**3.4 Viscosity**

The dynamics of LC is described by (i) velocities of the centres of the molecules *v* and (ii) director field *n*^. Generally, these variables obey equation of continuity in incompressible liquids, Navier–Stokes equation in anisotropic viscous liquid and the equation of rotation of director in nematic LC. While dealing with the rotation of director, backflow effect should be considered, which states that the rotation of molecules (after removing external field) induces a macroscopic translational motion in LCs. However, the mathematics associated with the above-mentioned equations is insufficient to explain the viscosity behaviour of different LC substances and their mixtures. But in order to develop new liquid crystalline low-viscosity materials, the following phenomenological rules should be remembered [39]:


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

5.Replacement of phenyl ring by a trans-cyclohexane ring results in reduced viscosity values.

The most useful compounds for reducing viscosity in LC materials are cyclohexane derivatives due to their high clearing temperature, good solubility and low viscosity.

#### **3.5 LC in electric and magnetic field**

The dependence of the free energy "*F*" of nematic LC on gradients of the director field is a unique property of LC. Therefore, the measurement of elastic constants in LC is a very crucial part in LC studies. The idea behind *Kii* measurement is related to the registration of spatial distortions in structure induced by different factors such as electric field, magnetic field and thermal and surface fluctuations for which the following methods can be employed:


constants in elastic energy. For nematic LCs, it is assumed that change in elastic energy is only due to splay, twist and bend type deformation (**Figure 13**). The increase of free energy F due to these deformations is described by the continuum theory. This theory was first developed by Oseen and Zocher and later reformulated by Frank. It was based on the balance laws for linear and angular momentum [4, 42]. The contribution of each deformation to the overall energy F is given by

<sup>2</sup> <sup>þ</sup> *<sup>K</sup>*22ð Þ *<sup>n</sup>:*<sup>∇</sup> � *<sup>n</sup>*

where *K*11, *K*<sup>22</sup> and *K*<sup>33</sup> are proportionality constants of splay, twist and bend deformations, respectively, often known as Frank elastic constants [19]. They were forced to splay, twist and bend until equilibrium. When the system is in equilibrium, it is in minimum energy state [15]. Other types of deformation are forbidden

The dynamics of LC is described by (i) velocities of the centres of the molecules *v* and (ii) director field *n*^. Generally, these variables obey equation of continuity in incompressible liquids, Navier–Stokes equation in anisotropic viscous liquid and the equation of rotation of director in nematic LC. While dealing with the rotation of director, backflow effect should be considered, which states that the rotation of molecules (after removing external field) induces a macroscopic translational motion in LCs. However, the mathematics associated with the above-mentioned equations is insufficient to explain the viscosity behaviour of different LC substances and their mixtures. But in order to develop new liquid crystalline low-viscosity materials, the following phenomenological rules should be

1.Alkyl end groups provide lower values of viscosity than alkoxy and acyloxy

3. Introducing the rings with heteroatoms increases viscosity compared to phenyl

4.The most viscous bridging groups are the ester group ▬COO▬, the simple bond

<sup>2</sup> h i

<sup>2</sup> <sup>þ</sup> *<sup>K</sup>*33ð Þ *<sup>n</sup>* � <sup>∇</sup> � *<sup>n</sup>*

(8)

*<sup>F</sup>* <sup>¼</sup> <sup>1</sup> 2

*(a) Splay, (b) twist and (c) bend deformation.*

*Liquid Crystals and Display Technology*

due to the symmetry and absent polarity.

**3.4 Viscosity**

**Figure 13.**

remembered [39]:

end groups.

analogues.

**24**

*K*11ð Þ ∇*:n*

2.The viscosity is lower for shorter molecules.

(as in biphenyls) and the ethane group ▬CH]CH▬.


Out of which the optical method based on Freedericksz transition is the simplest and most significant from the application point of view [40].

