**1. Definition and history of liquid crystals**

Liquid crystal (LC) is a thermodynamic phase of a condensed matter, intermediate of (in between) conventional isotropic liquid and three dimensionally ordered solid crystal with only orientational order but no positional order [1]. It holds

properties of liquid such as fluidity, coalescence and formation of droplets as well as crystalline properties such as order and anisotropy in optical, electrical and magnetic properties (as summarized in **Table 1**) [2]. The difference between molecular arrangement of solid, liquid crystal and liquid is shown in **Figure 1**.

relationships has been explained using principles commencing from swarm theory to continuum theory. Identification of mesophases, determination of transition temperatures and awareness about defect textures through polarizing optical microscope (POM) appreciably helped in developing a new era of LC applications [9]. The beginning of the third period (1960 to the present time) gives us a famous statistical Maier and Saupe mean field theory which states about the isotropicnematic phase transition [10, 11]. Synthesis of new LC materials is ongoing. Classification, molecular structure and properties of LCs, defects characterizing microscopic textures of LC phases and existence of blue phases are some topics, which are now well understood [12–14]. The decade of 1970 is known for

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

announcing application of LCs as display devices. Expansion of theories and their employment in practical applications give rise to new LC science from display world to beyond display technology as well. Having high resolution and high brightness and being lightweight, flexible and an energy saver make LC devices attractive and competitive in the high-tech world. LC science has been now well acknowledged and documented, but it is still thriving. Liquid crystal displays (LCDs) are like a milestone for the future world, but a continuous evolution via

This special class of materials are moderate-sized organic molecules, composed of flat segments like benzene rings, double bonds, strong dipole and easily polarizing groups [15]. Depending upon the molecular structure, LC compounds may have one or many phases (polymorphism), characterized by order and symmetry. LCs can be broadly classified into two generic classes: thermotropic and lyotropic [1]. Commonly found LCs from either group possess a remarkable polymorphism and give rise to various mesophases such as nematic, smectic, cholesteric, columnar and blue phases in thermotropic LC and discontinuous, hexagonal, lamellar, bicontinuous, reverse hexagonal and inverse cubic phases in lyotropic LC,

depending upon the type, amount and proportion of ordering in it [16]. Sometimes, thermotropic LCs are also cataloged as rod-like (calamatic) and disk-like (discotic). Thermotropic LC are single compounds, whereas lyotropic LC are always mixtures. The LiqCryst database accounts for more than 39,000 nematic phase compounds, about 18,000 chiral compounds and more than 6000 ferroelectric SmecticC\* phase compounds [17]. Some day-to-day life examples of LCs are soap solution, tobacco

Thermotropic LCs are comprised of rod-like organic molecules and exhibit phase transition into the LC phase as a function of temperature. At very low temperature, most LC materials are in anisotropic phase, but with the increase in temperature, these LC materials acquire isotropic phase along with so many intermediate phases such as smectic, nematic, cholesteric etc., which are described

As the temperature of isotropic phase (no positional or orientation order) is lowered, the LC material undergoes a transition to the nematic phase. It is a transparent or translucent low-viscosity liquid and a stable LC phase in a particular

dedicated research is still anticipated.

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

**2. Types and phases of liquid crystals**

mosaic virus, protein and cell membrane.

**2.1 Thermotropic liquid crystals**

below [1, 15].

