The three common states of matter, solid, liquid and gas, are different because the molecules in each state have a different degree of order.
In the (crystalline) solid state there exists a rigid arrangement of molecules which stay in a fixed position and orientation with a small amount of variation from molecular vibration. To maintain this arrangement there are large forces holding the molecules in place and therefore a solid is difficult to deform. In the liquid phase the molecules have no fixed position or orientation and are free to move in a random fashion and the liquid state has less order than the solid state. The random motions of the molecules mean that the intermolecular attractive forces that kept a solid together are now only strong enough to keep the liquid molecules fairly close together. A liquid can therefore be easily deformed. In the gas state the random motion of the molecules has increased to overcome the intermolecular forces and the molecules eventually spread out to fill any container that holds them. The order in a liquid which derived from the closeness of the molecules has therefore been lost in a gas which consequently has less order than the liquid. The probability of molecules in a certain region being in a rigid arrangement and of the same orientation can be used to define a positional and orientational order which is greatest in the solid state and least in the gaseous state.
The differences between the three states can be attributed to the temperature of the substance. Temperature is a measure of the randomness of the molecules and therefore the higher the temperature the less order exists and increasing temperature will cause the transition from a solid to a liquid and then to a gas.
A thermotropic liquid crystalline phase occurs in some substances in a temperature region between the solid and liquid states. In this state the substance possesses some properties of both liquids and solids. A liquid crystal is a fluid like a liquid but is anisotropic in its optical and electro-magnetic characteristics like a solid. When the liquid crystal is formed from the isotropic state some amount of positional or orientational order is gained. It is this order that accounts for the anisotropies of the substance.
In the following sections the main phases of thermotropic liquid crystals are described.Nematics
| By decreasing the temperature from the isotropic phase, in
which the molecules are randomly positioned and oriented (see Fig. 1), to
the nematic phase the material gains an amount of orientational order but
no positional order (Fig. 2). This reordering is thought to be due to the
packing constraints of the molecules. This claim is supported by the fact
that most liquid crystal molecules tend to be long thin molecules with a
rigid cental region. This orientational order allows us to define an
avarage direction of the molecules called the director and denoted by the vector n. The material
is still a fluid but at each point, r, in this fluid the molecules
prefer to orient along n(r). Thus the material is
anisotropic.
Another important variable in nematic liquid crystals is the order parameter which measures how aligned with the
director the molecules. The usual measure of this order is, |
  |
Chiral nematics
When the molecules that make up a nematic liquid crystal are chiral (i.e. they are not symmetric when reflected) then the chiral nematic phase will exist instead of the normal nematic. In this phase the molecules prefer to lie next to each other in a slightly skewed orientation. This induces a helical director configuration in which the director rotates through the material (Fig. 3).
This helical internal structure is key to the operation of Twisted Nematic (TN) liquid crystal displays. In such displays a nematic is placed between two crossed polarizers and the molecules at the cell surfaces are aligned such that the director lies parallel to the polarizers (see Fig. 4).
Without the liquid crystal present light entering from the top of the cell would not be transmitted through the cell due to the crossed polarizers. However the helical director structure guides the polarized light from the upper polarizer round so that the light may be transmitted through the lower polarizer. When a voltage is applied across the cell the molecules align with the electric field due to a dielectric interaction between the molecule and the electric field. This destroys the helical structure and the light cannot be transmitted. In a display the zero voltage, transmitting state is white and the non-zero voltage, non-transmitting state is black.
Smectics
|
At certain temperatures, generally below the nematic phase, the liquid crystal material may gain an amount of positional order. When this happens the liquid crystal forms into smectic phase where the molecules, although still forming a fluid, prefer to lie on average in layers (Fig. 5). Within each layer the liquid crystal is essentially a 2 dimensional nematic liquid crystal. This positional ordering may be described in terms of the
density of the centres of mass of the molecules, There are many types of smectic materials and Figs. 5-7
show just three examples. When the nematic-like director in each layer is
parallel to the layer normal the material is smectic
A (Fig. 5). If this director tilts away from the layer normal the
smectic C (Fig. 6) phase is formed and at lower
temperatures, in some materials, the direction of this tilt may alternate
to form a herringbone structure called a There also exists higher order smectics which form layers with positional ordering within the layers. For instance in smectic B materials the molecules in each layer for a hexatic structure. |
   |
Chiral smectics
In a similar way to chiral nematics there are chiral forms of smectic phases. Figure 8 shows a chiral smectic C material, denoted by smectic C*. The tilted director rotates from layer to layer forming a helical structure.
The discovery of liquid crystals is thought to have occurred nearly 150 years ago although its significance was not fully realised until over a hundred years later. Around the middle of the last century Virchow, Mettenheimer and Valentin found that the nerve fibre they were studying formed a fluid substance when left in water which exhibited a strange behaviour when viewed using polarized light. They did not realise this was a different phase but they are attributed with the first observation of liquid crystals. Later, in 1877, Otto Lehmann used a polarizing microscope with a heated stage to investigate the phase transitions of various substances. He found that one substance would change from a clear liquid to a cloudy liquid before crystallising but thought that this was simply an imperfect phase transition from liquid to crystalline. In 1888 Reinitzer conducted similar experiments and was the first to suggest that this cloudy fluid was a new phase of matter. He has consequently been given the credit for the discovery of the liquid crystalline phase. Up till 1890 all the liquid crystalline substances that had been investigated had been naturally occurring and it was then that the first synthetic liquid crystal, p-azoxyanisole, was produced by Gatterman and Ritschke. Subsequently more liquid crystals were synthesised and it is now possible to produce liquid crystals with specific predetermined material properties.
In the beginning of this century George Freidel conducted many experiments on liquid crystals and it was he who first explained the orienting effect of electric fields and the presence of defects in liquid crystals. In 1922 he proposed a classification of liquid crystals based upon the different molecular orderings of each substance. It was between 1922 and the World War II that Oseen and Zöcher developed a mathematical basis for the study of liquid crystals.
After the start of the war many scientists believed that the important features of liquid crystals had now been discovered and it wasn't until the 1950's that work by Brown in America, Chistiakoff in the Soviet Union and Gray and Frank in England led to a revival of interest in liquid crystals. Maier and Saupe formulated a microscopic theory of liquid crystals, Frank and later Leslie and Ericksen developed continuum theories for static and dynamic systems and in 1968 scientists from RCA first demonstrated a liquid crystal display. The interest in liquid crystals has grown ever since, partly due to the great variety of phenomena exhibited by liquid crystals and partly because of the enormous commercial interest and importance of liquid crystal displays.
A more in-depth study of the physical properties and theory of liquid crystals may be found in,
is the angle
between each molecule and the director. If the molecules are very well
aligned with the director then S=1 and if the molecules are randomly
oriented about n i.e. isotropic the S=0. So, the higher the order
parameter the more ordered the nematic liquid crystal. 
is the order
parameter. When 