Phases frustrated smectics

Figure C2.2.5. Frustrated smectic phases. Here the arrows denote longitudinal molecular dipoles. 

Another class of frustrated smectic phases are the incommensurate smectic A phases in which the competing periodicities coexist along the layer normal. The first example of such a phase was observed for a non-symmetric dimer, KI5 [144]... 

J. Wang, The Frustrated Smectic Phases in Liquid Crystals , thesis. University of Pennsylvania, 1985. 

Another class of frustrated phase results from the frustration between bend or twist deformations in smectic phases (Section 5.6) and the tendency to form a layered structure. Twisted grain boundary phases are frustrated smectic phases and both SmA and SmC versions have been observed. The phases are denoted TGBA and TGBC respectively and are formed by chiral mesogens. The phases are macroscopically chiral and result from arrays of screw dislocations (i.e. defects in lattice order) which lead to a twist in the director between grains of layers, i.e. to a helical rotation of layers. 

Frost showed that the properties and structures of frustrated smectics can be described by two order parameters [72, 82]. The first p(r) measures mass density modulation familiar in SmA phases [1 ]. The second (r), often referred to as a polarization wave, describes long range head-to-tail correlations of asymmetric molecules along the z axis... 

Figure 6. Mean field phase diagram obtained from the model of frustrated smectics for different values of the incommensurability parameter (a) Very weak incommensurability N, SmA, and SmA2 form the generic phase diagram of frustrated smectics. First calculated by Frost [82] this diagram is similar to the experimental one observed on the mixture DB5-TBBA [67].

Although not specific of liquid crystals, the re-entrant phenomenon (i.e. re-appearance of the phase of higher symmetry upon cooling) is often observed in frustrated smectics [80,106]. Theoretical analyses suggest that there is no universal explanation for re-en-trance in the N-SmA problem. 

Figure 15. Heat capacity of 80PCB0B near the nematic to smectic A1 phase transition. The smooth curve represents a fit to the data with Eq. (6) based on critical parameters in agreement with the three-dimensional XY model. The index 1 in SmA refers to the monolayer structure of this frustrated smectic compound [65].

A phenomenological model for frustrated smectics proposed that 2-D modulated smectic phases might arise as an escape from underlying incommensurability in the system [22,161,162]. The role of polar and steric molecular assymetry in smectic polymorphism has been comprehensively reviewed [23, 163]. The forms of the X-ray diffraction patterns from modulated and incommensurate smectic phases have been extensively discussed [20-23] and these papers should be consulted for earlier references and for details which will not be covered here. 

Modulated smectic phases are just one of a number of classes of frustrated smectic phases, all of which arise from the competition between different characteristic length scales but differ in the manner by which this frustration is relieved. In the incommensurate SmA phases the competing periodicities coexist along the layer normal and the first example of such a phase was observed for a nonsymmetric dimer, KI5 (see Fig. 1 g). In this phase the larger periodicity appears to correspond to the molec-... 

Fig. 9.22 (a) X-ray pattern of oriented smectic phase observed in BPCO3-011 fibers at 200 °C. The fiber specimen was prepared by pulling up the isotropic melt and its axis is placed in the vertical direction. It includes several other inner reflections except for the usual layer reflections, indicating the frustrated phase, (b) Tentative structural model of frustrated smectic phase. For convenience, the polymer chains in an all-trans conformation are illustrated... 

The steric frustrations have also been detected in LC polymers [66-68]. For example, the smectic A phase with a local two-dimensional lattice was found by Endres et al. [67] for combined main chain/side chain polymers containing no terminal dipoles, but with repeating units of laterally branched mesogens. A frustrated bilayer smectic phase was observed by Watanabe et al. [68] in main-chain polymers with two odd numbered spacers sufficiently differing in their length (Fig. 7). 

Thermotropic liquid crystals, 15 86-98 bent-core, 15 98 discotic phases of, 15 96 frustrated phases of, 15 94-96 metallomesogens, 15 97 nematic liquid crystals, 15 86-92 smectic liquid crystals, 15 92-94 Thermotropic mesophases, 20 79 Thermotropic polycarbonates, 19 804 Thermotropic polyesters, liquid-crystalline, 20 34... 

Fig. 6. However, these two structures are incompatible with one another and cannot co-exist and the molecules still fill space uniformly without forming defects. The matter is resolved by the formation of a periodic ordering of screw dislocations which enables a quasi-helical structure to co-exist with a layered structure. This is achieved by having small blocks/sheets of molecules, which have a local smectic structure, being rotated with respect to one another by a set of screw dislocations, thereby forming a helical structure [15]. As the macroscopic helix is formed with the aid of screw dislocations, the dislocations themselves must be periodic. It is predicted that rows of screw dislocations in the lattice will form grain boundaries in the phase, see Fig. 7, and hence this structurally frustrated phase, which was theoretically predicted by Renn and Lubensky [15], was called the twist grain boundary (TGB).

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