**2.2 Lyotropic liquid crystals**

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

Apart from the rod-like molecules, more advanced-shaped LCs are possible such as disk-like (**Figure 6(a)**) which can give rise to other types of ordering. They were first discovered in carbon precursor compounds with a transient existence by

Disk-shaped LC molecules can orient themselves in a layer-like manner termed as the discotic nematic phase. This phase is called as a discotic columnar, if their disks pack into stacks/columns. Again, these columns may organize themselves into rectangular or hexagonal arrays [31]. Discotic LCs are composed of an aromatic core surrounded by flexible chains as shown in **Figure 6(b)**. The aromatic cores allow charge transfers in the stacking direction through the π conjugate system, due to which these LCs become electrically semiconducting along the stacking direction.

Sterically induced packing of bent core (banana-shaped) LC molecules (**Figure 7(a)**)

is interesting from many viewpoints. These are the first ferroelectric and antiferroelectric LCs, which contain no chiral carbon atoms; however they can introduce chirality to the system [32]. One example of banana-shaped LC is shown in **Figure 7(b)**.

Brooks and Taylor in stable low molecular weight systems [29, 30].

of smectic phase.

*Liquid Crystals and Display Technology*

*2.1.5 Discotic phase*

*2.1.6 Banana-shaped LC*

*(a) Molecular arrangement and (b) example of disk-shaped LC.*

*(a) Molecular arrangement and (b) example of banana-shaped LC.*

**Figure 6.**

**Figure 7.**

**18**

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

**Figure 8.** *Molecular arrangement of (a) hexagonal phase, (b) micellar cubic phase and (c) lamellar phase of lyotropic LC.*

micellar phase (a bulk LC sample with spherical water cavities) [33, 34]. Different lyotropic phases are listed below:

where θ is the angle between the axis of an individual molecule and the local director *n*^ as shown in **Figure 9(a)**. It is the preferred direction in a volume element of a LC, and the average is taken over the complete ensemble. The bracket denotes both temporal and spatial average. For a completely isotropic sample, S = 0,

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whereas for a perfectly aligned sample, S = 1. For a typical LC sample, the value of S is 0.3 to 0.9, and for nematic LC, it is 0.5–0.7. **Figure 9(b)** shows the temperature dependence of order parameter (S), which follows an inverse relation [11, 35, 36].

LCs exhibit uniaxial symmetry around the director, which gives them shape anisotropy. The shape anisotropy of LC and their resulting interactions with the surrounding environment (applied fields) leads to an anisotropy in many other physical properties such as refractive index (RI), dielectric permittivity, magnetic

LCs are optically anisotropic materials and show birefringence. LCs have two direction-dependent refractive indices, ordinary RI ( *no*) and extraordinary RI ( *ne*)

> 1 3 *n*2 *<sup>e</sup>* þ 2*n*<sup>2</sup> *o*

*Indicatrix of optically uniaxially material: (a) positive birefringent material and (b) negative birefringent*

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

� � <sup>r</sup>

*nav* ¼

*Δn* ¼ *ne* � *no:* (5)

(6)

**3.2 Anisotropy in liquid crystals**

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

*3.2.1 Optical anisotropy*

with birefringence:

**Figure 10.**

*material.*

**21**

susceptibility, viscosity and conductivity.

Also, the average RI is given by

1.Hexagonal phase (hexagonal columnar phase) (middle phase) (**Figure 8(a)**)

2.Discontinuous cubic phase (micellar cubic phase) (**Figure 8(b)**)


5.Reverse hexagonal columnar phase

6. Inverse cubic phase (inverse micellar phase)

By varying concentration, even within the same phases, their self-assembled structures can be tuned. For example, in lamellar phases, distance between the layers increases with the solvent volume. Since lyotropic LCs indirectly depend on a subtle balance of intermolecular interactions, it is difficult to analyse their properties and structures as compared to those of thermotropic LCs. Similar type of phases and properties has been observed in immiscible diblock copolymers.
