Introduction To Liquid Crystals Engineering Essay Example

to distinguish between a substance being in a crystal or liquid crystal state. Crystalline substances display a three-dimensional periodic order, while isotropic liquids lack orientational order. However, there are substances that exhibit some degree of alignment but are not as ordered as solids, known as liquid crystals. To quantify the level of order in a substance, an order parameter (S) is defined. The conventional formula for the order parameter is: [Formula] where theta denotes the angle between the manager and the long axis of each molecule.

The brackets represent a norm across all molecules in the sample. In an isotropic liquid, the norm of the cosine footings is zero, meaning the order parameter is also zero. In a perfect crystal, the order parameter is equal to one. The order parameter of a liquid crystal typically ranges from 0.3 to 0.9, depending on temperature and kinetic molecular motion. The graph below illustrates this for a nematic liquid crystal material (to be discussed in the next section).

The liquid crystal molecules have a tendency to align along the manager, resulting in anisotropy. Anisotropy indicates that the properties of a material depend on how they are measured. For instance, cutting wood is easier along the grain rather than against it. The anisotropic nature of liquid crystals gives them unique optical properties that scientists and engineers utilize in various applications.

Qualifying Liquid Crystals

The structure of liquid crystals can be described by the following parameters:

• Positional order
• Orientational order
• Bond orientational order

Each parameter signifies the degree of ordering in the liquid crystal sample.

Positional order refers to the degree

of translational symmetry exhibited by a molecule or group of molecules, similar to the order seen in crystalline materials. On the other hand, orientational order indicates the extent to which molecules align along a specific direction over a long distance. Bond Orientational Order refers specifically to the alignment of neighboring molecules along a line connecting their centers, without requiring a regular spacing along that line. In other words, there is a relatively long-range order in terms of the center line, but only short-range positional order along that line itself. This concept is further discussed in texts such as Chandrasekhar's "Liquid Crystals" when exploring hexatic phases. It should be noted that most liquid crystal compounds display polymorphism, meaning they exhibit more than one phase in the liquid crystalline state.

The term mesophase refers to the "subphases" of liquid crystal materials. Mesophases are created by changing the level of order in the sample, either by imposing order in one or two dimensions or by allowing the molecules to have some degree of translational motion. The following section provides a more detailed explanation of the different mesophases of liquid crystals.

Liquid Crystal Phases:

There are various types of liquid crystal phases, depending on the degree of order in the material. This section will explain the phase behavior of liquid crystal materials, which is a distinct phase observed between the crystalline (solid) and isotropic (liquid) states.

Nematic Phases:

The nematic liquid crystal phase is characterized by molecules that have no positional order but tend to align in the same way (along the director). In the following diagram, observe that the molecules point vertically but are arranged without any specific

order. Liquid crystals are anisotropic materials, and the physical properties of the system change with the average alignment with the director. If the alignment is large, the material is highly anisotropic. Similarly, if the alignment is small, the material is nearly isotropic. The phase transition of a nematic liquid crystal is shown in the following video provided by Dr.

Mary Neubert, LCI-KSU, explains that the nematic stage can be identified by its marbleized texture. As the temperature increases, the substance transitions into a black, isotropous liquid. Within the category of nematic liquid crystals, there is a specific type called chiral nematic, which is capable of selectively reflecting one component of circularly polarized visible radiation. The terms chiral nematic and cholesteric are used interchangeably.

For more information about this mesophase, please refer to the subdivision on cholesteric liquid crystals.

Smectic Phases:

The term "smectic" is derived from the Greek word for soap. This apparently ambiguous beginning is explained by the fact that the middle, slippery substance often found at the bottom of a soap dish is actually a type of smectic liquid crystal. The smectic phase is another distinct mesophase of liquid crystal substances. Molecules in this phase show a degree of translational order not present in the nematic phase. In the smectic phase, the molecules maintain the general orientational order of nematics, but also tend to align themselves in layers or planes. Movement is restricted to within these planes, and separate planes are observed to flow past each other.

The smectic phase has increased order compared to the nematic phase. A polarising microscope is used to capture an image of a smectic stage. Multiple

types of smectic stages can be observed, with up to 12 of these fluctuations identified. However, only the most notable stages are discussed here.
In the smectic-A mesophase, the manager is perpendicular to the smectic plane and there is no specific positional order within the layer. Similarly, in the smectic-B mesophase, the manager is perpendicular to the smectic plane but the molecules form a hexagonal web within the layer. In the smectic-C mesophase, the molecules are arranged like in the smectic-A mesophase, but the manager is at a constant angle relative to the smectic plane. The smectic-C mesophase also includes a chiral state called C* similar to the nematic phase.

