Liquid Crystals

Chapter 1.3.3 - Thermotropic Liquid Crystals: Nematics, Cholesterics, and Smectics

1.3.3.   Thermotropic Liquid Crystals: Nematics, Cholesterics, and Smectics

The most widely used liquid crystals, and extensively studied for their linear as well
as nonlinear optical properties, are thermotropic liquid crystals. They exhibit various
liquid crystalline phases as a function of temperature. Although their molecular
structures, as discussed in Section 1.1, are, in general, quite complicated, they are

Figure 1.10. Polymeric liquid crystals: (a) main chain and (b) side chain.

often represented as “rigid rods.” These rigid rods interact with one another and form
distinctive ordered structures. There are three main classes of thermotropic liquid
crystals: nematic, cholesteric, and smectic. There are several subclassifications of
smectic liquid crystals in accordance with the positional and directional arrangements
of the molecules.

These mesophases are defined and characterized by many physical parameters such
as long- and short-range order, orientational distribution functions, and so on. They are
explained in greater detail in the following chapters. Here we continue to use the rigid-
rod model and pictorially describe these phases in terms of their molecular arrangement.

Figure 1.11a depicts schematically the collective arrangement of the rodlike liquid
crystal molecules in the nematic phase. The molecules are positionally random,
very much like liquids; x-ray diffraction from nematics does not exhibit any diffraction
peak. These molecules are, however, directionally correlated; they are aligned in
a general direction defined by a unit vector ñ, the so-called director axis.

In general, nematic molecules are centrosymmetric; their physical properties are
the same in the + ñ and the - ñ directions. In other words, if the individual molecules
carry a permanent electric dipole (such a polar nature is typically the case), they will
assemble in such a way that the bulk dipole moment vanishes.

Cholesterics, now often called chiral nematic liquid crystals, resemble nematic liquid
crystals in all physical properties except that the molecules tend to align in a helical
manner as depicted in Figure 1.11b. This property results from the synthesis of
cholesteric liquid crystals; they are obtained by adding a chiral molecule to a nematic
liquid crystal. Some materials, such as cholesterol esters, are naturally chiral.

Smectic liquid crystals, unlike nematics, possess positional order; that is, the position
of the molecules is correlated in some ordered pattern. Several subphases of
smectics have been “discovered,” in accordance with the arrangement or ordering of
the molecules and their structural symmetry properties.1,2 We discuss here three
representative ones: smectic-A, smectic-C, and smectic-C* (ferroelectrics).

Figure 1.11. Molecular alignments of liquid crystals: (a) nematic and (b) cholesteric or chiral nematic.

Figure 1.12a depicts the layered structure of a smectic-A liquid crystal. In each
layer the molecules are positionally random, but directionally ordered with their long
axis normal to the plane of the layer. Similar to nematics, smectic-A liquid crystals
are optically uniaxial, that is, there is a rotational symmetry around the director axis.

The smectic-C phase is different from the smectic-A phase in that the material is
optically biaxial, and the molecular arrangement is such that the long axis is tilted
away from the layer normal (see Fig. 1.12b).

In smectic-C* liquid crystals, as depicted in Figure 1.l2c, the director axis ñ is
tilted away from the layer normal and “precesses” around the axis in successive
layers. This is analogous to cholesterics and is due to the introduction of opticalactive
or chiral molecules to the smectic-C liquid crystals.

Smectic-C* liquid crystals are interesting in one important respect—namely, that
they comprise a system that permits, by the symmetry principle, the existence of a
spontaneous electric polarization. This can be explained simply in the following way.

The spontaneous electric polarization is a vector and represents a breakdown of
symmetry; that is, there is a directional preference. If the liquid crystal properties are
independent of the director axis direction (i.e., + is the same as - ), , if it exists,
must be locally perpendicular to . In the case of smectic-A, which possesses rotational
symmetry around , must therefore be vanishing. In the case of smectic-C, there is a
reflection symmetry (mirror symmetry) about the plane defined by the and axes, so
is also vanishing.

This reflection symmetry is broken if a chiral center is introduced to the molecule,
resulting in a smectic-C* system. By convention, is defined as positive if it is along
the direction of × , and as negative otherwise. Figure 1.12c shows that since
precesses around , also precesses around . If, by some external field, the helical

Figure 1.12. Molecular arrangements of liquid crystals: (a) smectic-A, (b) smectic-C, (c) smectic-C* or ferroelectric, and (d) unwound smectic-C*.

structure is unwound and points in a fixed direction, as in Figure 1.12d, then will
point in one direction. Clearly, this and other director axis reorientation processes are
accompanied by considerable change in the optical refractive index and other properties
of the system, and they can be utilized in practical electro- and opto-optical
modulation devices. A detailed discussion of smectic liquid crystals is given in
Chapter 4.


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