$D_2$-$D_1$ phase transition of columnar liquid crystals

The $D_2$-$D_1$ phase transition in columnar liquid crystals of the HAT series [e.g., HAT11 (triphenelene hexa-n-dodecanoate)] is discussed within the framework of Landau theory. The order parameters which describe the transition are abstracted from a tensor density function, and are associated with two irreducible representations of the symmetry group of the high-temperature $D_2$ phase. A mechanism for a first-order transition is then suggested in accordance with both theoretical considerations and the experimental result for the $D_2$-$D_1$ transition. Two possible arrangements of the herringbone structure of the $D_1$ phase are obtained, each of which gives six orientational states in the low-temperature $D_1$ phase.