Spontaneous Polarization Parallel to the Tilt Plane

Miyachi K, Matsushima J, Ishikawa K, Takezoe H, Fukuda A (1995) Spontaneous polarization parallel to the tilt plane in the antiferroelectric chiral smectic-CA phase of liquid-crystals as observed by polarized infrared-spectroscopy. Phys Rev E 52 R2153-R2156... 

An unanswered question is whether or not the Coulomb interaction among the permanent dipoles plays an important role. If the interaction is considered to result in in-plane spontaneous polarizations parallel to the tilt plane Px, we can designate this viewpoint as the Px model. For the stabilization of ferroelectric SmC, the Coulomb interaction among the permanent dipoles has not been considered essential, as insisted upon initially by Meyer [10]. It is also possible that this interaction does not play any essential role in the stabilization of SmC [24]. A... 

The local C2 symmetry in tilted chiral smectic layers leads to a polar inequivalence within the layers due to the chiral and polar nature of the individual molecules despite a considerable degree of molecular reorientation about the long axis (see Sec. 2 and 3 of this chapter) [19-22]. The consequence of this time-dependent alignment of the dipoles along the C2 axis is a spontaneous polarization (f s) parallel to the layer planes, which is averaged out macroscopically to... 

Similarly to the molecular engineering of calamitic molecules to produce ferroelectric smectic C phases [129], disk-like molecules with chiral peripheral chains tilted with respect to the columnar axis were predicted to lead to ferroelectric columnar mesophases [130]. Indeed, as it is the case with all flat disk-shaped mesogenic molecules, the tilt is mainly associated with the flat rigid aromatic cores of the molecules, the side-chains being in a disordered state around the columnar core. Thus, the nearest part of the chains from the cores makes an angle with the plane of the tilted aromatic part of the molecules. If the chiral centre and the dipole moment are located close to the core, then each column possesses a non-zero time averaged dipole moment, and therefore a spontaneous polarization. For reasons of symmetry, this polarization must be, on average, perpendicular to both the columnar axis and to the tilt direction in other words, the polarization is parallel to the axis about which the disk-shaped molecules rotate when they tilt as shown in Fig. 29. 

One result that stems from the above symmetry arguments is that the spontaneous polarization must have directionality [5, 6, 8, 9]. As the polarization acts along the normal to the tilt direction of the molecules and parallel to the layers, two directions for the spontaneous polarization become possible, as shown in Fig. 7. If the dipoles that produce the spontaneous polarization act along the positive y direction, when an object molecule is tilted to the right in the plane of the page, this results in positive polarization [Ps(+)j the reverse situation is denoted as negative polarization [Ps(-)]-... 

Figure 11-12. Crossed polarizing micrographic textures of spontaneous homeotropically aligned columnar phase of liquid crystalline porphyrin P8 at room temperature (A and B with different cooling rate. The dark areas are homeotropic alignment where the planes of the disk-shaped molecules are parallel to the substtates. Bright domains represent areas where the molecular planes are tilted with respect to the substtates.)...

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