Liquid crystals, nematic

Nematic liquid crystals (LCs) are a classical example of complex fluids. If we trust the small-load approximation as well as the matured theory of nema-todynamics [76], we must be able to predict the frequency shift induced by nematic LCs. The theory of nematic LCs in contact with the QCM has been worked out in detail by people who did not know about the QCM as a tool to probe these phenomena. These authors performed ultrasonic reflectometry. As we know from Sect. 5, the results of these studies can be transported to the QCM in a straightforward way by just using Eq. 39. 

In nematic liquid crystals, the viscosity depends on the relative orientation between the shear gradient and the orientation of the nematic phase. Close to a surface, the orientation is usually governed by surface orientational anchoring [77]. Anchoring transitions, for instance induced by the adsorption of an analyte molecule to the surface [78], can therefore be easily detected with the QCM [79,80]. This reorientation induced by adsorption amounts to an amplification scheme the expected shift in the resonance frequency and bandwidth 

The physics of shear waves in nematic liquid crystals is rather comph-cated. Because shear couples to reorientation, there are two separate modes— termed hydrodynamic and orientational —emanating from the oscillating crystal surface. The hydrodynamic mode mainly transports vorticity. This mode is known from simple hquids. The orientational modes mainly transport rotation of the director with regard to the background fluid. The penetration depth of the orientational mode is much smaller than the penetration depth of the hydrodynamic mode. While the amphtude of the orientational mode strongly depends on the strength of surface anchoring, the amplitude of the hydrodynamic mode does not [76]. 

As structured fluids such as liquid crystals are at least partially fluid, we also need to consider the forces and torques produced by friction. The frictional forces are given by a dissipative stress tensor, which is most conveniently derived from the dissipative function (j)F It is a homogeneous positive definite quadratic function of the time derivatives of the strains and rotations (the time derivatives of the torsions can be generally ignored) giving  

The viscosity tensors may have 81 + 27 elements. However, fortunately only those which are allowed by symmetry will be nonzero. The nonzero elements are determined so that the symmetry of the viscosity tensors must be compatible with the symmetry of the material (for example, a calamitic nematic and smectic A material with uniaxial symmetry will be invariant under n = -n ). 

Nematic liquid crystals are 3D anisotropic fluids, and as such they have no translational order, i.e., they do not support extensional or shear strains. For this reason, the rheology of nematic liquid crystals is similar to conventional organic liquids with similar size of molecules. The main difference is due to the anisotropic nature of the materials the director distortion results in elastic responses, and the magnitude of the viscosity depend on the relative orientation of the director with respect to the velocity gradient. 

The macroscopic theory that takes into accoimt the effect of the orientation order was developed by Ericksen, Leslie and Parodi, and usually is referred as ELP theory. A microscopic theory based on correlation functions, which then were translated to macroscopic terms and extended to other mesomorphic phases, was developed by the Harvard group. Although usually tire ELP flieory is accepted, it seems that the two approaches are equivalent. A continuum theory of biaxial nematics was developed by Saupe, who followed the description we give with (4.1)-(4.8). In the uniaxial situation, they reproduce the Leslie-Ericksen and Harvard theories. 

The elastic response to the distortion of the director is analogous to the elasticity of solids with positional ordering, and in complete absence of the lattice it can be described only by the term of (4.7) that is quadratic function of the rotation a, ( All other terms are not leading terms anymore. 

Nematics are the most widely studied liquid crystals. They are also the most widely used. As a matter of fact, nematics best exemplify the dual nature of liquid ciystals-fluidity and crystalline structure. To describe their liquidlike properties, one needs to invoke hydrodynamics. On the other hand, their crystalline properties necessitate theoretical formalisms pertaining to solids or crystals. To study their optical properties, it is also necessary that we invoke their electronic stractures and properties. 

In this chapter we discuss all three aspects of nematogen theory solid-state continuum theory, hydrodynamics, and electro-optical properties, in that order. 

Because of the orientational order, certain physical properties such as refractive index will vary depending on the direction at which the measurements are made with respect to the director. Thus, nematic phases appear birefringent when viewed through crossed polarizers and can strongly scat- 

FIGURE 1.1. (a) The ordered solid crystal, which can melt into (b) a nematic phase or (c) a smectic A phase, and (d) the completely disordered liquid phase. 

