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Liquid crystal

2007 Schools Wikipedia Selection. Related subjects: Materials science

   Schlieren texture of Liquid Crystal nematic phase
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   Schlieren texture of Liquid Crystal nematic phase

   Liquid crystals are substances that exhibit a phase of matter that has
   properties between those of a conventional liquid, and those of a solid
   crystal. For instance, a liquid crystal (LC) may flow like a liquid,
   but have the molecules in the liquid arranged and/or oriented in a
   crystal-like way. There are many different types of LC phases, which
   can be distinguished based on their different optical properties (such
   as birefringence). When viewed under a microscope using a polarized
   light source, different liquid crystal phases will appear to have a
   distinct texture. Each 'patch' in the texture corresponds to a domain
   where the LC molecules are oriented in a different direction. Within a
   domain, however, the molecules are well ordered. Liquid crystal
   materials may not always be in an LC phase (just as water is not always
   in the liquid phase: it may also be found in the solid or gas phase).
   Liquid crystals can be divided into thermotropic and lyotropic LCs.
   Thermotropic LCs exhibit a phase transition into the LC phase as
   temperature is changed, whereas lyotropic LCs exhibit phase transitions
   as a function of concentration of the mesogen in a solvent (typically
   water) as well as temperature.

Mesogens

   Molecules that exhibit liquid crystal phases are called mesogens. For a
   molecule to display an LC phase, it must generally be fairly rigid and
   anisotropic (i.e. longer in one direction than another). Most mesogens
   fall into the 'rigid-rod' class (calamitic mesogens), which orient
   based on their long axis. Disk-like (discotic) mesogens are also known,
   and these orient in the direction of their short axis. In addition to
   molecules, polymers and colloidal suspensions can also form LC phases.
   For instance, micrometre-sized objects (such as anisotropic colloids,
   latex particles, clay platelets, and even some viruses, such as the
   tobacco mosaic virus) can organize themselves in liquid crystal phases.
   These more exotic mesogens generally fall into the category of
   lyotropic liquid crystals.

Liquid crystal phases

   The various LC phases (called mesophases) can be characterized by the
   type of ordering that is present. One can distinguish positional order
   (whether or not molecules are arranged in any sort of ordered lattice)
   and orientational order (whether or not molecules are mostly pointing
   in the same direction), and moreover order can be either short-range
   (only between molecules close to each other) or long-range (extending
   to larger, sometimes macroscopic, dimensions). Most thermotropic LCs
   will have an isotropic phase at high temperature. That is, heating will
   eventually drive them into a conventional liquid phase characterized by
   random and isotropic molecular ordering (little to no long-range
   order), and fluid-like flow behaviour. Under other conditions (for
   instance, lower temperature), an LC might inhabit one or more phases
   with significant anisotropic orientational structure and long-range
   orientational order while still having an ability to flow.

   The ordering of liquid crystalline phases is extensive on the molecular
   scale. This order extends up to the entire domain size, which may be on
   the order of micrometres, but usually does not extend to the
   macroscopic scale as often occurs in classical crystalline solids.
   However, some techniques (such as the use of boundaries or an applied
   electric field) can be used to enforce a single ordered domain in a
   macroscopic liquid crystal sample. The ordering in a liquid crystal
   might extend along only one dimension, with the material being
   essentially disordered in the other two directions.

Thermotropic liquid crystals

   Thermotropic phases are those that occur in a certain temperature
   range. If the temperature is raised 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 a
   temperature, most LC materials will form a conventional (though
   anisotropic) crystal. Many thermotropic LCs exhibit a variety of phases
   as temperature is changed. For instance, a particular mesogen may
   exhibit various smectic and nematic (and finally isotropic) phases as
   temperature is increased.

Nematic phase

   One of the most common LC phases is the nematic, where the molecules
   have no positional order, but they do have long-range orientational
   order. Thus, the molecules flow and their centre of mass positions are
   randomly distributed as in a liquid, but they all point in the same
   direction (within each domain). Most nematics are uniaxial: they have
   one axis that is longer and preferred, with the other two being
   equivalent (can be approximated as cylinders). Some liquid crystals are
   biaxial nematics, meaning that in addition to orienting their long
   axis, they also orient along a secondary axis.