The tilt angle of the manager in the smectic-C phase is similar to that in the smectic-C*, with the difference being that in the smectic-C* phase, the angle rotates from one bed to the next, forming a spiral. This means that the manager is not parallel or perpendicular to the beds, but rather it rotates between them. The diagram below shows the turn of the manager in each bed, indicated by the green pointers. On the left is a conventional representation of a smectic C* stage, and on the right is the same stage shown along the axis.

In certain smectic mesophases, the molecules experience an influence from the various layers above and below them, resulting in a small amount of three-dimensional alignment being observed. An example that demonstrates this type of alignment is Smectic-G.

Cholesteric Phases:

The cholesteric (or chiral nematic) liquid crystal phase is typically made up of nematic mesogenic molecules that contain a chiral center. This produces intermolecular forces that promote alignment

between molecules at a slight angle to each other.

This results in the creation of a structure that can be imagined as a stack of extremely thin 2-D nematic-like layers, with each layer's orientation twisted in relation to the ones above and below. In this structure, the orientations of the layers form a continuous coiling pattern around the normal of the layer, as shown by the black pointer in the figure and animation below. The black pointer in the animation represents the orientation of the layers along the stack. The depicted molecules are representations of the many chiral nematic mesogens present in the thin slabs, with a range of orientations around the layer's orientation. It's important to note that this should not be confused with the flat arrangement found in smectic mesophases. One significant characteristic of the cholesteric mesophase is its pitch, denoted as P. The pitch is defined as the distance it takes for the layers to complete one full rotation in the spiral, as shown in the animation above.

A result of the coiling construction of the chiral nematic stage is its ability to selectively reflect visible radiation of wavelengths equal to the pitch length. This means that a color will be reflected when the pitch matches the corresponding wavelength of visible radiation in the visible spectrum. This consequence occurs because the gradual change in manager orientation between consecutive layers, as shown above, affects the pitch length and consequently changes the wavelength of reflected light depending on the temperature. The angle at which the manager changes can be increased by raising the temperature of the molecules, which tightens the pitch. On the other hand,

lowering the temperature of the molecules increases the pitch length of the chiral nematic liquid crystal. This characteristic allows for the creation of a liquid crystal thermometer that displays the temperature of its surroundings through reflected color. Mixtures of various types of these liquid crystals are commonly used in detectors with a wide range of responses to temperature variations.

Thermometers often use detectors in the form of heat sensitive films to detect defects in circuit board connections, fluid flow patterns, battery conditions, the presence of radiation, or in novelties like "mood" rings. In order to avoid degradation and possible contamination from placing chiral nematic liquid crystals directly on a black background, the crystals are encapsulated into very small particles. These particles are then treated with a binding material that contracts upon curing to flatten the microcapsules and produce optimal alignment for brighter colors. Chiral nematic liquid crystals that are less temperature sensitive can be used to create materials like clothing, dolls, inks, and pigments. The wavelength of reflected light can also be controlled by adjusting the chemical composition, as cholesterics can consist of either purely chiral molecules or nematic molecules with a dispersed chiral dopant.

In this case, the concentration of the dopant is utilized to determine the chirality and thus the pitch.

External Influences on Liquid Crystals:

Scientists and applied scientists can utilize liquid crystals in various applications because external disturbances can cause significant changes in the macroscopic properties of the liquid crystal system. Both electric and magnetic fields can induce these changes. The magnitude of the fields, as well as the speed at which the molecules align, are important factors in industry. Additionally, specific surface treatments can

be employed in liquid crystal devices to enforce specific orientations of the director.

Electric and Magnetic Field Effects:

The response of liquid crystal molecules to an electric field is the primary characteristic utilized in industrial applications.

The manager's ability to align with an external field is due to the electrical characteristics of its molecules, which have permanent electric dipoles. These dipoles consist of one end having a net positive charge and the other end having a net negative charge. When a liquid crystal comes into contact with an external electric field, the dipole molecules align themselves in the same direction as the field. In the given diagram, black arrows represent the vector of the electric field, while red arrows depict the force exerted on molecules by electricity. Even if a molecule does not have a permanent dipole, it can still be affected by an electric field.