**13**

*2.1.1 Nematic phase*

This phase of matter was discovered by the Austrian botanist Friedrich Reinitzer in the year 1888 while he was studying the compounds cholesteryl benzoate and cholesteryl acetate. He observed colored phenomena occurring in melts of cholesteryl acetate and cholesteryl benzoate. In addition, he reported that the compound cholesteryl benzoate has two distinct melting points. Its crystal transforms into hazy liquid at a temperature 145.5°C, and with the further increase in temperature, it suddenly turns into isotropic liquid at a temperature 178.5°C [3]. The word "liquid crystal" for this unusual phase of material was coined by German Physicist, Otto Lehmann, a specialist in polarizing optical microscopy [4]. Friedrich Reinitzer's and Otto Lehmann's studies revealed that liquid crystals (LCs) can rotate the direction of polarization of light and reflect circularly polarized light [5]. The history of the development of LCs can be divided into three phases: the first phase is from the discovery of LC (1888) to the acceptance of its existence (1925). Friedel's article about classification of LC, along with the publications on synthesis and studies of new LC materials by organic chemists in Germany, notably Vorlander [6, 7], provided a firm basis for the development of the subject. In the period from 1925 to about 1960, research in the field of LC was at a low level; however contribution of some devoted researcher has been summarized here: Vorlander synthesized a number of compounds forming LC phases, some of them showing up to three different mesophases. A lamellar and tilted lamellar structure was found by Herrmann for some thallium soaps [8]. In this period, the effect of external electric or magnetic field on the LC has been recognized, modifications of surface to orient LC has been done, and significance of anisotropic physical properties of aligned LC has been understood, which was the foundation of display technology of the future world. Synthesis of new LC materials and their structure–property


#### **Table 1.**

*Properties of solid, liquid crystal and liquid.*

**Figure 1.**

*Molecular arrangement of solid, liquid crystal and liquid.*

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

relationships has been explained using principles commencing from swarm theory to continuum theory. Identification of mesophases, determination of transition temperatures and awareness about defect textures through polarizing optical microscope (POM) appreciably helped in developing a new era of LC applications [9]. The beginning of the third period (1960 to the present time) gives us a famous statistical Maier and Saupe mean field theory which states about the isotropicnematic phase transition [10, 11]. Synthesis of new LC materials is ongoing. Classification, molecular structure and properties of LCs, defects characterizing microscopic textures of LC phases and existence of blue phases are some topics, which are now well understood [12–14]. The decade of 1970 is known for announcing application of LCs as display devices. Expansion of theories and their employment in practical applications give rise to new LC science from display world to beyond display technology as well. Having high resolution and high brightness and being lightweight, flexible and an energy saver make LC devices attractive and competitive in the high-tech world. LC science has been now well acknowledged and documented, but it is still thriving. Liquid crystal displays (LCDs) are like a milestone for the future world, but a continuous evolution via dedicated research is still anticipated.

### **2. Types and phases of liquid crystals**

This special class of materials are moderate-sized organic molecules, composed of flat segments like benzene rings, double bonds, strong dipole and easily polarizing groups [15]. Depending upon the molecular structure, LC compounds may have one or many phases (polymorphism), characterized by order and symmetry. LCs can be broadly classified into two generic classes: thermotropic and lyotropic [1]. Commonly found LCs from either group possess a remarkable polymorphism and give rise to various mesophases such as nematic, smectic, cholesteric, columnar and blue phases in thermotropic LC and discontinuous, hexagonal, lamellar, bicontinuous, reverse hexagonal and inverse cubic phases in lyotropic LC, depending upon the type, amount and proportion of ordering in it [16]. Sometimes, thermotropic LCs are also cataloged as rod-like (calamatic) and disk-like (discotic). Thermotropic LC are single compounds, whereas lyotropic LC are always mixtures. The LiqCryst database accounts for more than 39,000 nematic phase compounds, about 18,000 chiral compounds and more than 6000 ferroelectric SmecticC\* phase compounds [17]. Some day-to-day life examples of LCs are soap solution, tobacco mosaic virus, protein and cell membrane.

#### **2.1 Thermotropic liquid crystals**

Thermotropic LCs are comprised of rod-like organic molecules and exhibit phase transition into the LC phase as a function of temperature. At very low temperature, most LC materials are in anisotropic phase, but with the increase in temperature, these LC materials acquire isotropic phase along with so many intermediate phases such as smectic, nematic, cholesteric etc., which are described below [1, 15].

