as defects, impurities, voids and grain or phase boundaries. The accumulation of charges distorts the local electric field and causes permittivity. Interfacial polarization is most prevalent in heterogeneous system like polymer-LC composites and is usually observed at lower frequencies. In general, a given dielectric material exhibits more than one polarization mechanism, and the average dipole moment in a given material is the sum of all polarization contributions. All four types of polarization occur at low frequency. Each of the above-mentioned polarization processes has specific features in the frequency and temperature dependence of the real and imaginary part of the complex dielectric permittivity. **Figure 27** shows the

atoms, causing the separation of charges [90, 91].

**Figure 26.**

*Liquid Crystals and Display Technology*

**38**

*A Dielectric constant Spectrum over a wide range of frequencies.* ε<sup>0</sup> ð Þ ω *and* ε00ð Þ ω *denote real and imaginary part of the dielectric constant (relative permittivity) respectively.*

represented by a phase difference. For this reason, dielectric constant is often treated as a complex function of the angular frequency (ω) of the applied field [93, 94].

#### *5.5.1 Complex dielectric constant*

The frequency-dependent permittivity characterizes amplitude and timescale (via the relaxation time) of the charge-density fluctuations within the sample. For the evaluation of relaxation time (time required for LC droplet reorientation), dielectric permittivity is expressed as a complex function of angular frequency (*ω*) of applied field:

$$\text{i.e.}^\*(a) = \text{i.e.}^\prime(a) - i\varepsilon^\prime(a) \tag{14}$$

where *ε*<sup>0</sup> ð Þ *ω* and *ε*00ð Þ *ω* are real and imaginary parts of the complex dielectric constant.

Relaxation processes are characterized by a step-like decrease of the real part *ε*<sup>0</sup> and a peak in the imaginary part *<sup>ε</sup>*00of the complex dielectric function *<sup>ε</sup>* <sup>∗</sup> ð Þ *<sup>ω</sup>* with increasing frequency. The real part is related to stored energy also called as dispersion, whereas imaginary part is related to loss of energy or dissipation called as absorption of the system. It is reasonable to introduce here a quantity "loss tangent", which is a measure of the energy dissipated due to oscillating field also known by dissipation factor "D" [21, 92, 95]:

$$
tan \delta = \frac{\varepsilon''(o)}{\varepsilon'(o)}\tag{15}$$

For parallel plate capacitors with ideal dielectrics, the loss angle *δ* can be graphically expressed as shown in **Figure 28**.

Here, *V* is the applied voltage and *I*<sup>c</sup> and *I*<sup>R</sup> are the vector components of current *I*. The current *I*<sup>c</sup> represents a non-lossy capacitive current proportional to the charge stored in the capacitor; it is frequency dependent and leads voltage by 90°. The current IR is the alternating conduction current in phase with the applied voltage *V*, which represents the energy loss or power dissipated in the dielectric [96]. If ψ is the phase difference between the potential and current, then

$$
\delta = \Re \mathbf{0} - \boldsymbol{\mu} \tag{16}
$$

*ε*0

*DOI: http://dx.doi.org/10.5772/intechopen.91889*

**Figure 29(a)** and **(b)**, respectively.

been used, given by the equation

**Figure 29.**

*PSLC film.*

**41**

*<sup>ε</sup>* <sup>∗</sup> ð Þ¼ *<sup>ω</sup> <sup>ε</sup>*<sup>0</sup>

ð Þ¼ *ω ε*<sup>∞</sup> þ

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*<sup>ε</sup>* <sup>∗</sup> ð Þ¼ *<sup>ω</sup> <sup>ε</sup>*<sup>∞</sup> <sup>þ</sup>

