Editing Liquid crystal (section)

===Thermotropic liquid crystals===
{{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 crystal.<ref name=b2/><ref name=b1/> Many thermotropic LCs exhibit a variety of phases as temperature is changed. For instance, a particular type of LC molecule (called a [[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-azoxyanisole]].<ref name="Shao">{{cite journal|title=Phase Transitions of Liquid Crystal PAA in Confined Geometries|journal=Journal of Physical Chemistry B|date=1998|volume=102|issue=18|pages=3387–3394|doi=10.1021/jp9734437| vauthors = Shao Y, Zerda TW }}</ref>

====Nematic phase====
{{see also|Biaxial nematic|Twisted nematic field effect}}
[[File:LiquidCrystal-MesogenOrder-Nematic.jpg|thumb|left|120px|Alignment in a nematic phase]]
[[File:Smectic nematic.jpg|thumb|Phase transition between a nematic (left) and smectic A (right) phases observed between crossed [[polarizers]]. The black color corresponds to isotropic medium.]]

The simplest liquid crystal phase is the nematic. In a nematic phase, {{linktext|calamitic}} (rod-like) organic 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.<ref>{{cite journal |url=http://www.csupomona.edu/~jarego/pubs/RD2_LC.pdf |title=Asymmetric synthesis of a highly soluble 'trimeric' analogue of the chiral nematic liquid crystal twist agent Merck S1011 | vauthors = Rego JA, Harvey JA, MacKinnon AL, Gatdula E |s2cid=95102727 |journal=Liquid Crystals |volume=37 |issue=1 |date=January 2010 |pages=37–43 |doi=10.1080/02678290903359291 |url-status=dead |archive-url=https://web.archive.org/web/20121008152304/http://www.csupomona.edu/~jarego/pubs/RD2_LC.pdf |archive-date=October 8, 2012 |df=mdy-all }}</ref> 

The word ''nematic'' comes from the [[Greek language|Greek]] {{lang|el|νήμα}} (''{{langx|el|nema}}''), which means "thread". This term originates from the [[disclination]]s: thread-like [[topological defect]]s observed in nematic phases.  

Nematics also exhibit so-called "hedgehog" [[topological defect]]s. In two dimensions, there are topological defects with [[topological charge]]s {{math|+{{sfrac|1|2}}}} and {{math|-{{sfrac|1|2}}}}. Due to hydrodynamics, the {{math|+{{sfrac|1|2}}}} defect moves considerably faster than the {{math|-{{sfrac|1|2}}}} defect. When placed close to each other, the defects attract; upon collision, they annihilate.<ref>{{cite journal |vauthors=Géza T, Denniston C, Yeomans JM|title=Hydrodynamics of Topological Defects in Nematic Liquid Crystals |journal=Physical Review Letters |date=26 February 2002 |volume=88 |issue=10 |pages=105504 |doi=10.1103/PhysRevLett.88.105504|pmid=11909370 |arxiv=cond-mat/0201378 |bibcode=2002PhRvL..88j5504T |s2cid=38594358 }}</ref><ref>{{cite journal|vauthors=Géza T, Denniston C, Yeomans JM|title=Hydrodynamics of domain growth in nematic liquid crystals |journal=Physical Review E |date=21 May 2003 |volume=67 |issue=5 |pages=051705 |doi=10.1103/PhysRevE.67.051705|pmid=12786162 |arxiv=cond-mat/0207322 |bibcode=2003PhRvE..67e1705T |s2cid=13796254 }}</ref> 

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 are [[biaxial nematic]], meaning that in addition to orienting their long axis, they also orient along a secondary axis.<ref>{{cite journal | vauthors = Madsen LA, Dingemans TJ, Nakata M, Samulski ET | title = Thermotropic biaxial nematic liquid crystals | journal = Physical Review Letters | volume = 92 | issue = 14 | pages = 145505 | date = April 2004 | pmid = 15089552 | doi = 10.1103/PhysRevLett.92.145505 | bibcode = 2004PhRvL..92n5505M }}</ref> 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 in [[liquid-crystal display]]s (LCD).<ref name=castellano>{{cite book| last = Castellano | first = Joseph A. | name-list-style = vanc |title =Liquid Gold: The Story of Liquid Crystal Displays and the Creation of an Industry| publisher=World Scientific Publishing|date =2005| isbn = 978-981-238-956-5}}</ref>

