Why are liquid crystals so interesting?

Nematic liquid crystal media have uniaxial symmetry, which means that in a homogeneous liquid crystal medium a rotation around the director does not make a difference. The bulk ordering has a profound influence on the way light and electric fields behave in the material. Uniaxial anisotropy results in different electrical and optical parameters if considered along the director or in a plane perpendicular to it. This gives rise to interesting technological possibilities. Two unusual phenomena are the following: the reorientation of the molecules in an electric field and optical birefringence of the molecules.

Reorientation of the molecules in electric fields

As a result of the uniaxial anisotropy, an electric field experiences a different dielectric constant when oscillating in a direction parallel or perpendicular to the director. The difference is called the dielectric anisotropy. If the dielectric constant along the director is larger than in the direction perpendicular to it, one speaks of positive anisotropy.

Due to the anisotropy, the dielectric displacement and the induced dipole moment are not parallel to the electric field, except when the director is parallel or perpendicular to the electric field. As a result, a torque is exerted on the director. For materials with positive anisotropy, the director prefers to align parallel to the electric field. Liquid crystals with a negative anisotropy tend to orient themselves perpendicularly to the electric field.

The effect of an electric field on a liquid crystal medium with positive anisotropy is illustrated in the pictures below. Originally the orientation is almost horizontal. When an electric field with direction along the blue arrow is applied, a torque (represented in green) rising from the dielectric anisotropy, acts on the molecule. The torque tends to align the molecule parallel to the field. When the field strength is increased, the molecule will reorient parallel to the field.

Original position of the liquid crystal molecule Tork on the liquid crystal molecule due to the electric field
Original orientation Situation in electric field
Rotation of the liquid crystal molecule Rotation of the liquid crystal molecule in a strong electric field
Result electric field Result strong electric field

The technological importance of the reorientation is obvious: it gives a switchable medium by simply varying the applied electric field in the liquid crystal medium. In most applications a liquid crystal is used in a thin layer between two glass surfaces. To generate the electric field, thin electrodes layers are deposited on the bottom and/or top glass surface. For optical devices transparent electrodes are used, made from Indium Tin Oxide (ITO). If the generated field is strong enough, the molecules will reorient to follow its direction.

Optical birefringence

Applications of liquid crystals almost always involve optics. Optical waves also involve electric fields, but the associated frequencies are much higher than those of the fields generated by the applied voltages. Therefore the dielectric constants, which arise from the electronic response of the molecules to the externally applied fields, are different. To make the distinction, the refractive index is usually given for optical waves instead of the dielectric constant.

Optical waves can also reorient the liquid crystal director in an analogue manner as the electrically applied fields. In a display this can be neglected, since both the optical dielectric anisotropy and the intensity of the optical fields are typically much lower than those used in the static case. Therefore the optical transmission is mostly independent of the director calculations.

To understand the influence of birefringence on the propagation of light through a liquid crystal, the light must be represented by an electric field. This electric field is described by a wave vector in each point. At a certain time and location, the direction and the length of the vector correspond with the direction and magnitude of the electric field. For a plane wave propagating in a specific direction, the electric field vector in an isotropic medium describes an ellipse in the plane perpendicular to the propagation direction. This ellipse represents the polarization of the light. Some special cases are the linear polarization and the circular polarization where this ellipse is distorted to a straight line or a perfect circle. Generally each ellipsoidal polarization can be decomposed as a superposition of linear polarizations along two perpendicular axes. In an isotropic medium, both linear polarizations move with the same speed. The speed of the wave is determined by the refractive index of the medium.

Light propagation in an isotropic medium
Light propagation in an isotropic medium

For the uniaxial liquid crystal medium, an electric field feels a different refractive index when it oscillates in the plane perpendicular to the director or along the director. This uniaxial anisotropy of the refractive index is called birefringence. Birefringence allows to manipulate the polarization of the light propagating through the medium.

The elliptical polarization of light entering a liquid crystal medium must be decomposed into two linear polarizations called the ordinary and the extra-ordinary mode. Along these two directions, the two linearly polarized modes feel a different refractive index. Therefore, they propagate through the liquid crystal with a different speed as illustrated in the picture below.

Light propagation in an anisotropic medium
Light propagation in a birefringent medium

In the isotropic medium, the two parts propagated with the same speed. Combining them back together will result in the same polarization ellipse as the original. In birefringent media, the different speed of the ordinary and extra-ordinary waves results in a phase difference between the two modes (= retardation). At the end of the medium this phase difference between the two oscillations will result in a different polarization ellipse.

Switchable birefringence

To observe the influence of birefringence, polarized light must be used. Most light sources such as a light bulb or a fluorescent lamp produce unpolarized light. Optical applications often required polarized light with a known oscillation direction of the light. To obtain polarized light, ordinary light sources can be used in combination with polarizers.