*<sup>ε</sup>*00ð Þ¼ *<sup>ω</sup> δε*<sup>0</sup> ð Þ*ωτ*

Debye relaxation is usually expressed in terms of the complex dielectric constant *<sup>ε</sup>* <sup>∗</sup> ð Þ *<sup>ω</sup>* of a medium. On putting values from Eqs. (18) and (19) in (14), we get:

where *δε*<sup>0</sup> ¼ *ε<sup>s</sup>* � *ε*<sup>∞</sup> is dielectric strength of the material, which is the voltage a material can withstand before breakdown occurs. *ε<sup>s</sup>* and *ε*<sup>∞</sup> are static (at 20 Hz frequency) and optical (at relaxation frequency *f*) values of the relative dielectric constant, respectively, which were obtained by experimental relaxation spectra [91, 99–101]. The frequency dependence of real and imaginary components of complex dielectric constant of PSLC film is shown in

b. Cole-Cole model: To describe secondary relaxations, Cole-Cole model has

ð Þ� *ω iε*00ð Þ¼ *ω ε*<sup>∞</sup> þ

*Frequency dependence of (a) real component and (b) imaginary component of complex dielectric constant of*

where *α* is known as the distribution parameter and other terms are the same as in Debye model. The exponent *α* characterizes the breadth of the relaxation time distribution and ranges from 0 (infinitely broad distribution) to 1 (Debye's single relaxation time limit), describing different spectral shapes. When *α* = 0, the Cole-Cole model reduces to the Debye model. The graph drawn between imaginary part *<sup>ε</sup>*″ and the real part <sup>ε</sup><sup>0</sup> of the dielectric constant with frequency as a parameter, shown in **Figure 30**, is known as a Cole-Cole plot [102, 103]. It is useful for the interpretation of molecular dynamics of materials which possess one or more well-separated relaxation processes with comparable magnitudes. How well the *<sup>ε</sup>*<sup>0</sup> and <sup>ε</sup>″ are fitted to form semicircle is an indication of the nature of relaxation behaviour. All the above-mentioned parameters were determined from fitting the experimental data of dielectric spectra with

*δε*<sup>0</sup> ð Þ

*δε*<sup>0</sup> ð Þ

<sup>1</sup> <sup>þ</sup> *<sup>ω</sup>*<sup>2</sup>*τ*<sup>2</sup> (18)

<sup>1</sup> <sup>þ</sup> *<sup>ω</sup>*<sup>2</sup>*τ*<sup>2</sup> (19)

<sup>1</sup> <sup>þ</sup> ð Þ *<sup>i</sup>ωτ* (20)

*δε*<sup>0</sup> ð Þ

<sup>1</sup> <sup>þ</sup> ð Þ *<sup>i</sup>ωτ* <sup>1</sup>�*<sup>α</sup>* (21)

To promote maximum energy storage in a capacitor, the dielectric loss, originating from interfacial, dipolar, distortional and conduction losses, should be minimal [87]. In general, dielectric loss increases with increase in humidity, temperature, frequency and amplitude of the applied voltage for most of the materials.

#### *5.5.2 Macroscopic models for dielectric spectra*

Dielectric relaxation processes are usually analyzed using model functions. Starting from the Debye function, several formulas for both the frequency and the time domain have been suggested to describe the experimentally observed spectra. The most important approaches are discussed below [97, 98].

a. Debye model: It is a method to study the dielectric behaviour of a material by measuring the complex dielectric permittivity versus frequency at constant temperature and ambient pressure. As the dielectric spectrum is obtained in a frequency domain, it is called as a frequency domain dielectric spectroscopy (FDDS). If a single relaxation is considered, it is known as Debye-type relaxation, and the time assumed for it is Debye relaxation time which is inversely related to the critical relaxation frequency. It is the point where dissipation factor is maximum. The relaxation frequency *f* is related to relaxation time τ by the relation

$$
\pi = \frac{1}{\alpha} = \frac{1}{2\pi f} \tag{17}
$$

The dispersion and absorption terms for single relaxation as a function of the field angular frequency ω and relaxation time τ are given as

**Figure 28.** *Graphical representation of loss tangent.*

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$$
\varepsilon'(o) = \varepsilon\_{\infty} + \frac{(\delta \varepsilon')}{1 + o^2 \tau^2} \tag{18}
$$

$$
\epsilon''(\boldsymbol{\omega}) = \frac{(\delta \epsilon')\alpha \sigma}{1 + \alpha^2 \sigma^2} \tag{19}
$$