Nematic phases are also known in non-molecular systems: at high magnetic fields, electrons flow in [[charge density wave|bundles or stripes]] to create an "electronic nematic" form of matter.<ref>{{cite journal|department=Letters to Nature|title=Electronic liquid-crystal phases of a doped Mott insulator|first1=SA|last1=Kivelson|first2=E|last2=Fradkin|first3=VJ|last3=Emery|journal=Nature|volume=393|date=11 June 1998|issue=6685 |publisher=Macmillan|pages=550–553|doi=10.1038/31177 |arxiv=cond-mat/9707327 |bibcode=1998Natur.393..550K |s2cid=4392009 |url=https://www.nature.com/articles/31177.pdf|name-list-style=vanc}}</ref><ref>{{cite journal|title=Nematic Fermi Fluids in Condensed Matter Physics|first1=Eduardo|last1=Fradkin|first2=Steven A|last2=Kivelson|first3=Michael J|last3=Lawler|first4=James P|last4=Eisenstein|first5=Andrew P|last5=Mackenzie|name-list-style=vanc|journal=Annual Review of Condensed Matter Physics|date=May 4, 2010|volume=1|pages=153–178|doi=10.1146/annurev-conmatphys-070909-103925|arxiv=0910.4166|bibcode=2010ARCMP...1..153F|s2cid=55917078|url=https://authors.library.caltech.edu/20497/|access-date=August 5, 2022|archive-date=September 14, 2020|archive-url=https://web.archive.org/web/20200914003558/https://authors.library.caltech.edu/20497/|url-status=dead}}</ref>

====Smectic phases====
[[File:LiquidCrystal-MesogenOrder-SmecticPhases.jpg|thumb|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 properties.<ref>{{cite web| title=smectic| url=http://www.merriam-webster.com/dictionary/smectic| publisher=Merriam-Webster Dictionary| access-date=April 26, 2013| archive-date=July 31, 2013| archive-url=https://web.archive.org/web/20130731023631/http://www.merriam-webster.com/dictionary/smectic| url-status=live}}</ref>
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.<ref name=b2/><ref name=b1/> Beyond organic molecules, Smectic ordering has also been reported to occur within colloidal suspensions of 2-D materials or nanosheets.<ref name="Swollen liquid-crystalline lamellar">{{cite journal | vauthors = Gabriel JC, Camerel F, Lemaire BJ, Desvaux H, Davidson P, Batail P | s2cid = 4416985 | title = Swollen liquid-crystalline lamellar phase based on extended solid-like sheets | journal = Nature | volume = 413 | issue = 6855 | pages = 504–8 | date = October 2001 | pmid = 11586355 | doi = 10.1038/35097046 | bibcode = 2001Natur.413..504G | url = https://hal-cea.archives-ouvertes.fr/cea-03194654/file/24-Article.pdf | access-date = September 8, 2021 | archive-date = July 15, 2021 | archive-url = https://web.archive.org/web/20210715065520/https://hal-cea.archives-ouvertes.fr/cea-03194654/file/24-Article.pdf | url-status = live }}</ref><ref>{{cite journal | vauthors = Davidson P, Penisson C, Constantin D, Gabriel JP | title = Isotropic, nematic, and lamellar phases in colloidal suspensions of nanosheets | journal = Proceedings of the National Academy of Sciences of the United States of America | volume = 115 | issue = 26 | pages = 6662–6667 | date = June 2018 | pmid = 29891691 | pmc = 6042086 | doi = 10.1073/pnas.1802692115 | bibcode = 2018PNAS..115.6662D | doi-access = free }}</ref> One example of smectic LCs is [[p,p-dinonylazobenzene|''p,p'''-dinonylazobenzene]].<ref>{{Cite book |last1=Vertogen |first1=Ger |page=13 |url=https://books.google.com/books?id=7SHrCAAAQBAJ&dq=examples+of+smectic+liquid+crystals&pg=PA13 |title=Thermotropic Liquid Crystals, Fundamentals |last2=Jeu |first2=Wim H. de |oclc=851375789 |date=2012-12-06 |publisher=Springer Science & Business Media |isbn=9783642831331 |access-date=March 21, 2023 |archive-date=October 17, 2023 |archive-url=https://web.archive.org/web/20231017052201/https://books.google.com/books?id=7SHrCAAAQBAJ&dq=examples+of+smectic+liquid+crystals&pg=PA13 |url-status=live }}</ref>

