Bent-core molecules liquid crystals

It is possible for chiral mesogens to produce essentially achiral mesophases. For instance, in certain ranges of concentration and molecular weight, DNA will form an achiral line hexatic phase. A curious recent observation is of the formation of chiral mesophases from achiral mesogens. Specifically, bent-core molecules (sometimes called banana LCs) have been shown to form liquid crystal phases that are chiral. In any particular sample, various domains will have opposite handedness, but within any given domain, strong chiral ordering will be present. 

The free energy density terms introduced so far are all used in the description of the smectic phases made by rod-like molecules, the electrostatic term (6) being characteristic for the ferroelectric liquid crystals made of chiral rod-like molecules. To describe phases made by bent-core molecules one has to add symmetry allowed terms which include the divergence of the polar director (polarization splay) and coupling of the polar director to the nematic director and the smectic layer normal ... 

Earl DJ, Osipov MA, Takezoe H, Takanishi Y, Wilson MR (2005) Induced and spontaneous deracemization in bent-core liquid crystal phases and in other phases doped with bent-core molecules. Phys Rev E 71 021706-1-11... 

The bent core molecules do not only exhibit spontaneous resolution in smectic phases. One achiral derivative resolves in a nematic phase in this fluid state [ 145], while a substituted oxadiazole which forms a biaxial nematic phase also segregates [ 146]. The bent core clearly has a special stereochemical influence as a result of the effects it induces beyond the molecule, at least for liquid crystals. 

Liquid crystals are interesting supramolecular systems which can show second harmonic generation when they are aligned appropriately. Ferroelectric LCs [250] as well as bent-core molecules have been used to this purpose, and show reasonable second harmonic generation [251]. These materials combine non-linear optical effects with simple processing procedures on account of their liquid crystalline flow characteristics and the possibility of organising them with electric and magnetic fields. 

General expressions for the flexocoefiicients of nematic liquid crystals have been obtained in terms of the direct correlation function using the powerful density functional approach. These expressions have been used to obtain some interesting numerical results using the Perkus-Yevic approximation for the pair correlation function. The results from the density functional theory have also been used in computer simulations of flexoelectricity using model bent-core molecules interacting via the Gay-Berne potential. Alternative general expressions for the flexocoefiicients have... 

A. Jakli, J. Harden and N. Eber, Chapter 3. Flexoelectricity of bent-core molecules. In eds. A. Buka and N. Eber, Flexoelectricity in Liquid Crystals. Theory, Experiments and Applications, Imperial College Press, London, 2012. pp. 61-99. 

Lee, J. H. Yoona, T. H. Choi, E. J. Flexoelectric effect of arod-like nematic liquid crystal doped with highly kinked bent-core molecules for energy converting components. Soft Matter 2012, 8, 2370. 

Ortega, J. Gallastegui, J. A. Folcia, C. L. Etxebarria, J. Gimeno, N. Ros, M. B. Second harmonic generation measurements in aligned samples of liquid crystals composed of bent-core molecules. Liq. Cryst. 2004, 31, 579-584. 

Jakli, A., Rauch, S., Lotzsch, D., Fleppke, G. Uniform textures of smectic liquid-crystal phase formed by bent-core molecules. Phys. Rev. E. 1998, 57, 6737—6740. 

Thermotropic liquid crystals are most often composed of elongated rod-like or plane disc-like organic molecules cf. Fig. 3.1, top part). However, the molecules may also take other geometries as long as they are anisotropic, e.g. a banana-like shape as found for bent-core molecules [1]. This anisotropic shape is essential, as orientational order cannot be defined for building blocks with an isotropic shape. 

It is important to note that also nonchiral molecules are capable of forming chiral mesophases. In particular, molecules with a bent core ( bananashaped molecules) can build polar, and even chiral liquid crystal structures [75]-[78]. Bent-core molecules form a variety of new phases (B1-B7, Table 1.3) which differ from the usual smectic and columnar phases (see also Chapter 8). As a consequence of the polar arrangement, antiferroelectric-like switching was observed in the B2 phase formed by bent-core molecules, and second harmonic generation was found in both the B2 phase and the B4 phase. The latter phase is probably a solid crystal. It consists of two domains showing selective reflection with opposite handedness. In the liquid crystalline B2 phase, the effective nonlinear susceptibility can be modulated by an external dc field [79] (Figure 1.15). 