Debye relaxation is usually expressed in terms of the complex dielectric constant *<sup>ε</sup>* <sup>∗</sup> ð Þ *<sup>ω</sup>* of a medium. On putting values from Eqs. (18) and (19) in (14), we get:

$$
\varepsilon^\*\left(w\right) = \varepsilon\_\infty + \frac{(\delta\varepsilon')}{1 + (i\alpha\tau)}\tag{20}
$$

where *δε*<sup>0</sup> ¼ *ε<sup>s</sup>* � *ε*<sup>∞</sup> is dielectric strength of the material, which is the voltage a material can withstand before breakdown occurs. *ε<sup>s</sup>* and *ε*<sup>∞</sup> are static (at 20 Hz frequency) and optical (at relaxation frequency *f*) values of the relative dielectric constant, respectively, which were obtained by experimental relaxation spectra [91, 99–101]. The frequency dependence of real and imaginary components of complex dielectric constant of PSLC film is shown in **Figure 29(a)** and **(b)**, respectively.

b. Cole-Cole model: To describe secondary relaxations, Cole-Cole model has been used, given by the equation

$$\varepsilon^\*\left(a\right) = \varepsilon'(a) - i\varepsilon''(a) = \varepsilon\_\infty + \frac{\left(\delta\varepsilon'\right)}{\mathbf{1} + \left(i\alpha\tau\right)^{1-a}}\tag{21}$$

where *α* is known as the distribution parameter and other terms are the same as in Debye model. The exponent *α* characterizes the breadth of the relaxation time distribution and ranges from 0 (infinitely broad distribution) to 1 (Debye's single relaxation time limit), describing different spectral shapes. When *α* = 0, the Cole-Cole model reduces to the Debye model. The graph drawn between imaginary part *<sup>ε</sup>*″ and the real part <sup>ε</sup><sup>0</sup> of the dielectric constant with frequency as a parameter, shown in **Figure 30**, is known as a Cole-Cole plot [102, 103]. It is useful for the interpretation of molecular dynamics of materials which possess one or more well-separated relaxation processes with comparable magnitudes. How well the *<sup>ε</sup>*<sup>0</sup> and <sup>ε</sup>″ are fitted to form semicircle is an indication of the nature of relaxation behaviour. All the above-mentioned parameters were determined from fitting the experimental data of dielectric spectra with

**Figure 29.** *Frequency dependence of (a) real component and (b) imaginary component of complex dielectric constant of PSLC film.*

Here, *V* is the applied voltage and *I*<sup>c</sup> and *I*<sup>R</sup> are the vector components of current *I*. The current *I*<sup>c</sup> represents a non-lossy capacitive current proportional to the charge stored in the capacitor; it is frequency dependent and leads voltage by 90°. The current IR is the alternating conduction current in phase with the applied voltage *V*, which represents the energy loss or power dissipated in the dielectric [96]. If ψ is

To promote maximum energy storage in a capacitor, the dielectric loss, originating from interfacial, dipolar, distortional and conduction losses, should be min-

Dielectric relaxation processes are usually analyzed using model functions. Starting from the Debye function, several formulas for both the frequency and the time domain have been suggested to describe the experimentally observed spectra.

a. Debye model: It is a method to study the dielectric behaviour of a material by measuring the complex dielectric permittivity versus frequency at constant temperature and ambient pressure. As the dielectric spectrum is obtained in a frequency domain, it is called as a frequency domain dielectric spectroscopy (FDDS). If a single relaxation is considered, it is known as Debye-type relaxation, and the time assumed for it is Debye relaxation time which is inversely related to the critical relaxation frequency. It is the point where dissipation factor is maximum. The relaxation frequency *f* is related to relaxation time τ by the relation

*<sup>τ</sup>* <sup>¼</sup> <sup>1</sup>

field angular frequency ω and relaxation time τ are given as

*<sup>ω</sup>* <sup>¼</sup> <sup>1</sup>

The dispersion and absorption terms for single relaxation as a function of the

imal [87]. In general, dielectric loss increases with increase in humidity, temperature, frequency and amplitude of the applied voltage for most of the

*δ* ¼ 90 � *ψ* (16)

<sup>2</sup>*π<sup>f</sup>* (17)

the phase difference between the potential and current, then

The most important approaches are discussed below [97, 98].

*5.5.2 Macroscopic models for dielectric spectra*

*Liquid Crystals and Display Technology*

materials.

