DEVELOPABLE DOMAINS IN HEXAGONAL LIQUID-CRYSTALS

Configurations without strain (as opposed to curvature) in a mesomorphic phase made of long thin rods (like hexagonal liquid crystals) are characterized by local frames of reference undistorted with respect to the ground state and by absence of splay deformation (div t equals 0). These constraints lead to an important class of solutions, without twist deformation (t. rot t equals 0), with bend deformation (t x rot t does not equal 0). It is shown that this class of solutions is characterized by the existence of physical planes perpendicular to the rods, enveloping a developable surface. This is the solution first devised by Bouligand. The geometrical properties are studied in detail and the problem of obtaining all the so-called developable domains by using a plane representation of the space configuration is solved giving methods to calculate its energy. Two simple examples are given, one in which the developable domain is equivalent to a disclination, another one in which it is equivalent to a singular point.