Classical Liquid Crystals

The spontaneous formation of surfactant aggregate structures or micelles at relatively low concentrations opens the door to a veritable zoo of larger, more structurally complex, and certainly more theoretically complex self-assembled structures that inhabit our natural world, and make life as we know it possible. While the concepts presented in Chapter 4 to explain micelle formation in aqueous and nonaqu-eous solutions are relatively straightforward, chemically speaking, it should be obvious that there is a great deal of room for complications to set in as a system becomes more complex. 

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A general theory of curvature-elasticity in the molecularly uniaxial liquid crystals, similar to that of Oseen, is established on a revised basis. There are certain significant differences in particular one of his coefficients is shown to be zero in the classical liquid crystals. Another, which he did not recognize, does not interfere with the determination of the three principal coefficients. The way is therefore open for exact experimental determination of these coefficients, giving unusually direct information regarding the mutual orienting effect of molecules. 

It fits nicely into the picture of dual structure-phase views of biomesogenic organizations that objects of rod-like appearance , for instance the little world of the tobacco mosaic virus (which - its overall design reduced to a simple rod-like entity - became the starting point of Onsager s theory [37]), as well as much simpler protein and nucleic acid helices are typical mesophase formers in the classical liquid-crystal phase... 

Liquid crystals constitute a distinct thermodynamic state of condensed matter, which combines the fluidity of ordinary liquids with the macroscopic anisotropy of solid crystals. They are quintessential soft matter materials, which are today best known to the broad public for their ubiquitous application as electro-optical material in flat panel liquid aystal displays (LCDs). Systems exhibiting liquid crystalline order range from small rod- or disc-shaped organic molecules (e.g., the classic liquid crystals used in LCD devices), over polymers, biological membranes, dispersions of micelles and nanoparticles to certain quantum electronic materials. 

Local Molecular Orientation Occurrence and Description The local molecular orientations (LMOs) are detectable by TEM as a clustering of the bright dots (Figure 1.30a). These clusters are self-associations of BSUs in almost parallel preferred orientation. They are equivalent to classical liquid crystals described by Brooks and Taylor [96]. LMOs are limited by digitized contours and have a roughly isometrical shape in diameter and thickness, determined by... 

The structures of extra-chain liquid crystalline polymers present applicative interest today for other reasons than those of intra-chain LCP. Coupling of the mesogene with basic chain caused a classical liquid crystal behavior. On the other hand, these structures exhibit characteristics of processability and a mechanical behavior similar with that of polymers, having the same sensitivity to various external sohcitations (electric and/or magnetic field) as simple mesogenes, which recommends the utilization of liquid crystaline polymers with extra-chain mesophase for electro-optic applications [29-32]. 

Rod-like liquid crystals [1] have been known for more than a hundred years, the first one, cholesteryl benzoate, being discovered in 1888 by Reinitzer. In materials of this type, nematic N, cholesteric N and different lamellar mesophases such as SmA, SmC, SmF, and SmI are obtained. Beside these classical liquid crystals, thermotropic mesophases - consisting of two-dimensional aromatic flat molecules - that exhibit various columnar phases (e.g., Col, Coif, Colob) have been known since 1977 [2, 3], In these two types of systems, the lamellar and columnar phases are observed separately. So, it was interesting to examine the mesomorphic properties of the hybrid molecules, i.e., molecules with a long rodlike rigid core ending in two half-disc moieties (Fig. 1). In fact, the phasmids [4,5] fill... 

Historically, microemulsions were discussed as a separate family of colloids that formed essentially spontaneously and were thermodynamically stable. However, microemulsions must, by definition, contain at least three components—solvent, amphiphile, and dispersed phase—and quite often contain a fourth, the so-called cosolvent. More recent experimental and theoretical work has tended to move them into the larger family of surfactant aggregates, their complex composition notwithstanding. That convention will be followed here, although there still remain a number of points of contention that need to be resolved on their classification as surfactant mesophases on a par with classical liquid crystals. 

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. 

The present method is successful with a wide variety of ketones (see Table). Cyclic ketones (entries 1-4, 8) produce benzoannelated products in excellent overall yields. There is no need to purify the intermediate both the nucleophilic addition of methallylmagnesium chloride and the aromatic cyclization take place cleanly. Acyclic ketones (entries 5-7) also provide high yields of benzoannelated product. Aromatic ketones are particularly interesting substrates for this reaction since they provide substituted biphenyls, which are potentially useful materials for liquid crystal synthesis and whose preparation through classical methodology is often not straightforward. The conditions for the cationic cyclization step can be modified to accommodate acid-sensitive functionality. For example, cyclization of 3 to 4, the latter a precursor for 3-methyl-8,14-dehydromorphinan, was accomplished in 77% yield by treatment of 3 at... 