====Chiral phases or twisted nematics====
[[File:LiquidCrystal-MesogenOrder-ChiralPhases.jpg|thumb|left|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 [[Chirality (chemistry)|chiral]] [[nematic]] phase exhibits [[Chirality (chemistry)|chirality]] (handedness). This phase is often called the [[Cholesteric liquid crystal|''cholesteric'']] phase because it was first observed for [[cholesterol]] derivatives. Only [[Chirality (chemistry)|chiral molecules]] 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 normal, hence they are also called ''twisted nematics''.<ref name=b1/><ref name=b4/><ref name=b5/>

[[File:Cholesterinisch.png|thumb|Chiral nematic phase. The numerator ''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,<ref name="Kopp1998"/> and these properties are exploited in a number of optical applications.<ref name=b3>{{cite book | vauthors = Sluckin TJ, Dunmur DA, Stegemeyer H |title=Crystals That Flow – classic papers from the history of liquid crystals|location=London|date=2004|publisher=Taylor & Francis|isbn=978-0-415-25789-3|url=https://books.google.com/books?id=iMEMAuxrhFcC}}
</ref><ref name=b4/> 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 obliquely.<ref>{{cite book| title = Introduction to Liquid Crystals| vauthors = Priestley EB, Wojtowicz PJ, Sheng P | publisher=Plenum Press|date =1974| isbn = 978-0-306-30858-1}}</ref>
[[File:Wikipedia LCD prototype.jpg|thumb|211x211px|A planar cell, filled with achiral LC host doped with an optically active Tröger base analog, placed between a pair of parallel (A) and crossed (B) linear polarizers. This doped mesogenic phase forms self-organized helical superstructures, that allow specific wavelengths of light to pass through the crossed polarizers, and selectively reflects a particular wavelength of light.<ref>{{cite journal|last=Kazem-Rostami|first=Masoud | name-list-style = vanc |date=2019|title=Optically active and photoswitchable Tröger's base analogs|journal=New Journal of Chemistry|volume=43|issue=20|pages=7751–7755|doi=10.1039/C9NJ01372E|s2cid=164362391 }}</ref>]]

====Blue phases====
Blue phases are liquid crystal phases that appear in the temperature range between a [[Chirality (chemistry)|chiral]] [[nematic]] phase and an [[Isotropy|isotropic]] liquid phase. Blue phases have a regular three-dimensional cubic structure of defects with [[Crystal structure|lattice]] periods of several hundred nanometers, and thus they exhibit selective [[Bragg's law|Bragg reflections]] in the wavelength range of visible light corresponding to the [[Cubic phase|cubic lattice]]. It was theoretically predicted in 1981 that these phases can possess icosahedral symmetry similar to [[quasicrystal]]s.<ref>{{cite journal | title = Lattice Textures in Cholesteric Liquid Crystals | vauthors = Kleinert H, Maki K | author-link = Hagen Kleinert | journal = Fortschritte der Physik | volume = 29 | issue = 5 | pages = 219–259 | date = 1981 | doi = 10.1002/prop.19810290503 | url = http://www.physik.fu-berlin.de/~kleinert/75/75.pdf | bibcode = 1981ForPh..29..219K | access-date = October 7, 2011 | archive-date = April 26, 2020 | archive-url = https://web.archive.org/web/20200426005943/http://users.physik.fu-berlin.de/~kleinert/75/75.pdf | url-status = live }}</ref><ref>{{cite journal|url=http://chemgroups.northwestern.edu/seideman/Publications/The%20liquid-crystalline%20blue%20phases.pdf|title=The liquid-crystalline blue phases|journal=Rep. Prog. Phys.|volume=53|date=1990|pages=659–705|bibcode=1990RPPh...53..659S|doi=10.1088/0034-4885/53/6/001|vauthors=Seideman T|issue=6|citeseerx=10.1.1.397.3141|s2cid=250776819|access-date=October 7, 2011|archive-date=March 30, 2012|archive-url=https://web.archive.org/web/20120330204736/http://chemgroups.northwestern.edu/seideman/Publications/The%20liquid-crystalline%20blue%20phases.pdf|url-status=live}}</ref>

