anisotropy

An anisotropic substance has, as opposed to an isotropic one, different properties in different directions. An example you certainly are acquainted with is meat; try cutting it along and perpendicular to the fibers respectively and you'll get quite different results! The anisotropy of liquid crystals concerns for instance their interaction with light. Light plane polarized parallel to the so called optic axis of the substance sees a different material than light polarized perpendicular to it.

azimuthal angle

To describe the different instants of a rotatory motion you need the azimuthal angle. This is the angle between the rotating object at a particular instant of time, and some reference direction. For instance, at 3 o'clock the little finger of your watch (provided you don't have a digital watch) will have an azimuthal angle of 90° relative to the straight-up (12 o'clock) position. In chiral liquid crystal phases where a helix forms, the azimuthal angle of the director is changing continuously as you go along the helix axis.

chirality

A chiral object is mirror asymmetric, that is, it cannot be superposed on its mirror image. A well known chiral object is the human hand, which has also given the property its name (the word chiral is derived from the Greek word for hand). Objects which are mirror symmetric are called achiral.

cholesteric

Chiral nematics are often called cholesterics. The first observations of liquid crystals were made on cholesterol benzoate (thereby the name cholesteric) which is a chiral mesogen with a nematic phase between the solid and liquid states.

cohesion

The sticking together by molecular forces, characteristic of all matter at sufficiently small distances between atoms or molecules.

crystallinity

A crystal is a solid characterized by a periodic arrangement of the constituents on a microscopic level, as opposed to an amorphous solid, which has a more or less random positioning of the constituents.

density

The mass of a substance per unit volume.

dielectric constant

The size of the dielectric constant reflects how much a material can be polarized by an electric field. The dielectric constant is in the general case a tensor, so for anisotropic materials the magnitude is different in different directions

dipole

An electric dipole has a negative charge in one end and a positive in the other.

director

The director n is an entity specific for liquid crystals. It is a unit vector describing the direction around which the molecules fluctuate. It has no sign; n = -n.

helix

A helical structure exhibits a twist in a plane perpendicular to the helix axis. A cork screw is an example.

isotropic

An isotropic substance has the same properties in all directions.

monoclinic

There is one distinct direction towards which the molecules tilt.

mesogen

A substance showing liquid crystalline phases is called a mesogen.

mesophase

Liquid crystalline phases are also called mesophases.

nematic

The simplest liquid crystalline phase. In the nematic phase the molecules have random positional order but are on the average oriented along one specific direction. The word is derived from the Greek word for thread, which stems from the threadlike defect lines characteristic of nematic liquid crystals viewed under a polarizing microscope.

normal

The normal to a plane is the unit vector perpendicular to the plane.

optic axis

An optically anisotropic substance has one extreme refractive index in a certain direction, and the other extreme refractive index in the directions perpendicular to this. This direction is labelled the optic axis. In liquid crystals the optic axis often coincides with the director.

phase (thermodynamic)

The phases of a substance are its thermodynamic states of matter, differing in degree and kind of order. There are solid, liquid crystalline, liquid and gas phases. Most materials do not exhibit any liquid crystalline phases.

phase (in wave equations)

If two waves with the same frequency oscillate such that they at all instants in time are at the same part of their period, they oscillate in phase. However, if one wave is always slightly ahead of the other, there is a phase difference between the two waves.

polar

A polar molecule is a dipole.

polarizer

An optical component which lets through light polarized in a certain way, for instance linearly polarized in a specific direction, and blocks all other light.

polymer

Substances whose molecules are made up of a great number of identical parts (monomers).

refractive indicex

The refractive index of a material is a measure of the light speed in the material. The higher value, the lower the light speed.

smectics

Smectic phases are characterized by a layered structure. The molecules are often free to move within the layers, but much less free to move from layer to layer. The word is derived from the Greek word for soap, which is due to the liquid soap-like appearance of smectics when viewed with the naked eye.

vector

An entity with both magnitude and direction. Velocity is for instance a vector, while mass is a so called scalar, i.e. it does not have a direction, only a magnitude. Vectors are often written with bold face, like the director n, to distinguish them from scalars which are written with plain font.