#### *3.5.1 Freedericksz transition*

In the absence of any surface alignment or external field, LC directors of nematic molecules are free to point in any direction. However, it is possible to force the director to point in a specific direction by introducing an outside agent to the system. For example, when a thin layer of polymer (usually a polyimide (PI)) is coated on a glass substrate and rubbed in a single direction with a velvet cloth, it is observed that LC molecules in contact with that surface get aligned along the rubbing direction and achieve uniform director configuration. Upon application of magnetic or electric field for any distortion to occur (to overcome the elastic and viscoelastic forces of LC), the strength of the applied field has to be larger than certain threshold value [21]. Initially, when electric field is low, no change in alignment occurs. However, as we increase electric field above threshold, the LC director changes its orientation from one molecule to the next, and deformation occurs. This threshold is called the Freedericksz threshold, and the transition from a uniform director configuration to deformed director configuration is named as Freedericksz transition. To find out various elastic constants, we need to understand geometry of confined LC molecules and applied external field. The external field may be either electric or magnetic; it is more convenient and accurate to record electric field because measurement of magnetic field near to the sample is a tricky procedure due to the field inhomogeneity, and temperature dependence of Hall probe, etc.

Consider two, coated and rubbed (along *X* direction), conducting glass plates, separated by a distance "*d*". Due to this, LC director tends to align along the direction parallel to the flat surface (*X* direction). Now we consider the following cases which give rise to splay, bend and twist geometries [20].

#### *3.5.1.1 Twist geometry*

An electric field is applied perpendicular to the *x*-axis. Let this be the *y*-axis. If the anisotropy of the dielectric susceptibility is positive, then the director tends to align along the direction of electric field, rotating away from the *x*-axis towards the *y*-axis. Let us call the angle between the director and the *x*-axis be θ. If we consider the dimensions of the flat pieces of glass to be much larger than the separation, then *θ* should not be a function of *x* or *y* but should depend on *z* (an axis normal to the surfaces of the glass). This geometry is illustrated in **Figure 14**.

*Et* <sup>¼</sup> *<sup>π</sup> d*

*Bt* <sup>¼</sup> *<sup>π</sup> d*

diamagnetic susceptibility.

**Figure 16.**

(planar) and homeotropic.

*3.6.1 Homogeneous alignment*

**27**

**3.6 Alignment of liquid crystals**

*reorientation, (c) deformation induced by electric field.*

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

ffiffiffiffiffiffiffiffiffiffi *Kii* ε0Δε

ffiffiffiffiffiffiffiffiffiffiffiffiffi *Kii μ*�<sup>1</sup> <sup>0</sup> *Δχ*

(9)

(10)

r

*Bend deformation in nematic LC molecules: (a) initially oriented homeotropic cell, (b) sketch of molecular*

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

s

where *Kii* is elastic constant; *ii* = 11, 22, 33 corresponds to splay, bend and twist deformations respectively; *μ*<sup>0</sup> is permeability of free space and *Δχ* is anisotropic

To manufacture LC device with desired electro-optic (EO) effect, confinement and alignment of LC molecules in a specific direction is very essential. Mauguin reported that LC domains could be aligned by placing them in contact with a crystal surface. The structure of LC nearby interface is different from that in the bulk. The interfacial LC molecules change the boundary conditions and influence the LC in bulk. By controlling the LC directors at the surface, reproducible director orientations can be obtained. The different interaction (anchoring) conditions of LC molecules with their neighboring phase (solid substrate) give rise to different types of liquid crystal display (LCD) devices with varied properties [4, 31, 38, 43–46]. Various types of LC molecule alignment can be induced by treating the supporting substrate differently. The most common types of alignment are homogeneous

This is also called as planar alignment (**Figure 17(a)**). Here, directors of LC molecules are oriented parallel to the electrode surface. Homogeneous alignment refers to the unidirectional orientation of the molecular axis in the planar mode and displays birefringence with excellent optical quality [47]. It can be achieved using surface treatment methods, such as obliquely evaporated SiO*x* layers, Langmuir– Blodgett films, photoalignment and rubbed polymer films [48–50]. Out of which photoalignment and mechanical rubbing are more promising techniques. In photoalignment, materials like polyvinyl alcohol (PVA) or polyvinyl cinnamate (PVC) are coated on indium tin oxide (ITO)-coated glass plates. These materials are illuminated with polarized ultraviolet light, which forces the LC directors to align parallel to the specific surface direction. Another method is rubbing, invented by Mauguin in 1911; in this method electrode is coated with transparent polymeric

**Figure 14.**

*Twist deformation in nematic LC molecules: (a) initially oriented planar cell, (b) sketch of molecular reorientation, and (c) deformation induced by electric field.*

#### *3.5.1.2 Splay geometry*

A director is oriented along the *x*-axis, but now the electric field is applied in the *z* direction. The director now has *x* and *z* components, and *θ*(*z*) is measured from the *x*-axis to the director in the *xz* plane as shown in **Figure 15**.