#### *2.1.1 Nematic phase*

As the temperature of isotropic phase (no positional or orientation order) is lowered, the LC material undergoes a transition to the nematic phase. It is a transparent or translucent low-viscosity liquid and a stable LC phase in a particular

properties of liquid such as fluidity, coalescence and formation of droplets as well as crystalline properties such as order and anisotropy in optical, electrical and magnetic properties (as summarized in **Table 1**) [2]. The difference between molecular

This phase of matter was discovered by the Austrian botanist Friedrich Reinitzer in the year 1888 while he was studying the compounds cholesteryl benzoate and cholesteryl acetate. He observed colored phenomena occurring in melts of

cholesteryl acetate and cholesteryl benzoate. In addition, he reported that the compound cholesteryl benzoate has two distinct melting points. Its crystal transforms into hazy liquid at a temperature 145.5°C, and with the further increase in temperature, it suddenly turns into isotropic liquid at a temperature 178.5°C [3]. The word "liquid crystal" for this unusual phase of material was coined by German Physicist,

Reinitzer's and Otto Lehmann's studies revealed that liquid crystals (LCs) can rotate the direction of polarization of light and reflect circularly polarized light [5]. The history of the development of LCs can be divided into three phases: the first phase is from the discovery of LC (1888) to the acceptance of its existence (1925). Friedel's article about classification of LC, along with the publications on synthesis and studies of new LC materials by organic chemists in Germany, notably Vorlander [6, 7], provided a firm basis for the development of the subject. In the period from 1925 to about 1960, research in the field of LC was at a low level; however contribution of some devoted researcher has been summarized here: Vorlander synthesized a number of compounds forming LC phases, some of them showing up to three different mesophases. A lamellar and tilted lamellar structure was found by Herrmann for some thallium soaps [8]. In this period, the effect of external electric or magnetic field on the LC has been recognized, modifications of surface to orient LC has been done, and significance of anisotropic physical properties of aligned LC has been understood, which was the foundation of display technology of the future world. Synthesis of new LC materials and their structure–property

**Solid Liquid crystal Liquid** Anisotropic Anisotropic Isotropic Rigidity Fluidity Fluidity Ordered Ordered Disordered 3-D lattice 0/1/2 lattice No lattice

**Table 1.**

**Figure 1.**

**12**

*Properties of solid, liquid crystal and liquid.*

*Molecular arrangement of solid, liquid crystal and liquid.*

Otto Lehmann, a specialist in polarizing optical microscopy [4]. Friedrich

arrangement of solid, liquid crystal and liquid is shown in **Figure 1**.

*Liquid Crystals and Display Technology*

temperature range. It is the most common LC phase of calamatic or rod-shaped organic molecules, as shown in **Figure 2(a)** [4].

and their associated elastic constants are *K*11, *K*<sup>22</sup> and *K*33, respectively. The free

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

!*:*<sup>∇</sup> � *<sup>n</sup>* ! <sup>2</sup>

The cholesteric LC phase is typically composed of nematic mesogenic molecules containing chiral centres. Chiral molecules have no internal planes of symmetry and produce a twist in the nematic structure by inducing intermolecular forces which favour alignment between molecules at a slight angle to one another. They are composed of quasi-nematic layers. Their individual directors are turned by a fixed angle on proceeding from one layer to the next as shown in **Figure 3(a)**. The rotation is constrained in a plane perpendicular to the pitch direction. The pitch (p) is the distance over which the director of LC molecules undergoes a full twist of 2π angle. As the phase directors at 0° and 180° are equivalent, the arrangement of molecules in the chiral nematic phase repeats at every half pitch (p/2). Due to this strong twisting effect, in a definite spectral range, cholesteric phase shows a selective reflection of the circularly polarized light of wavelength equal to pitch length. The pitch length *p* can be altered by varying temperature or adding other materials in LC host. With the increase in temperature, the angle at which the director changes increases, which in turn decreases the pitch length and vice versa [4, 20, 21]. The free energy of distortions in cholesteric LC is given by Eq. (2)

