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Liquid crystal

liquid crystal, liquid crystal display
Liquid crystals LCs are matter in a state which has properties between those of conventional liquids and those of solid crystals1 For instance, a liquid crystal may flow like a liquid, but its molecules may be oriented in a crystal-like way There are many different types of liquid-crystal phases, which can be distinguished by their different optical properties such as birefringence When viewed under a microscope using a polarized light source, different liquid crystal phases will appear to have distinct textures The contrasting areas in the textures correspond to domains where the liquid-crystal molecules are oriented in different directions Within a domain, however, the molecules are well ordered LC materials may not always be in a liquid-crystal phase just as water may turn into ice or steam

Liquid crystals can be divided into thermotropic, lyotropic and metallotropic phases Thermotropic and lyotropic liquid crystals consist mostly of organic molecules, although a few minerals are also known Thermotropic LCs exhibit a phase transition into the liquid-crystal phase as temperature is changed Lyotropic LCs exhibit phase transitions as a function of both temperature and concentration of the liquid-crystal molecules in a solvent typically water Metallotropic LCs are composed of both organic and inorganic molecules; their liquid-crystal transition depends not only on temperature and concentration, but also on the inorganic-organic composition ratio

Examples of liquid crystals can be found both in the natural world and in technological applications Most contemporary electronic displays use liquid crystals Lyotropic liquid-crystalline phases are abundant in living systems but can also be found in the mineral world For example, many proteins and cell membranes are liquid crystals Other well-known examples of liquid crystals are solutions of soap and various related detergents, as well as the tobacco mosaic virus, and some clays

Contents

  • 1 History
  • 2 Design of liquid crystalline materials
  • 3 Liquid-crystal phases
    • 31 Thermotropic liquid crystals
      • 311 Nematic phase
      • 312 Smectic phases
      • 313 Chiral phases
      • 314 Discotic phases
      • 315 Bowlic phases
    • 32 Lyotropic liquid crystals
    • 33 Metallotropic liquid crystals
    • 34 Laboratory analysis of mesophases
  • 4 Biological liquid crystals
  • 5 Mineral liquid crystals
  • 6 Pattern formation in liquid crystals
  • 7 Theoretical treatment of liquid crystals
    • 71 Director
    • 72 Order parameter
    • 73 Onsager hard-rod model
    • 74 Maier–Saupe mean field theory
    • 75 McMillan's model
    • 76 Elastic continuum theory
  • 8 External influences on liquid crystals
    • 81 Electric and magnetic field effects
    • 82 Surface preparations
    • 83 Fredericks transition
  • 9 Effect of chirality
  • 10 Applications of liquid crystals
  • 11 See also
  • 12 References
  • 13 External links

Historyedit

In 1888, Austrian botanical physiologist Friedrich Reinitzer, working at the Karl-Ferdinands-Universität, examined the physico-chemical properties of various derivatives of cholesterol which now belong to the class of materials known as cholesteric liquid crystals Previously, other researchers had observed distinct color effects when cooling cholesterol derivatives just above the freezing point, but had not associated it with a new phenomenon Reinitzer perceived that color changes in a derivative cholesteryl benzoate were not the most peculiar feature

Chemical structure of cholesteryl benzoate molecule

He found that cholesteryl benzoate does not melt in the same manner as other compounds, but has two melting points At 1455 °C 2939 °F it melts into a cloudy liquid, and at 1785 °C 3533 °F it melts again and the cloudy liquid becomes clear The phenomenon is reversible Seeking help from a physicist, on March 14, 1888, he wrote to Otto Lehmann, at that time a Privatdozent in Aachen They exchanged letters and samples Lehmann examined the intermediate cloudy fluid, and reported seeing crystallites Reinitzer's Viennese colleague von Zepharovich also indicated that the intermediate "fluid" was crystalline The exchange of letters with Lehmann ended on April 24, with many questions unanswered Reinitzer presented his results, with credits to Lehmann and von Zepharovich, at a meeting of the Vienna Chemical Society on May 3, 18882

By that time, Reinitzer had discovered and described three important features of cholesteric liquid crystals the name coined by Otto Lehmann in 1904: the existence of two melting points, the reflection of circularly polarized light, and the ability to rotate the polarization direction of light

After his accidental discovery, Reinitzer did not pursue studying liquid crystals further The research was continued by Lehmann, who realized that he had encountered a new phenomenon and was in a position to investigate it: In his postdoctoral years he had acquired expertise in crystallography and microscopy Lehmann started a systematic study, first of cholesteryl benzoate, and then of related compounds which exhibited the double-melting phenomenon He was able to make observations in polarized light, and his microscope was equipped with a hot stage sample holder equipped with a heater enabling high temperature observations The intermediate cloudy phase clearly sustained flow, but other features, particularly the signature under a microscope, convinced Lehmann that he was dealing with a solid By the end of August 1889 he had published his results in the Zeitschrift für Physikalische Chemie3

