With liquid-crystalline order description

In this Chapter we introduce some of the theoretical approaches for studying thin nematic liqnid crystalline systems, both on the microscopic and macroscopic level. In the former, one models the microscopic interactions between the constituing molecules, leaves the system to evolve, and then determines its macroscopic properties. If the obtained macroscopic behaviour is in agreement with the experimental evidence the modeled interaction is considered appropriate. On the other hand, the macroscopic description takes into account the universal properties of systems in the vicinity of phase and structural transitions. This means that they are based on the fact that in the vicinity of phase changes the macroscopic properties of the system do not depend on the details of the microscopic interactions but on the symmetry properties and dimensionality of the system in question. Most of our attention is focused on the effects of confinement on to liquid crystalline order. Finally, we will be interested in the resulting disjoining pressure. The evidences in experiments will be briefly mentioned. 

In this chapter we will discuss possible realizations of liquid crystalline ordering in conductive polymers. Section II presents basic properties of conducting polymers with a brief description of charge transport mechanisms in those systems. Section III discusses structural types and defects in liquid crystals, and Section IV covers some experimental results of the structural analysis of mesophases in polymers with flexible side chains and polymer/surfactant systems. Sections III and IV are presented to emphasize the properties important to conducting polymers. In Section V experimental data on liquid crystallinity in conductive polymers will be reviewed. Conclusion will be given in Section VI,... 

In the following we focus our attention to the most complete study of birefringence so far [74] instead of completely reviewing all research on polymer dispersions in liquid crystals. We show how one can, with a rather simple experimental method combined with the phenomenological description of liquid crystalline ordering, point out important details about the polymer network structure on both the micro and macro levels. 

The second type of impurity, substitution of a lattice atom with an impurity atom, allows us to enter the world of alloys and intermetallics. Let us diverge slightly for a moment to discuss how control of substitutional impurities can lead to some useful materials, and then we will conclude our description of point defects. An alloy, by definition, is a metallic solid or liquid formed from an intimate combination of two or more elements. By intimate combination, we mean either a liquid or solid solution. In the instance where the solid is crystalline, some of the impurity atoms, usually defined as the minority constituent, occupy sites in the lattice that would normally be occupied by the majority constituent. Alloys need not be crystalline, however. If a liquid alloy is quenched rapidly enough, an amorphous metal can result. The solid material is still an alloy, since the elements are in intimate combination, but there is no crystalline order and hence no substitutional impurities. To aid in our description of substitutional impurities, we will limit the current description to crystalline alloys, but keep in mind that amorphous alloys exist as well. 

In the above study it could be shown that the relaxation of triplets in conjugated polymers is in quantitative agreement with predictions based on the concept of random walk in a disordered solid. Meanwhile, this theoretical framework for the description of migration of triplets in disordered solids has been applied to PFO (polyfluorene with octyl side chains) [168] as well. PFO contains liquid crystalline domains in the polymer that leads to the formation of highly ordered domains (fi phase). This ft phase plays an essential role in the photophysics of this polymer, notably on triplet migration. 

However, even without structural studies, Friberg et al. [32], Shinoda [33], and others noted that the broad existence range with respect to the water/oil ratio could not be consistent with a micellar-only picture. Also, the rich polymorphism in general in surfactant systems made such a simplified picture unreasonable. It was natural to try to visualize microemulsions as disordered versions of the ordered liquid crystalline phases occurring under similar conditions, and the rods of hexagonal phases, the layered structure of lamellar phases, and the minimal surface structure of bicontinuous cubic phases formed a starting point. We now know that the minimal surfaces of zero or low mean curvature, as introduced in the field by Scriven [34], offer an excellent description of balanced microemulsions, i.e., microemulsions containing similar volumes of oil and water. 

In this Chapter the basic approaches used to describe nematic liquid crystalline (NLC) systems in slab geometries under the effect of confinement are introduced. We review both, the microscopic and macroscopic approaches, however, the emphasis is on the latter. We also show the correspondence between the approaches on different levels. Special attention is devoted to effects of the confinement on the LC order and consequently to the interactions arising from that. More precise descriptions of the techniques and also more detailed results have been already published elsewhere [9-12,15-18]. In the following Section we first shortly review the microscopic origin of order and define the appropriate order parameter. Then we review the basic microscopic and macroscopic theoretical approaches to describe LC systems. In the third Section we describe in short the effect of confinement in two different types of NLC systems. The fourth Section is devoted to macroscopic interactions between confining walls, especially the ones characteristic for ordered systems. We conclude the Chapter with the discussion on the observability of structural and fluctuation forces in NLC systems. 

In the following we will discuss some unconventional properties of macrocyclic metal complexes, preferentially semiconductive and liquid crystalline behavior. There are several reviews available on low-dimensional conductive compounds based on these macrocycles [21]. A detailed description of newer developments in the field of bridged macrocyclic metal complexes especially with transition metals was published recently [22]. In order to use the 7t-electrons in these macrocyclic systems for a conduction pathway, polymerization of the metallo-macrocycles is necessary. A polymerization can be carried out in three different ways as explained in Sections 1.2.1-1.2.3. 

The above mentioned unlimited self-assembly structures in ID, 2D or 3D are referred to as liquid crystalline structures. The latter behave as fluids and are usually highly viscous. At the same time. X-ray studies of these phases yield a small number of relatively sharp lines which resemble those produced by crystals [25-29]. Since they are fluids they are less ordered than crystals, but because of the X-ray lines and their high viscosity it is also apparent that they are more ordered than ordinary liquids. Thus, the term liquid crystalline phase is very appropriate for describing these self-assembled structures. Below a brief description of the various liquid crystalline structures that can be produced with surfactants is given and Table 1.4 shows the most commonly used notation to describe these systems. 

The parameters average values (amplitudes). Note that is the Hermans orientation function. The full description of uniaxial orientation /(0) cannot thus be attained by a single measurement of birefringence. The Hermans orientation function can be given a simple interpretation. A sample with orientation f may be considered to consist of perfectly aligned molecules of the mass fraction / and randomly oriented molecules of the mass fraction 1 — /. Liquid-crystalline polymers are often characterized by their order parameter, denoted S (Chapter 6). This quantity is equivalent to the Hermans orientation function. 

The detailed descriptions of the structures of calamitic phases allow us to classify the mesomorphic liquid crystal state, and to place this state in context with the crystalline and amorphous liquid states [3]. Table 1 describes the relationship between ordered crystals, disordered or soft crystals, liquid crystals and the isotropic liquid. 

---