þ *K*<sup>33</sup> *n*

! <sup>2</sup> (1)

! � <sup>∇</sup> � *<sup>n</sup>*

þ *K*<sup>22</sup> *n*

energy of distortions of nematic LC is given by Eq. (1) [19]:

*K*<sup>11</sup> ∇*:n* ! <sup>2</sup>

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

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

*2.1.2 Cholesteric phase*

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

where *<sup>q</sup>*<sup>0</sup> <sup>¼</sup> <sup>2</sup>*<sup>π</sup>*

**Figure 3.**

**15**

*K*<sup>11</sup> ∇*:n* ! <sup>2</sup>

þ *K*<sup>22</sup> *n*

**Figure 3(b)** represents example of cholesteric LC.

*(a) Molecular arrangement and (b) example of cholesteric LC phase*.

!*:*<sup>∇</sup> � *<sup>n</sup>*

infinite; therefore *q*<sup>0</sup> vanishes from free energy equation of nematic LC [22].

! <sup>þ</sup> *<sup>q</sup>*<sup>0</sup> <sup>2</sup>

! <sup>2</sup> (2)

*<sup>p</sup>* corresponds to the intrinsic twist of the system. For nematics *p* is

þ *K*<sup>33</sup> *n*

! � <sup>∇</sup> � *<sup>n</sup>*

The structure of a typical nematic LC is shown in **Figure 2(b)**, and each entity has exclusive function. The terminal group (e.g. (C6H13)*n*) determines dielectric constant and anisotropy, and benzene rings provide short-range molecular forces which affect electrical and elastic properties; the linkage group stabilizes LC against moisture, UV radiation and chemicals, and the side chain (e.g. cyano group) influences the elastic constants and transition temperature of LC. **Figure 2(c)** represents example of nematic LC. Nematic LCs lack positional order, but have self-aligning long-range directional order with their long axes almost parallel, characterized by a nematic director *n*^, which is the average direction of the ensemble of molecules [15]. The director *n*^ is a function of space with unit magnitude and *n*^ = *n*^. Thus, the LC molecules in nematic phase are free to flow with three translational degrees of freedom, and their centre of mass positions is randomly distributed as in a liquid, but still maintains their long-range directional order. In nematic phase of LC, one axis is generally longer and preferred than the other two, i.e., they are uniaxial and can be approximated as cylinders and rods. The easy alignment of these uniaxial nematic LC using electric or magnetic field makes them optically uniaxial and prominent in display devices. However, some LCs are biaxial nematic, i.e., in addition to orienting along their long axis, they also orient along a secondary axis [1, 18]. As the nematic LC is relatively a low-viscosity fluid, it easily gets deformed by small external forces. In a deformed LC, the director direction *n*^ changes from point to point. These LC deformations can be explained using three basic deformations: splay, twist and bend,

**Figure 2.** *(a) Molecular arrangement, (b) general chemical structure and (c) example of nematic liquid crystal.*

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

and their associated elastic constants are *K*11, *K*<sup>22</sup> and *K*33, respectively. The free energy of distortions of nematic LC is given by Eq. (1) [19]:

$$F = \frac{1}{2} \left[ K\_{11} \left( \nabla. \overrightarrow{n} \right)^2 + K\_{22} \left( \overrightarrow{n}. \nabla \times \overrightarrow{n} \right)^2 + K\_{33} \left( \overrightarrow{n} \times \nabla \times \overrightarrow{n} \right)^2 \right] \tag{1}$$

#### *2.1.2 Cholesteric phase*

temperature range. It is the most common LC phase of calamatic or rod-shaped

*(a) Molecular arrangement, (b) general chemical structure and (c) example of nematic liquid crystal.*