**Figure 28.**

**40**

*Graphical representation of loss tangent.*

**Figure 30.** *Cole-Cole plot of PSLC film at 25°C temperature.*


**Table 3.**

*Fitting parameters of various PSLC films.*

Cole-Cole approach of the Debye equation and are shown in **Table 3**. The frequency corresponding to the top point of this semicircle curve is the relaxation frequency *f* of orientational polarization of LC domains. At this point dielectric heating is maximum due to which dissipation factor is also maximum. The angle φ between arc radius and ε<sup>0</sup> -axis gives distribution parameter *α*:

$$
\varphi = \frac{a\pi}{2} \tag{22}
$$

optically isotropic polymer matrix first introduced by Fergason in 1984 [61, 113, 114]. The composite of these two is technologically very important because it encompasses various unique properties of LCs, which are mechanically and structurally strengthened by polymer matrix. The operation of these composite films is based on birefringence property of LC. For LC with positive birefringence, *Δn*>0, in the OFF state as the LC droplets are randomly oriented, light repetitively refract/ scatters at multiple polymer-LC interfaces. Due to which most of the light incident on PDLC device scatters, and the film becomes/appears opaque (**Figure 31(a)**). On the contrary, in the ON state as the directors in LC droplets align along the direction of electric field and if the RI, *np* of polymer matrix, matches with the ordinary RI, *no* of LC, most of the normally incident light on PDLC device behaves as an ordinary light and transmits through it, and the film becomes a transparent one [22, 115] (**Figure 31(b)**). In a similar manner, for LC with negative birefringence, Δ*n* < 0, in the ON state extraordinary RI *ne* comes into picture [34]. The LC droplet structure, their interaction with the polymer matrix and their optical and dielectric anisotropy play crucial role in shaping/modeling system properties. Although LC droplets are spherical in shape, they get deformed when embedded inside a polymer matrix. The polymer is supposed to act as a mere matrix for the LC aggregates, but their physical interactions can influence the formation of mesophases. The LC droplet morphology depends on many physical parameters such as refractive indices, conductivity, type and proportion of materials used, phase separation method, rate of diffusion, viscosity and solubility of the LC in the polymer, addition of dopant or dye molecules, etc. [116–121]. Unlike other LC technologies, PDLC do not require alignment layers and polarizers. This reduces cost; simplifies design; increases device lifetime in high-temperature and highhumidity conditions; increases transmittance, contrast ratio, flexibility and mechanical strength; and reduces response time. Also, the large surface-tovolume ratio of the composite film supports the construction of large area

*An Overview of Polymer-Dispersed Liquid Crystal Composite Films and Their Applications*

*DOI: http://dx.doi.org/10.5772/intechopen.91889*

PDLC devices [19].

**6.1 Fabrication of PDLC films**

*PDLC in (a) OFF state and (b) ON state.*

encapsulation.

**43**

**Figure 31.**

For the uniform dispersion of micron-sized nematic LC droplets inside polymer matrix, principally two methods have been enlisted, namely, phase separation and

If the centre of the semicircle lies on the ε<sup>0</sup> -axis, then the distribution parameter *α* = 0 (Debye type), and if the centre is below the ε<sup>0</sup> -axis, then *α* 6¼ 0 (non-Debye type), while if *α* > 0.5, there could be more than one relaxation process. The calculated value of *α* indicates that the PSLC film exhibits non-Debyetype relaxation process [104–106].

#### **5.6 Conclusions of PSLC study**

PSLC is a reverse to the conventional PDLC but identical to the twisted nematic liquid crystal cell having maximum and minimum transmittance under crossed polarizer in the OFF and ON states, respectively. However, the threshold voltages of PSLC are much lower than TNLC [107–109]. The PSLC are useful for bi-stable reflective displays and normal- and reverse-mode light shutters [68, 110]. In order to improve electro-optic responses of PSLC devices, LC material are doped with dye and nanoparticles [111, 112].

