Liquid crystal
![](https://upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Nematische_Phase_Schlierentextur.jpg/300px-Nematische_Phase_Schlierentextur.jpg)
Condensed matter physics |
---|
![]() |
Liquid crystal(LC) is astate of matterwhose properties are between those of conventionalliquidsand those of solidcrystals.For example, a liquid crystal can flow like a liquid, but itsmoleculesmay be oriented in a common direction as in a solid. There are many types of LCphases,which can be distinguished by theiropticalproperties (such astextures). The contrasting textures arise due to molecules within one area of material ( "domain" ) being oriented in the same direction but different areas having different orientations. An LC material may not always be in an LC state of matter (just as water may be ice or water vapor).
Liquid crystals can be divided into three main types:thermotropic,lyotropic,andmetallotropic.Thermotropic and lyotropic liquid crystals consist mostly oforganic molecules,although a few minerals are also known. Thermotropic LCs exhibit aphase transitioninto the LC phase as temperature changes. Lyotropic LCs exhibit phase transitions as a function of both temperature andconcentrationof molecules in asolvent(typically water). Metallotropic LCs are composed of both organic and inorganic molecules; their LC transition additionally depends on the inorganic-organic composition ratio.
Examples of LCs exist both in the natural world and in technological applications. Lyotropic LCs abound in living systems; many proteins and cell membranes are LCs, as well as thetobacco mosaic virus[citation needed].LCs in the mineral world include solutions ofsoapand various relateddetergents,and someclays.Widespreadliquid-crystal displays(LCD) use liquid crystals.
History
[edit]In 1888, Austrian botanical physiologistFriedrich Reinitzer,working at theKarl-Ferdinands-Universität,examined the physico-chemical properties of variousderivativesofcholesterolwhich 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 thefreezing point,but had not associated it with a new phenomenon. Reinitzer perceived that color changes in a derivativecholesteryl benzoatewere not the most peculiar feature.
![](https://upload.wikimedia.org/wikipedia/commons/thumb/9/9a/Cholesteryl_benzoate.png/250px-Cholesteryl_benzoate.png)
He found that cholesteryl benzoate does notmeltin the same manner as other compounds, but has twomelting points.At 145.5 °C (293.9 °F) it melts into a cloudy liquid, and at 178.5 °C (353.3 °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 toOtto Lehmann,at that time aPrivatdozentinAachen.They exchanged letters and samples. Lehmann examined the intermediate cloudy fluid, and reported seeingcrystallites.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, 1888.[1]
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 ofcircularly 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 incrystallographyandmicroscopy.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 inpolarized 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 theZeitschrift für Physikalische Chemie.[2]
![](https://upload.wikimedia.org/wikipedia/commons/thumb/5/51/Otto_Lehmann.jpg/180px-Otto_Lehmann.jpg)
Lehmann's work was continued and significantly expanded by the German chemistDaniel Vorländer,who from the beginning of the 20th century until he retired 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 years.[3]
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 bookMolecular Structure and the Properties of Liquid Crystals[4]became a guidebook on the subject. One of the first U.S. chemists to study liquid crystals was Glenn H. Brown, starting in 1953 at theUniversity of Cincinnatiand later atKent 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 materials.[5][6]
Liquid crystal materials became a focus of research in the development of flat panel electronic displays beginning in 1962 atRCALaboratories.[7]When physical chemist Richard Williams applied an electric field to a thin layer of anematicliquid crystal at 125 °C, he observed the formation of a regular pattern that he called domains (now known as Williams Domains). This led his colleagueGeorge H. Heilmeierto perform research on a liquid crystal-based flat panel display to replace the cathode ray vacuum tube used in televisions. But thepara-azoxyanisolethat 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 ofSchiff basecompounds resulted in a material that had a nematic range of 22–105 °C.[8]Operation at room temperature enabled the first practical display device to be made.[9]The team then proceeded to prepare numerous mixtures of nematic compounds many of which had much lower melting points. This technique of mi xing nematic compounds to obtain wideoperating temperaturerange eventually became the industry standard and is still used to tailor materials to meet specific applications.
![](https://upload.wikimedia.org/wikipedia/commons/thumb/7/78/MBBA_cleaner.svg/220px-MBBA_cleaner.svg.png)
In 1969, Hans Kelker succeeded in synthesizing a substance that had a nematic phase at room temperature,N-(4-methoxybenzylidene)-4-butylaniline(MBBA), which is one of the most popular subjects of liquid crystal research.[10]The next step to commercialization of liquid-crystal displays was the synthesis of further chemically stable substances (cyanobiphenyls) with low melting temperatures byGeorge Gray.[11]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 laboratory and some appearing spontaneously in nature. Since then, two new types of LC molecules have been synthesized:disc-shaped(bySivaramakrishna Chandrasekharin India in 1977)[12]and cone or bowl shaped (predicted by Lui Lam in China in 1982 and synthesized in Europe in 1985).[13]
In 1991, when liquid crystal displays were already well established,Pierre-Gilles de Gennesworking at theUniversité Paris-Sudreceived 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 materials
[edit]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: discotic, conic (bowlic), and rod-shaped molecules. Discotics are disc-like molecules consisting of a flat core of adjacent aromatic rings, whereas the core in a conic LC is not flat, but is shaped like a rice bowl (a three-dimensional object).[15][16]This allows for two dimensional columnar ordering, for both discotic and conic LCs. Rod-shaped molecules have an elongated, anisotropic geometry which allows forpreferential alignmentalong one spatial direction.
- The molecular shape should be relatively thin, flat or conic, especially within rigid molecular frameworks.
- The molecular length should be at least 1.3 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 conic LC.
