Crystal flexoelectric

Binary molecular co-crystals of 2,5-bis(3-pyridyl)-l,3,4-oxadiazole and 2,5-bis-(4-pyridyl)-l,3,4-oxadiazole with benzene-1,3,5-tricarboxylic and benzene-1,2,4,5-tetracarboxylic acids were studied by X-ray and thermogravimetric analysis of mass loss <2005MI1247>. Dipole moments were used to study the flexoelectric effect in guest-host mixtures of 2,5-(4-pentylbenzene)-l,3,4-oxadiazole with commercial liquid crystal hosts <2005CM6354>. The luminescence properties of many other copolymers were also investigated (see Section 5.06.12.3). 

A series of model nematic liquid crystals (among them oxadiazole derivatives) with transverse dipole moments were used to study the flexoelectric effect in guest-host mixtures with a commercial liquid crystal host <2005CM6354>. 

The third electro-optical effect using calamitic nematic liquid crystals makes use of a flexoelectric effect manifested by a curved asymmetrical nematic medium. This corresponds to piezoelectricity in crystals. The existence of flexoelectricity in a nematic phase under certain boundary conditions was predicted in the late 1960s and then confirmed experimentally several years later. However, LCDs using this effect, such as bistable nematic displays are only in the development stage and as such they will not be discussed in this monograph. 

As noted earlier, the incorporation of chiral groups in the liquid crystal moieties can have the effect of inducing non-linear properties, which include thermochromism, ferroelectricity, antiferroelectricity, electrostriction, and flexoelectricity. In a now classical study, Hult [82] demonstrated that it was possible for supermolecular material 34 to exhibit two-state ferroelectric switching. The remarkable material he investigated, shown in Fig. 30, was found to exhibit two hitherto unclassified mesophases between the smectic... 

The aim of these studies is to understand and control the electrical properties of surfaces on a micrometric scale, that might be extremely useful for the application of these materials in the field of liquid crystal display (LCD) technology. In fact, it is well known that the LC anchoring properties depend not only on the substrate morphology but also on its electrical properties [68]. The electric polarization in nematic and other non-polar liquid crystals has essentially three origins flexoelectricity [65], orderelectricity [66,67] (related to the gradient in the order parameter) and the polarization of the substrate... 

Flexoelectricity - what is it How does it arise in liquid crystals What are its consequences What role does it play in liquid crystal phases, structures, and textures How is it measiu-ed What is its role, both realized and potential, in applications of liquid crystals How was it discovered and what is its history in the context of the development of liquid crystal science and technology in the last 50 years The name flexoelectricity clearly indicates the dual role of curvature distortions and electrical effects in liquid crystals, but just how are these two fundamental sets of concepts related by this phenomenon This book attempts to lay out the answers to these questions, with a combination of broad reviews and focused insights into the role of flexoelectricity in the science and technology of liquid crystals. In this introduction there is first a little informal review of history along with some general comments on the fundamentals and the special challenges presented by this phenomenon, and then there is a brief sketch of the chapters of this book. 

In this book the flexoelectric effect is mainly considered from the phenomenological point of view. At the same time it is very interesting and important to reveal the molecular origin of flexoelectricity and, in particular, to consider different types of intermolecular interactions that may be responsible for the dipolar ordering in a deformed liquid crystal, and to study the effects of intermolecular correlations and the molecular structure. This problem can only be solved using a molecular-statistical theory, which eventually allows us to express the flexoelectric coefficients in terms of molecular model parameters using various approximations. 

It should be noted, however, that the flexoelectric effect is not necessarily related to the ordering of molecular dipoles. Frost and Marcerou proposed another microscopic mechanism of the flexoelectric effect, which requires neither the asymmetry of the molecular shape nor the permanent molecular dipole. The macroscopic polarization may simply appear in the direction of the gradient of average density of the molecular quadrupole moments. The quadrupole mechanism of flexoelectricity is more general because, in principle, it should manifest itself in any anisotropic material with a non-zero quadrupole density including solid crystals d and elastomers. 

Molecular Theory of Flexoelectricity in Nematic Liquid Crystals... 

During recent decades the molecular theory of flexoelectricity in nematic liquid crystals was developed further by various authors. " In particular, explicit expressions for the flexocoefiicients were obtained using the molecular-field approximation taking into account both steric repulsion and attraction between the molecules of polar shape. The influence of dipole-dipole correlations and molecular flexibility was later considered. Recently flexoelectric coefficients have been calculated numerically using the mean-field theory based on a simple surface intermolecular interaction model. This approach allows us to take into consideration the real molecular shape and to evaluate the flexocoefiicients for mesogenic molecules of different structures including dimers with flexible spacers. 

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 molecular-statistical theory of the flexoelectric effect in the nematic phase can be derived in a general way using the density-functional approach to the theory of liquid crystals. In this approach, the free energy of a liquid crystal, F, is a functional of the density po(a ) = Po/(w) where /(w) is the orientational distribution fimction. The general structure of the functional F p) is not known, but the functional derivatives are known and are related to the direct correlation functions of the nematic phase. 

The results of Straley can be obtained by neglecting the pair attraction interaction potential V(xi, X2, ri2) in the equation for the direct correlation function. Indeed, the Straley theory of flexoelectricity was developed for the system of hard polar rods, while for thermotropic liquid crystals both the molecular shape and the intermolecular attraction are important. 

Secondly, it follows from Eqs (1.31) and (1.32) that the longitudinal molecular dipole d provides a much smaller contribution to the flexocoef-ficients than the transverse dipole d , since A/k 10. Thus we conclude that the dipole flexoeffect is expected to be important only for molecules with large transverse dipoles. Note that the significant dipole flexoeffect has indeed been determined for nematics composed of molecules with large transverse dipoles. For cyanobiphenyl liquid crystals Marcerou and Frost did not find any dipolar flexoelectric effect, which may be determined not only by the tendency to form dimers with antiparallel dipoles but also by a relatively small contribution from transverse molecular dipoles to the flexoelectric coefficients. 

The expressions for the flexoelectric coefficients presented in this section are derived using the molecular-field approximation. Therefore, care should be taken in the description of nematic liquid crystals composed of strongly polar molecules. In such liquid crystal materials (for example, cyanobiphenyls) the flexoelectric coefficients may be strongly affected by the short-range dipole-dipole correlations, which are considered in the following section. 

It follows from Eq. (1.45) that the contribution from the dipole-dipole correlations strongly depends on the value of the molecular dipoles, i.e. A dj (i if d > d . Therefore the correlation contribution can be substantial in liquid crystal materials composed of strongly polar molecules. The effect of dipole-dipole correlations on the flexoelectric coefficients has been discussed in experimental papers. 

A.K. Tagantsev, Pyroelectric, piezoelectric, flexoelectric, and thermal polarization effects in ionic crystals, Sov. Phys. Uspekhi, 30(7), 588-603, (1987). doi 10.1070/PU1987v030n07 ABEH002926... 

M.A. Osipov, Molecular theory of flexoelectric effect in nematic liquid crystals, Sov. Phys. JETP 58(6), 1167-1171, (1983). 

M.A. Osipov, The order parameter dependence of the flexoelectric coefficients in nematic liquid crystals, J. Physique Lett. 45(16), 823-826, (1984). 

A. Ferrarini, C. Greco and G.R. Luckhurst, On the flexoelectric coefficients of liquid crystal monomers and dimers A computational methodology bridging length-scales, J. Mater. Chem. 17(11), 1039-1042, (2007). 

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