   Liquid crystals are a phase of matter whose order is intermediate
   between that of a liquid and that of a crystal. The molecules are
   typically rod-shaped organic moieties about 25 angstroms (2.5
   nanometers) in length and their ordering is a function of temperature.
   The nematic phase, for example, is characterized by the orientational
   order of the constituent molecules. The molecular orientation (and
   hence the material's optical properties) can be controlled with applied
   electric fields. Nematics are (still) the most commonly used phase in
   liquid crystal displays (LCDs), with many such devices using the
   twisted nematic geometry. The smectic phases, which are found at lower
   temperatures than the nematic, form well-defined layers that can slide
   over one another like soap. 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 the layer normal. These phases, which are liquid-like within
   the layers, are illustrated below. There is a very large number of
   different smectic phases, all characterized by different types and
   degrees of positional and orientational order.

Chiral phases

   The chiral nematic phase exhibits chirality (handedness). This phase is
   often called the cholesteric phase because it was first observed for
   cholesterol derivatives. Only chiral molecules (i.e.: those that lack
   inversion symmetry) can give rise to such a phase. This phase exhibits
   a twisting of the molecules along the director, with the molecular axis
   perpendicular 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, the molecules
   orient roughly along the director, with a finite tilt angle, and a
   twist relative to other mesogens. This results in, again, a spiral
   twisting of molecular axis along the director.

   The chiral pitch refers to the distance (along the director) over which
   the mesogens undergo a full 360° twist (but note that the structure
   repeats itself every half-pitch, since the positive and negative
   directions along the director are equivalent). The pitch may be varied
   by adjusting temperature or adding other molecules to the LC fluid. For
   many types of liquid crystals, the pitch is on the same order as the
   wavelength of visible light. This causes these systems to exhibit
   unique optical properties, such as selective reflection. These
   properties are exploited in a number of optical applications.

Discotic phases

   Disk-shaped mesogens 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 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.

Lyotropic liquid crystals

   A lyotropic liquid crystal consists of two or more components that
   exhibit liquid-crystalline properties in certain concentration ranges.
   In the lyotropic phases, solvent molecules fill the space around the
   compounds to provide fluidity to the system. 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 which has two immiscible hydrophilic and hydrophobic parts
   within the same molecule is called an amphiphilic molecule. 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 into micelles or vesicles. 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 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 concentration, 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 phase)
     * Hexagonal columnar phase (middle phase)
     * Bicontinuous cubic phase
     * Lamellar phase
     * Bicontinuous cubic 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
   diblock copolymers.

Metallotropic liquid crystals

   Liquid crystal phases can also be based on low-melting inorganic phases
   like ZnCl[2] that have a structure formed of linked tetrahedra and
   easily form glasses. The addition of long chain soaplike molecules
   leads to a series of new phases that show a variety of liquid
   crystalline behaviour both as a function of the inorganic-organic
   composition ratio and of temperature. This class of materials has been
   named metallotropic ^J.D. Martin et al.

Biological liquid crystals

   Lyotropic liquid-crystalline nanostructures are abundant in living
   systems. Accordingly, lyotropic liquid crystals attract particular
   attention in the field of biomimetic chemistry. In particular,
   biological membranes and cell membranes are a form of liquid crystal.
   Their constituent rod-like molecules (e.g., phospholipids) are
   organized perpendicularly to the membrane surface, yet the membrane is
   fluid and elastic. The constituent molecules can flow in-plane quite
   easily, but tend not to leave the membrane, and can flip from one side
   of the membrane to the other with some difficulty. These liquid crystal
   membrane phases can also host important proteins such as receptors
   freely "floating" inside, or partly outside, the membrane.

   Many other biological structures exhibit LC behaviour. For instance,
   the concentrated protein solution that is extruded by a spider to
   generate silk is, in fact, a liquid crystal phase. The precise ordering
   of molecules in silk is critical to its renowned strength. DNA and many
   polypeptides can also form LC phases. Since biological mesogens are
   usually chiral, chirality often plays a role in these phases.

Theoretical treatment of liquid crystals

   Microscopic theoretical treatment of fluid phases can become quite
   involved, owing to the high material density, which means 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 complicate analysis. There are a number of fairly
   simple theories, however, that can at least predict the general
   behaviour of the phase transitions in liquid crystal systems.