- 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 rings.[17]
Liquid-crystal phases
[edit]The various liquid-crystal phases (calledmesophasestogether withplastic crystalphases) 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). Liquid crystals are characterized by orientational order, but only partial or completely absent positional order. In contrast, materials with positional order but no orientational order are known asplastic crystals.[18]Most thermotropic LCs will have anisotropicphase at high temperature: heating will eventually drive them into a conventional liquid phase characterized by random and isotropic molecular ordering andfluid-like flow behavior. Under other conditions (for instance, lower temperature), a LC might inhabit one or more phases with significantanisotropicorientational structure and short-range orientational order while still having an ability to flow.[19][20]
The ordering of liquid crystals extends up to the entire domain size, which may be on the order of micrometers, but usually not to the macroscopic scale as often occurs in classicalcrystallinesolids. However some techniques, such as the use of boundaries or an appliedelectric field,can be used to enforce a single ordered domain in a macroscopic liquid crystal sample.[21]The orientational ordering in a liquid crystal might extend along only onedimension,with the material being essentially disordered in the other two directions.[22][23]
Thermotropic liquid crystals
[edit]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 crystal.[19][20]Many thermotropic LCs exhibit a variety of phases as temperature is changed. For instance, a particular type of LC molecule (called amesogen) 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 ispara-azoxyanisole.[24]
Nematic phase
[edit]![](https://upload.wikimedia.org/wikipedia/commons/thumb/8/80/LiquidCrystal-MesogenOrder-Nematic.jpg/120px-LiquidCrystal-MesogenOrder-Nematic.jpg)
![](https://upload.wikimedia.org/wikipedia/commons/thumb/6/67/Smectic_nematic.jpg/220px-Smectic_nematic.jpg)
The simplest liquid crystal phase is the nematic. In a nematic phase,calamiticorganic molecules lack a crystalline positional order, but do self-align with their long axes roughly parallel. The molecules are free to flow and their center of mass positions are randomly distributed as in a liquid, but their orientation is constrained to form a long-range directional order.[25]
The wordnematiccomes from theGreekνήμα(Greek:nema), which means "thread". This term originates from thedisclinations:thread-liketopological defectsobserved in nematic phases.
Nematics also exhibit so-called "hedgehog" topological defects. In two dimensions, there are topological defects with topological charges+1/2and-1/2.Due to hydrodynamics, the+1/2defect moves considerably faster than the-1/2defect. When placed close to each other, the defects attract; upon collision, they annihilate.[26][27]
Most nematic phases are uniaxial: they have one axis (called a directrix) that is longer and preferred, with the other two being equivalent (can be approximated as cylinders or rods). However, some liquid crystals arebiaxial nematic,meaning that in addition to orienting their long axis, they also orient along a secondary axis.[28]Nematic crystals 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 inliquid-crystal displays(LCD).[7]
Nematic phases are also known in non-molecular systems: at high magnetic fields, electrons flow inbundles or stripesto create an "electronic nematic" form of matter.[29][30]
Smectic phases
[edit]![](https://upload.wikimedia.org/wikipedia/commons/thumb/f/f2/LiquidCrystal-MesogenOrder-SmecticPhases.jpg/220px-LiquidCrystal-MesogenOrder-SmecticPhases.jpg)
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 properties.[31] 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 order.[19][20]Beyond organic molecules, Smectic ordering has also been reported to occur within colloidal suspensions of 2-D materials or nanosheets.[32][33]One example of smectic LCs isp,p'-dinonylazobenzene.[34]
Chiral phases or twisted nematics
[edit]![](https://upload.wikimedia.org/wikipedia/commons/thumb/b/bf/LiquidCrystal-MesogenOrder-ChiralPhases.jpg/220px-LiquidCrystal-MesogenOrder-ChiralPhases.jpg)
Thechiralnematicphase exhibitschirality(handedness). This phase is often called thecholestericphase because it was first observed forcholesterolderivatives. Onlychiral moleculescan 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 normal, hence they are also calledtwisted nematics.[20][22][23]
![](https://upload.wikimedia.org/wikipedia/commons/d/d2/Cholesterinisch.png)
Thechiral 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 thewavelengthofvisible light.This causes these systems to exhibit unique optical properties, such asBragg reflectionand low-thresholdlaseremission,[35]and these properties are exploited in a number of optical applications.[3][22]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 andelliptically polarizedif it comes in obliquely.[36]
![](https://upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Wikipedia_LCD_prototype.jpg/211px-Wikipedia_LCD_prototype.jpg)
Blue phases
[edit]Blue phases are liquid crystal phases that appear in the temperature range between achiralnematicphase and anisotropicliquid phase. Blue phases have a regular three-dimensional cubic structure of defects withlatticeperiods of several hundred nanometers, and thus they exhibit selectiveBragg reflectionsin the wavelength range of visible light corresponding to thecubic lattice.It was theoretically predicted in 1981 that these phases can possess icosahedral symmetry similar toquasicrystals.[38][39]
Although blue phases are of interest for fast light modulators or tunablephotonic crystals,they exist in a very narrow temperature range, usually less than a fewkelvins.Recently the stabilization of blue phases over a temperature range of more than 60 K including room temperature (260–326 K) has been demonstrated.[40][41]Blue phases stabilized at room temperature allow electro-optical switching with response times of the order of 10−4s.[42]In May 2008, the firstblue phase mode LCDpanel had been developed.[43]
Blue phase crystals, being a periodic cubic structure with a bandgap in the visible wavelength range, can be considered as3D photonic crystals.Producing ideal blue phase crystals in large volumes is still problematic, since the produced crystals are usually polycrystalline (platelet structure) or the single crystal size is limited (in the micrometer range). Recently, blue phases obtained as ideal 3D photonic crystals in large volumes have been stabilized and produced with different controlled crystal lattice orientations.[44]
Discotic phases
[edit]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 adiscotic columnar.The columns themselves may be organized into rectangular or hexagonal arrays. Chiral discotic phases, similar to the chiral nematic phase, are also known.
Conic phases
[edit]Conic 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. Conic phases, except nonpolar nematic, are polar phases.[45]
Lyotropic liquid crystals
[edit]![](https://upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Lipid_bilayer_and_micelle.svg/250px-Lipid_bilayer_and_micelle.svg.png)
Alyotropic liquid crystalconsists of two or more components that exhibit liquid-crystalline properties in certain concentration ranges. In thelyotropicphases,solventmolecules fill the space around the compounds to providefluidityto the system.[46]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 immisciblehydrophilicandhydrophobicparts within the same molecule is called anamphiphilicmolecule. 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 intomicellesorvesicles.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 cubicphase)
- Hexagonal phase(hexagonal columnar phase) (middle phase)
- Lamellar phase
- Bicontinuouscubic 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 diblockcopolymers.
Metallotropic liquid crystals
[edit]Liquid crystal phases can also be based on low-melting inorganic phases likeZnCl2that 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 metallotropic.[47]
Laboratory analysis of mesophases
[edit]Thermotropicmesophasesare detected and characterized by two major methods, the original method was use of thermal optical microscopy,[48][49]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),[48]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 ofmesogenin order to analyze that impact.
