The molecules in most crystals are arranged on a regular lattice, with even spacings between them, and they typically point in well defined directions.
In contrast, in a liquid, the molecules are disordered, in the sense that their positions and orientations are not correlated with each other. More precisely, the positions and orientations of molecules in a liquid are independent of each other when the molecules are far apart; molecules close together will always show some correlation between each other, because of the direct interactions between them.
Also, liquids flow, and the molecules find it easy to diffuse around, in contrast to their behaviour in solids.
In a liquid crystal, the positions of the molecules are still disordered, but the orientations align in a preferred direction. This occurs spontaneously, without the need to apply any external fields, although in the laboratory it is often convenient to apply a field so as to dictate the direction of alignment, or director as it is known. This alignment gives liquid crystals their interesting properties and makes them technologically useful, for example in display devices. The molecules still diffuse freely, and the substance flows, so it is a liquid.
We study nematic, smectic, and twisted or chiral liquid crystal phases.