Helical defects in smectic- A and smectic- A∗ phases
Abstract
There are two categories of helical line defects in Sm- A phases: screw dislocations of small Burgers vectors and double helices (DHs), whose macroscopic configuration constitutes a mode of splitting of screw dislocations of giant Burgers vectors. Their counterparts in Sm- A∗ ’s (Sm- A ’s with chiral molecules) show a number of differences with the former and are investigated theoretically on the basis of recent observations [C. Meyer , Liq. Cryst. 37, 1047 (2010)10.1080/02678291003782846]. The first part of the paper is a short review of the main features of helical defects in Sm- A ’s proper. In Sm- A∗ ’s, small Burgers vector screw dislocations with the same chirality as the high-temperature N∗ phase are favored over the opposite ones, a result that is related to the defect core singularity. This is also true for the macroscopic DH∗ s for a more subtle reason; we advance that the DH∗ nucleation at the N∗→Sm-A∗ transition stems from a peculiar texture of the cybotactic groups, akin in the ideal case to a set of two twisted χ disclinations in the N∗ phase, linked by a stacking fault of continuous disclinations. This stacking fault vanishes in the Sm- A∗ phase, and one recovers a DH∗ much similar to a DH but with the appropriate chirality. Cases that differ from ideality are described: they involve small Burgers vector screw dislocations and can be evoked to explain the numerous observed distorted double helices (the Darboux condition is not obeyed) and twisted ribbons. The case when the N∗→Sm-A∗ transition is type II (presence of a twist grain boundary phase in between) is briefly discussed.
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