Tilt plane bilayer smectics

From this discussion the clear similarity between the SmAPA and SmCsPA structures is easily seen. In addition, the suggestion of Brand et al.29 that a bilayer smectic with all anticlinic layer interfaces (the SmAPF) would produce an achiral ferroelectric smectic follows directly. The unanticipated tilt of the director in the tilt plane, leading to a chiral layer structure, seems to be a general response of the bent-core mesogens to the spontaneous nonpolar symmetry breaking occurring in these rigid dimer structures. 

Figure 8.29 Illustration showing how all-anticlinic bilayer smectic should be ferroelectric is given. In case of covalent dimers (bent-core mesogens), equilibrium tilt of director combined with anti clinic layer interfaces in bow plane provides SmCsPF ferroelectric banana structure.

The earliest approach to explain tubule formation was developed by de Gen-nes.168 He pointed out that, in a bilayer membrane of chiral molecules in the Lp/ phase, symmetry allows the material to have a net electric dipole moment in the bilayer plane, like a chiral smectic-C liquid crystal.169 In other words, the material is ferroelectric, with a spontaneous electrostatic polarization P per unit area in the bilayer plane, perpendicular to the axis of molecular tilt. (Note that this argument depends on the chirality of the molecules, but it does not depend on the chiral elastic properties of the membrane. For that reason, we discuss it in this section, rather than with the chiral elastic models in the following sections.)... 

Liquid crystals can be in the smectic, nematic, or isotropic states. In the smectic liquid crystalline state there is a long-range order in the direction of the long axis of the molecules. These molecules may be in single- or bilayer conformation, have molecular axis normal or tilted to the plane of the layer, and frozen or melted chains. In the nematic liquid crystalline state the molecules are aligned side by side but not in specific layers. The isotropic liquid crystalline state is more or less a liquid state, but where clusters with short-range order persist (Small, 1986, pp. 49-51). 

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