Liquid crystals symmetry breaking

We start with some elementary information about anisotropic intermolec-ular interactions in liquid crystals and molecular factors that influence the smectic behaviour. The various types of molecular models and commonly accepted concepts reproducing the smectic behaviour are evaluated. Then we discuss in more detail the breaking of head-to-tail inversion symmetry in smectic layers formed by polar and (or) sterically asymmetric molecules and formation of particular phases with one and two dimensional periodicity. We then proceed with the description of the structure and phase behaviour of terminally fluorinated and polyphilic mesogens and specific polar properties of the achiral chevron structures. Finally, different possibilities for bridging the gap between smectic and columnar phases are considered. 

So far we have considered the formation of tubules in systems of fixed molecular chirality. It is also possible that tubules might form out of membranes that undergo a chiral symmetry-breaking transition, in which they spontaneously break reflection symmetry and select a handedness, even if they are composed of achiral molecules. This symmetry breaking has been seen in bent-core liquid crystals which spontaneously form a liquid conglomerate composed of macroscopic chiral domains of either handedness.194 This topic is extensively discussed in Walba s chapter elsewhere in this volume. Some indications of this effect have also been seen in experiments on self-assembled aggregates.195,196... 

Spontaneous Reflection Symmetry Breaking in Liquid Crystals... 

The author was supported by the Ferroelectric Liquid Crystal Materials Research Center (National Science Foundation MRSEC award No. DMR-9809555) during the writing of this chapter. The author thanks Professors Tom Lubensky, Leo Radzihovsky, and Joseph Gal for helpful discussions around the issue of terminology for reflection symmetry breaking, and especially Professor Noel Clark for his help on this and many other banana-phase issues. The author also thanks Dr. Renfan Shao for the photomicrographs shown in Figures 8.32 and 8.33. 

This volume of Topics in Stereochemistry could not be complete without hearing about ferroelectric liquid crystals, where chirality is the essential element behind the wide interest in this mesogenic state. In Chapter 8, Walba, a pioneering contributor to this area, provides a historical overview of the earlier key developments in this field and leads us to the discovery of the unique banana phases. This discussion is followed by a view of the most recent results, which involve, among others, the directed design of chiral ferroelectric banana phases, which display spontaneous polar symmetry breaking in a smectic liquid crystal. 

The existence of the layers and director tilt in the achiral smectic C liquid crystal phase are experimental facts. Given these, the maximum possible symmetry of the phase would be Ci, with a C2 axis normal to the tilt plane, and a a plane congruent with the tilt plane. In fact, there is no fundamental reason why a given C phase must possess either of these symmetry elements. But, breaking of either of the symmetry elements would afford polar symmetry, and no C phase has ever been shown to possess any property associated with polar symmetry (e.g. pyroelectricity). Therefore, we can say that all known C phases indeed possess the maximum possible symmetry consistent with the layers and tilt. 

Vaupotic N, Copic M (2005) Polarization modulation instability in liquid crystals with spontaneous chiral symmetry breaking. Phys Rev E 72 031701-1-031701-4... 

Walba DM, Korblova E, Huang C-C, Shao R, Nakata M, Clark NA (2006) Reflection symmetry breaking in achiral rod-shaped smectic liquid crystals J Am Chem Soc 128 5318-5319... 

Prasang C, Whitwood AC, Bruce DW (2008) Spontaneous symmetry-breaking in halogen-bonded, bent-core liquid crystals observation of a chemically driven Iso-N-N phase sequence. Chem Commun 2008 2137-2139... 

Supramolecular chemistry can be used to create the bent cores that give rise to the symmetry breaking in this family of liquid crystals [139]. The formation of a complex between a calamitic benzoic acid derivative and a bent core terminated with a pyridyl group—neither of which display mesomorphic behaviour—gave rise to a material which displayed SmCP mesophases. The achiral bent cores can also give rise to symmetry breaking when they are attached to flexible polymeric chains, such as poly(siloxane) [140]. 

Keywords liquid crystals, metastability, symmetry breaking, weak disorder, Irmy-Ma scaling... 

There is another class of liquid crystals, the bowlic liquid crystal phase, whose molecules are bowl-like or pyramid-like, as is shown in Figure 1.13. Because of the breaking down of the up-down symmetry, the bowlic phase shows an even higher order and may be able to show ferroelectricity (Lam, 1986 Wang et al., 1989). 

S.P. Palto, N.J. Mottram and M.A. Osipov, Flexoelectric instability and spontaneous chiral-symmetry breaking in a nematic liquid crystal with asymmetric boundary conditions, Phys. Rev. E 75(6), 061707/1-8, (2007). 

For some special kind of magnetic-liquids and liquid crystals the symmetry of the hydrodynamic stress tensor, P, breaks down (Slattery 1978). In the case of classical fluids P is a symmetric tensor - there is not micro-moments acting on the fluid element. The stress tensor P becomes a superposition of two contributions - an isotropic thermodynamic pressure, p, and... 

The interfaces in general, and particularly with solid substrates break the head-to-tail symmetry of a liquid crystal phase and induce polar orientational order. The symmetry is reduced to the conical group Coov The latter allows a finite value of the second-order nonlinear susceptibility X2 responsible for the second optical harmonic generation [11]. This phenomenon has been observed in experiments on generation of the second harmonic in a ultrathin nematic layers on a solid substrate as shown in Fig. 10.9. 

Since discovery of chiral ferroelectrics in 1975, a search for the achiral analogues of liquid crystal ferro- and antiferroeiectrics was a challenge to researchers, both theoreticians and experimentalists and recently there was a great progress in this area. The idea was to find a way to break non-polar symmetry Dooh or C2h of... 

Since the discovery of spontaneous break of mirror symmetry [39, 43], many new, so-called banana-form compounds have been synthesised and hundreds of papers published on that subject [44]. It became a hot topic in modem physics and chemistry of liquid crystals. In the present book there is no space for discussirm of different aspects of this fascinating phenomenon and I have decided to finish my narration here. I believe very soon the books shall appear devoted solely to this important subject related not only to liquid crystals, but to the general problems of chirality of the matter. 

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