When an external field is present, molecules can undergo limited rearrangement of electrons and protons, resulting in the creation of an induced electric dipole. Despite being weaker than permanent dipoles, alignment with the external field still occurs. The effect of magnetic fields on liquid crystal molecules is similar to that of electric fields. As magnetic fields are produced by moving electric charges, the movement of electrons around atoms leads to the formation of permanent magnetic dipoles. When a magnetic field is applied, the molecules tend to align either parallel or anti-parallel to the field.

Methods for Preparing Surfaces:

In situations without an external field, liquid crystals have free orientation. However, it is possible to impose a specific orientation by introducing an external agent into the system.

When a thin polymer coating, usually a polyimide, is applied

to a glass substrate and rubbed using a fabric, it is observed that the liquid crystal molecules in contact with the surface align in the same direction as the rubbing motion. The current belief is that this alignment occurs through an epitaxial growth of the liquid crystal layers on the partially aligned polymer chains in the surface layers of the polyimide.

Freedericksz Passage:

The competition between surface anchoring and electric field effects is often utilized in liquid crystal devices. An example of this is when the liquid crystal molecules align parallel to the surface while an electric field is applied perpendicular to the cell, as depicted in the following diagram.

Initially, there is no change in alignment as the electric field increases in magnitude. However, once the electric field reaches a certain threshold, distortion occurs. This distortion happens when the orientation of the molecules changes from one to the next. This transition from an aligned to a distorted state is known as Freedericksz passage and can also be induced by applying a sufficiently strong magnetic field. The Freedericksz passage plays a crucial role in the functionality of many liquid crystal displays since the orientation of the molecules (and thus their properties) can be easily controlled through field application.

Mention the applications subdivision for more information about liquid crystals used in shows.

Light and Polarization:

This subdivision will present some of the basic constructs that are important in understanding the optical behavior of liquid crystals. This is by no means a complete discussion of the subject; it is only intended to be used in the context of liquid crystal optical behavior. Please refer to Jenkins and White for a detailed treatment.

Light and Polarization:

Light is an electromagnetic wave composed of perpendicular electric and magnetic fields. In the diagram below, the left side illustrates the electric field in the xy plane, the magnetic field in the xz plane, and the propagation direction of the wave in the z direction. The right half of the diagram shows the path traced by the electric field vector as it propagates. Typically, only the electric field vector is considered as the magnetic field component behaves similarly. This oscillating electric field can be visualized as a rope held by two children at opposite ends. The children move their ends in a way that causes the rope to move in a specified plane, such as up and down or left and right, or at any angle in between.

Ordinary white visible radiation is composed of waves oscillating in all possible directions. When light is "linearly polarized," it means that the waves only oscillate in one particular plane. It is similar to a rope passing through a fence with vertical openings, where the rope can move up and down but is restricted from any other direction. A polarizer is a material that selectively allows light with a specific vibrating angle to pass through.

The path of variation that the polarizer follows is known as the "easy" axis. When two polarizers are arranged in a series with parallel optical axes, light passes through both. However, when the axes are positioned 90 degrees apart (crossed), the polarized light from the first polarizer is blocked by the second. As the angle rotates from 0 to 90 degrees, the amount of transmitted

light decreases.

This consequence is illustrated in the following diagram. The polarizers are parallel at the top and crossed at the bottom.

Polarized Light:

Linear polarization is just a specific case of circularly polarized visible radiation. Consider two light waves, one polarized in the YZ plane and the other in the XY plane.

When the waves reach their maximum and minimum points simultaneously (in phase), their vector sum results in one wave that is linearly polarized at 45 degrees. This is illustrated in the diagram below. Similarly, when two waves are out of phase by 180 degrees, the resultant wave is linearly polarized at 45 degrees but in the opposite direction. If the two waves are out of phase by 90 degrees (one wave at its peak and the other wave at its trough), the resulting wave is circularly polarized.

The electric field vector of the constituents rotates around the beginning as the moving wave propagates. This can be seen in the diagram below, which illustrates the electric field vectors for two different waves. In the most general case, the phase difference between the vectors can be at any angle, not just 90 or 180 degrees. When this occurs, it is referred to as elliptical polarization, as the electric field vector traces out an oval shape instead of a straight line or circle as previously described.

) These concepts can instead abstract the first clip they are presented. The following simulation allows the user to adjust the stage displacement to an arbitrary value to detect the associated polarization state.

