Anisotropic Intermolecular Interactions in Liquid Crystals

The starting point for a theory of the anisotropic intermolecular interaction in liquid crystals is the Maierand Saupe theory [114,115,116,118].This theory is based on the assumption that the intermolecular interaction potential in nematic liquid crystals is determined primarily by Lx)ndon dispersion forces. The effective anisotropic potential U of a molecule C in the anisotropic dispersion field generated by its oriented neighbors s is calculated by averaging the pair potential between two molecules C and s over all orientations of the solvent molecules s and over all... 

We start with the microscopic definitions and discussion of the nematic and smectic order parameters and then proceed with some elementary information about anisotropic intermolecular interactions in liquid crystals. Then we discuss in more detail the main molecular theories of the nematic-isotropic phase transition and conclude with a consideration of molecular models for smectic A and smectic C phases. 

The liquid crystal state (LCS) shows order in one or two dimensions it lacks the three-dimensional long-range order of the crystalline state. LCS has characteristics intermediate between those of the crystalline and the disordered amorphous states. These phases are called liquid crystals because many of them can flow like ordinary liquids but they display-birefringence and other properties characteristic of crystalline soHds. In liquid crystal phases the molecules can move but the orientational order is conserved in at least ne direction. The LCS can be displayed by small molecules and by polymersj but in both cases a characteristic chemical structure is needed. The existence of the liquid crystal state is related to the molecular asymmetry and the presence of strong anisotropic intermolecular interactions (19-21). Thus, molecules with a rigid rod structure can form highly ordered... 

Another classification of methods for measuring anisotropies is that of partially oriented molecules, the most important examples of which are the liquid crystals. The utility of this method lies in the fact that many molecules can be dissolved in liquid crystals without destroying the liquid crystal phase.12-15 The solute molecules are able to translate relatively freely in one direction-along the optic axis. As a result of this motion the intermolecular dipole-dipole interactions are averaged to zero but the intramolecular interactions are not. Also since the solute molecules cannot rotate equally in all directions, there will be an anisotropic contribution to the observed shielding. 

Both the degree of order in liquid crystals and the average orientation of guest molecules in liquid crystals are closely related to the anisotropy of the intermolecular forces. The measurements of the solute or the solvent order are therefore most important in order to test theoretical models of the forces acting between non-spherical molecules. The use of nematic phases as model systems for the investigation of anisotropic intermole.cular interaction potentials is another important scientific application of liquid crystals. 

As the temperature is decreased, the chains become increasingly rigid zc then approaches 1 if we assume that there is only one fully ordered crystalline structure and Zconf for the liquid becomes smaller than 1. This means that, at this level of approximation, the disordered state becomes less favorable than the crystalline ground state. A first-order disorder-order phase transition is expected to occur under these conditions. Flory interpreted this phase transition as the spontaneous crystallization of bulk semiflexible polymers [12], However, since the intermolecular anisotropic repulsion essential in the Onsager model is not considered in the calculation, only the short-range intramolecular interaction is responsible for this phase transition. 

As its name suggests, a liquid crystal is a fluid (liquid) with some long-range order (crystal) and therefore has properties of both states mobility as a liquid, self-assembly, anisotropism (refractive index, electric permittivity, magnetic susceptibility, mechanical properties, depend on the direction in which they are measured) as a solid crystal. Therefore, the liquid crystalline phase is an intermediate phase between solid and liquid. In other words, macroscopically the liquid crystalline phase behaves as a liquid, but, microscopically, it resembles the solid phase. Sometimes it may be helpful to see it as an ordered liquid or a disordered solid. The liquid crystal behavior depends on the intermolecular forces, that is, if the latter are too strong or too weak the mesophase is lost. Driving forces for the formation of a mesophase are dipole-dipole, van der Waals interactions, 71—71 stacking and so on. 

Fig. 13.19 Intermolecular interactions responsible for formation of different liquid crystal phases attractive anisotropic van der Waals and repulsive steric interactions for nematics (a), van der Waals (bifilic) and steric for SmA (b), steric quadrupolar interaction for SmC (c) and SmC A (d) owed to molecular biaxiality. The density is increasing in a sequence orthogonal (b), synclinic (c) and anticlinic (d) phases. An interlayer steric correlations in SmC (e) are shown by displacements of grey molecules . Note that the displacement of gray molecules may influence the next to nearest layer via a kind of relay race mechanism...

Viscosity, especially rotational viscosity (yi), plays a crucial role in the LCD response time. The response time of a nematic LC device is linearly proportional to yi [45]. The rotational viscosity of an aligned liquid crystal depends on the detailed molecular constituents, structure, intermolecular association, and temperature. As the temperamre increases, viscosity decreases rapidly. Several theories, rigorous or semi-empitical, have been developed in an attempt to account for the origin of the LC viscosity [46,47]. However, owing to the complicated anisotropic attractive and steric repulsive interactions among LC molecules, these theoretical results are not completely satisfactory [48,49]. 

The results of several molecular theories that describe the smectic ordering in a system of hard spherocylinders enable us to conclude that the contribution from hardcore repulsion can be described by the smoothed-density approximation. On the other hand, a realistic theory of thermotropic smectics can only be developed if the intermolecular attraction is taken into account, The interplay between hard-core repulsion and attraction in smectic A liquid crystals has been considered by Kloczkow-ski and Stecki [17] using a very simple model of hard spherocylinders with an ad-ditonal attractive r potential. Using the Onsager approximation, the authors have obtained equations for the order parameters that are very similar to the ones found in the McMillan theory but with explicit expressions for the model parameters. The more general analysis has been performed by Me-deros and Sullivan [76] who have treated the anisotropic attraction interaction by the mean-field approximation while the hardcore repulsion has been taken into account using the nonlocal density functional approach proposed by Somoza and Tarazona. 

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