Otto Lehmann

Lehmann's work was continued and significantly expanded by the German chemist Daniel Vorländer, who from the beginning of 20th century until his retirement in 1935, had synthesized most of the liquid crystals known However, liquid crystals were not popular among scientists and the material remained a pure scientific curiosity for about 80 years4

After World War II work on the synthesis of liquid crystals was restarted at university research laboratories in Europe George William Gray, a prominent researcher of liquid crystals, began investigating these materials in England in the late 1940s His group synthesized many new materials that exhibited the liquid crystalline state and developed a better understanding of how to design molecules that exhibit the state His book Molecular Structure and the Properties of Liquid Crystals5 became a guidebook on the subject One of the first US chemists to study liquid crystals was Glenn H Brown, starting in 1953 at the University of Cincinnati and later at Kent State University In 1965, he organized the first international conference on liquid crystals, in Kent, Ohio, with about 100 of the world’s top liquid crystal scientists in attendance This conference marked the beginning of a worldwide effort to perform research in this field, which soon led to the development of practical applications for these unique materials67

Liquid crystal materials became a focus of research in the development of flat panel electronic displays beginning in 1962 at RCA Laboratories8 When physical chemist Richard Williams applied an electric field to a thin layer of a nematic liquid crystal at 125 °C, he observed the formation of a regular pattern that he called domains now known as Williams Domains This led his colleague George H Heilmeier to perform research on a liquid crystal-based flat panel display to replace the cathode ray vacuum tube used in televisions But the para-Azoxyanisole that Williams and Heilmeier used exhibits the nematic liquid crystal state only above 116 °C, which made it impractical to use in a commercial display product A material that could be operated at room temperature was clearly needed

In 1966, Joel E Goldmacher and Joseph A Castellano, research chemists in Heilmeier group at RCA, discovered that mixtures made exclusively of nematic compounds that differed only in the number of carbon atoms in the terminal side chains could yield room-temperature nematic liquid crystals A ternary mixture of Schiff base compounds resulted in a material that had a nematic range of 22–105 °C9 Operation at room temperature enabled the first practical display device to be made10 The team then proceeded to prepare numerous mixtures of nematic compounds many of which had much lower melting points This technique of mixing nematic compounds to obtain wide operating temperature range eventually became the industry standard and is used to this very day to tailor materials to meet specific applications

Chemical structure of N-4-Methoxybenzylidene-4-butylaniline MBBA molecule

In 1969, Hans Kelker succeeded in synthesizing a substance that had a nematic phase at room temperature, MBBA, which is one of the most popular subjects of liquid crystal research11 The next step to commercialization of liquid crystal displays was the synthesis of further chemically stable substances cyanobiphenyls with low melting temperatures by George Gray12 That work with Ken Harrison and the UK MOD RRE Malvern, in 1973, led to design of new materials resulting in rapid adoption of small area LCDs within electronic products

These molecules are rod-shaped, some created in the lab and some appearing spontaneously in nature Since then, two new types of LC molecules have been discovered, both man-made: disc-shaped created by S Chandrasekhar's group in India, 1977citation needed and bowl-shaped invented by Lui Lam13 in China, 1982, and synthesized in Europe three years later

In 1991, when liquid crystal displays were already well established, Pierre-Gilles de Gennes working at the Université Paris-Sud received the Nobel Prize in physics "for discovering that methods developed for studying order phenomena in simple systems can be generalized to more complex forms of matter, in particular to liquid crystals and polymers"14

Design of liquid crystalline materialsedit

A large number of chemical compounds are known to exhibit one or several liquid crystalline phases Despite significant differences in chemical composition, these molecules have some common features in chemical and physical properties There are three types of thermotropic liquid crystals: discotics, bowlics and rod-shaped molecules Discotics are flat disc-like molecules consisting of a core of adjacent aromatic rings; the core in a bowlic is not flat but like a rice bowl a three-dimensional object1516 This allows for two dimensional columnar ordering, for both discotics and bowlics Rod-shaped molecules have an elongated, anisotropic geometry which allows for preferential alignment along one spatial direction

The molecular shape should be relatively thin, flat or bowl-like, especially within rigid molecular frameworks
The molecular length should be at least 13 nm, consistent with the presence of long alkyl group on many room-temperature liquid crystals
The structure should not be branched or angular, except for the bowlics
A low melting point is preferable in order to avoid metastable, monotropic liquid crystalline phases Low-temperature mesomorphic behavior in general is technologically more useful, and alkyl terminal groups promote this

An extended, structurally rigid, highly anisotropic shape seems to be the main criterion for liquid crystalline behavior, and as a result many liquid crystalline materials are based on benzene rings17

