Liquid crystals

In the fundamental physics, such as high school physics or university physics, everyone has been taught that substance only exists three phases: solid, liquid, and gas. In particular, some organic materials do not show a single transition from solid phase to liquid phase. The mechanical and the symmetry properties of these new phases are intermediate between those of a liquid and those of a solid.

Therefore, these new phases are often called “liquid crystals”. Liquid crystals can be divided into three different phase depending on the physical properties, such as thermotropic, lyotropic and metallotropic phases. The thermotropic liquid crystals exhibit a phase transition into the liquid crystal phase as temperature is changed. The phase transition of the lyotropic liquid crystals depends on both temperature and concentration of the liquid crystal molecules in a solvent, such as water. Most of the thermotropic and lyotropic liquid crystals consist of organic molecules. The metallotropic liquid crystals are composed of not only organic but also inorganic molecules. The liquid crystal transition of the metallotropic liquid crystal depends not only on temperature and concentration, but also on the inorganic-organic composition ratio.

According to the different arrangement of liquid crystal molecules, the thermotropic liquid crystals can also be distinguished into three different types:

nematic, smectic, and cholesteric. Figure 1-1 shows the schematic of liquid crystal alignment in these three different phases. In the nematic phase, the liquid crystal molecules have no positional order, but have long-range orientational order. Therefore, the center of mass positions of the liquid crystal molecules are randomly distributed as a liquid, but they all point to the same direction. The smectic phase usually forms several well-defined layers, and is usually found at

lower temperature than the nematic phase. There are many different smectic phases. All of these smectic phases are characterized by different types and degrees of positional and orientational order. [1] The cholesteric phase, also called the chiral nematic phase, exhibits chirality or handedness. The first cholesteric phase was observed for cholesterol derivatives. Most of the liquid crystals which have the cholesteric phase are chiral molecules that are without inversion symmetry.[1] In this work, nematic liquid crystal is used in most of our experiment.

The well arrangement of the anisotropic rodlike molecules directly results in the anisotropy of mechanical, electric, magnetic, and optical properties. In the liquid crystal displays applications, the most important anisotropic properties are the optical and electric properties. As a result of the orientational ordering of the nematic liquid crystals molecules, the nematic liquid crystals are uniaxial with the symmetric axis parallel to the axes of the molecules, called the director nˆ. Because of the uniaxial symmetry, the dielectric constants are different in value parallel to (ε_//) and perpendicular to (ε_⊥) the director. The dielectric anisotropy is defined as

− ⊥

=

Δε ε_// ε _{. (1-1)}

The sign and magnitude of the dielectric anisotropy are both important in liquid crystal displays application by using the various electric fields to control the liquid crystal displays. Usually, the macroscopic dielectric constant is often proportional to the molecular polarizability. For the rodlike molecules, such as the nematic liquid crystal molecules, the longitudinal polarizability (parallel to molecular axis) is often larger than the transverse polarizability (perpendicular to axis). Most of the rodlike molecules have induced dipole in the applied electric field. Because the induced dipole is parallel to the director, the dielectric anisotropy is positive, Δε >0, and ε_// >ε_⊥. 4`-n-pentyl-4-cyanobiphenyl (5CB) is one of the most common positive nematic liquid crystals in literatures.[2] Some

polar liquid crystal compounds have the permanent dipole moment. Depending on the angle between the permanent dipole moment and the molecular axis, the additional contributions increase or decrease the dielectric constant. The increase or decrease of the dielectric anisotropy Δ results in the negative value of the ε dielectric anisotropy, called the negative liquid crystals (e.g., p-Methoxybenzylidene-p`-n-butylaniline, MBBA).[1] The dielectric anisotropy also depends on the temperature. ε_// and ε_⊥ approaches to each other near the clearing point T_c. Beyond the clearing point, the dielectric constant becomes the mean dielectric constant

3

// +2 ⊥

=ε ε

ε . (1-2)

Figure 1-2 shows the characteristic of the dielectric constants for 5CB.[3]

Here, ε is calculated from the measured values of ε_//, ε_⊥ and Equation (1-2).

The dashed line denotes the extrapolated value of the dielectric anisotropy in isotropic state, ε_iso.[4]

On the other hand, the nematic liquid crystals also show the anisotropic properties in optical region, called the optical anisotropy. Without proper boundaries or the applied field (magnetic field or electric field), the directors and the refractive index of liquid crystal molecules are random, and the incident light is scattered. Because of the discontinuity of the refractive indices at the domain boundaries, the nematic liquid crystals usually appear as a milky fluid. A nematic liquid crystal cell with the proper treated alignment layers exhibits the optical properties as an uniaxial crystal with two principal refractive indices n_o and n_e. The ordinary refractive index n_o is for light with the polarization of the electric field perpendicular to the director. The extraordinary refractive index n_e is for light with the polarization of the electric field parallel to the director. The optical anisotropy, also called the birefringence, is defined as

o

e n

n n= −

Δ . (1-3)

If Δn>0⇒n_e >n_o, the liquid crystal has positive birefringence, whereas if

o

e n

n n< ⇒ <

Δ 0 , the liquid crystal has negative birefringence. For most liquid crystals, the ordinary refractive index n is around 1.5, and the birefringence is _o from 0.05 to 0.45. This optical anisotropy plays an essential role in changing the polarization state of light in liquid crystals. Figure 1-3 shows the characteristic of n , e n and _o Δn of 5CB.[5] It clearly shows the similar behavior as the dielectric constants. It is because that the refractive index is also related to the molecular polarizability at optical frequencies and the anisotropic molecular structure.