Twist-grain-boundary phases near the nematic–smectic-A–smectic-Cpoint in liquid crystals

We generalize the Chen-Lubensky model for the point where the nematic, smectic-A, and smectic-C liquid-crystalline phases meet (the NAC point) to include the effects of molecular chirality. We calculate the phase diagram for this model when the possibility of a twist-grain-boundary (TGB) phase is included and when it is not. In the latter case, we find that the NAC multicritical point becomes a critical end point where first-order cholesteric to smectic-A and cholesteric to chiral-smectic-C phase boundaries meet a second-order smectic-A to chiral-smectic-C phase boundary. In the former case, we find that the TGB phase always intervenes between the cholesteric and smectic-A phases near the NAC multicritical point of the nonchiral system. The connection between these results and the recent observations of a chiral smectic phase near the NAC point by Goodby and co-workers Nature 337, 449 (1988); J. Am. Chem. Soc. 111, 8119 (1989) is discussed briefly.