FIGURE 1.2. Some examples of nematogens p-azoxyanisole (PAA), p-methoxy-benzylidene-p-n-butylaniline (MBBA), and p-pentyl-p -cyanobiphenyl (5CB). Transition temperatures are in °C. 

Cholesteryl benzoate belongs to a special type of nematics because the molecule is chiral. Chiral means that the rod-like molecules have a handedness like a screw, which is usually right-handed but could be left-handed. Chiral molecules in a nematic phase can impart a gentle rotation on their 

FIGURE 1.3. Schematic picture of a chiral nematic phase. Perfect alignment is assumed for the sake of clarity. 

The rigidity of the central core structure is often achieved using aromatic rings, as in the case of 4-cyano-4 -ra-pentylbiphenyl (10) or 4-cyano-4 - -pentyl-p-terphenyl (11)  

The biphenyl shows transitions C-N at 22.5 °C and N-I at 35 °C, whereas the terphenyl shows transitions C-N at 130 °C and N-I at 239 °C. In these molecules, planarity of the two aromatic rings is inhibited by strong interactions between the hydrogen atoms in the a-position to the C-C bond. Mesogenic behaviour is observed if the aromatic rings are joined by one of the following entities 

These linkages allow delocalization of electron density between the terminal aromatic rings, and have the effect if retaining the rigidity and planarity of the central core. The delocalized electron density can enhance the molecules anisotropic polarizability. Interestingly, the analogue of the above molecule in which the two aromatic rings are joined by a double bonded rather than a triple bond does not necessarily form a liquid crystal phase. The tram isomer retains the overall linear profile and can form a liquid crystalline phase whereas the cis does not.  

The importance of the effect of the length of the central rigid core of the structure on the thermal stability is illustrated by the following comparison  

Molecule (12) exhibits transitions C-N at 148 °C and N I at 143 °C, whereas (13) has transitions C N at 172 °C and N-I at 199 °C. Replacement of a single p-phenylene ring by a 4,4 -biphenyl or 2,6-naphthalene ring system strongly increases the N I temperature as illustrated in the following eompounds  

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A nematic liquid crystal cell, based on Merck Licrilite E202, was used in these experiments. The rod like liquid crystal molecules preferentially aligned themselves with each other and to an alignment surface in the liquid crystal device. Any birefringence. An, was given as the difference between the two orthogonal refractive indices. As a consequence, any resulting... 

The method has been extended to mixtures of hard spheres, to hard convex molecules and to hard spherocylinders that model a nematic liquid crystal. For mixtures m. subscript) of hard convex molecules of the same shape but different sizes. Gibbons [38] has shown that the pressure is given by... 

Allen M P, Warren M A, Wilson M R, Sauron A and Wiliam S 1996 Molecular dynamics calculation of elastic constants in Gay-Berne nematic liquid crystals J. Chem. Phys. 105 2850-8... 

We consider first the Maier-Saupe tlieory and its variants. In its original foniiulation, tills tlieory assumed tliat orientational order in nematic liquid crystals arises from long-range dispersion forces which are weakly anisotropic [60, 61 and 62]. However, it has been pointed out [63] tliat tlie fonii of tlie Maier-Saupe potential is equivalent to one in... 

An aligned monodomain of a nematic liquid crystal is characterized by a single director n. However, in imperfectly aligned or unaligned samples the director varies tlirough space. The appropriate tensor order parameter to describe the director field is then... 

Figure C2.2.11. (a) Splay, (b) twist and (c) bend defonnations in a nematic liquid crystal. The director is indicated by a dot, when nonnal to the page. The corresponding Frank elastic constants are indicated (equation(C2.2.9)).

C2.2.12 and Ae is the anisotropy in pennittivity in the nematic liquid crystal. Note that in equation (C2.2.16) the tlireshold voltage, that is the relevant quantity for display operation, is independent of cell thickness. 

Luckhurst G R and Zannoni C 1977 Why is the Maier-Saupe theory of nematic liquid crystals so successful Nature 267 412-14... 

Humphries R L, James P G and Luckhurst G R 1972 Molecular field treatment of nematic liquid crystals J. Chem. Soc. Faraday Trans. II 68 1031-44... 

Stannarius R 1998 Elastic properties of nematic liquid crystals 1998 Handbook of Liquid Crystals Vol 2A. Low Molecular Weight Liquid Crystals led D Demus, J Goodby, G W Gray, Fl-W Speiss and V Vill (New York Wiley-VCH)... 