Double refraction in Liquid Crystals:

The previous section introduced the concepts of polarized radiation and polarizers. This section will demonstrate how these ideas

are important to liquid crystals.

Liquid crystals exhibit birefringence due to their anisotropic properties, meaning they have the ability to refract light in two different ways. When light is polarized parallel to the manager, it has a different refractive index and travels at a different speed compared to light polarized perpendicular to the manager. In the following diagram, the blue lines represent the manager field and the pointers indicate the polarization vector.

When visible radiation enters a birefringent material, such as a nematic liquid crystal sample, it is divided into two components: the fast beam (known as the ordinary beam) and the slow beam (known as the extraordinary beam). These components travel at different speeds, causing a phase difference. As the beams exit the birefringent material and are recombined, the polarization state is altered due to this phase difference. The direction that light takes through a birefringent medium depends on its polarization. The double refraction of a material is characterized by the difference, Dn, in the indices of refraction for the ordinary and extraordinary beams. To express this more quantitatively, the index of refraction of a material is defined as the ratio of the velocity of light in a vacuum to its velocity in the material. In this case, we have ne = c/V| | and no = c/V^ for the velocities of a wave traveling parallel and perpendicular to the director, respectively. Thus, the maximum value for double refraction is Dn = ne - no.

We will not cover here the general instance of a moving wave traveling in an arbitrary way relative to the manager in a liquid crystal sample, except to note that Dn

varies from zero to the maximum value, depending on the direction of travel. The condition Ne & gt; no describes a positive uniaxial material, so that nematic liquid crystals fall into this category. For typical nematic liquid crystals, no is approximately 1.5 and the maximum difference, Dn, may range between 0.05 and 0.5. The length of the sample is another important parameter because the phase displacement accumulates as long as the light propagates in the birefringent material. Any polarization state can be produced with the right combination of the double refraction and length parameters. It is convenient here to introduce the concept of optical path in media since for the above two wave components traveling with different velocities in a birefringent material, the difference in optical paths will lead to a change in the polarization state of the wave as it progresses through the medium.

We define the optical path for a moving wave with distance L in a crystal as nL, so that the optical path difference for the two wave components mentioned above will be L (ne - no) = LDn. The corresponding phase difference between the two components (the amount by which the slow, extraordinary component slows down behind the fast, ordinary one) is only 2p LDn/lv where lv is the wavelength in vacuum. The following simulation demonstrates the optical properties of a birefringent material. A linearly polarized light wave enters a crystal whose extraordinary (slow) index of refraction can be controlled by the user.

The sample's length can be varied, and the outgoing polarization state is displayed. The concept of optical path difference and its impact on polarization state can also be investigated

here. This leads to a discussion on optical retardation plates or phase retarders within the simulation.

Application to Liquid Crystals' Polarized Light Studies:

Observe the scenario where a liquid crystal sample is inserted between crossed polarizers with transmission axes aligned at an angle between the material's fast and slow axes. Due to the sample's birefringent nature, the incoming linearly polarized light transforms into elliptically polarized light, as previously observed in the simulation. When this beam reaches the second polarizer, there is now a component that can pass through, resulting in a bright region.

The magnitude of the phase difference for monochromatic light depends on the length and double refraction of the material. When the material is thin, the ordinary and extraordinary components do not have a significant phase difference. Conversely, when the material is thick, the phase difference can be large. If the phase difference equals 360 degrees, the wave returns to its original polarization state and is blocked by the second polarizer.

The strength of the familial light is determined by the size of the stage displacement. If the transmittal axis of the first polarizer is parallel to either the ordinary or extraordinary waies, no alteration in the polarisation province occurs and the radiation is not broken up into constituents. In this instance, there is no familial constituent and the part appears dark. In a typical liquid crystal, the double refraction and length are not constant over the entire sample. Therefore, some areas appear light while others appear dark, as shown in the microscope image below. These light and dark areas indicate differences in manager orientation, double refraction, and length.

Image courtesy of E. Merck Company The Schlieren texture,

also known as the peculiar agreement of the nematic stage, displays dark parts called coppices that represent alignment analogue or perpendicular to the manager. The following subdivision will provide a more detailed depiction of the textures of liquid crystals. However, before exploring that, let's examine how double refraction can result in various images when liquid crystals are scrutinized under polarized white visible radiation.