**Figure 15.**

*Splay deformation in nematic LC molecules: (a) initially oriented planar cell, (b) sketch of molecular reorientation, and (c) deformation induced by electric field.*

#### *3.5.1.3 Bend geometry*

The last geometry also involves both splay and bend. As shown in **Figure 16**, the boundary conditions are such that the undistorted director points along the *z*-axis and the electric field is applied along the *x*-axis. The angle *θ*(*z*) now is measured from the *z*-axis to the director in the *xz* plane.

The threshold value for deformations of the director *n*^ in the electric (*Et*) and magnetic field (*Bt*) is given by

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

**Figure 16.**

*3.5.1.1 Twist geometry*

*Liquid Crystals and Display Technology*

*3.5.1.2 Splay geometry*

**Figure 14.**

*3.5.1.3 Bend geometry*

**Figure 15.**

**26**

from the *z*-axis to the director in the *xz* plane.

*reorientation, and (c) deformation induced by electric field.*

magnetic field (*Bt*) is given by

An electric field is applied perpendicular to the *x*-axis. Let this be the *y*-axis. If the anisotropy of the dielectric susceptibility is positive, then the director tends to align along the direction of electric field, rotating away from the *x*-axis towards the *y*-axis. Let us call the angle between the director and the *x*-axis be θ. If we consider the dimensions of the flat pieces of glass to be much larger than the separation, then *θ* should not be a function of *x* or *y* but should depend on *z* (an axis normal to the

A director is oriented along the *x*-axis, but now the electric field is applied in the *z* direction. The director now has *x* and *z* components, and *θ*(*z*) is measured from

*Twist deformation in nematic LC molecules: (a) initially oriented planar cell, (b) sketch of molecular*

The last geometry also involves both splay and bend. As shown in **Figure 16**, the boundary conditions are such that the undistorted director points along the *z*-axis and the electric field is applied along the *x*-axis. The angle *θ*(*z*) now is measured

*Splay deformation in nematic LC molecules: (a) initially oriented planar cell, (b) sketch of molecular*

The threshold value for deformations of the director *n*^ in the electric (*Et*) and

surfaces of the glass). This geometry is illustrated in **Figure 14**.

the *x*-axis to the director in the *xz* plane as shown in **Figure 15**.

*reorientation, and (c) deformation induced by electric field.*

*Bend deformation in nematic LC molecules: (a) initially oriented homeotropic cell, (b) sketch of molecular reorientation, (c) deformation induced by electric field.*

$$E\_t = \frac{\pi}{d} \sqrt{\frac{K\_{ii}}{\varepsilon\_0 \Delta \varepsilon}}\tag{9}$$

$$B\_t = \frac{\pi}{d} \sqrt{\frac{K\_{ii}}{\mu\_0^{-1} \Delta \chi}} \tag{10}$$

where *Kii* is elastic constant; *ii* = 11, 22, 33 corresponds to splay, bend and twist deformations respectively; *μ*<sup>0</sup> is permeability of free space and *Δχ* is anisotropic diamagnetic susceptibility.

### **3.6 Alignment of liquid crystals**

To manufacture LC device with desired electro-optic (EO) effect, confinement and alignment of LC molecules in a specific direction is very essential. Mauguin reported that LC domains could be aligned by placing them in contact with a crystal surface. The structure of LC nearby interface is different from that in the bulk. The interfacial LC molecules change the boundary conditions and influence the LC in bulk. By controlling the LC directors at the surface, reproducible director orientations can be obtained. The different interaction (anchoring) conditions of LC molecules with their neighboring phase (solid substrate) give rise to different types of liquid crystal display (LCD) devices with varied properties [4, 31, 38, 43–46]. Various types of LC molecule alignment can be induced by treating the supporting substrate differently. The most common types of alignment are homogeneous (planar) and homeotropic.