Liquid-crystal phasesedit

The various liquid-crystal phases called mesophases can be characterized by the type of ordering One can distinguish positional order whether molecules are arranged in any sort of ordered lattice and orientational order whether molecules are mostly pointing in the same direction, and moreover order can be either short-range only between molecules close to each other or long-range extending to larger, sometimes macroscopic, dimensions Most thermotropic LCs will have an isotropic phase at high temperature That is that heating will eventually drive them into a conventional liquid phase characterized by random and isotropic molecular ordering little to no long-range order, and fluid-like flow behavior Under other conditions for instance, lower temperature, a LC might inhabit one or more phases with significant anisotropic orientational structure and short-range orientational order while still having an ability to flow118

The ordering of liquid crystalline phases is extensive on the molecular scale This order extends up to the entire domain size, which may be on the order of micrometers, but usually does not extend to the macroscopic scale as often occurs in classical crystalline solids However some techniques, such as the use of boundaries or an applied electric field, can be used to enforce a single ordered domain in a macroscopic liquid crystal sample The ordering in a liquid crystal might extend along only one dimension, with the material being essentially disordered in the other two directions1920

Thermotropic liquid crystalsedit

See also: Thermotropic crystal

Thermotropic phases are those that occur in a certain temperature range If the temperature rise is too high, thermal motion will destroy the delicate cooperative ordering of the LC phase, pushing the material into a conventional isotropic liquid phase At too low temperature, most LC materials will form a conventional crystal118 Many thermotropic LCs exhibit a variety of phases as temperature is changed For instance, on heating a particular type of LC molecule called mesogen may exhibit various smectic phases followed by the nematic phase and finally the isotropic phase as temperature is increased An example of a compound displaying thermotropic LC behavior is para-azoxyanisole21

Nematic phaseedit

See also: Biaxial nematic and Twisted nematic field effect Alignment in a nematic phase Phase transition between a nematic left and smectic A right phases observed between crossed polarizers The black color corresponds to isotropic medium

One of the most common LC phases is the nematic The word nematic comes from the Greek νήμα Greek: nema, which means "thread" This term originates from the thread-like topological defects observed in nematics, which are formally called 'disclinations' Nematics also exhibit so-called "hedgehog" topological defects In a nematic phase, the calamitic or rod-shaped organic molecules have no positional order, but they self-align to have long-range directional order with their long axes roughly parallel22 Thus, the molecules are free to flow and their center of mass positions are randomly distributed as in a liquid, but still maintain their long-range directional order Most nematics are uniaxial: they have one axis that is longer and preferred, with the other two being equivalent can be approximated as cylinders or rods However, some liquid crystals are biaxial nematics, meaning that in addition to orienting their long axis, they also orient along a secondary axis23 Nematics have fluidity similar to that of ordinary isotropic liquids but they can be easily aligned by an external magnetic or electric field Aligned nematics have the optical properties of uniaxial crystals and this makes them extremely useful in liquid crystal displays LCD8

Smectic phasesedit

Schematic of alignment in the smectic phases The smectic A phase left has molecules organized into layers In the smectic C phase right, the molecules are tilted inside the layers

The smectic phases, which are found at lower temperatures than the nematic, form well-defined layers that can slide over one another in a manner similar to that of soap The word "smectic" originates from the Latin word "smecticus", meaning cleaning, or having soap-like properties24 The smectics are thus positionally ordered along one direction In the Smectic A phase, the molecules are oriented along the layer normal, while in the Smectic C phase they are tilted away from it These phases are liquid-like within the layers There are many different smectic phases, all characterized by different types and degrees of positional and orientational order118

Chiral phasesedit

Schematic of ordering in chiral liquid crystal phases The chiral nematic phase left, also called the cholesteric phase, and the smectic C phase right

The chiral nematic phase exhibits chirality handedness This phase is often called the cholesteric phase because it was first observed for cholesterol derivatives Only chiral molecules ie, those that have no internal planes of symmetry can give rise to such a phase This phase exhibits a twisting of the molecules perpendicular to the director, with the molecular axis parallel to the director The finite twist angle between adjacent molecules is due to their asymmetric packing, which results in longer-range chiral order In the smectic C phase an asterisk denotes a chiral phase, the molecules have positional ordering in a layered structure as in the other smectic phases, with the molecules tilted by a finite angle with respect to the layer normal The chirality induces a finite azimuthal twist from one layer to the next, producing a spiral twisting of the molecular axis along the layer normal181920

Chiral nematic phase; p refers to the chiral pitch see text

The chiral pitch, p, refers to the distance over which the LC molecules undergo a full 360° twist but note that the structure of the chiral nematic phase repeats itself every half-pitch, since in this phase directors at 0° and ±180° are equivalent The pitch, p, typically changes when the temperature is altered or when other molecules are added to the LC host an achiral LC host material will form a chiral phase if doped with a chiral material, allowing the pitch of a given material to be tuned accordingly In some liquid crystal systems, the pitch is of the same order as the wavelength of visible light This causes these systems to exhibit unique optical properties, such as Bragg reflection and low-threshold laser emission,25 and these properties are exploited in a number of optical applications419 For the case of Bragg reflection only the lowest-order reflection is allowed if the light is incident along the helical axis, whereas for oblique incidence higher-order reflections become permitted Cholesteric liquid crystals also exhibit the unique property that they reflect circularly polarized light when it is incident along the helical axis and elliptically polarized if it comes in obliquely26