The structure of a typical nematic LC is shown in **Figure 2(b)**, and each entity has exclusive function. The terminal group (e.g. (C6H13)*n*) determines dielectric constant and anisotropy, and benzene rings provide short-range molecular forces which affect electrical and elastic properties; the linkage group stabilizes LC against moisture, UV radiation and chemicals, and the side chain (e.g. cyano group) influences the elastic constants and transition temperature of LC. **Figure 2(c)** represents example of nematic LC. Nematic LCs lack positional order, but have self-aligning long-range directional order with their long axes almost parallel, characterized by a nematic director *n*^, which is the average direction of the ensemble of molecules [15]. The director *n*^ is a function of space with unit magnitude and *n*^ = *n*^. Thus, the LC molecules in nematic phase are free to flow with three translational degrees of freedom, and their centre of mass positions is randomly distributed as in a liquid, but still maintains their long-range directional order. In nematic phase of LC, one axis is generally longer and preferred than the other two, i.e., they are uniaxial and can be approximated as cylinders and rods. The easy alignment of these uniaxial nematic LC using electric or magnetic field makes them optically uniaxial and prominent in display devices. However, some LCs are biaxial nematic, i.e., in addition to orienting along their long axis, they also orient along a secondary axis [1, 18]. As the nematic LC is relatively a low-viscosity fluid, it easily gets deformed by small external forces. In a deformed LC, the director direction *n*^ changes from point to point. These LC deformations can be explained using three basic deformations: splay, twist and bend,

organic molecules, as shown in **Figure 2(a)** [4].

*Liquid Crystals and Display Technology*

**Figure 2.**

**14**

The cholesteric LC phase is typically composed of nematic mesogenic molecules containing chiral centres. Chiral molecules have no internal planes of symmetry and produce a twist in the nematic structure by inducing intermolecular forces which favour alignment between molecules at a slight angle to one another. They are composed of quasi-nematic layers. Their individual directors are turned by a fixed angle on proceeding from one layer to the next as shown in **Figure 3(a)**. The rotation is constrained in a plane perpendicular to the pitch direction. The pitch (p) is the distance over which the director of LC molecules undergoes a full twist of 2π angle. As the phase directors at 0° and 180° are equivalent, the arrangement of molecules in the chiral nematic phase repeats at every half pitch (p/2). Due to this strong twisting effect, in a definite spectral range, cholesteric phase shows a selective reflection of the circularly polarized light of wavelength equal to pitch length. The pitch length *p* can be altered by varying temperature or adding other materials in LC host. With the increase in temperature, the angle at which the director changes increases, which in turn decreases the pitch length and vice versa [4, 20, 21]. The free energy of distortions in cholesteric LC is given by Eq. (2)

$$F = \frac{1}{2} \left[ K\_{11} \left( \nabla . \overrightarrow{n} \right)^2 + K\_{22} \left( \overrightarrow{n} . \nabla \times \overrightarrow{n} + q\_0 \right)^2 + K\_{33} \left( \overrightarrow{n} \times \nabla \times \overrightarrow{n} \right)^2 \right] \tag{2}$$

where *<sup>q</sup>*<sup>0</sup> <sup>¼</sup> <sup>2</sup>*<sup>π</sup> <sup>p</sup>* corresponds to the intrinsic twist of the system. For nematics *p* is infinite; therefore *q*<sup>0</sup> vanishes from free energy equation of nematic LC [22]. **Figure 3(b)** represents example of cholesteric LC.