Order parameter

   The description of liquid crystals involves an analysis of order. To
   make this quantitative, an orientational order parameter is usually
   defined based on the average of the second Legendre polynomial:

          S = \langle P_2(\cos \theta) \rangle = \left \langle \frac{3
          \cos^2 \theta-1}{2} \right \rangle

   where θ is the angle between the mesogen molecule axis and the local
   director (which is the 'preferred direction' in a liquid crystal
   sample). 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, S is 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 one undergoes a
   phase transition from an LC phase into the isotropic phase. The order
   parameter can be measured experimentally in a number of ways. For
   instance, diamagnetism, birefringence, Raman scattering, and NMR can
   also be used to determine S.

   One could also characterize the order of a liquid crystal 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.

Onsager hard-rod model

   A very simple model which predicts lyotropic phase transitions is the
   hard-rod model proposed by Lars 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 where the approaching cylinder's centre-of-mass cannot enter
   (due to the hard-rod repulsion between the two idealized objects).
   Thus, this angular arrangement sees a decrease in the net positional
   entropy of the approaching cylinder (there are fewer states available
   to it).

   The fundamental insight here is that that while parallel arrangements
   of anisotropic objects leads 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. Recently
   this theory is used to observe the phase transition between nematic and
   smectic-A at very high concentration also ^Hanif et al.. Although this
   model is conceptually helpful, its mathematical formulation makes
   several assumptions that limit its applicability to real systems.

Maier-Saupe mean field theory

   This statistical theory includes contributions from an attractive
   intermolecular potential. The anisotropic attraction stabilizes
   parallel alignment of neighboring molecules, and the theory then
   considers a mean-field average of the interaction. Solved
   self-consistently, this theory predicts thermotropic phase transitions,
   consistent with experiment.

Elastic continuum theory

   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. 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 mesogen axis. All three of these types of distortions incur an
   energy penalty. They are defects that often occur near domain walls or
   boundaries of 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.

Effect of chirality

   As already described, chiral mesogens usually give rise to chiral
   mesophases. For molecular mesogens, this means that the molecule must
   possess an asymmetric carbon atom. An additional requirement is that
   the system not be racemic: a mixture of right- and left-handed versions
   of the mesogen 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 mesogens. If the
   pitch of this twist is on the order of the wavelength of visible light,
   then interesting optical interference effects will be observed. The
   chiral twisting that occurs in chiral LC phases also makes the system
   respond differently to right- and left-handed circularly polarized
   light. These materials can thus be used as polarization filters.

   It is possible for chiral mesogens to produce essentially achiral
   mesophases. For instance, in certain ranges of concentration and
   molecular weight, DNA will form an achiral line hexatic phase. A
   curious recent observation is of the formation of chiral mesophases
   from achiral mesogens. Specifically, bent-core molecules (sometimes
   called banana liquid crystals) have been shown to form liquid crystal
   phases that are chiral. 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 are ferroelectric and anti-
   ferroelectric, both of which are of interest for applications.

Applications of liquid crystals

   Liquid crystals find wide use in liquid crystal displays, which rely on
   the optical properties of certain liquid crystalline molecules in the
   presence or absence of an electric field. In a typical device, a liquid
   crystal layer sits between two polarizers that are crossed (oriented at
   90° to one another). The liquid crystal is chosen so that its relaxed
   phase is a twisted one. This twisted phase reorients light that has
   passed through the first polarizer, allowing it to be transmitted
   through the second polarizer and reflected back to the observer. The
   device thus appears clear. When an electric field is applied to the LC
   layer, all the mesogens align (and are no longer twisting). In this
   aligned state, the mesogens do not reorient light, so the light
   polarized at the first polarizer is absorbed at the second polarizer,
   and the entire device appears dark. In this way, the electric field can
   be used to make a pixel switch between clear or dark on command. Color
   LCD systems use the same technique, with colour filters used to
   generate red, green, and blue pixels. Similar principles can be used to
   make other liquid crystal based optical devices.

   Thermotropic chiral LCs whose pitch varies strongly with temperature
   can be used as crude 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. Other liquid crystal
   materials change colour 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 for failure analysis in the semiconductor industry. Liquid
   crystal memory units with extensive capacity were used in Space Shuttle
   navigation equipment.

   It is also worth noting that many common fluids are in fact liquid
   crystals. Soap, for instance, is a liquid crystal, and forms a variety
   of LC phases depending on its concentration in water.

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