Phase Transitions in the Systems of Identical Rigid Molecules in Perfect Alignment-Relations of the Smectic A and Columnar Orderings in Liquid Crystals and the Crystalline Ordering to the Molecular Shape

The method of symmetry breaking potential is applied to the system of identical rigid molecules with simple typical shapes (rod with square cross-section, square plate and cube), which are perfectly aligned, to examine the occurrences of such various types of spatial ordering as in smectic, columnar and crystalline phases in relation to the molecular shape. A smectic A phase occurs in the system of rigid rod molecules much more easily than the close packed crystal structure does in the system of rigid sphere molecules. Columnar and crystalline phases do also similarly in the system of molecules of square plate and cube, respectively. It is also shown that the nematic-smectic A transition in the case of rigid rod molecules in perfect alignment is the second order one, in contrast with those in the others of typical first order transitions. The effect of orientational fluctuation is discussed in short.