Biological liquid crystals
[edit]Lyotropic liquid-crystalline phases are abundant in living systems, the study of which is referred to aslipid polymorphism.Accordingly, lyotropic liquid crystals attract particular attention in the field of biomimetic chemistry. In particular,biological membranesandcell membranesare a form of liquid crystal. Their constituent molecules (e.g.phospholipids) are perpendicular to the membrane surface, yet the membrane is flexible.[50]These lipids vary in shape (see page onlipid 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 byflippasesand 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, e.g. CTP:phosphocholine cytidylyltransferase (CCT).
Many other biological structures exhibit liquid-crystal behavior. For instance, the concentratedproteinsolution that is extruded by a spider to generatesilkis, in fact, a liquid crystal phase. The precise ordering of molecules in silk is critical to its renowned strength.DNAand manypolypeptides,including actively-driven cytoskeletal filaments,[51]can also form liquid crystal phases. Monolayers of elongated cells have also been described to exhibit liquid-crystal behavior, and the associated topological defects have been associated with biological consequences, including cell death and extrusion.[52]Together, these biological applications of liquid crystals form an important part of current academic research.
Mineral liquid crystals
[edit]Examples of liquid crystals can also be found in the mineral world, most of them being lyotropic. The first discovered wasvanadium(V) oxide,by Zocher in 1925.[53]Since then, few others have been discovered and studied in detail.[54]The existence of a truenematicphase in the case of the smectiteclaysfamily was raised by Langmuir in 1938,[55]but remained an open question for a very long time and was only confirmed recently.[56][57]
With the rapid development of nanosciences, and the synthesis of many new anisotropicnanoparticles,the number of such mineral liquid crystals is increasing quickly, with, for example, carbon nanotubes and graphene. A lamellar phase was even discovered, H3Sb3P2O14,which exhibits hyperswelling up to ~250 nm for the interlamellar distance.[32]
Pattern formation in liquid crystals
[edit]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 patterns.[58]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 change.[59]Since growth is controlled by heat diffusion, anisotropy in thermal conductivity favors growth in specific directions, which has also an effect on the final shape.[60]
Theoretical treatment of liquid crystals
[edit]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.
Director
[edit]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 vectorncalled thedirector,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,nand-nare fully equivalent.[20]
Order parameter
[edit]![](https://upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Nematic-Director.png/220px-Nematic-Director.png)
The description of liquid crystals involves an analysis of order. A second rank symmetric traceless tensor order parameter, theQ tensoris used to describe the orientational order of the most generalbiaxial nematicliquid crystal. However, to describe the more common case of uniaxial nematic liquid crystals, a scalar order parameter is sufficient.[61]To make this quantitative, an orientational order parameter is usually defined based on the average of the secondLegendre polynomial:
whereis the angle between the liquid-crystal molecular axis and thelocal director(which is the 'preferred direction' in a volume element of a liquid crystal sample, also representing itslocal 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,Sis on the order of 0.3 to 0.8, 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 phase.[62]The order parameter can be measured experimentally in a number of ways; for instance,diamagnetism,birefringence,Raman scattering,NMRandEPRcan be used to determine S.[23]
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 ordering.[19]
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 thez-axis the densityis often given by:
The complex positional order parameter is defined asandthe 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 nematicand for a smectic phasewill 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 transitions.[20]
Onsager hard-rod model
[edit]A simple model which predicts lyotropic phase transitions is the hard-rod model proposed byLars 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 adecreasein the net positionalentropyof the approaching cylinder (there are fewer states available to it).[63][64]
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 systems.[64]An extension of Onsager Theory was proposed by Flory to account for non entropic effects.
Maier–Saupe mean field theory
[edit]This statistical theory, proposed byAlfred Saupeand Wilhelm Maier, includes contributions from an attractive intermolecular potential from an induced dipole moment between adjacent rod-like liquid crystal molecules. The anisotropic attraction stabilizes parallel alignment of neighboring molecules, and the theory then considers amean-fieldaverage of the interaction. Solved self-consistently, this theory predicts thermotropic nematic-isotropic phase transitions, consistent with experiment.[65][66][67]Maier-Saupe mean field theory is extended to high molecular weight liquid crystals by incorporating thebending stiffnessof the molecules and using the method ofpath integrals in polymer science.[68]
McMillan's model
[edit]McMillan's model, proposed by William McMillan,[69]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 secondLegendre polynomialand the second order parameter is given by:
The valueszi,θi,anddare 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:
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 crystal.[23]
Elastic continuum theory
[edit]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 theFrank 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 an effective tool for modeling liquid crystal devices and lipid bilayers.[70][71]
External influences on liquid crystals
[edit]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 effects
[edit]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.[72]
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 response of any system to an external electrical field is
where,andare the components of the electric field, electric displacement field and polarization density. The electric energy per volume stored in the system is
(summation over the doubly appearing index). In nematic liquid crystals, the polarization, and electric displacement both depend linearly on the direction of the electric field. The polarization should be even in the director since liquid crystals are invariants under reflexions of.The most general form to expressis
(summation over the index) withandthe electricpermittivityparallel and perpendicular to the director.Then density of energy is (ignoring the constant terms that do not contribute to the dynamics of the system)[73]
(summation over). Ifis positive, then the minimum of the energy is achieved whenandare parallel. This means that the system will favor aligning the liquid crystal with the externally applied electric field. Ifis negative, then the minimum of the energy is achieved whenandare perpendicular (in nematics the perpendicular orientation is degenerated, making possible the emergence of vortices[74]).
The differenceis called dielectrical anisotropy and is an important parameter in liquid crystal applications. There are bothandcommercial liquid crystals.5CBandE7 liquid crystal mixtureare twoliquid crystals commonly used.MBBAis a commonliquid crystal.
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. Electromagnetic radiation, e.g. UV-Visible light, can influence light-responsive liquid crystals which mainly carry at least a photo-switchable unit.[75]
Surface preparations
[edit]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.
Several liquid crystal chemicals also align to a 'command surface' which is in turn aligned by electric field of polarized light. This process is calledphotoalignment.
Fréedericksz transition
[edit]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 aFréedericksz transitionand can also be produced by the application of a magnetic field of sufficient strength.
The Fréedericksz 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 chirality
[edit]As already described,chiralliquid-crystal molecules usually give rise to chiral mesophases. This means that the molecule must possess some form of asymmetry, usually astereogeniccenter. An additional requirement is that the system not beracemic: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 aspolarization filters.[76]
It is possible for chiral LC molecules to produce essentially achiral mesophases. For instance, in certain ranges of concentration andmolecular 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 chiral.[77]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 beferroelectricor anti-ferroelectric, both of which are of interest for applications.[78][79]
Chirality can also be incorporated into a phase by adding a chiraldopant,which may not form LCs itself.Twisted-nematicorsuper-twisted nematicmixtures often contain a small amount of such dopants.