Parodi O 1970 Stress tensor for a nematic liquid crystal J.PhysiqueZ 581-4... 

Brochard F, Pieranski P and Guyon E 1972 Dynamics of the orientation of a nematic-liquid-crystal film in a variable magnetic field Phys.Rev.Lett 2S 1681-3... 

Pieranski P, Brochard F and Guyon E 1973 Static and dynamic behavior of a nematic liquid crystal in a magnetic field. Part II Dynamics J.Physique 34 35-48... 

Schadt M and Flelfrich W 1971 Voltage-dependent optical activity of a twisted nematic liquid crystal Appl. Phys. Lett. 18 127-8... 

NEMA Grade G-11 Nemathelminthes Nematic liquid crystal Nemato cide Nemato cides... 

Table 3. Technologically Important Nematic Liquid Crystals...

The direct coupling constants (A/) of pyridine, obtained from a spectrum of the molecule in a nematic liquid crystal solvent, are listed in Batterham s monograph (B-73NMR, p. lo). These data provide information about the geometry of the molecule, as the couplings are proportional to the inverse cube of the distance (r,/) between the nuclei. 

The europium shift NMR spectra of both parents have also been studied (710MR(3)575), as has the nematic liquid crystal behaviour of pyrido[2,3-f ]pyrazine (760MR(8)155). 

FT-IR POLARIZED SPECTROSCOPY OE 9-ELUORENONE AND DEUTERATED 9-ELUORENONE ORIENTED IN NEMATIC LIQUID CRYSTAL... 

The rigid nature of the mesophase pitch molecules creates a strong relationship between flow and orientation. In this regard, mesophase pitch may be considered to be a discotic nematic liquid crystal. The flow behavior of liquid crystals of the nematic type has been described by a continuum theory proposed by Leslie [36] and Ericksen [37]. 

The conservation equations developed by Ericksen [37] for nematic liquid crystals (of mass, linear momentum, and angular momentum, respectively) are ... 

S. Blenk, W. Muschik. Orientational balances for nematic liquid crystals. J Non-Equilib Thermodyn 7(5 67-87, 1991. 

T. Gruhn, M. Schoen. Substrate-induced order in confined nematic liquid-crystal films. J Chem Phys 705 9124-9136, 1998. 

The formation of ECC is not only an extension of a portion of the macromolecule but also a mutual orientational ordering of these portions belonging to different molecules (intermolecular crystallization), as a result of which the structure of ECC is similar to that of a nematic liquid crystal. After the melt is supercooled below the melting temperature, the processes of mutual orientation related to the displacement of molecules virtually cannot occur because the viscosity of the system drastically increases and the chain mobility decreases. Hence, the state of one-dimensional orientational order should be already attained in the melt. During crystallization this ordering ensures the aggregation of extended portions to crystals of the ECC type fixed by intermolecular interactons on cooling. 

The present appendix represents a detailed derivation of the kinetic equations of the fluctuating liquid cage model in the classical formalism. A natural generalization is done for the case of partially ordered media, e.g. nematic liquid crystals. One of the simplest ways to take into account the back reaction is demonstrated, namely to introduce friction. 

Leslie, F. M., "Theory of Flow in Nematic Liquid Crystals, The Breadth and Depth of Continuum Mechanics—A Collection of Papers Dedicated To J. L. Ericksen, C. M. Da-fermos, D. D. Joseph, andF. M. Leslie, Eds., Springer-Verlag, Berlin, 1986. 

Mixtures of a nematic liquid crystal (LC or LC ) with small quantities of gold nanoparticles coated with alkylthiolates (<5 wt%) including an alkylthiolate functionalized with a chiral group have been studied (Figure 8.29) [72]. All mixtures show nematic mesophases with transition temperatures and phase stability very similar to those oftheliquid crystal precursors LC or LC. The introduction ofachiral center into the mixtures (mixtures of Au ) produce chiral nematic mesophases. A similar result is obtained in mixtures of Au and LC doped with the chiral dopant (s)-Naproxen. 

Qi, H. and Hegmann, T. (2006) Formation of periodic stripe patterns in nematic liquid crystals doped with functionalized gold nanopartides. Journal of Materials Chemistry, 16, 4197-4205. 

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