#### *3.6.1 Homogeneous alignment*

This is also called as planar alignment (**Figure 17(a)**). Here, directors of LC molecules are oriented parallel to the electrode surface. Homogeneous alignment refers to the unidirectional orientation of the molecular axis in the planar mode and displays birefringence with excellent optical quality [47]. It can be achieved using surface treatment methods, such as obliquely evaporated SiO*x* layers, Langmuir– Blodgett films, photoalignment and rubbed polymer films [48–50]. Out of which photoalignment and mechanical rubbing are more promising techniques. In photoalignment, materials like polyvinyl alcohol (PVA) or polyvinyl cinnamate (PVC) are coated on indium tin oxide (ITO)-coated glass plates. These materials are illuminated with polarized ultraviolet light, which forces the LC directors to align parallel to the specific surface direction. Another method is rubbing, invented by Mauguin in 1911; in this method electrode is coated with transparent polymeric

**Figure 17.**

*(a) Homogeneous and (b) homeotropic alignment of liquid crystals. [1, PI coated ITO glass plate; 2, LC molecules].*

material (generally PI), followed by baking and rubbing [45, 51]. The thin layer of PI is known for its exceptionally strong and outstanding heat, mechanical and chemical resistivity [52]. The mechanical treatment such as unidirectional rubbing modifies surface topography by breaking the symmetry and creating linear microgrooves on the polymer surface [48, 53, 54]. The rubbing direction on one ITO plate is 0° or 90° with respect to other depending upon the parallel/antiparallel or twisted mode, respectively [55, 56].

**4.1 Transmissive LCD**

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

**Figure 18.** *Classification of LCD.*

**29**

tion of light beams passing through it [43, 63].

*4.1.1 Twisted nematic liquid crystal cell*

A transmissive LCD transmits a backlight for illuminating the LCD panel, which results in high contrast ratio and high brightness. As their viewing angle is limited, they are more suitable for single-viewer applications, such as games and notebook computers. To make them applicable for multiple viewers, such as televisions and desktop computers, a phase compensation film should be introduced in them. They can also be used for projection displays, for which a high-power arc lamp or a lightemitting diode (LED) array is used as a light source. The most common and finest example of transmissive LCD is twisted nematic liquid crystal (TNLC) cells which are extensively used for notebook computers, where viewing angle is not critical. Its operating principle is based on the ability of the nematic LC to rotate the polariza-

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

It was first invented by Schadt and Helfrich and demonstrated by Fergason in 1971 [64, 65]. It consists of two ITO-coated glass substrates, additionally coated with transparent alignment layers, usually PI. These PI-coated glass plates are rubbed with velvet cloth in one direction; as a result, the LC molecules orient parallel to the rubbing direction. The rubbing directions on two substrates are perpendicular to each other. These glass plates are arranged in such a way that a 90° twist of director from one substrate to the other is formed inside the cell. The cell is kept in between two crossed polarisers in such a way that their polarization is parallel to the rubbing direction of the same glass substrate. In the absence of electric field, the top LC alignment is parallel to the optical axis of the top polarizer, while the bottom LC directors are rotated 90° and parallel to the optical axis of the bottom polarizer (analyzer) as shown in **Figure 19(a)**. When *dΔn* ≫ 0.5λ (the Gooch-Tarry's first minimum condition) is satisfied, the incoming linearly polarized light will follow closely the molecular twist and transmit the crossed analyzer. Here *Δn* is the birefringence of LC, *d* is the cell gap, and λ is the wavelength of the light. This is called the normally white (NW) mode, since light is transmitted without application of any voltage. In the voltage-on state (**Figure 19(b)**), the LC molecules undergo a Freedericksz transition. In this state, the director of the nematic LC is parallel to the field and no longer twisted. When polarized light enters a cell in such a configuration, it is not twisted and is absorbed/blocked by the analyser, resulting in a dark state. Regions where an electric field is applied appear dark against a bright