Although blue phases are of interest for fast light modulators or tunable [[photonic crystal]]s, they exist in a very narrow temperature range, usually less than a few [[kelvin]]s. Recently the stabilization of blue phases over a temperature range of more than 60&nbsp;K including room temperature (260–326&nbsp;K) has been demonstrated.<ref>{{cite journal | vauthors = Coles HJ, Pivnenko MN | s2cid = 4307675 | title = Liquid crystal 'blue phases' with a wide temperature range | journal = Nature | volume = 436 | issue = 7053 | pages = 997–1000 | date = August 2005 | pmid = 16107843 | doi = 10.1038/nature03932 | bibcode = 2005Natur.436..997C }}</ref><ref>{{cite journal | vauthors = Yamamoto J, Nishiyama I, Inoue M, Yokoyama H | s2cid = 4432184 | title = Optical isotropy and iridescence in a smectic 'blue phase' | journal = Nature | volume = 437 | issue = 7058 | pages = 525–8 | date = September 2005 | pmid = 16177785 | doi = 10.1038/nature04034 | bibcode = 2005Natur.437..525Y }}</ref> Blue phases stabilized at room temperature allow electro-optical switching with response times of the order of 10<sup>−4</sup>&nbsp;s.<ref>{{cite journal | vauthors = Kikuchi H, Yokota M, Hisakado Y, Yang H, Kajiyama T | s2cid = 31419926 | title = Polymer-stabilized liquid crystal blue phases | journal = Nature Materials | volume = 1 | issue = 1 | pages = 64–8 | date = September 2002 | pmid = 12618852 | doi = 10.1038/nmat712 | bibcode = 2002NatMa...1...64K }}</ref> In May 2008, the first [[Blue Phase Mode LCD|blue phase mode LCD]] panel had been developed.<ref>{{cite news| url = http://www.physorg.com/news129997960.html| title = Samsung Develops World's First 'Blue Phase' Technology to Achieve 240&nbsp;Hz Driving Speed for High-Speed Video| access-date = April 23, 2009| archive-date = March 15, 2012| archive-url = https://web.archive.org/web/20120315124810/http://www.physorg.com/news129997960.html| url-status = live}}</ref>

Blue phase crystals, being a periodic cubic structure with a bandgap in the visible wavelength range, can be considered as [[Photonic crystal|3D 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.<ref>{{cite journal | vauthors = Otón E, Yoshida H, Morawiak P, Strzeżysz O, Kula P, Ozaki M, Piecek W | title = Orientation control of ideal blue phase photonic crystals | journal = Scientific Reports | volume = 10 | issue = 1 | pages = 10148 | date = June 2020 | pmid = 32576875 | pmc = 7311397 | doi = 10.1038/s41598-020-67083-6 | bibcode = 2020NatSR..1010148O }}</ref>

====Discotic phases====
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 [[columnar phase|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.

====Conic phases====
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.<ref name=Bowlics>{{cite journal|vauthors=Wang L, Huang D, Lam L, Cheng Z |s2cid = 126256863|title = Bowlics: history, advances and applications|journal=Liquid Crystals Today|doi = 10.1080/1358314X.2017.1398307|volume = 26|date = 2017|issue =4|pages=85–111|doi-access = free}}</ref>