Smectic antiphases

So far we have discussed 2D density modulated phases that are formed by deformation or breaking of the layers. However, there are also 2D phases with more subtle electron density modulations. In some cases additional peaks observed in the XRD pattern (Fig. 10) are related to a double layer periodicity in the structure. As double layer periodicity was observed in the bent-core liquid crystals formed by the asymmetric as well as symmetric molecules [22-25] it should be assumed that the mechanism leading to bilayers must be different from that of the pairing of longitudinal dipole moments of molecules from the neighboring layers, which is valid for smectic antiphases made by asymmetric rod-like molecules. 

The smectic antiphase SmA, first discovered by Sigaud et al. [74] exhibits a periodic modulation of the antiferroelectric order along a direction x parallel to the plane of the layers. The incommensurate wavevectors tilt over to lock in in two dimensions (Fig. 5). 

Notice that this structure has already been reported to describe the ribbon structure observed with sodium soaps [60], with the Sa antiphase [61], and for the two-dimensional smectic structure of dissymmetrical and highly polar mesogens [62]. 

Let us consider smectic A phases in which the molecules form a regular stack of infinite 2D liquid-like ordered layers with their director perpendicular to the layer the presence of longitudinal dipoles raises the question of their orientation within each layer. Over the past few years five Sa modifications have been defined which involve different overlapping structures of the molecules e.g. A (monolayer), A2 (bilayer), A (interdigitated bilayer) and A and A (antiphase and crenelated phase, in-plane modulated structuring) (Fig. 2.12). In the A phase the dipoles are randomly oriented in each layer, the period is then equal to the molecular length. In the Sa phase, the dipoles are all in the same... 

Fig. 2.12. Interdigitated bilayer (Sa j) nionolayer (SaJ, bilayer Sa2 and antiphase (Sa) smectic A phases.

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