Applications of liquid crystals
[edit]![](https://upload.wikimedia.org/wikipedia/commons/thumb/d/dc/LCD_layers.svg/220px-LCD_layers.svg.png)
![](https://upload.wikimedia.org/wikipedia/commons/thumb/1/12/Wikipedia_Liquid_Crystal_Display_Arduino.jpg/220px-Wikipedia_Liquid_Crystal_Display_Arduino.jpg)
Liquid crystals find wide use in liquid crystal displays, which rely on theopticalproperties of certain liquid crystalline substances in the presence or absence of anelectric field.In a typical device, a liquid crystal layer (typically 4 μm thick) sits between twopolarizersthat are crossed (oriented at 90° to one another). The liquid crystal alignment is chosen so that its relaxed phase is a twisted one (seeTwisted nematic field effect).[7]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 pixels.[7]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 devices.[80]
Liquid crystal tunable filtersare used aselectro-opticaldevices,[81][82]e.g., inhyperspectral imaging.
Thermotropicchiral LCs whose pitch varies strongly with temperature can be used as crudeliquid 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 baths.[83]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 forfailure analysisin thesemiconductorindustry.[84]
Liquid crystal lenses converge or diverge the incident light by adjusting the refractive index of liquid crystal layer with applied voltage or temperature. Generally, the liquid crystal lenses generate a parabolic refractive index distribution by arranging molecular orientations. Therefore, a plane wave is reshaped into a parabolic wavefront by a liquid crystal lens. Thefocal lengthof liquid crystal lenses could be continuously tunable when the external electric field can be properly tuned. Liquid crystal lenses are a kind ofadaptive optics.Imaging systems can benefit from focusing correction, image plane adjustment, or changing the range ofdepth-of-fieldordepth of focus.The liquid crystal lense is one of the candidates to develop vision correction devices formyopiaandpresbyopia(e.g., tunable eyeglass and smart contact lenses).[85][86]Being an opticalphase modulator,a liquid crystal lens feature space-variantoptical path length(i.e., optical path length as the function of its pupil coordinate). In different imaging system, the required function ofoptical path lengthvaries from one to another. For example, to converge a plane wave into a diffraction limited spot, for a physically-planar liquid crystal structure, the refractive index of liquid crystal layer should be spherical or paraboloidal underparaxial approximation.As for projecting images or sensing objects, it may be expected to have the liquid crystal lens with aspheric distribution of optical path length across its aperture of interest. Liquid crystal lenses with electrically tunable refractive index (by addressing the different magnitude of electric field on liquid crystal layer) have potentials to achieve arbitrary function ofoptical path lengthfor modulating incoming wavefront; current liquid crystalfreeformoptical elements were extended from liquid crystal lens with same optical mechanisms.[87]The applications of liquid crystals lenses includes pico-projectors, prescriptions lenses (eyeglasses or contact lenses), smart phone camera, augmented reality, virtual reality etc.
Liquid crystal lasersuse a liquid crystal in thelasing mediumas a distributed feedback mechanism instead of external mirrors. Emission at aphotonic bandgapcreated by the periodic dielectric structure of the liquid crystal gives a low-threshold high-output device with stable monochromatic emission.[35][88]
Polymer dispersed liquid crystal(PDLC) sheets and rolls are available as adhesive backedSmart filmwhich can be applied to windows and electrically switched between transparent and opaque to provide privacy.
Many common fluids, such assoapy water,are in fact liquid crystals. Soap forms a variety of LC phases depending on its concentration in water.[89]
Liquid crystal films have revolutionized the world of technology. Currently they are used in the most diverse devices, such as digital clocks, mobile phones, calculating machines and televisions. The use of liquid crystal films in optical memory devices, with a process similar to the recording and reading ofCDsandDVDsmay be possible.[90][91]
Liquid crystals are also used as basic technology to imitatequantum computers,usingelectric fieldsto manipulate the orientation of the liquid crystalmolecules,to store data and to encode a different value for every different degree of misalignment with other molecules.[92][93]
See also
[edit]- Biaxial nematic
- Columnar phase
- LCD classification
- Liquid-crystal display– Display that uses the light-modulating properties of liquid crystals
- Liquid crystal on silicon– Type of display technology
- Liquid-crystal polymer– Class of extremely unreactive, inert and fire-resistant polymers
- Liquid crystal tunable filter
- Lyotropic liquid crystal
- Pattern formation– Study of how patterns form by self-organization in nature
- Plastic crystal– non-classical state of matter
- Smart glass– Glass with electrically switchable opacity
- Thermochromism– Property of substances to change colour due to a change in temperature
- Thermotropic crystal
- Twisted nematic field effect– Type of thin-film-transistor liquid-crystal display technology
- Nematicon
- Liquid crystal thermometer
- Mood ring– A ring that contains a thermochromic element
- Active fluid
References
[edit]- ^Reinitzer F (1888)."Beiträge zur Kenntniss des Cholesterins".Monatshefte für Chemie.9(1): 421–441.doi:10.1007/BF01516710.S2CID97166902.Archivedfrom the original on November 4, 2022.RetrievedSeptember 8,2021.
- ^Lehmann O (1889). "Über fliessende Krystalle".Zeitschrift für Physikalische Chemie.4:462–72.doi:10.1515/zpch-1889-0434.S2CID92908969.
- ^abSluckin TJ, Dunmur DA, Stegemeyer H (2004).Crystals That Flow – classic papers from the history of liquid crystals.London: Taylor & Francis.ISBN978-0-415-25789-3.
- ^Gray GW (1962).Molecular Structure and the Properties of Liquid Crystals.Academic Press.
- ^Stegemeyer H (1994)."Professor Horst Sackmann, 1921 – 1993".Liquid Crystals Today.4:1–2.doi:10.1080/13583149408628630.
- ^"Liquid Crystals".King Fahd University of Petroleum & Minerals.Archived fromthe originalon August 5, 2012.
- ^abcdCastellano JA (2005).Liquid Gold: The Story of Liquid Crystal Displays and the Creation of an Industry.World Scientific Publishing.ISBN978-981-238-956-5.
- ^US 3540796,Goldmacher JE, Castellano JA, "Electro-optical Compositions and Devices", issued 17 November 1970, assigned to RCA Corp
- ^Heilmeier GH, Zanoni LA, Barton LA (1968). "Dynamic Scattering in Nematic Liquid Crystals".Applied Physics Letters.13(1): 46–47.Bibcode:1968ApPhL..13...46H.doi:10.1063/1.1652453.
