Liquid crystal
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 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, a liquid crystal material 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.
Molecules that exhibit liquid crystal phases are called mesogens. For a molecule to display an LC phase, it must generally be 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.
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 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 behavior. 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 orientational order may be quasicrystalline.

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 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) as temperature is increased.
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 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.

The smectic phase is one where in addition to orientation order, the mesogens are grouped into layers, enforcing long-range positional order in one direction. In the smectic A phase, the molecules point perpendicular to the layer planes, whereas in the smectic C phase, the molecules are tilted with respect to the layer planes. In hexatic phases, the mesogens in a particular layer take on a roughly hexagonal close-packed ordering, with typically no registry between adjacent smectic layers. It is also possible to find examples of liquid crystals where the registry between layers is fairly strong, hence there is three dimensional positional (and possibly even orientational) order. These phases are called crystal mesophases, and are in fact nearly as ordered as solid crystals (although they still exhibit fluid-like flow).
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 360º 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.
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.

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) or lecithins 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 behavior. 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.

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