Liquid Crystalline Blue Phases - Liquid Crystalline Functional Assemblies and Their Supramolecular Structures - page 103

around its long axis, and the intermolecular interaction should therefore work
isotropically in all of the lateral directions. For this reason, the interaction is
expected to induce twist arrangements for all the neighboring molecules in
the lateral directions. It should be noted, however, that a simple twist results in
directions, perpendicular to the helical axis, in which no twisting is induced.
That is to say, the molecular interaction to be twisted isotropically in all of the
lateral directions is not satisfied in the simple twist. Why does the chiral ne-
matic phase form a simple twist despite of the unsatisfactory arrangement?
Now let us consider the geometrical continuity of twisting arrangements. As
shown in Fig. 2, the rod-shaped molecules are arranged so that their long axes
are parallel to the x -axis, with no twisting along the long axis of molecules.
Then, beginning at Point A on the x -axis, the molecules are arranged in a twist
along the y -axis. Similarly, the twisting arrangement along the y -axis begins
with Point B on the x -axis, separated from Point A. When the angle of twisting
reaches 90 ◦ , the molecules are arranged along the x -axis so that they meet each
other from either direction. In the case of a simple twist along the x -axis, the
molecules are not twisted along the y -axis. Thus, the angles of the molecules
from Points A and B match, as shown in Fig. 2a in the meeting point. This
holds true even if the molecule twisting angle is other than 90 ◦ at the points
where the angle changes. If, however, the molecules are twisted along both
the y -and x -axes (double twist), the angles of molecules from both points
are mismatched (Fig. 2b) in the meeting point, except the distance between
Points A and B coincidentally corresponds to half the helical pitch. Next, let us
expand such twisting arrangements globally to the entire space. In the case of
the simple twist, when the angle of one molecule is determined at one point,
the angle of a molecule at any given position can be determined regardless of
Fig. 2 Frustration in twisted arrangements. a Inthecaseofsimpletwists,arrangements
from Points A and B, which are separated, do not result in inconsistency. b Double twists
result in inconsistency