The properties of smectic

An interesting modification of smectic C is the S, phase, which has a twist axis normal to the layers (fig. 5.10.1 (a)). The possibility of such a structure being formed by the addition of optically active molecules to the ordinary 

Both Sc and Si (the chiral forms of Sp and Sj) were shown to be ferroelectric. 

In the molecules are upright, and since there is no head-to-tail ordering (the director being apolar) there is no polarization normal to the layers. Moreover, even if the molecules themselves are chiral, there is equal probability of their assuming any orientation about their long axes. Hence the transverse component of the dipole moment is averaged out and there is no net polarization parallel to the layers. 

In the phase, on the other hand, the molecules are tilted, and their rotation about their long axes is biased. The symmetry plane of the ordinary structure (fig. S.8.1) is now absent because the molecules are chiral. The only symmetry element that remains is a twofold axis parallel to the layers and normal to the long molecular direction. This allows the existence of a permanent dipole moment parallel to this axis. (Of course, these arguments apply to the S,. phase as well.) 

Thus in S. each layer is spontaneously polarized. Since the structure has a twist about the layer normal, the tilt and the polarization direction rotate from one layer to the next (fig. 5.10.1(a)). This implies that there is a constant bend around the helical axis, which gives rise to a flexoelectric contribution to the polarization. 

---

The important information about the properties of smectic layers can be obtained from the relative intensities of the (OOn) Bragg peaks. The electron density profile along the layer normal is described by a spatial distribution function p(z). The function p(z) may be represented as a convolution of the molecular form factor F(z) and the molecular centre of mass distribution f(z) across the layers [43]. The function F(z) may be calculated on the basis of a certain model for layer organization [37, 48]. The distribution function f(z) is usually expanded into a Fourier series f(z) = cos(nqoz), where the coefficients = (cos(nqoz)) are the de Gennes-McMillan translational order parameters of the smectic A phase. According to the convolution theorem, the intensities of the (OOn) reflections from the smectic layers are simply proportional to the square of the translational order parameters t ... 

---