Blue phases are liquid crystal phases that appear in the temperature range between a chiral nematic phase and an isotropic liquid phase Blue phases have a regular three-dimensional cubic structure of defects with lattice periods of several hundred nanometers, and thus they exhibit selective Bragg reflections in the wavelength range of visible light corresponding to the cubic lattice It was theoretically predicted in 1981 that these phases can possess icosahedral symmetry similar to quasicrystals2728

Although blue phases are of interest for fast light modulators or tunable photonic crystals, they exist in a very narrow temperature range, usually less than a few kelvin Recently the stabilization of blue phases over a temperature range of more than 60 K including room temperature 260–326 K has been demonstrated2930 Blue phases stabilized at room temperature allow electro-optical switching with response times of the order of 10−4 s31

In May 2008, the first Blue Phase Mode LCD panel had been developed32

Discotic phasesedit

Disk-shaped LC molecules can orient themselves in a layer-like fashion known as the discotic nematic phase If the disks pack into stacks, the phase is called a discotic columnar The columns themselves may be organized into rectangular or hexagonal arrays Chiral discotic phases, similar to the chiral nematic phase, are also known

Bowlic phasesedit

Bowl-shaped LC molecules, like in discotics, can form columnar phases Other phases, such as nonpolar nematic, polar nematic, stringbean, donut and onion phases, have been predicted Bowlic phases, except nonpolar nematic, are polar phases

Lyotropic liquid crystalsedit

See also: Lyotropic liquid crystal and Columnar phase Structure of lyotropic liquid crystal The red heads of surfactant molecules are in contact with water, whereas the tails are immersed in oil blue: bilayer left and micelle right

A lyotropic liquid crystal consists of two or more components that exhibit liquid-crystalline properties in certain concentration ranges In the lyotropic phases, solvent molecules fill the space around the compounds to provide fluidity to the system33 In contrast to thermotropic liquid crystals, these lyotropics have another degree of freedom of concentration that enables them to induce a variety of different phases

A compound that has two immiscible hydrophilic and hydrophobic parts within the same molecule is called an amphiphilic molecule Many amphiphilic molecules show lyotropic liquid-crystalline phase sequences depending on the volume balances between the hydrophilic part and hydrophobic part These structures are formed through the micro-phase segregation of two incompatible components on a nanometer scale Soap is an everyday example of a lyotropic liquid crystal

The content of water or other solvent molecules changes the self-assembled structures At very low amphiphile concentration, the molecules will be dispersed randomly without any ordering At slightly higher but still low concentration, amphiphilic molecules will spontaneously assemble into micelles or vesicles This is done so as to 'hide' the hydrophobic tail of the amphiphile inside the micelle core, exposing a hydrophilic water-soluble surface to aqueous solution These spherical objects do not order themselves in solution, however At higher concentration, the assemblies will become ordered A typical phase is a hexagonal columnar phase, where the amphiphiles form long cylinders again with a hydrophilic surface that arrange themselves into a roughly hexagonal lattice This is called the middle soap phase At still higher concentration, a lamellar phase neat soap phase may form, wherein extended sheets of amphiphiles are separated by thin layers of water For some systems, a cubic also called viscous isotropic phase may exist between the hexagonal and lamellar phases, wherein spheres are formed that create a dense cubic lattice These spheres may also be connected to one another, forming a bicontinuous cubic phase

The objects created by amphiphiles are usually spherical as in the case of micelles, but may also be disc-like bicelles, rod-like, or biaxial all three micelle axes are distinct These anisotropic self-assembled nano-structures can then order themselves in much the same way as thermotropic liquid crystals do, forming large-scale versions of all the thermotropic phases such as a nematic phase of rod-shaped micelles

For some systems, at high concentrations, inverse phases are observed That is, one may generate an inverse hexagonal columnar phase columns of water encapsulated by amphiphiles or an inverse micellar phase a bulk liquid crystal sample with spherical water cavities

A generic progression of phases, going from low to high amphiphile concentration, is:

  • Discontinuous cubic phase micellar cubic phase
  • Hexagonal phase hexagonal columnar phase middle phase
  • Lamellar phase
  • Bicontinuous cubic phase
  • Reverse hexagonal columnar phase
  • Inverse cubic phase Inverse micellar phase

Even within the same phases, their self-assembled structures are tunable by the concentration: for example, in lamellar phases, the layer distances increase with the solvent volume Since lyotropic liquid crystals rely on a subtle balance of intermolecular interactions, it is more difficult to analyze their structures and properties than those of thermotropic liquid crystals