Colors Originating From Polarized Light Studies:

So far, we have only dealt with monochromatic visible radiation when considering the optical properties of materials. To understand the origin of colors observed in studies of liquid crystals placed between crossed linear polarizers, it would be helpful to refer back to the examples of retarding plates discussed in the Birefringence Simulation.

They are designed for a specific wavelength and therefore produce desired results for a limited range of wavelengths around that particular value. For example, if a full-wave plate designed for wavelength lA? is placed between crossed polarizers at any orientation and illuminated with white light, only the wavelength lA? will not be affected by the retarder and will be absorbed by the analyze. However, all other wavelengths will experience some delay and exit the full-wave plate with different polarization states. The light that passes through the analyze will then form the complementary color to lA?. Color patterns observed in the polarizing microscope, along with the extinctions discussed earlier in relation to Birefringence Simulations, are very useful in studying liquid crystals in various situations, including identifying textures, liquid crystal phases, and observing phase changes.

Textures and Defects:

The optical properties of liquid crystals alone allow them to be used in various applications. This section explains

how these properties arise.

Liquid Crystal Textures

The term texture refers to the alignment of liquid crystal molecules near a surface. Each liquid crystal mesophase can form its own characteristic textures, which are useful in identification. We focus on nematic textures here, deferring discussion of cholesteric textures until the section on polymer stabilized cholesteric liquid crystals.

If mesogenic materials are contained between closely spaced rubbed surfaces (as described above) and oriented with rubbing directions parallel, the entire liquid crystal sample can be oriented in a planar texture, as shown in the following diagram. Mesogens can also be oriented perpendicular to a surface using appropriate polymer films or in the presence of an electric field applied perpendicular to the surface, resulting in the homeotropic texture, as depicted below.

Chemical Properties of Liquid Crystals:

Liquid crystals can be classified into two main categories: thermotropic liquid crystals and lyotropic liquid crystals. These two types of liquid crystals are distinguished by the mechanisms that drive their self-organization, but they are also similar in many ways. Thermotropic transitions occur in most liquid crystals and are defined by the fact that the transitions to the liquid crystalline state are induced thermally. In other words, one can reach the liquid crystalline state by increasing the temperature of a solid and/or decreasing the temperature of a liquid.

Thermotropic liquid crystals can be categorized into two types: enantiotropic and monotropic. Enantiotropic liquid crystals can transition into the liquid crystal phase by either lowering the temperature of a liquid or raising the temperature of a solid. Monotropic liquid crystals, on the other hand, can only transition into the liquid crystal phase by either increasing the temperature

of a solid or decreasing the temperature of a liquid, but not both simultaneously. The occurrence of thermotropic mesophases is generally due to anisotropic scattering forces between molecules and packing interactions. In contrast, lyotropic liquid crystal transitions are influenced by solvents rather than temperature changes. Lyotropic mesophases form when the component mesogens are assembled into micellar structures through solvent-induced aggregation. Lyotropic mesogens are typically composed of both lyophilic (solvent-attracting) and lyophobic (solvent-repelling) parts, which cause them to form micellar structures when dissolved in a solvent. In these structures, the lyophobic ends stay together while the lyophilic ends extend outward towards the solution.

As the concentration of the solution increases and it is cooled, the size of the micelles increase and eventually blend. This separates the newly formed liquid crystalline region from the solvent. A large number of chemical compounds are known to exhibit one or several liquid crystalline phases, despite differences in their chemical composition. These molecules have common characteristics in terms of their chemical and physical properties. There are two types of thermotropic liquid crystals: discotics and bacillar molecules. Discotics are flat, disc-shaped molecules composed of a nucleus made up of adjacent aromatic rings. This structure allows for two-dimensional columnar arrangement.

Bacillar molecules are elongated and anisotropic, allowing for selective alignment in one spatial direction. The rod-like low molar mass ( LMM ) liquid crystals, like 5CB shown in the diagram below, require an extended shape of the molecule. This shape is maintained by the rigidity and one-dimensionality of its components. In order for a molecule to exhibit liquid crystal properties, it must be both stiff and bacillar. To achieve this, two stiff cyclic units are

interconnected. The connecting group should result in a compound with a linear planar shape. Connecting units can include multiple bonds such as - ( CH=N ) - , -N=N- , - ( CH=CH ) n- , -CH=N-N=CH- , etc.

The use of html tags restricts the freedom of rotary motion which can be conjugated with phenylene rings to increase the anisotropic polarizability and maintain the molecular length and rigidness.

Applications of Liq