A polarizer is a special type of birefringent layer. The ordinary wave propagates unmodified through the medium, whereas the extra-ordinary wave is absorbed in the medium. An arbitrarily polarized wave entering such a medium will result in a linearly polarized wave at the back of the medium. In the picture above the effect of a polarizer is illustrated for two different orientations of the absorbing direction.


Polarizer with vertical transmission axis
Polarizer with vertical transmission axis
Polarizer with horizontal transmission axis
Polarizer with horizontal transmission axis

If two polarizers with orthogonal absorption direction are used, all light emitted by the light source is absorbed. This is typically referred to as a set of crossed polarizers.

Polarizer with vertical transmission axis
Crossed polarizers

Birefringence is important for modifying and controlling the polarization of light propagating through the medium. A liquid crystal layer inserted between crossed polarizers can change the polarization of the light propagating through, which results in light transmission after the crossed polarizers.

Polarizer with vertical transmission axis
A liquid crystal layer between crossed polarizers

Because the director can be controlled using an electric field, a liquid crystal is a controllable birefringent medium. Therefore, the polarization state of the light after the liquid crystal layer can be changed and hence the intensity of the transmission through the crossed polarizers is adapted.

Choosing the preferential direction of the molecules

In a glass vessel a liquid crystal appears as an opaque milky fluid. The random variation of the director in the material on a micrometer scale is the main cause of the light scattering.

For applications, it is important to obtain a region free of defects with a known director distribution. Therefore, liquid crystals are usually handled in thin layers between two substrates. Control of the director at the surfaces allows reproducible director orientations as illustrated below. The fixed orientation of the surface director forces the director in the bulk to follow this direction. Two commonly used types of alignment are planar and homeotropic alignment. In planar alignment the surface director is oriented parallel to the surface, for homeotropic alignment it is oriented perpendicular to the surface.

Planar alignment Homeotropic alignment Alignment by rubbing
Planar alignment Homeotropic alignment Alignment by rubbing

Another simple and widely used process to achieve planar alignment is rubbing. A polymer layer (e.g. polyimide, nylon or polyvinylalcohol) is deposited on the surface and rubbed with a soft tissue. A liquid crystal deposited on the rubbed polymer surface will exhibit a surface director parallel to the direction of rubbing. One could say that microscopic grooves are created in the surface which align the director. The direction of rubbing and the resulting surface director are shown below.

Alignment along the rubbing direction
Alignment along the rubbing direction

The alignment with the surface is not perfect, there is a small angle of 1 or 2 degrees between the surface and the molecule director which is called the pretilt. The pretilt depends on the strength of the rubbing.

Pretilt originating from the rubbing process
Pretilt originating from the rubbing process

Liquid crystals are generally used in thin layers between two glass parallel substrates. The distance, between the top and bottom substrate in a liquid crystal cell ranges typically from 1 to 100 µm, depending on the used liquid crystal and the intended application. The two surfaces are kept parallel at a constant distance by spacers: microscopic spheres or rods made of polymer or glass. The spacers are mixed in the glue that holds the two substrates together and if necessary also spread on the whole substrate surface by spinning.

The figure below shows three examples of liquid crystal layers sandwiched between two substrates. On the surfaces in contact with the liquid crystal, rubbed alignment layers are deposited. In the left picture, the alignment layers of both surfaces were rubbed in the same direction. This is called a Π-cell or splay cell. The obtained director distribution is inhomogeneous and shows a splay distortion.

Parallel rubbed liquid crystal cell Anti-parallel rubbed liquid crystal cell Twisted nematic liquid crystal cell
Splay-cell Anti-parallel rubbed Twisted nematic

A homogeneous director distribution is obtained when the top and bottom substrate are rubbed in opposite direction as illustrated in the middle picture. An angle of 90° between the rubbing at the top and bottom substrate results in a linear variation of the twist angle along the surface normal. This is referred to as a twisted nematic cell.

Calculation of the director pattern in a liquid crystal medium

A liquid crystal medium prefers a uniform director distribution. A variation of the director in space induces an increase of the free energy. According to the elastic theory for liquid crystals, the elastic energy related to the variation of the director 'n' in space can be written as

    Elastic energy due to the distribution of the molecule orienation

with the three elastic constants k11, k22 and k33. This equation is known as the Oseen-Frank distortion energy. The three terms in the equation are related to distortion due to splay, twist and bend respectively as illustrated in the figure below. General deformations are a mixture of these three types.

Twist, bend and splay of liquid crystal molecules

Calculations of the equilibrium director distribution involve minimizing the total free energy of the volume. The total energy of a liquid crystal is made up of three components: the elastic energy density (as described above), the interface energy

    Interface energy at the borders

related to the alignment of the director at the surfaces of the considered volume and the electric energy density

    Electric energy due to the tork of the electric field

related to the interaction of the applied electric field and the director of the liquid crystal molecule.

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Liquid crystal tutorial written by Chris Desimpel, based on the introduction of his Ph.D. thesis and literature.