- ^Kelker H, Scheurle B (1969). "A Liquid-crystalline (Nematic) Phase with a Particularly Low Solidification Point".Angew. Chem. Int. Ed.8(11): 884.doi:10.1002/anie.196908841.
- ^Gray GW, Harrison KJ, Nash JA (1973). "New family of nematic liquid crystals for displays".Electronics Letters.9(6): 130.Bibcode:1973ElL.....9..130G.doi:10.1049/el:19730096.
- ^Chandrasekhar S, Sadashiva BK, Suresh KA (1977). "Liquid crystals of disc-like molecules".Pramana.9(5): 471–480.Bibcode:1977Prama...9..471C.doi:10.1007/bf02846252.S2CID98207805.
- ^Collyer AA (2012).Liquid Crystal Polymers: From Structures to Applications.Springer Science & Business Media. p. 21.ISBN978-94-011-1870-5.
The names pyramidic or bowlic were proposed, but eventually it was decided to adopt the name conic.
- ^de Gennes PG (1992). "Soft Matter(Nobel Lecture)".Angewandte Chemie International Edition.31(7): 842–845.doi:10.1002/anie.199208421.
- ^Lam L (1994). "Bowlics". In Shibaev VP, Lam L (eds.).Liquid Crystalline and Mesomorphic Polymers.Partially Ordered Systems. New York: Springer. pp. 324–353.doi:10.1007/978-1-4613-8333-8_10.ISBN978-1-4613-8333-8.
- ^Lei L (1987). "Bowlic Liquid Crystals".Molecular Crystals and Liquid Crystals.146:41–54.doi:10.1080/00268948708071801.
- ^"Chemical Properties of Liquid Crystals".Case Western Reserve University. Archived fromthe originalon November 25, 2012.RetrievedJune 13,2013.
- ^Gennes, Pierre-Gilles de (1974).The physics of liquid crystals.Oxford [Eng.] Clarendon Press. p. 2.ISBN978-0-19-851285-1.
- ^abcdChandrasekhar S(1992).Liquid Crystals(2nd ed.). Cambridge: Cambridge University Press.ISBN978-0-521-41747-1.[permanent dead link]
- ^abcdefde Gennes PG,Prost J (1993).The Physics of Liquid Crystals.Oxford: Clarendon Press.ISBN978-0-19-852024-5.
- ^Carroll, Gregory T.; Lee, Kyung Min; McConney, Michael E.; Hall, Harris J. (2023)."Optical control of alignment and patterning in an azobenzene liquid crystal photoresist".Journal of Materials Chemistry C.11(6): 2177–2185.doi:10.1039/D2TC04869H.S2CID256151872.Archivedfrom the original on April 20, 2023.RetrievedApril 16,2023.
- ^abcDierking I (2003).Textures of Liquid Crystals.Weinheim: Wiley-VCH.ISBN978-3-527-30725-8.
- ^abcdCollings PJ, Hird M (1997).Introduction to Liquid Crystals.Bristol, PA: Taylor & Francis.ISBN978-0-7484-0643-2.
- ^Shao Y, Zerda TW (1998). "Phase Transitions of Liquid Crystal PAA in Confined Geometries".Journal of Physical Chemistry B.102(18): 3387–3394.doi:10.1021/jp9734437.
- ^Rego JA, Harvey JA, MacKinnon AL, Gatdula E (January 2010)."Asymmetric synthesis of a highly soluble 'trimeric' analogue of the chiral nematic liquid crystal twist agent Merck S1011"(PDF).Liquid Crystals.37(1): 37–43.doi:10.1080/02678290903359291.S2CID95102727.Archived fromthe original(PDF)on October 8, 2012.
- ^Géza T, Denniston C, Yeomans JM (February 26, 2002). "Hydrodynamics of Topological Defects in Nematic Liquid Crystals".Physical Review Letters.88(10): 105504.arXiv:cond-mat/0201378.Bibcode:2002PhRvL..88j5504T.doi:10.1103/PhysRevLett.88.105504.PMID11909370.S2CID38594358.
- ^Géza T, Denniston C, Yeomans JM (May 21, 2003). "Hydrodynamics of domain growth in nematic liquid crystals".Physical Review E.67(5): 051705.arXiv:cond-mat/0207322.Bibcode:2003PhRvE..67e1705T.doi:10.1103/PhysRevE.67.051705.PMID12786162.S2CID13796254.
- ^Madsen LA, Dingemans TJ, Nakata M, Samulski ET (April 2004). "Thermotropic biaxial nematic liquid crystals".Physical Review Letters.92(14): 145505.Bibcode:2004PhRvL..92n5505M.doi:10.1103/PhysRevLett.92.145505.PMID15089552.
- ^Kivelson SA, Fradkin E, Emery VJ (June 11, 1998)."Electronic liquid-crystal phases of a doped Mott insulator"(PDF).Letters to Nature.Nature.393(6685). Macmillan: 550–553.arXiv:cond-mat/9707327.Bibcode:1998Natur.393..550K.doi:10.1038/31177.S2CID4392009.
- ^Fradkin E, Kivelson SA, Lawler MJ, Eisenstein JP, Mackenzie AP (May 4, 2010)."Nematic Fermi Fluids in Condensed Matter Physics".Annual Review of Condensed Matter Physics.1:153–178.arXiv:0910.4166.Bibcode:2010ARCMP...1..153F.doi:10.1146/annurev-conmatphys-070909-103925.S2CID55917078.Archived fromthe originalon September 14, 2020.RetrievedAugust 5,2022.
- ^"smectic".Merriam-Webster Dictionary.Archivedfrom the original on July 31, 2013.RetrievedApril 26,2013.
- ^abGabriel JC, Camerel F, Lemaire BJ, Desvaux H, Davidson P, Batail P (October 2001)."Swollen liquid-crystalline lamellar phase based on extended solid-like sheets"(PDF).Nature.413(6855): 504–8.Bibcode:2001Natur.413..504G.doi:10.1038/35097046.PMID11586355.S2CID4416985.Archived(PDF)from the original on July 15, 2021.RetrievedSeptember 8,2021.
- ^Davidson P, Penisson C, Constantin D, Gabriel JP (June 2018)."Isotropic, nematic, and lamellar phases in colloidal suspensions of nanosheets".Proceedings of the National Academy of Sciences of the United States of America.115(26): 6662–6667.Bibcode:2018PNAS..115.6662D.doi:10.1073/pnas.1802692115.PMC6042086.PMID29891691.
