**6.2 Nematic configurations in PDLC films**

The nematic material confined in a droplet in a PDLC is in a particular arrangement, called the director configuration. LC droplets are usually spherical because of surface tension, but due to photopolymerization reaction the texture changes significantly to adopt different configurations. When LCs are confined to small cavities, curved surfaces deform the director field, inducing three basic Frank elastic deformations in the director structure, namely, splay, twist and bend. The contribution of each deformation to the overall energy density *F* is given by [19, 125]

$$F = \frac{1}{2} \left[ K\_{11} \left( \nabla . \overrightarrow{n} \right)^2 + K\_{22} \left( \overrightarrow{n} . \nabla \times \overrightarrow{n} \right)^2 + K\_{33} \left( \overrightarrow{n} \times \nabla \times \overrightarrow{n} \right)^2 \right] \tag{23}$$

where the proportionality constants *K*11*, K*<sup>22</sup> and *K*<sup>33</sup> are associated with splay, twist and bend deformations, respectively. It is usually not possible to pack the nematic director field into curvatures without creating one or more defects. These defects are responsible for the transformation of LC droplet from one configuration to another. Different defect structures are classified on the basis of their twodimensional structure often known as "strength (*s*)" of the defect. "*s*" is defined by the rotation of the nematic director on a closed path around the defect; *s* indicates how many times of 2π the director rotates. Since +*n* and – *n* of the director are equivalent, half-integer values of *s* are allowed. The light scattering and dielectric properties of different droplet configurations can vary considerably, which is an important factor in the PDLC devices. Accordingly, the configuration of confined LCs is an area of both scientific and technological interest [19, 126]. The configuration adopted by the nematic director field within a droplet reflects the subtle interplay of a number of forces, such as shape and size of cavity containing LC

material, alignment properties of the LC at the polymer surface, elastic constants of the bulk nematic, temperature and the presence of external fields. Out of these factors, preferred alignment of the nematic at the surface of the polymer-LC interface determines the droplet configuration. If the anchoring energy is stronger than the elastic forces inside LC droplets, then the nematic director adopts a uniform tilt angle either (0° or 90°) at all points on the droplet surface, and the final configuration of nematic director within LC droplet is to minimize the total free energy. However, if the anchoring energy is weaker than the elastic forces inside LC droplets, then the tilt angle of the nematic varies spatially within the droplet to minimize curvature in the bulk of the droplet. Strong or weak anchoring conditions depend on the chemical nature of the polymer interface up to a certain degree. However, typically anchoring energy is more influential. Anchoring effects are magnified in small droplets, because of their shorter length scale and increased surface-to-volume ratio. Along with anchoring energy, balance of elastic constants is an imperative factor in determining the director configuration. Contribution of elastic constants to the system's free energy determines whether director configuration inside the droplet is simple or complex. The shape and size of cavity affects droplet structure. In submicron-sized droplets, the close proximity of surfaces and defects can distort the nematic structure throughout the droplet, whereas in large-sized droplets, it is easy to form multiple defect structures. The director configuration is isomorphic in a symmetric cavity and unpredictable in irregular-shaped cavity. The presence of external fields may influence the alignment direction of a nematic without altering the director configuration. Four commonly found director configurations in PDLCs [127–129] are illustrated in **Figure 32**.

structure is a splay deformation with a point defect (*s* = 1) in the volume centre known as hedgehog [19, 130]. This is shown in **Figure 33**. The defects (also known as disclinations) arise when the elastic energy density of a nematic grows sufficiently large, and the orientation of the nematic director becomes indistinct [131]. Radial structure is generally found by dispersing LC in low-surface energy fluids like polysiloxane or in glycerine containing a

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

b. Axial configuration (**Figure 32(b)**): This configuration was found in director field which are weakly anchored perpendicular (homeotropic) to the droplet wall, smaller in radii than radial droplets and in those radial droplets which were exposed to electric or magnetic field [132]. The director field possesses cylindrical symmetry, with a line defect perpendicular to the preferred orientation direction at the droplet equator as shown in **Figure 32(b)**.

c. Bipolar configuration (**Figure 32(c)**): In this configuration, director field is anchored tangential (parallel or homogeneous) to the droplet wall. The director field possesses cylindrical symmetry, with the symmetry axis defined by two-point defects called *boojums*, which lie at opposite ends (poles) of the droplet. *Boojums* can exist only at the surface and cannot move into the volume of the droplet. In a bipolar droplet, both splay and bend deformations are present, with splay-type *boojums* located at the surface near the poles of the droplet, as shown in **Figure 33**. The bend deformation dominates throughout the rest of the drop along the lines connecting the two poles.

d. Toroidal configuration (**Figure 32(d)** and **(e)**): In the case of multiple elastic constants, the toroidal configuration exists when the splay energy becomes too large in comparison with the bend energy in the droplet. For a value of *K*11/*K*<sup>33</sup> > 0.7, a droplet with the toroidal configuration is a stable structure as it has a lower free energy than a bipolar structure. The toroidal structure possesses a line defect running along the droplet diameter, and the nematic director is everywhere perpendicular to this line arranged in a series of

*A schematic illustration of splay and bend elastic deformations dictating the nematic ordering in radial and*

small amount of lecithin.

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

concentric circles.

**Figure 33.**

**47**

*bipolar LC droplets.*

a. Radial configuration (**Figure 32(a)**): In this configuration, director field is anchored perpendicular (homeotropic) to the droplet wall. A radial droplet possesses spherical symmetry, and the only elastic deformation present in this

**Figure 32.**

*Director configurations in a droplet of PDLC (a) radial, (b) axial, (c) bipolar, (d) toroidal and (e) threedimensional view of the toroidal configuration.*