**Figure 3.** *(a) Molecular arrangement and (b) example of cholesteric LC phase*.

#### *2.1.3 Blue phase*

The blue phases are a set of thermodynamically distinct phases that occur at the boundary of the helical phase and isotropic phase of highly chiral LCs within a small temperature range. It was first observed by Reinitzer in 1888 as an unstable phase, and after a century (in 1975), they were shown to be stable and distinct thermodynamic phase by Armitage and Price [23, 24]. In the absence of electric fields, in the order of increasing temperature, there can be three blue phases: BPI\*, BPII\* and BPIII\*. BPI\* has body-centred cubic symmetry, BPII\* possess simple cubic symmetry and BPIII\* is with a local cubic lattice only. BPI\* and BPII\* reflect blue light, as their name suggest, whereas BPIII\* phase is observed at highest temperature and appears fogy because of which it is called as fog phase or blue fog [25, 26]. The building structure element of BPI\* and BPII\* phase is double-twist cylinders (**Figure 4(a)**). The double-twist cylinder is a local structure of minimum free energy with local director rotating around any given radius of the cylinders. Free energy of blue phases is lower than the free energy of chiral nematic phase because here molecules twist in two dimensions simultaneously (**Figure 4(b)**). As the local twist is increased, the cylinder becomes strained and distorted. Therefore, blue phase cannot have a single, large double-twist structure; instead it consists of many of these double-twist structures arranged in a lattice with cubic symmetry. But for elastic reasons, it is only possible by introducing a lattice of topological defects [27, 28] as shown in **Figure 4(c)**.

molecules show relatively high mobility. The thickness of layer is equal to molecular length. The SmA LCs are optically positive and uniaxial with the optic axis parallel to the molecular long axes. The layers of the SmA LC can be bended in a way causing splay deformation. Bend and twist deformations are prohibited in this LC

*Molecular arrangement in (a) smectic A phase, (b) smectic B phase, (c) smectic C phase, (d) smectic C\* phase*

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

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

*K*<sup>11</sup> ∇*:n*

Upon further cooling, the smectic B (SmB) (**Figure 5(b)**) and smectic C (SmC) (**Figure 5(c)**) phases are formed. The SmB mesophase orients with the director perpendicular to the smectic plane, but the molecules are arranged into a network of hexagons within the layer. In the SmC mesophase, molecules are arranged as in the SmA mesophase, but the director is at a constant tilt angle measured normally to the smectic plane. For some material the tilt angle is constant, but for others it is temperature dependent. The centre of mass of the molecules is randomly oriented/ ordered, and the molecules are free to rotate around their long axes. SmC phases are optically biaxial. If the molecules of SmC LC are in chiral state, then they are designated as smectic C\* (SmC\*) (**Figure 5(d)**) state, and the direction of the director projection is rotated from layer to layer forming a helix. Therefore, these phases appear optically positive uniaxial and show optical activity and selective reflection similar to the cholesteric phase. The SmC\* shows ferroelectric properties if their molecules have permanent dipole moment perpendicular to their long axes. In some smectic phases (e.g. Smectic G phase), the molecules are affected by the various layers above and below them. Therefore, a small amount of

! <sup>2</sup> (3)

phase. The free energy density equation is given by Eq. (3)

**Figure 5.**

**17**

*and (e) example of smectic phase.*

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

#### **Figure 4.**

*(a) Double twisted structure with two helical axes, h1 and h2 in a blue phase LC, the directors perform a rotation of 90o across the diameter. (b) Perspective view of the double twist cylinder, the angle of directors at the outer edge of the cylinder is 45°, relative to the central axis. (c) Local arrangement of three double twist cylinders forming a defect region, which eventually leads to the three-dimensional, cubic lattice of defects observed in blue phases.*

### *2.1.4 Smectic phase*

Upon cooling, nematic phase LC transforms into smectic phase. The distinguished feature of smectic phase LC is their stratification. In addition to the orientational order, their molecules form well-defined layers which can slide over one another. Thus, they are positionally ordered along one direction with two translational degrees of freedom. The increased order indicates that the smectic phase is more solid-like than the nematic. Several different smectic classes (phases) have been discovered so far, and some of them are discussed here. In the smectic A (SmA) phase, on average, the molecules are parallel to one another possessing orientational order and are arranged in layers, with the long axes perpendicular to the layer plane. The orientational order is characterized by the director *n*^ analogous to the nematic LC but restricted within a specific layer/plane. Within the layers the centre of mass of the molecules is ordered at random and has no correlation between intra-plane centres of masses. Thus, the SmA phase (**Figure 5(a)**) possesses the one-dimensional quasi long-range positional order, and within the layers, *An Overview of Polymer-Dispersed Liquid Crystal Composite Films and Their Applications DOI: http://dx.doi.org/10.5772/intechopen.91889*

**Figure 5.**

*2.1.3 Blue phase*

*Liquid Crystals and Display Technology*

[27, 28] as shown in **Figure 4(c)**.