Table 1.2. Nonlinear susceptibilities observed in ferroelectric liquid crystals and in the phases B2 and B4 formed by bent-core molecules. The indices are given in the following coordinates y-axis spontaneous polarization z-axis smectic layer normal x-axis projection of the director in the plane of the smectic layers. For comparison, the values of two NLO crystals are given.

Ferroelectricity in Liquid Crystal Phases of Nonchiral Bent-Core Molecules... 

A special example of chiral liquid crystals is the tilted smectic phases of bent-core molecules, which can be chiral even though the molecules do not contain any stereo-center carbons. The reason is that a bent-core tilted layer structure with polar order has a three-dimensional structure defined by the polar vector and the tilt direction, which can be illustrated either by our left or right hands of Figure 1.12. We note that the latest investigations indicate other sources of chirality of bent-core molecules, which are termed conformational chirality, due to a propeller type configuration of the two molecular legs. ... 

As described in Chapter 1, smectic liquid crystal phases of bent-core molecules can form polar strcutures. 

Thisayukta J, Nakayama Y, Kawauchi S, Takezoe H, Watanabe J (2000) Distinct formation of a chiral smectic phase in achiral banana-shaped molecules with a central core based on a 2,7-dihydroxynaphthalene unit. J Am Chem Soc 122 7441-7448 Tschierske C, Dantlgraber G (2003) From antiferroelectricity to ferroelectricity in smectic mesophases formed by bent-core molecules. Pramana J Phys 61 455-481 Ungar G, Percec V, Zuber M (1992) Liquid crystalline polyethers based on conformational isomerism. 20. Nematic-nematic transition in polyethers and copolyethers based on l-(4-hydroxyphenyl)2-(2-R-4-hydroxyphenyl)ethane with R=lluoro, chloro and methyl and flexible spacers containing an odd number of methylene units. Macromolecules 25 75-80 Urayama K (2007) Issues in liquid crystal elastomers and gels. Macromolecules 40 2277-2288 Vorlander D (1908) About transparently clear, crystalline liquids. Rep Ger Chem Soc 41 2033-2052... 

First it was argued to be due to a chiral molecular configuration characteristic of the particular type of bent-shape molecules, such as twisted or propeller shape (conformational chirality). The concept of conformational chirality was supported by simulations by Earl et al. [61], and was demonstrated by the observation that doping calamitic cholesteric liquid crystal by achiral bent-core molecules can lead to a decrease of the helical pitch, indicating an enhanced rotatory power of the mixture [62]. Unfortunately there is no proof that the decrease of the pitch is not due to a decrease of the twist elastic constant caused by the addition of bent-core units. Although the conformational chirality is usually not questioned in the solid B4 phase [20], its role has been questioned by Walba et al. [20] by arguing that these chiral conformations have very short lifetime, therefore they average out in fluid smectic, such as SmCP or SmCo phases. 

As a summary, we have reviewed the main experimental results and concepts concerning the physical properties of the liquid crystals of bent-core molecules. We demonstrated that a number of seminal findings and basically new concepts emerged in the field in the last decade. However scientists regularly explore unusual , surprising and not understood phenomena, and there are more unexplained observations than well understood ones. We are completely sure that the next decade of the physics of bent-core liquid crystals will bring new physics, and will be as rich in beautiful observations as was the first decade. 

An accepted experimental proof for the existence of a biaxial nematic phase in a thermotropic liquid crystal remained missing for a very long time. However, in recent years, biaxial nematic phases have been found in liquid crystalline polymers as well as in liquid crystals made of rod-disc mesogens, banana-shaped (bent-core) molecules, and organo-siloxane tetrapodes. Here, some characteristics of these systems and the corresponding experimental procedure for the investigation of phase biaxiality will be introduced. Further details for the individual systems can be found in the cited literature. 

