Editing Liquid crystal (section)

====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>]]