A theoretical investigation on the relative stability of the columnar hexagonal and columnar square phases of discotic molecules

We have employed a mean field theory, which is a modified Ginzburg-Landau expansion in terms of the scalar order parameter Φ(r), to stabilize the ordered phases such as square and hexagonal phases of the discotic molecules. The Φ(r) represents the local volume fraction differential between the stiff core and the outside alkyl chain regions of the discotic molecules. The current theoretical analysis stabilizes the ordered phases, particularly the square (S) and 2D hexagonal (H) phases. The present study also identifies the direct hexagonal (HI) and reverse hexagonal (HII) phases, with the phases occurring in the following order: disorder(D) - HI - S - HII - disorder(D) with increase in the average volume fraction difference, Φo. Contrarily, the stability area of the S phase accounts for around 10% of the total area of the ordered phase, whereas the HI and HII phases each occupy about 45% of the total area of the ordered phase.