Editing Liquid crystal (section)

==External influences on liquid crystals==
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===
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>

===Surface preparations===
{{See also|Alignment layers}}
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 called [[photoalignment]].

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