*2.1.4 Smectic phase*

*observed in blue phases.*

**Figure 4.**

**16**

The blue phases are a set of thermodynamically distinct phases that occur at the boundary of the helical phase and isotropic phase of highly chiral LCs within a small temperature range. It was first observed by Reinitzer in 1888 as an unstable phase, and after a century (in 1975), they were shown to be stable and distinct thermodynamic phase by Armitage and Price [23, 24]. In the absence of electric fields, in the order of increasing temperature, there can be three blue phases: BPI\*, BPII\* and BPIII\*. BPI\* has body-centred cubic symmetry, BPII\* possess simple cubic symmetry and BPIII\* is with a local cubic lattice only. BPI\* and BPII\* reflect blue light, as their name suggest, whereas BPIII\* phase is observed at highest temperature and appears fogy because of which it is called as fog phase or blue fog [25, 26]. The building structure element of BPI\* and BPII\* phase is double-twist cylinders (**Figure 4(a)**). The double-twist cylinder is a local structure of minimum free energy with local director rotating around any given radius of the cylinders. Free energy of blue phases is lower than the free energy of chiral nematic phase because here molecules twist in two dimensions simultaneously (**Figure 4(b)**). As the local twist is increased, the cylinder becomes strained and distorted. Therefore, blue phase cannot have a single, large double-twist structure; instead it consists of many of these double-twist structures arranged in a lattice with cubic symmetry. But for elastic reasons, it is only possible by introducing a lattice of topological defects

Upon cooling, nematic phase LC transforms into smectic phase. The distinguished feature of smectic phase LC is their stratification. In addition to the orientational order, their molecules form well-defined layers which can slide over one another. Thus, they are positionally ordered along one direction with two translational degrees of freedom. The increased order indicates that the smectic phase is more solid-like than the nematic. Several different smectic classes (phases) have been discovered so far, and some of them are discussed here. In the smectic A (SmA) phase, on average, the molecules are parallel to one another possessing orientational order and are arranged in layers, with the long axes perpendicular to the layer plane. The orientational order is characterized by the director *n*^ analogous to the nematic LC but restricted within a specific layer/plane. Within the layers the

*(a) Double twisted structure with two helical axes, h1 and h2 in a blue phase LC, the directors perform a rotation of 90o across the diameter. (b) Perspective view of the double twist cylinder, the angle of directors at the outer edge of the cylinder is 45°, relative to the central axis. (c) Local arrangement of three double twist cylinders forming a defect region, which eventually leads to the three-dimensional, cubic lattice of defects*

centre of mass of the molecules is ordered at random and has no correlation between intra-plane centres of masses. Thus, the SmA phase (**Figure 5(a)**) possesses the one-dimensional quasi long-range positional order, and within the layers,

*Molecular arrangement in (a) smectic A phase, (b) smectic B phase, (c) smectic C phase, (d) smectic C\* phase and (e) example of smectic phase.*

molecules show relatively high mobility. The thickness of layer is equal to molecular length. The SmA LCs are optically positive and uniaxial with the optic axis parallel to the molecular long axes. The layers of the SmA LC can be bended in a way causing splay deformation. Bend and twist deformations are prohibited in this LC phase. The free energy density equation is given by Eq. (3)

$$F = \frac{1}{2} \left[ K\_{11} \left( \nabla. \overrightarrow{n} \right)^{2} \right] \tag{3}$$