- ^Vertogen, Ger; Jeu, Wim H. de (December 6, 2012).Thermotropic Liquid Crystals, Fundamentals.Springer Science & Business Media. p. 13.ISBN9783642831331.OCLC851375789.Archivedfrom the original on October 17, 2023.RetrievedMarch 21,2023.
- ^abKopp VI, Fan B, Vithana HK, Genack AZ (November 1998). "Low-threshold lasing at the edge of a photonic stop band in cholesteric liquid crystals".Optics Letters.23(21): 1707–9.Bibcode:1998OptL...23.1707K.doi:10.1364/OL.23.001707.PMID18091891.
- ^Priestley EB, Wojtowicz PJ, Sheng P (1974).Introduction to Liquid Crystals.Plenum Press.ISBN978-0-306-30858-1.
- ^Kazem-Rostami M (2019). "Optically active and photoswitchable Tröger's base analogs".New Journal of Chemistry.43(20): 7751–7755.doi:10.1039/C9NJ01372E.S2CID164362391.
- ^Kleinert H,Maki K (1981)."Lattice Textures in Cholesteric Liquid Crystals"(PDF).Fortschritte der Physik.29(5): 219–259.Bibcode:1981ForPh..29..219K.doi:10.1002/prop.19810290503.Archived(PDF)from the original on April 26, 2020.RetrievedOctober 7,2011.
- ^Seideman T (1990)."The liquid-crystalline blue phases"(PDF).Rep. Prog. Phys.53(6): 659–705.Bibcode:1990RPPh...53..659S.CiteSeerX10.1.1.397.3141.doi:10.1088/0034-4885/53/6/001.S2CID250776819.Archived(PDF)from the original on March 30, 2012.RetrievedOctober 7,2011.
- ^Coles HJ, Pivnenko MN (August 2005). "Liquid crystal 'blue phases' with a wide temperature range".Nature.436(7053): 997–1000.Bibcode:2005Natur.436..997C.doi:10.1038/nature03932.PMID16107843.S2CID4307675.
- ^Yamamoto J, Nishiyama I, Inoue M, Yokoyama H (September 2005). "Optical isotropy and iridescence in a smectic 'blue phase'".Nature.437(7058): 525–8.Bibcode:2005Natur.437..525Y.doi:10.1038/nature04034.PMID16177785.S2CID4432184.
- ^Kikuchi H, Yokota M, Hisakado Y, Yang H, Kajiyama T (September 2002). "Polymer-stabilized liquid crystal blue phases".Nature Materials.1(1): 64–8.Bibcode:2002NatMa...1...64K.doi:10.1038/nmat712.PMID12618852.S2CID31419926.
- ^"Samsung Develops World's First 'Blue Phase' Technology to Achieve 240 Hz Driving Speed for High-Speed Video".Archivedfrom the original on March 15, 2012.RetrievedApril 23,2009.
- ^Otón E, Yoshida H, Morawiak P, Strzeżysz O, Kula P, Ozaki M, Piecek W (June 2020)."Orientation control of ideal blue phase photonic crystals".Scientific Reports.10(1): 10148.Bibcode:2020NatSR..1010148O.doi:10.1038/s41598-020-67083-6.PMC7311397.PMID32576875.
- ^Wang L, Huang D, Lam L, Cheng Z (2017)."Bowlics: history, advances and applications".Liquid Crystals Today.26(4): 85–111.doi:10.1080/1358314X.2017.1398307.S2CID126256863.
- ^Liang Q, Liu P, Liu C, Jian X, Hong D, Li Y (2005). "Synthesis and Properties of Lyotropic Liquid Crystalline Copolyamides Containing Phthalazinone Moieties and Ether Linkages".Polymer.46(16): 6258–6265.doi:10.1016/j.polymer.2005.05.059.
- ^Martin JD, Keary CL, Thornton TA, Novotnak MP, Knutson JW, Folmer JC (April 2006). "Metallotropic liquid crystals formed by surfactant templating of molten metal halides".Nature Materials.5(4): 271–5.Bibcode:2006NatMa...5..271M.doi:10.1038/nmat1610.PMID16547520.S2CID35833273.
- ^ab Tomczyk W, Marzec M, Juszyńska-Gałązka E, Węgłowska D (2017). "Mesomorphic and physicochemical properties of liquid crystal mixture composed of chiral molecules with perfluorinated terminal chains".Journal of Molecular Structure.1130:503–510.Bibcode:2017JMoSt1130..503T.doi:10.1016/j.molstruc.2016.10.039.
- ^Juszyńska-Gałązka E, Gałązka M, Massalska-Arodź M, Bąk A, Chłędowska K, Tomczyk W (December 2014). "Phase Behavior and Dynamics of the Liquid Crystal 4'-butyl-4-(2-methylbutoxy)azoxybenzene (4ABO5*)".The Journal of Physical Chemistry B.118(51): 14982–9.doi:10.1021/jp510584w.PMID25429851.
- ^Templer, Richard; Seddon, John (May 18, 1991)."The World of Liquid Crystals".New Scientist.Archivedfrom the original on December 15, 2023.RetrievedDecember 15,2023.
You might be surprised to find out that cell membranes are liquid crystals. In fact, the first recorded observations of the liquid crystalline phase were of myelin, the material that coats nerve fibres.
- ^Wensink HH, Dunkel J, Heidenreich S, Drescher K, Goldstein RE,Löwen H,Yeomans JM (September 2012)."Meso-scale turbulence in living fluids".Proceedings of the National Academy of Sciences of the United States of America.109(36): 14308–13.Bibcode:2013PNAS..110.4488S.doi:10.1073/pnas.1215368110.PMC3607014.PMID22908244.
- ^Saw TB, Doostmohammadi A, Nier V, Kocgozlu L, Thampi S, Toyama Y, et al. (April 2017)."Topological defects in epithelia govern cell death and extrusion".Nature.544(7649): 212–216.Bibcode:2017Natur.544..212S.doi:10.1038/nature21718.PMC5439518.PMID28406198.
- ^Zocher H (1925). "Uber freiwillige Strukturbildung in Solen. (Eine neue Art anisotrop flqssiger Medien)".Z. Anorg. Allg. Chem.147:91.doi:10.1002/zaac.19251470111.
- ^Davidson P, Gabriel JC (2003). "Mineral Liquid Crystals from Self-Assembly of Anisotropic Nanosystems".Top Curr Chem.226:119.doi:10.1007/b10827.
