Crystal bulk phase

As with solid phase decompositions (Sect. 1), the kinetic characteristics of solid—solid interactions are controlled by the properties of lattice imperfections, though here many systems of interest involve the migration, in a crystal bulk of a mobile participant, from one interface to another. Kinetic measurements have been determined for reactions in a number of favourable systems, but there remain many possibilities for development in a field that is at present so largely unexplored. 

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]. 

In the previous sections, we have seen how computer simulations have contributed to our understanding of the microscopic structure of liquid crystals. By applying periodic boundary conditions preferably at constant pressure, a bulk fluid can be simulated free from any surface interactions. However, the surface properties of liquid crystals are significant in technological applications such as electro-optic displays. Liquid crystals also show a number of interesting features at surfaces which are not seen in the bulk phase and are of fundamental interest. In this final section, we describe recent simulations designed to study the interfacial properties of liquid crystals at various types of interface. First, however, it is appropriate to introduce some necessary terminology. 

A very different model of tubules with tilt variations was developed by Selinger et al.132,186 Instead of thermal fluctuations, these authors consider the possibility of systematic modulations in the molecular tilt direction. The concept of systematic modulations in tubules is motivated by modulated structures in chiral liquid crystals. Bulk chiral liquid crystals form cholesteric phases, with a helical twist in the molecular director, and thin films of chiral smectic-C liquid crystals form striped phases, with periodic arrays of defect lines.176 To determine whether tubules can form analogous structures, these authors generalize the free-energy of Eq. (5) to consider the expression... 

Polymers that are not crystallizable in the bulk phase, or only very weakly crystal lizable, are not so well understood. 

Lipids with a suitable hydrophilic-lipophilic balance (HLB) are known to spread on the surface of water to form monolayer films. It is obvious that if the lipid-like molecule is highly soluble in water, it will disappear into the bulk phase (as observed for SDS). Thus, the criteria for a monolayer formation are that it exhibits very low solubility in water. The alkyl part of the lipid points away from the water surface. The polar group is attracted to the water molecules and is inside this phase at the surface. This means that the solid crystal, when placed on the surface of water, is in equilibrium with the him spread on the surface. A detailed analysis of this equilibrium has been given in the literature (Gaines, 1966 Adamson and Gast, 1997 Birdi, 2009). The thermodynamics allows one to obtain extensive physical data on this system. It is thus apparent that, by studying only one monolayer of the substance, the effect of temperature can be very evident. 

The analysis of such patterns reveals that the microcrystals are preferentially oriented with their (021) planes, the contact planes, parallel to the substrate s surface. The interesting point is that, in order to satisfy such orientation, the hydrogen bonds of the dimers at the interface have to be broken and in addition some reorganization of the molecules is needed (see Fig. 5.6(g)). In conclusion, the molecule-substrate interactions are sufficiently strong (larger yuns and y nv values) to induce COO Aik bonds, where Aik represents sodium and potassium, but the growing crystals adapt their structure in order to crystallize in the known monoclinic bulk phase. 

A phase can be defined as a domain bounded by a closed surface in which parameters such as composition, temperature, pressure and refractive index are constant but change abruptly at the interface. The principal phases in milk are its serum and fat and the most important interfaces are air/serum and fat/serum. If present, air bubbles, and ice, fat or lactose crystals will also constitute phases. Forces acting on molecules or particles in the bulk of a phase differ from those at an interface since the former are attracted equally in all directions while those at an interface experience a net attraction towards the bulk phase (Figure 11.6). 

The crystallinity of liquid crystal phases refers to the large assortment of ways these micellar structures can be organized within a bulk phase. For example, spherical micelles of... 

By a change of temperature or pressure, it is often possible to cross the phase limits of a homogeneous crystal. It supersaturates with respect to one or several of its components, and the supersaturated components eventually precipitate. This is an additive reaction. It occurs either externally at the surfaces, or in the crystal bulk by nucleation and growth. Reactions of this kind from initially homogeneous and supersaturated solid solutions will be discussed in Chapter 12 on phase transformations. Internal reactions in the sense of the present chapter occur after crystal A has been brought into contact with reactant B, and the product AB forms isothermally in the interior of A or B. Point defect fluxes are responsible for the matter transport during internal reactions, and local equilibrium is often established throughout. 

The equilibrium interfaces of fluid systems possess one variant chemical potential less than isolated bulk phases with the same number of components. This is due to the additional condition of heterogeneous equilibrium and follows from Gibbs phase rule. As a result, the equilibrium interface of a binary system is invariant at any given P and T, whereas the interface between the phases a and /3 of a ternary system is (mono-) variant. However, we will see later that for multiphase crystals with coherent boundaries, the situation is more complicated. 

After discussing the thermodynamic properties of the boundary, let us concentrate on the change in thermodynamic potentials across the boundary. For this, we formulate the Gibbs energy for the bulk phase a of an ionic crystal as the sum... 

In many non-equilibrium situations, this local equilibrium assumption holds for the crystal bulk. However, its verification at the phase boundaries and interfaces (internal and external surfaces) is often difficult. This urges us to pay particular attention to the appropriate kinetic modeling of interfaces, an endeavour which is still in its infancy. 

Materials that have a nonzero second-order susceptibility will produce light at twice the incident frequency. The magnitude of this effect is small, and has been a practical consideration only since the advent of lasers. If the symmetry of a crystal or other medium is such that it has a center of inversion, no SHG effect will be observed. However, surfaces by their very nature break this inversion symmetry. Hence, an SHG signal may arise at the electrode-solution interface even though both bulk phases may be considered centrosymmetric [66], The magnitude of the SHG signal is sensitive to surface conditions (e.g., electrode potential, ionic or molecular adsorption, etc.). Surface spectroscopy is also feasible since the SHG signal will be enhanced if either the incident frequency (to) or SHG (2co) corresponds to an electronic absorption of a surface species [66]. 

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