Upon further cooling, the smectic B (SmB) (**Figure 5(b)**) and smectic C (SmC) (**Figure 5(c)**) phases are formed. The SmB mesophase orients with the director perpendicular to the smectic plane, but the molecules are arranged into a network of hexagons within the layer. In the SmC mesophase, molecules are arranged as in the SmA mesophase, but the director is at a constant tilt angle measured normally to the smectic plane. For some material the tilt angle is constant, but for others it is temperature dependent. The centre of mass of the molecules is randomly oriented/ ordered, and the molecules are free to rotate around their long axes. SmC phases are optically biaxial. If the molecules of SmC LC are in chiral state, then they are designated as smectic C\* (SmC\*) (**Figure 5(d)**) state, and the direction of the director projection is rotated from layer to layer forming a helix. Therefore, these phases appear optically positive uniaxial and show optical activity and selective reflection similar to the cholesteric phase. The SmC\* shows ferroelectric properties if their molecules have permanent dipole moment perpendicular to their long axes.

In some smectic phases (e.g. Smectic G phase), the molecules are affected by the various layers above and below them. Therefore, a small amount of

three-dimensional order is observed in them [1, 2, 15, 21]. **Figure 5(a**–**d)** shows the molecular arrangement in all types of smectic phases, and **Figure 5(e)** is an example of smectic phase.

**2.2 Lyotropic liquid crystals**

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

**Figure 8.**

**19**

*lyotropic LC.*

Another class of LCs is named as lyotropic LCs, having two distinct parts/ building blocks—hydrophobic and hydrophilic. Their properties depend on the concentration in the solvent and the shape of the molecule. Soaps and detergents are some common examples of lyotropic LCs. It consists of two or more components that exhibit phase transition into the LC phase as a function of both temperature and concentration of the molecules in a solvent (generally water). The solvent molecules fill the space around the compounds and provide fluidity to the system. In lyotropics, along with temperature, concentration is another degree of freedom that enables them to induce a variety of different phases. A compound which has two immiscible hydrophobic and hydrophilic parts within the same molecule is termed as an amphiphilic molecule. Depending on the volume balances between the hydrophobic part and hydrophilic part, many amphiphilic molecules show lyotropic liquid-crystalline phase sequences. These structures are formed because of the micro-phase segregation of two incompatible components on a nanometre scale. At very low amphiphile concentration, the molecules are randomly dispersed in a solvent without any order. At slightly higher concentration, amphiphilic molecules spontaneously assemble into micelles or vesicles. This is done to "hide" the hydrophobic tail of the amphiphile inside the micelle core, exposing a hydrophilic (watersoluble) surface to aqueous solution. However, these spherical objects do not order themselves in solution. At higher concentration, the assemblies are well ordered. An example of such phase is a hexagonal columnar phase (**Figure 8(a)**). In this phase, the amphiphiles form long cylinders (again with a hydrophilic surface) that arrange themselves into a roughly hexagonal lattice. This is called the middle soap phase. At further higher concentration, a lamellar phase (**Figure 8(c)**) (neat soap phase) may form. In this phase extended sheets of amphiphiles are separated by thin layers of water. For some systems in between the hexagonal and lamellar phases, a cubic phase (**Figure 8(b)**) (viscous isotropic) may exist. In this phase spheres are formed that create a dense cubic lattice. These spheres may also be connected to one another, forming a bicontinuous cubic phase. The objects created by amphiphiles are usually spherical (as in the case of micelles), but sometimes disk-like (bicelles), rod-like or biaxial (all three micelle axes are distinct) objects are also possible. These anisotropic self-assembled nanostructures can then order themselves in similar way as thermotropic LCs do, forming large-scale versions of all the thermotropic phases (such as a nematic phase of rod-shaped micelles). For some systems, at high concentrations, inverse phases are observed, i.e., one may generate an inverse hexagonal columnar phase (columns of water encapsulated by amphiphiles) or an inverse

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

*Molecular arrangement of (a) hexagonal phase, (b) micellar cubic phase and (c) lamellar phase of*