- ^Langmuir I (1938). "The role of attractive and repulsive forces in the formation of tactoids, thixotropic gels, protein crystals and coacervates".J Chem Phys.6(12): 873.Bibcode:1938JChPh...6..873L.doi:10.1063/1.1750183.
- ^Gabriel JC, Sanchez C, Davidson P (1996). "Observation of Nematic Liquid-Crystal Textures in Aqueous Gels of Smectite Clays".J. Phys. Chem.100(26): 11139.doi:10.1021/jp961088z.
- ^Paineau E, Philippe AM, Antonova K, Bihannic I, Davidson P, Dozov I, et al. (2013). "Liquid–crystalline properties of aqueous suspensions of natural clay nanosheets".Liquid Crystals Reviews.1(2): 110.doi:10.1080/21680396.2013.842130.S2CID136533412.
- ^Buka A, Palffy-Muhoray P, Rácz Z (October 1987). "Viscous fingering in liquid crystals".Physical Review A.36(8): 3984–3989.Bibcode:1987PhRvA..36.3984B.doi:10.1103/PhysRevA.36.3984.PMID9899337.
- ^González-Cinca R, Ramirez-Piscina L, Casademunt J, Hernández-Machado A, Kramer L, Katona TT, et al. (1996). "Phase-field simulations and experiments of faceted growth in liquid crystal".Physica D.99(2–3): 359.Bibcode:1996PhyD...99..359G.doi:10.1016/S0167-2789(96)00162-5.
- ^González-Cinca R, Ramırez-Piscina L, Casademunt J, Hernández-Machado A, Tóth-Katona T, Börzsönyi T, Buka Á (1998). "Heat diffusion anisotropy in dendritic growth: phase field simulations and experiments in liquid crystals".Journal of Crystal Growth.193(4): 712.Bibcode:1998JCrGr.193..712G.doi:10.1016/S0022-0248(98)00505-3.
- ^Chaikin, P. M.; Lubensky, T. C. (1995).Principles of condensed matter physics.Cambridge: Cambridge University Press. p. 168.ISBN9780521794503.
- ^Ghosh SK (1984). "A model for the orientational order in liquid crystals".Il Nuovo Cimento D.4(3): 229.Bibcode:1984NCimD...4..229G.doi:10.1007/BF02453342.S2CID121078315.
- ^Onsager L (1949). "The effects of shape on the interaction of colloidal particles".Annals of the New York Academy of Sciences.51(4): 627.Bibcode:1949NYASA..51..627O.doi:10.1111/j.1749-6632.1949.tb27296.x.S2CID84562683.
- ^abVroege GJ, Lekkerkerker HN (1992)."Phase transitions in lyotropic colloidal and polymer liquid crystals"(PDF).Rep. Prog. Phys.55(8): 1241.Bibcode:1992RPPh...55.1241V.doi:10.1088/0034-4885/55/8/003.hdl:1874/22348.S2CID250865818.
- ^Maier W, Saupe A (1958)."Eine einfache molekulare theorie des nematischen kristallinflussigen zustandes".Z. Naturforsch. A(in German).13(7): 564.Bibcode:1958ZNatA..13..564M.doi:10.1515/zna-1958-0716.S2CID93402217.
- ^Maier W, Saupe A (1959)."Eine einfache molekular-statistische theorie der nematischen kristallinflussigen phase.1".Z. Naturforsch. A(in German).14(10): 882.Bibcode:1959ZNatA..14..882M.doi:10.1515/zna-1959-1005.S2CID201840526.
- ^Maier W, Saupe A (1960)."Eine einfache molekular-statistische theorie der nematischen kristallinflussigen phase.2".Z. Naturforsch. A(in German).15(4): 287.Bibcode:1960ZNatA..15..287M.doi:10.1515/zna-1960-0401.S2CID97407506.
- ^Ciferri A (1991).Liquid crystallinity in polymers: principles and fundamental properties.Weinheim: VCH Publishers.ISBN3-527-27922-9.
- ^McMillan W (1971). "Simple Molecular Model for the Smectic A Phase of Liquid Crystals".Phys. Rev. A.4(3): 1238.Bibcode:1971PhRvA...4.1238M.doi:10.1103/PhysRevA.4.1238.
- ^Leslie FM (1992). "Continuum theory for nematic liquid crystals".Continuum Mechanics and Thermodynamics.4(3): 167.Bibcode:1992CMT.....4..167L.doi:10.1007/BF01130288.S2CID120908851.
- ^Watson MC, Brandt EG, Welch PM, Brown FL (July 2012)."Determining biomembrane bending rigidities from simulations of modest size".Physical Review Letters.109(2): 028102.Bibcode:2012PhRvL.109b8102W.doi:10.1103/PhysRevLett.109.028102.PMID23030207.
- ^Takezoe H (2014). "Historical Overview of Polar Liquid Crystals".Ferroelectrics.468(1): 1–17.Bibcode:2014Fer...468....1T.doi:10.1080/00150193.2014.932653.S2CID120165343.
- ^Oswald P, Pieranski P (2005).Nematic and Cholesteric Liquid Crystals: Concepts and Physical Properties Illustrated by Experiments.CRC Press.ISBN9780415321402.Archivedfrom the original on May 15, 2019.RetrievedMay 15,2019.
- ^Barboza R, Bortolozzo U, Assanto G, Vidal-Henriquez E, Clerc MG,Residori S(October 2012). "Vortex induction via anisotropy stabilized light-matter interaction".Physical Review Letters.109(14): 143901.Bibcode:2012PhRvL.109n3901B.doi:10.1103/PhysRevLett.109.143901.hdl:10533/136047.PMID23083241.
- ^Kazem-Rostami M (2017). "photoswitchable liquid crystal design".Synthesis.49(6): 1214–1222.doi:10.1055/s-0036-1588913.S2CID99913657.
- ^Fujikake H, Takizawa K, Aida T, Negishi T, Kobayashi M (1998). "Video camera system using liquid-crystal polarizing filter toreduce reflected light".IEEE Transactions on Broadcasting.44(4): 419.doi:10.1109/11.735903.
- ^Achard MF, Bedel JP, Marcerou JP, Nguyen HT, Rouillon JC (February 2003). "Switching of banana liquid crystal mesophases under field".The European Physical Journal E.10(2): 129–34.Bibcode:2003EPJE...10..129A.doi:10.1140/epje/e2003-00016-y.PMID15011066.S2CID35942754.