Similar phases and characteristics can be observed in immiscible diblock copolymers

Metallotropic liquid crystalsedit

Liquid crystal phases can also be based on low-melting inorganic phases like ZnCl2 that have a structure formed of linked tetrahedra and easily form glasses The addition of long chain soap-like molecules leads to a series of new phases that show a variety of liquid crystalline behavior both as a function of the inorganic-organic composition ratio and of temperature This class of materials has been named metallotropic34

Laboratory analysis of mesophasesedit

Thermotropic mesophases are detected and characterized by two major methods, the original method was use of thermal optical microscopy, in which a small sample of the material was placed between two crossed polarizers; the sample was then heated and cooled As the isotropic phase would not significantly affect the polarization of the light, it would appear very dark, whereas the crystal and liquid crystal phases will both polarize the light in a uniform way, leading to brightness and color gradients This method allows for the characterization of the particular phase, as the different phases are defined by their particular order, which must be observed The second method, differential scanning calorimetry DSC, allows for more precise determination of phase transitions and transition enthalpies In DSC, a small sample is heated in a way that generates a very precise change in temperature with respect to time During phase transitions, the heat flow required to maintain this heating or cooling rate will change These changes can be observed and attributed to various phase transitions, such as key liquid crystal transitions

Lyotropic mesophases are analyzed in a similar fashion, though these experiments are somewhat more complex, as the concentration of mesogen is a key factor These experiments are run at various concentrations of mesogen in order to analyze that impact

Biological liquid crystalsedit

Lyotropic liquid-crystalline phases are abundant in living systems, the study of which is referred to as lipid polymorphism Accordingly, lyotropic liquid crystals attract particular attention in the field of biomimetic chemistry In particular, biological membranes and cell membranes are a form of liquid crystal Their constituent molecules eg phospholipids are perpendicular to the membrane surface, yet the membrane is flexible These lipids vary in shape see page on lipid polymorphism The constituent molecules can inter-mingle easily, but tend not to leave the membrane due to the high energy requirement of this process Lipid molecules can flip from one side of the membrane to the other, this process being catalyzed by flippases and floppases depending on the direction of movement These liquid crystal membrane phases can also host important proteins such as receptors freely "floating" inside, or partly outside, the membrane, eg CCT

Many other biological structures exhibit liquid-crystal behavior For instance, the concentrated protein solution that is extruded by a spider to generate silk is, in fact, a liquid crystal phase The precise ordering of molecules in silk is critical to its renowned strength DNA and many polypeptides can also form LC phases and this too forms an important part of current academic research

Mineral liquid crystalsedit

Examples of liquid crystals can also be found in the mineral world, most of them being lyotropics The first discovered was VanadiumV oxide, by Zocher in 192535 Since then, few others have been discovered and studied in detail36 The existence of a true nematic phase in the case of the smectic clays family was raised by Langmuir in 1938,37 but remained open for a very long time and was only solved recently3839 With the rapid development of nanosciences, and the synthesis of many new anisotropic nanoparticles, the number of such mineral liquid crystals is quickly increasing, with, for example, carbon nanotubes and graphene A lamellar phase was even discovered, H3Sb3P2O14, which exhibits hyperswelling up to ~250 nm for the interlamellar distance40

Pattern formation in liquid crystalsedit

See also: Pattern formation

Anisotropy of liquid crystals is a property not observed in other fluids This anisotropy makes flows of liquid crystals behave more differentially than those of ordinary fluids For example, injection of a flux of a liquid crystal between two close parallel plates viscous fingering causes orientation of the molecules to couple with the flow, with the resulting emergence of dendritic patterns41 This anisotropy is also manifested in the interfacial energy surface tension between different liquid crystal phases This anisotropy determines the equilibrium shape at the coexistence temperature, and is so strong that usually facets appear When temperature is changed one of the phases grows, forming different morphologies depending on the temperature change42 Since growth is controlled by heat diffusion, anisotropy in thermal conductivity favors growth in specific directions, which has also an effect on the final shape43

Theoretical treatment of liquid crystalsedit

Microscopic theoretical treatment of fluid phases can become quite complicated, owing to the high material density, meaning that strong interactions, hard-core repulsions, and many-body correlations cannot be ignored In the case of liquid crystals, anisotropy in all of these interactions further complicates analysis There are a number of fairly simple theories, however, that can at least predict the general behavior of the phase transitions in liquid crystal systems

Directoredit

As we already saw above, the nematic liquid crystals are composed of rod-like molecules with the long axes of neighboring molecules aligned approximately to one another To describe this anisotropic structure, a dimensionless unit vector n called the director, is introduced to represent the direction of preferred orientation of molecules in the neighborhood of any point Because there is no physical polarity along the director axis, n and -n are fully equivalent18

Order parameteredit

The local nematic director, which is also the local optical axis, is given by the spatial and temporal average of the long molecular axes

