Mesophases of liquid crystals

The mesophase state of liquid crystals is normally opaque due to relatively large sizes of ordered domains. Its transition point to the isotropic melt state is called the clear point T,. The DSC scanning curves of liquid crystals can exhibit either enantiotropic or monotropic phenomena. For the thermodynamically stable mesophases of liquid crystals, they occur between the melt and the crystal states during both cooling and heating processes, as illustrated in Fig. 10.5. When both the cooling and heating curves show two symmetric consecutive phase transitions, it is known as the enantiotropic phenomenon. In contrast, for the metastable mesophase... 

X-ray diffractometry, polarization microscopy and mixture testingt are important in the identification of mesophases of liquid crystals while DSC and DTA are the most valuable aids in revealing and confirming phase transition. Simultaneous polarization microscopy-DSC instruments are now commercially available. 

Linear and nonlinear optical properties of liquid crystals in their mesophases have been studied in several contexts, in both fundamental and application-oriented pursuits. In the context of nonlinear optical processes, they have recently received considerable renewed interests as a result of the newly discovered extraordinarily large optical nonlinearity due to the laser-induced molecular reorientation, and a renewed effort explicitly at the large thermal index effect in liquid crystals. In the last few years, several groups [2]-[10] have looked at the optical nonlinearity in the mesophases of liquid crystals and the associated nonlinear processes. A brief review of some of these nonlinear optical processes and the fundamental mechanisms in both the liquid crystal and the isotropic phases has recently appeared [1]. In this paper, therefore, we will concentrate only on optical wave mixing processes that are relevant to this Special Issue. 

We have presented a discussion of the theories and experiments on laser-induced optica nonlinearities and some recently observed wave-mixing processes in nematic liquid crystals based on the phase grating induced by two laser pulses. These studies have demonstrated again the unique and interesting physical characteristics of liquid crystals that have attracted the attention of fundamental and applied researchers alike. It is also clear that some practically useful nonlinear optical devices could be constructed. The nematic phase is but one of the several mesophases of liquid crystal that possess these interesting nonlinearities. Cholesterics and smectics [4] and other hybrid forms of nematics [6] also possess large nonlinearities. We anticipate that many more effects will be observed in the near future. 

NMR can, in principle, provide complementary information on motional processes in liquid crystals. The dipole-dipole interaction between a C-H pair and the quadrupolar interaction when the proton is replaced with a deuteron share the same principal interaction axis. In the case where the carbon is not directly bonded to a proton, there is still dipole-dipole relaxation by nearby protons, but it is also necessary to include an additional relaxation mechanism, the modulation of the chemical shift anisotropy. Proton spin decoupling is necessary to give well-resolved chemically shifted lines in the mesophase of liquid crystals. Furthermore, it is not practical to determine individual spectral density parameters from measured relaxation rates. Proton-proton dipolar interactions may not be ignored even when observation is exclusively confined to the resonant spin [5.31]. This is because proton relaxation causes population flow among the proton spin levels through dipolar (or scalar) coupling. As a consequence, cross-... 

R. J. Mansfield, P. LoPresti, Dynamics of picosecond laser-induced density, temperature, and flow-reorientation effects in the mesophases of liquid crystals, J. Appl. Phys. 1991, 29, 2972-2976. 

In this and the next chapters, laser-induced changes in the director axis orientation 9(r, t), density p(r, t temperature T r, t), and flows are separately discussed for all the principal mesophases of liquid crystals. An intense laser pulse can also generate electronic nonlinearities in liquid crystals. This is treated separately in Chapter 10. 

Chapters 1-5 cover the basic physics and optical properties of liquid crystals intended for beginning workers in liquid crystal related areas. Although the major focus is on nematics, we have included sufficient discussions on other mesophases of liquid crystals such as the smectics, ferroelectrics, and cholesterics to enable the readers to proceed to more advanced or specialized topics elsewhere. New sections have also been added. For example, in Chapter 4, a particularly important addition is a quantitative discussion of the optical properties and fundamentals of one-dimensional photonic crystal band stractures. Dispersion is added to fill in an important gap in most treatments of cholesteric liqrrid crystals. 

Molecules tliat are capable of fonning liquid crystal phases are called mesogens and have properties tliat are mesogenic. From the same root, tire tenn mesophase can be used instead of liquid crystal phase. A substance in a liquid crystal phase is tenned a liquid crystal. These conventions follow tliose in tire Handbook of Liquid Crystals, [4, 5 and 6] tire nomenclature of which [7] for various liquid crystal phases is adopted elsewhere in tliis section. 

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 rapid rise in computer speed over recent years has led to atom-based simulations of liquid crystals becoming an important new area of research. Molecular mechanics and Monte Carlo studies of isolated liquid crystal molecules are now routine. However, care must be taken to model properly the influence of a nematic mean field if information about molecular structure in a mesophase is required. The current state-of-the-art consists of studies of (in the order of) 100 molecules in the bulk, in contact with a surface, or in a bilayer in contact with a solvent. Current simulation times can extend to around 10 ns and are sufficient to observe the growth of mesophases from an isotropic liquid. The results from a number of studies look very promising, and a wealth of structural and dynamic data now exists for bulk phases, monolayers and bilayers. Continued development of force fields for liquid crystals will be particularly important in the next few years, and particular emphasis must be placed on the development of all-atom force fields that are able to reproduce liquid phase densities for small molecules. Without these it will be difficult to obtain accurate phase transition temperatures. It will also be necessary to extend atomistic models to several thousand molecules to remove major system size effects which are present in all current work. This will be greatly facilitated by modern parallel simulation methods that allow molecular dynamics simulations to be carried out in parallel on multi-processor systems [115]. 

Drug molecules with amphiphilic character may form lyotropic mesophases, and amphiphilic excipients in drug formulations also form lyotropic liquid crystals. Especially surfactants, which are commonly used as emulsifiers in dermal formulations, associate to micelles after dissolution in a solvent. With increasing concentration of these micelles the probability of interaction between these micelles increases and thus the formation of liquid crystals. 

Collective segmental rotation is considered to be the natural form gaining conformational entropy as the essential factor for stabilizing mesophases or liquid-crystalline structures. Despite the approximate character of our conception it should be possible to identify the significant characteristics of the intermolecular segmental arrangement in mesophases, in liquid crystals or in a polymer melt. 

In order to avoid this section becoming too abstract, a selection of molecules which can form nematic or smectic liquid crystals is illustrated in Figure 7.2. For a discussion of how particular molecular structures lead to formation of particular mesophases, reference should be made to the work by Gray and Goodby [402] already cited or to Chapters 1 and 12 of Molecular Physics of Liquid Crystals edited by Luckhurst and Gray [28]. 

As is known, the question of how to predict the type of mesophase on the basis of the molecular structure of liquid crystals alone is not yet solved in spite of its vital importance for low-molecular crystals. Researchers rely only on some empirical... 

For a nematic polymer in a transition region from LC to isotropic state, maximal viscosity is observed at low shear rates j. For a smectic polymer in the same temperature range only a break in the curve is observed on a lgq — 1/T plot. This difference is apparently determined by the same reasons that control the difference in rheological behaviour of low-molecular nematics and smectics 126). A polymeric character of liquid crystals is revealed in higher values of the activation energy (Ef) of viscous flow in a mesophase, e.g., Ef for a smectic polymer is 103 kJ/mole, for a nematic polymer3 80-140kJ/mole. 

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