- ^Baus M, Colot JL (November 1989)."Ferroelectric nematic liquid-crystal phases of dipolar hard ellipsoids".Physical Review A.40(9): 5444–5446.Bibcode:1989PhRvA..40.5444B.doi:10.1103/PhysRevA.40.5444.PMID9902823.Archivedfrom the original on April 27, 2021.RetrievedMarch 4,2021.
- ^Uehara H, Hatano J (2002). "Pressure-Temperature Phase Diagrams of Ferroelectric Liquid Crystals".J. Phys. Soc. Jpn.71(2): 509.Bibcode:2002JPSJ...71..509U.doi:10.1143/JPSJ.71.509.
- ^Alkeskjold TT, Scolari L, Noordegraaf D, Lægsgaard J, Weirich J, Wei L, Tartarini G, Bassi P, Gauza S, Wu ST, Bjarklev A (2007). "Integrating liquid crystal based optical devices in photonic crystal".Optical and Quantum Electronics.39(12–13): 1009.doi:10.1007/s11082-007-9139-8.S2CID54208691.
- ^Ciofani G, Menciassi A (2012).Piezoelectric Nanomaterials for Biomedical Applications.Springer Science & Business Media.ISBN9783642280443.
- ^A.D. Chandra & A. Banerjee (2020)."Rapid phase calibration of a spatial light modulator using novel phase masks and optimization of its efficiency using an iterative algorithm".Journal of Modern Optics.67(7). Journal of Modern Optics, Volume 67, Issue 7, 18 May 2020: 628–637.arXiv:1811.03297.Bibcode:2020JMOp...67..628C.doi:10.1080/09500340.2020.1760954.S2CID219646821.Archivedfrom the original on April 10, 2022.RetrievedJanuary 7,2021.
- ^US 4738549,Plimpton RG, "Pool thermometer", issued 1988-04-19
- ^"Hot-spot detection techniques for ICs".acceleratedanalysis.Archived fromthe originalon February 11, 2009.RetrievedMay 5,2009.
- ^Sato S (1979). "Liquid-Crystal Lens-Cells with Variable Focal Length".Japanese Journal of Applied Physics.18(9): 1679–1684.Bibcode:1979JaJAP..18.1679S.doi:10.1143/JJAP.18.1679.S2CID119784753.
- ^Lin YH, Wang YJ, Reshetnyak V (2017). "Liquid crystal lenses with tunable focal length".Liquid Crystals Reviews.5(2): 111–143.doi:10.1080/21680396.2018.1440256.S2CID139938136.
- ^Wang, Yu-Jen; Lin, Yi-Hsin; Cakmakci, Ozan; Reshetnyak, Victor (2020)."Phase modulators with tunability in wavefronts and optical axes originating from anisotropic molecular tilts under symmetric electric field II: Experiments".Optics Express.28(6): 8985–9001.Bibcode:2020OExpr..28.8985W.doi:10.1364/OE.389647.PMID32225513.S2CID214734642.
- ^Dolgaleva K, Wei SK, Lukishova SG, Chen SH, Schwertz K, Boyd RW (2008). "Enhanced laser performance of cholesteric liquid crystals doped with oligofluorene dye".Journal of the Optical Society of America.25(9): 1496–1504.Bibcode:2008JOSAB..25.1496D.doi:10.1364/JOSAB.25.001496.
- ^Luzzati V, Mustacchi H, Skoulios A (1957). "Structure of the Liquid-Crystal Phases of the Soap–water System: Middle Soap and Neat Soap".Nature.180(4586): 600.Bibcode:1957Natur.180..600L.doi:10.1038/180600a0.S2CID4163714.
- ^Silva MC, Sotomayor J, Figueirinhas J (September 2015). "Effect of an additive on the permanent memory effect of polymer dispersed liquid crystal films".Journal of Chemical Technology & Biotechnology.90(9): 1565–9.doi:10.1002/jctb.4677.
- ^da Silva MC, Figueirinhas JL, Sotomayor JC (January 2016). "Improvement of permanent memory effect in PDLC films using TX-100 as an additive".Liquid Crystals.43(1): 124–30.doi:10.1080/02678292.2015.1061713.S2CID101996816.
- ^Padavic-Callaghan, Karmela (August 19, 2022)."Computer made from liquid crystals would ripple with calculations".Science Advances.8(33).New Scientist:eabp8371.doi:10.1126/sciadv.abp8371.hdl:1721.1/145669.PMC9390992.PMID35984880.Archivedfrom the original on August 24, 2022.RetrievedAugust 24,2022.
- ^"Researchers claim that ripples and imperfections in liquid crystals like those found in LCD TVs could be used to build a new type of computer".Engineering and Technology.August 22, 2022.Archivedfrom the original on August 26, 2022.RetrievedAugust 24,2022.
External links
[edit]![](https://upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png)
- "History and Properties of Liquid Crystals".Nobelprize.org.Archivedfrom the original on August 30, 2009.RetrievedJune 6,2009.
- Definitions of basic terms relating to low-molar-mass and polymer liquid crystals (IUPAC Recommendations 2001)ArchivedOctober 3, 2009, at theWayback Machine
- An intelligible introduction to liquid crystalsfrom Case Western Reserve University
- Liquid Crystal Physics tutorialArchivedAugust 5, 2007, at theWayback Machinefrom the Liquid Crystals Group, University of Colorado
- Liquid Crystals & Photonics Group – Ghent University (Belgium)ArchivedJune 13, 2007, at theWayback Machine,good tutorial
- Simulation of light propagation in liquid crystals[permanent dead link],free program
- Liquid Crystals Interactive OnlineArchivedMarch 18, 2021, at theWayback Machine
- Liquid Crystal InstituteArchivedSeptember 20, 2017, at theWayback MachineKent State University
- Liquid CrystalsArchivedJanuary 22, 2004, at theWayback Machinea journal by Taylor&Francis
- Molecular Crystals and Liquid Crystalsa journal by Taylor & Francis
- Hot-spot detection techniques for ICs
- What are liquid crystals?from Chalmers University of Technology, Sweden
- Progress in liquid crystal chemistryArchivedJune 16, 2010, at theWayback MachineThematic series in the Open Access Beilstein Journal of Organic Chemistry
- DoITPoMS Teaching and Learning Package- "Liquid Crystals"ArchivedAugust 4, 2010, at theWayback Machine
- Bowlic liquid crystalArchivedMay 18, 2015, at theWayback Machinefrom San Jose State University
- Phase calibration of a Spatial Light ModulatorArchivedOctober 29, 2021, at theWayback Machine