The description of liquid crystals involves an analysis of order A second rank symmetric traceless tensor order parameter is used to describe the orientational order of a nematic liquid crystal, although a scalar order parameter is usually sufficient to describe uniaxial nematic liquid crystals To make this quantitative, an orientational order parameter is usually defined based on the average of the second Legendre polynomial:

S = ⟨ P 2 cos ⁡ θ ⟩ = ⟨ 3 cos 2 ⁡ θ − 1 2 ⟩ \cos \theta \rangle =\left\langle \theta -1\right\rangle

where θ is the angle between the liquid-crystal molecular axis and the local director which is the 'preferred direction' in a volume element of a liquid crystal sample, also representing its local optical axis The brackets denote both a temporal and spatial average This definition is convenient, since for a completely random and isotropic sample, S = 0, whereas for a perfectly aligned sample S=1 For a typical liquid crystal sample, S is on the order of 03 to 08, and generally decreases as the temperature is raised In particular, a sharp drop of the order parameter to 0 is observed when the system undergoes a phase transition from an LC phase into the isotropic phase44 The order parameter can be measured experimentally in a number of ways; for instance, diamagnetism, birefringence, Raman scattering, NMR and EPR can be used to determine S20

The order of a liquid crystal could also be characterized by using other even Legendre polynomials all the odd polynomials average to zero since the director can point in either of two antiparallel directions These higher-order averages are more difficult to measure, but can yield additional information about molecular ordering1

A positional order parameter is also used to describe the ordering of a liquid crystal It is characterized by the variation of the density of the center of mass of the liquid crystal molecules along a given vector In the case of positional variation along the z-axis the density ρ z is often given by:

ρ r = ρ z = ρ 0 + ρ 1 cos ⁡ q s z − φ + ⋯ =\rho z=\rho _+\rho _\cosq_z-\varphi +\cdots \,

The complex positional order parameter is defined as ψ r = ρ 1 r e i φ r =\rho _\mathbf e^ and ρ 0 the average density Typically only the first two terms are kept and higher order terms are ignored since most phases can be described adequately using sinusoidal functions For a perfect nematic ψ = 0 and for a smectic phase ψ will take on complex values The complex nature of this order parameter allows for many parallels between nematic to smectic phase transitions and conductor to superconductor transitions18

Onsager hard-rod modeledit

Unsolved problem in physics:
Can the nematic to smectic A phase transition in liquid crystal states be characterized as a universal phase transition
more unsolved problems in physics

A simple model which predicts lyotropic phase transitions is the hard-rod model proposed by Lars Onsager This theory considers the volume excluded from the center-of-mass of one idealized cylinder as it approaches another Specifically, if the cylinders are oriented parallel to one another, there is very little volume that is excluded from the center-of-mass of the approaching cylinder it can come quite close to the other cylinder If, however, the cylinders are at some angle to one another, then there is a large volume surrounding the cylinder which the approaching cylinder's center-of-mass cannot enter due to the hard-rod repulsion between the two idealized objects Thus, this angular arrangement sees a decrease in the net positional entropy of the approaching cylinder there are fewer states available to it4546

The fundamental insight here is that, whilst parallel arrangements of anisotropic objects lead to a decrease in orientational entropy, there is an increase in positional entropy Thus in some case greater positional order will be entropically favorable This theory thus predicts that a solution of rod-shaped objects will undergo a phase transition, at sufficient concentration, into a nematic phase Although this model is conceptually helpful, its mathematical formulation makes several assumptions that limit its applicability to real systems46

Maier–Saupe mean field theoryedit

This statistical theory, proposed by Alfred Saupe and Wilhelm Maier, includes contributions from an attractive intermolecular potential from an induced dipole moment between adjacent liquid crystal molecules The anisotropic attraction stabilizes parallel alignment of neighboring molecules, and the theory then considers a mean-field average of the interaction Solved self-consistently, this theory predicts thermotropic nematic-isotropic phase transitions, consistent with experiment474849

McMillan's modeledit

McMillan's model, proposed by William McMillan,50 is an extension of the Maier–Saupe mean field theory used to describe the phase transition of a liquid crystal from a nematic to a smectic A phase It predicts that the phase transition can be either continuous or discontinuous depending on the strength of the short-range interaction between the molecules As a result, it allows for a triple critical point where the nematic, isotropic, and smectic A phase meet Although it predicts the existence of a triple critical point, it does not successfully predict its value The model utilizes two order parameters that describe the orientational and positional order of the liquid crystal The first is simply the average of the second Legendre polynomial and the second order parameter is given by:

σ = ⟨ cos ⁡ 2 π z i d 3 2 cos 2 ⁡ θ i − 1 2 ⟩ \right\left\cos ^\theta _-\right\right\rangle

The values zi, θi, and d are the position of the molecule, the angle between the molecular axis and director, and the layer spacing The postulated potential energy of a single molecule is given by:

U i θ i , z i = − U 0 S + α σ cos ⁡ 2 π z i d 3 2 cos 2 ⁡ θ i − 1 2 \theta _,z_=-U_\leftS+\alpha \sigma \cos \left\right\right\left\cos ^\theta _-\right

Here constant α quantifies the strength of the interaction between adjacent molecules The potential is then used to derive the thermodynamic properties of the system assuming thermal equilibrium It results in two self-consistency equations that must be solved numerically, the solutions of which are the three stable phases of the liquid crystal20

Elastic continuum theoryedit

In this formalism, a liquid crystal material is treated as a continuum; molecular details are entirely ignored Rather, this theory considers perturbations to a presumed oriented sample The distortions of the liquid crystal are commonly described by the Frank free energy density One can identify three types of distortions that could occur in an oriented sample: 1 twists of the material, where neighboring molecules are forced to be angled with respect to one another, rather than aligned; 2 splay of the material, where bending occurs perpendicular to the director; and 3 bend of the material, where the distortion is parallel to the director and molecular axis All three of these types of distortions incur an energy penalty They are distortions that are induced by the boundary conditions at domain walls or the enclosing container The response of the material can then be decomposed into terms based on the elastic constants corresponding to the three types of distortions Elastic continuum theory is a particularly powerful tool for modeling liquid crystal devices 51 and lipid bilayers52

External influences on liquid crystalsedit

Scientists and engineers are able to use liquid crystals in a variety of applications because external perturbation can cause significant changes in the macroscopic properties of the liquid crystal system Both electric and magnetic fields can be used to induce these changes The magnitude of the fields, as well as the speed at which the molecules align are important characteristics industry deals with Special surface treatments can be used in liquid crystal devices to force specific orientations of the director

Electric and magnetic field effectsedit

The ability of the director to align along an external field is caused by the electric nature of the molecules Permanent electric dipoles result when one end of a molecule has a net positive charge while the other end has a net negative charge When an external electric field is applied to the liquid crystal, the dipole molecules tend to orient themselves along the direction of the field

Even if a molecule does not form a permanent dipole, it can still be influenced by an electric field In some cases, the field produces slight re-arrangement of electrons and protons in molecules such that an induced electric dipole results While not as strong as permanent dipoles, orientation with the external field still occurs The effects of magnetic fields on liquid crystal molecules are analogous to electric fields Because magnetic fields are generated by moving electric charges, permanent magnetic dipoles are produced by electrons moving about atoms When a magnetic field is applied, the molecules will tend to align with or against the field

Surface preparationsedit

In the absence of an external field, the director of a liquid crystal is free to point in any direction It is possible, however, to force the director to point in a specific direction by introducing an outside agent to the system For example, when a thin polymer coating usually a polyimide is spread on a glass substrate and rubbed in a single direction with a cloth, it is observed that liquid crystal molecules in contact with that surface align with the rubbing direction The currently accepted mechanism for this is believed to be an epitaxial growth of the liquid crystal layers on the partially aligned polymer chains in the near surface layers of the polyimide

Fredericks transitionedit

The competition between orientation produced by surface anchoring and by electric field effects is often exploited in liquid crystal devices Consider the case in which liquid crystal molecules are aligned parallel to the surface and an electric field is applied perpendicular to the cell At first, as the electric field increases in magnitude, no change in alignment occurs However at a threshold magnitude of electric field, deformation occurs Deformation occurs where the director changes its orientation from one molecule to the next The occurrence of such a change from an aligned to a deformed state is called a Fredericks transition and can also be produced by the application of a magnetic field of sufficient strength

The Fredericks transition is fundamental to the operation of many liquid crystal displays because the director orientation and thus the properties can be controlled easily by the application of a field

Effect of chiralityedit

As already described, chiral liquid-crystal molecules usually give rise to chiral mesophases This means that the molecule must possess some form of asymmetry, usually a stereogenic center An additional requirement is that the system not be racemic: a mixture of right- and left-handed molecules will cancel the chiral effect Due to the cooperative nature of liquid crystal ordering, however, a small amount of chiral dopant in an otherwise achiral mesophase is often enough to select out one domain handedness, making the system overall chiral

Chiral phases usually have a helical twisting of the molecules If the pitch of this twist is on the order of the wavelength of visible light, then interesting optical interference effects can be observed The chiral twisting that occurs in chiral LC phases also makes the system respond differently from right- and left-handed circularly polarized light These materials can thus be used as polarization filters53

It is possible for chiral LC molecules to produce essentially achiral mesophases For instance, in certain ranges of concentration and molecular weight, DNA will form an achiral line hexatic phase An interesting recent observation is of the formation of chiral mesophases from achiral LC molecules Specifically, bent-core molecules sometimes called banana liquid crystals have been shown to form liquid crystal phases that are chiral54 In any particular sample, various domains will have opposite handedness, but within any given domain, strong chiral ordering will be present The appearance mechanism of this macroscopic chirality is not yet entirely clear It appears that the molecules stack in layers and orient themselves in a tilted fashion inside the layers These liquid crystals phases may be ferroelectric or anti-ferroelectric, both of which are of interest for applications5556

