Editing Liquid crystal (section)

===Electric and magnetic field effects===
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.<ref>{{cite journal|date=2014|title=Historical Overview of Polar Liquid Crystals|journal=Ferroelectrics|volume=468|pages=1–17|doi=10.1080/00150193.2014.932653|last1=Takezoe|first1=Hideo |issue=1 |bibcode=2014Fer...468....1T | name-list-style = vanc |s2cid=120165343}}</ref>

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

: <math>D_i = \epsilon_0 E_i + P_i</math>

where <math>E_i</math>, <math>D_i</math> and <math>P_i</math> are the components of the electric field, electric displacement field and polarization density. The electric energy per volume stored in the system is

: <math>f_\text{elec} = -\frac{1}{2} D_i E_i</math>

(summation over the doubly appearing index <math>i</math>). 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 <math>n</math>. The most general form to express <math>D</math> is

: <math>D_i = \epsilon_0 \epsilon_\bot E_i + \left(\epsilon_\parallel - \epsilon_\bot\right) n_i n_j E_j </math>

(summation over the index <math>j</math>) with <math>\epsilon_\bot</math> and <math>\epsilon_\parallel</math> the electric [[permittivity]] parallel and perpendicular to the director <math>n</math>. Then density of energy is (ignoring the constant terms that do not contribute to the dynamics of the system)<ref>{{cite book |last1=Oswald |first1=Patrick |last2=Pieranski |first2=Pavel |name-list-style=vanc |title=Nematic and Cholesteric Liquid Crystals: Concepts and Physical Properties Illustrated by Experiments |date=2005 |publisher=CRC Press |isbn=9780415321402 |url=https://www.crcpress.com/Nematic-and-Cholesteric-Liquid-Crystals-Concepts-and-Physical-Properties/Oswald-Pieranski/p/book/9780415321402 |access-date=May 15, 2019 |archive-date=May 15, 2019 |archive-url=https://web.archive.org/web/20190515040953/https://www.crcpress.com/Nematic-and-Cholesteric-Liquid-Crystals-Concepts-and-Physical-Properties/Oswald-Pieranski/p/book/9780415321402 |url-status=live }}</ref>

: <math>f_\text{elec} = -\frac{1}{2}\epsilon_0\left(\epsilon_\parallel - \epsilon_\bot\right)\left(E_i n_i\right)^2</math>

(summation over <math>i</math>). If <math>\epsilon_\parallel - \epsilon_\bot</math> is positive, then the minimum of the energy is achieved when <math>E</math> and <math>n</math> are parallel. This means that the system will favor aligning the liquid crystal with the externally applied electric field. If <math>\epsilon_\parallel - \epsilon_\bot</math> is negative, then the minimum of the energy is achieved when <math>E</math> and <math>n</math> are perpendicular (in nematics the perpendicular orientation is degenerated, making possible the emergence of vortices<ref>{{cite journal | vauthors = Barboza R, Bortolozzo U, Assanto G, Vidal-Henriquez E, Clerc MG, [[Stefania Residori|Residori S]] | title = Vortex induction via anisotropy stabilized light-matter interaction | journal = Physical Review Letters | volume = 109 | issue = 14 | pages = 143901 | date = October 2012 | pmid = 23083241 | doi = 10.1103/PhysRevLett.109.143901 | bibcode = 2012PhRvL.109n3901B | hdl = 10533/136047 }}</ref>).

The difference <math>\Delta\epsilon = \epsilon_\parallel - \epsilon_\bot</math> is called dielectrical anisotropy and is an important parameter in liquid crystal applications. There are both <math>\Delta\epsilon > 0</math> and <math>\Delta\epsilon < 0</math> commercial liquid crystals. [[5CB]] and [[E7 liquid crystal mixture]] are two <math>\Delta\epsilon > 0</math> liquid crystals commonly used. [[MBBA]] is a common <math>\Delta\epsilon < 0</math> liquid 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.<ref>{{cite journal|date=2017|title=photoswitchable liquid crystal design|journal=Synthesis|volume=49|issue=6|pages=1214–1222|doi=10.1055/s-0036-1588913|last1=Kazem-Rostami|first1=Masoud|s2cid=99913657 | name-list-style = vanc }}</ref>