G. Vertogen and W. H. De Jeu. Thermotropic Liquid Crystals, Fundamentals Springer Series in Classical Physics, Springer-Verlag, Berlin (1988), Vol. 45. 

The classical cholesteric phase materials show only a weak anisotropic interaction with electric fields and hence are of limited use in electro-optical response applications. Cholesteric phases for these outlets are consequently produced by adding chiral dopants to nematic liquid crystals. 

Colloids hold a considerable potential for applications that are unusual in the classical sense. Most of us are familiar with imaging devices such as the picture tube in a television set. These tubes are bulky and consume large amounts of electrical power. There is, therefore, a large incentive to develop compact imaging devices, known as flat-panel devices, that are easily portable and have lower power requirements. (Displays based on liquid crystal technology fall in this class.)... 

There are two basic approaches to the computer simulation of liquid crystals, the Monte Carlo method and the method known as molecular dynamics. We will first discuss the basis of the Monte Carlo method. As is the case with both these methods, a small number (of the order hundreds) of molecules is considered and the difficulties introduced by this restriction are, at least in part, removed by the use of artful boundary conditions which will be discussed below. This relatively small assembly of molecules is treated by a method based on the canonical partition function approach. That is to say, the energy which appears in the Boltzman factor is the total energy of the assembly and such factors are assumed summed over an ensemble of assemblies. The summation ranges over all the coordinates and momenta which describe the assemblies. As a classical approach is taken to the problem, the summation is replaced by an integration over all these coordinates though, in the final computation, a return to a summation has to be made. If one wishes to find the probable value of some particular physical quantity, A, which is a function of the coordinates just referred to, then statistical mechanics teaches that this quantity is given by... 

From macroscopic observations, it appears that in the DMDBTDMA-dodecane system the nature of the third phase (liquid, gel, or solid) (140) depends to a large extent on the extracted species. In some cases, microphase separations can be obtained, that is, the coexistence of a more crystalline phase with domains of diluted phase that do not separate upon centrifugation. In classical colloidal literature (141), this situation is described as a dispersion of tactoids in the form of small amounts of liquid crystals, giving macroscopically a gel. 

The phase behavior of surfactant systems is particularly complex because of the existence of numerous lyotropic (solvent-induced) liquid crystal phases (3). These phases, like liquids and crystals, are discrete states of matter. They are fluids, but their x-ray patterns display sharp lines signifying the existence of considerable structure. They are often extremely viscous because of their high viscosities and for other reasons they are difficult to study using conventional methods. This is evident from the fact that serious errors in the presumably well-established classical aqueous phase diagrams of soaps, sodium alkyl sulfates, monoglycerides, and... 

The model of a dipole in a spherical cavity can only provide qualitative insights into the behaviour of real molecules moreover, it cannot explain the effect of electrostatic interactions in the case of apolar molecules. More accurate predictions require a more detailed representation of the molecular charge distribution and of the cavity shape this is enabled by the theoretical and computational tools nowadays available. In the following, the application of these tools to anisotropic liquids will be presented. First, the theoretical background will be briefly recalled, stressing those issues which are peculiar to anisotropic fluids. Since most of the developments for liquid crystals have been worked out in the classical context, explicit reference to classical methods will be made however, translation into the quantum mechanical framework can easily be performed. Then, the main results obtained for nematics will be summarized, with some illustrative... 

One of the most classic examples of chiral expression in thermotropic liquid crystals is that of the stereospecific formation of helical fibres by di-astereomers of tartaric acid derivatised either with uracil or 2,6-diacylamino pyridine (Fig. 9) [88]. Upon mixing the complementary components, which are not liquid crystals in their pure state, mesophases form which exist over very broad temperature ranges, whose magnitude depend on whether the tartaric acid core is either d, l or meso [89]. Electron microscopy studies of samples deposited from chloroform solutions showed that aggregates formed by combination of the meso compounds gave no discernable texture, while those formed by combinations of the d or l components produced fibres of a determined handedness [90]. The observation of these fibres and their dimensions makes it possible that the structural hypothesis drawn schematically in Fig. 9 is valid. This example shows elegantly the transfer of chirality from the molecular to the supramolecular level in the nanometer to micrometer regime. 

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