Chirality can also be incorporated into a phase by adding a chiral dopant, which may not form LCs itself Twisted-nematic or super-twisted nematic mixtures often contain a small amount of such dopants

Applications of liquid crystalsedit

See also: Liquid crystal display Structure of liquid crystal display: 1 – vertical polarization filter, 2,4 – glass with electrodes, 3 – liquid crystals, 5 – horizontal polarization filter, 6 – reflector "Wikipedia" displayed on an LCD

Liquid crystals find wide use in liquid crystal displays, which rely on the optical properties of certain liquid crystalline substances in the presence or absence of an electric field In a typical device, a liquid crystal layer typically 4 μm thick sits between two polarizers that are crossed oriented at 90° to one another The liquid crystal alignment is chosen so that its relaxed phase is a twisted one see Twisted nematic field effect8 This twisted phase reorients light that has passed through the first polarizer, allowing its transmission through the second polarizer and reflected back to the observer if a reflector is provided The device thus appears transparent When an electric field is applied to the LC layer, the long molecular axes tend to align parallel to the electric field thus gradually untwisting in the center of the liquid crystal layer In this state, the LC molecules do not reorient light, so the light polarized at the first polarizer is absorbed at the second polarizer, and the device loses transparency with increasing voltage In this way, the electric field can be used to make a pixel switch between transparent or opaque on command Color LCD systems use the same technique, with color filters used to generate red, green, and blue pixels8 Chiral smectic liquid crystals are used in ferroelectric LCDs which are fast-switching binary light modulators Similar principles can be used to make other liquid crystal based optical devices57

Liquid crystal tunable filters are used as electrooptical devices, eg, in hyperspectral imaging

Thermotropic chiral LCs whose pitch varies strongly with temperature can be used as crude liquid crystal thermometers, since the color of the material will change as the pitch is changed Liquid crystal color transitions are used on many aquarium and pool thermometers as well as on thermometers for infants or baths58 Other liquid crystal materials change color when stretched or stressed Thus, liquid crystal sheets are often used in industry to look for hot spots, map heat flow, measure stress distribution patterns, and so on Liquid crystal in fluid form is used to detect electrically generated hot spots for failure analysis in the semiconductor industry59

Liquid crystal lasers use a liquid crystal in the lasing medium as a distributed feedback mechanism instead of external mirrors Emission at a photonic bandgap created by the periodic dielectric structure of the liquid crystal gives a low-threshold high-output device with stable monochromatic emission6061

Polymer dispersed liquid crystal PDLC sheets and rolls are available as adhesive backed Smart film which can be applied to windows and electrically switched between transparent and opaque to provide privacy

Many common fluids, such as soapy water, are in fact liquid crystals Soap forms a variety of LC phases depending on its concentration in water62

Bowlic columns could be used for fast switches63

See alsoedit

  • Biaxial nematic
  • Columnar phase
  • Chromonic
  • LCD classification
  • Liquid crystal display
  • Liquid crystal on silicon
  • Liquid crystal polymer
  • Liquid crystal tunable filter
  • Lyotropic liquid crystal
  • Pattern formation
  • Plastic crystal
  • Smart glass
  • Thermochromics
  • Thermotropic crystal
  • Twisted nematic field effect
  • Nematicon
  • Liquid crystal thermometer
  • Mood ring

Referencesedit

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External linksedit

  • "History and Properties of Liquid Crystals" Nobelprizeorg Retrieved June 6, 2009 
  • Definitions of basic terms relating to low-molar-mass and polymer liquid crystals IUPAC Recommendations 2001
  • An intelligible introduction to liquid crystals from Case Western Reserve University
  • Liquid Crystal Physics tutorial from the Liquid Crystals Group, University of Colorado
  • Liquid Crystals & Photonics Group – Ghent University Belgium, good tutorial
  • Simulation of light propagation in liquid crystals, free program
  • Liquid Crystals Interactive Online
  • Liquid Crystal Institute Kent State University
  • Liquid Crystals a journal by Taylor&Francis
  • Molecular Crystals and Liquid Crystals a journal by Taylor & Francis
  • Hot-spot detection techniques for ICs
  • What are liquid crystals from Chalmers University of Technology, Sweden
  • H Kleinert & K Maki 1981 "Lattice Textures in Cholesteric Liquid Crystals" PDF Fortschritte der Physik 29 5: 219 Bibcode:1981ForPh29219K doi:101002/prop19810290503 
  • Progress in liquid crystal chemistry Thematic series in the Open Access Beilstein Journal of Organic Chemistry
  • DoITPoMS Teaching and Learning Package- "Liquid Crystals"
  • Bowlic liquid crystal from San Jose State University

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