### **6. Polymer-dispersed liquid crystal**

Polymer-dispersed liquid crystal is a smart, inhomogeneous thin composite film of micron-sized nematic LC droplets, randomly dispersed and embedded in

*An Overview of Polymer-Dispersed Liquid Crystal Composite Films and Their Applications DOI: http://dx.doi.org/10.5772/intechopen.91889*

optically isotropic polymer matrix first introduced by Fergason in 1984 [61, 113, 114]. The composite of these two is technologically very important because it encompasses various unique properties of LCs, which are mechanically and structurally strengthened by polymer matrix. The operation of these composite films is based on birefringence property of LC. For LC with positive birefringence, *Δn*>0, in the OFF state as the LC droplets are randomly oriented, light repetitively refract/ scatters at multiple polymer-LC interfaces. Due to which most of the light incident on PDLC device scatters, and the film becomes/appears opaque (**Figure 31(a)**). On the contrary, in the ON state as the directors in LC droplets align along the direction of electric field and if the RI, *np* of polymer matrix, matches with the ordinary RI, *no* of LC, most of the normally incident light on PDLC device behaves as an ordinary light and transmits through it, and the film becomes a transparent one [22, 115] (**Figure 31(b)**). In a similar manner, for LC with negative birefringence, Δ*n* < 0, in the ON state extraordinary RI *ne* comes into picture [34]. The LC droplet structure, their interaction with the polymer matrix and their optical and dielectric anisotropy play crucial role in shaping/modeling system properties. Although LC droplets are spherical in shape, they get deformed when embedded inside a polymer matrix. The polymer is supposed to act as a mere matrix for the LC aggregates, but their physical interactions can influence the formation of mesophases. The LC droplet morphology depends on many physical parameters such as refractive indices, conductivity, type and proportion of materials used, phase separation method, rate of diffusion, viscosity and solubility of the LC in the polymer, addition of dopant or dye molecules, etc. [116–121]. Unlike other LC technologies, PDLC do not require alignment layers and polarizers. This reduces cost; simplifies design; increases device lifetime in high-temperature and highhumidity conditions; increases transmittance, contrast ratio, flexibility and mechanical strength; and reduces response time. Also, the large surface-tovolume ratio of the composite film supports the construction of large area PDLC devices [19].

**Figure 31.** *PDLC in (a) OFF state and (b) ON state.*

#### **6.1 Fabrication of PDLC films**

For the uniform dispersion of micron-sized nematic LC droplets inside polymer matrix, principally two methods have been enlisted, namely, phase separation and encapsulation.

Cole-Cole approach of the Debye equation and are shown in **Table 3**. The frequency corresponding to the top point of this semicircle curve is the relaxation frequency *f* of orientational polarization of LC domains. At this point dielectric heating is maximum due to which dissipation factor is also maximum.

**Sample** *f* **(MHz)** *ε<sup>s</sup> ε***<sup>∞</sup>** *δε*<sup>0</sup> *τ* **(s)** *α* **A** 13.2 29.9 2.53 27.4 1.21 E � 08 0.022

*<sup>φ</sup>* <sup>¼</sup> *απ*

Debye type), while if *α* > 0.5, there could be more than one relaxation process. The calculated value of *α* indicates that the PSLC film exhibits non-Debye-

PSLC is a reverse to the conventional PDLC but identical to the twisted nematic liquid crystal cell having maximum and minimum transmittance under crossed polarizer in the OFF and ON states, respectively. However, the threshold voltages of PSLC are much lower than TNLC [107–109]. The PSLC are useful for bi-stable reflective displays and normal- and reverse-mode light shutters [68, 110]. In order to improve electro-optic responses of PSLC devices, LC material are doped with dye

Polymer-dispersed liquid crystal is a smart, inhomogeneous thin composite film

of micron-sized nematic LC droplets, randomly dispersed and embedded in


<sup>2</sup> (22)



The angle φ between arc radius and ε<sup>0</sup>

*Cole-Cole plot of PSLC film at 25°C temperature.*

*Liquid Crystals and Display Technology*

*Fitting parameters of various PSLC films.*

type relaxation process [104–106].

**5.6 Conclusions of PSLC study**

**Figure 30.**

**Table 3.**

and nanoparticles [111, 112].

**42**

**6. Polymer-dispersed liquid crystal**

If the centre of the semicircle lies on the ε<sup>0</sup>

eter *α* = 0 (Debye type), and if the centre is below the ε<sup>0</sup>