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... 

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. 

Takanishi Y, Shin GJ, Jung JC, Choi S-W, Ishikawa K, Watanabe J, Takezoe H, Toledano P (2005) Observation of very large chiral domains in a liquid crystal phase formed by mixtures of achiral bent-core and rod molecules. J Mater Chem 15 4020-4024... 

While such a general model is quite appropriate to describe many known liquid-crystal species, it is increasingly inadequate, not because it is inaccurate, but rather because developments in the synthetic chemistry of liquid crystals have been such that, in reality, the usefulness of such general models might be called into question. For example, a new and significant area of research concerns on so-called bent-core (or banana) liquid crystals where the structural anisotropy rules given above simply do not hold and a 120° bend in the molecule is effectively a requirement. Some other developments may be found elsewhere. 

The dipolar mechanism is sensitive to the molecular shape. By dimensional considerations one can estimate the flexocoefficients due to dipolar mechanism as ei, 63 < /Xe/a, where /Xg 1-5 debye (1 D = 3.3x 10 Cm) is the molecular dipole moment and a 2-4 nm is the typical molecular dimension for a low molecular weight liquid crystal. This means that e and 63 are expected to be of the order of pCm. Assuming a random three-dimensional distribution of the centre of masses of the constituent bent-core (banana-shaped) molecules, Helfrich and Derzhanski and Petrov derived a more precise expression for the macroscopically testable bend fiexo-electric coefficient ... 

S.H. Hong, R. Verduzco, J.T. Gleeson, S. Sprunt and A. Jakli, Nanostructures of liquid crystal phases in mixtures of bent-core and rod-shaped molecules, Phys. Rev. E 83(6), 061702/1-5, (2011). 

Bent-core liquid crystal elastomers have shown to exhibit large values of flexoelectricity as many as three orders of magnitude larger than liquid crystal elastomers containing rod-shaped molecules [44]. These high responses are attributed to a piezoelectric phenomenon. Liquid crystal elastomers combine elasticity and flexibility inherent to rubbers and the optical and electrical properties of liquid crystals, and are promising materials for applications such as electrooptics, flexible electronics, and actuator technologies for biomedical applications. 

This phenomenon has been discovered in the liquid crystal phases consisting of so-called banana (or bent-core) shape molecules [17, 27]. A mechanical model in Fig. 4.39a illustrates the idea. Each of the two dumb-bells has symmetry Do h with infinite number of mirror planes containing the longitudinal rotation axis and one mirror plane perpendicular to that axis. Imagine now that one of the dumb-bells is lying on the table and we try to put another one on the top of the first one parallel to... 

A survey of recent studies of biaxial liquid crystals, in the context of the reported biaxial nematic phase in low molecular mass bent-core mesogens, with emphasize on the use of NMR spectroscopy is available. A discussion of orientational order parameters particularly in smectic-C and biaxial nematic phases and their determination by various techniques including NMR has been presented. The relation between molecular dynamics and biaxiality of nematic polymers and elastomers has been studied by H NMR spectroscopy. "" It was observed that the side-on attachment of the mesogens hinder the rotation of the molecules around their long axes and that in nematic polymers and elastomers phase biaxiality... 

Finally here, it is important to note that the supramolecular nature of liquid crystal mesophases, in conjunction with polarity, can also lead to the induction of chirality in nonchiral materials. Current interest dates back to 2006 when Niori et a/. reported the observation of ferroelectric switching in some achiral, bent-core liquid crystals. The molecules are shown in Figure 6 and are unusual inasmuch as convention suggests that liquid-crystalline molecules should be highly anisotropic. Matsnnaga eta/. had prepared these materials in the 1990s and had noted that they did indeed form a liquid crystal phase. However, what Niori et al. showed was that the symmetry of the liquid crystal phases must be broken in order to observe a ferroelectric response and further that chiral domains could be observed. ... 

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