Anisotropic shape

There are many ingenious and successful routes now developed for nanocry stalline syntliesis some rely on gas phase reactions followed by product dispersal into solvents [7, 9,13,14 and 15]. Otliers are adaptations of classic colloidal syntlieses [16,17,18 and 19]. Electrochemical and related template metliods can also be used to fomi nanostmctures, especially tliose witli anisotropic shapes [20, 21, 22 and 23]. Ratlier tlian outline all of tlie available metliods, this section will focus on two different techniques of nanocrystal syntliesis which together demonstrate tlie general strategies. 

Figure C2.17.5. Transmission electron micrograph of a field of anisotropic gold nanocrystals. In tliis example, a lower magnification image of gold nanocrystals reveals tlieir anisotropic shapes and faceted surfaces [36],...

In summary, control of the surface chemistry and the presence of clean surfaces allow the coalescence of initially isotropic nanoparticles into regular, often monodisperse, nano-objects of anisotropic shape (cubes, rods, wires). It is possible that the inclusion of the initially present nanoparticles into superlattices play an important role in these coalescence processes. 

Liquid crystal behavior is a genuine supramolecular phenomenon based on the existence of extended weak interactions (dipole-dipole, dispersion forces, hydrogen bonding) between molecules. For the former two to be important enough, it is usually necessary for the molecules to have anisotropic shapes, able to pack efficiently so that these weak interactions can accumulate and co-operate, so as to keep the molecules associated in a preferred orientation, but free enough to move and slide, as they are not connected by rigid bonds. 

When a nanoporous Ti02 film consisting of Ti02 nanoparticles is used instead of the single crystal, the extinction band of silver nanoparticles deposited by UV-irradiation is much broader. This is probably because the nanopores in the Ti02 film mold the silver nanoparticles into various anisotropic shapes [9], although direct observation of the particles in the nanopores is difficult. 

There have been a number of past attempts to unify hardness measurements but they have not succeeded. In several cases, hardness numbers have been compared with scalar properties that is, with cohesive energies (Plendl and Gielisse, 1962) or bulk moduli (Cohen, 1988). But hardness is not based on scalar behavior, since it involves a change of shape and is anisotropic. Shape changes (shears) are vector quantities requiring a shear plane, and a shear direction for their definition. In this book, the fact that plastic... 

Hematite derived from dehydroxylation of FeOOH at temperatures below 600 °C shows marked, non-uniform (differential) broadening of the XRD lines. Some authors have attributed this effect to the anisotropic shape of the coherently diffracting domains of hematite (Duvigneaud Derie, 1980), and others to the development... 

That growth at the steps is much faster than at the steps has been confirmed in a number of experiments. It also helps explain the highly anisotropic shapes of islands that form on the flat Si(lOO) surface. Growth takes place primarily at the ends of the islands. Little growth takes place at the sides, because these edges, which resemble the steps, simply cannot localize the adatoms there. 

Almond and Axelson have introduced an approach of some resemblance to TRAMITE, but based on the molecule s gyration tensor, which more closely reflects molecular shape and thus provides higher accuracy for molecules of highly anisotropic shape.104 They propose that the eigenvalues of the order tensor can be predicted to an accuracy which nearly matches SSIA, according to the simple relationship,... 

Transmission electron microscopy ( ) analysis reveals that these materials crystallize as hexagonal planar particles with marked anisotropic shape,8,37 as shown in Figure 6. When appropriate preparation methods are used, plate-like crystals are obtained with small thickness of about 20-30 nm and an aspect ratio D/h=5-10. Selected area diffraction (SAD) patterns of incident beams perpendicular and parallel to the large hexagonal facet show that they correspond to the crystallographic planes perpendicular to the c axis. The anisotropic shape of the... 

Gels are very soft and can be easily deformed into anisotropic shapes. In such states, phase transitions and separation are of great interest. Similar problems have been treated in the metallurgical literature [57-59]. In this subsection, we are mainly interested in the structure factor in such deformed states, so we will neglect possible macroscopic instabilities (which can occur if gels are allowed to swell at least in two directions as will be discussed in Sect. 5). 

In natural systems (lakes, oceans, atmosphere) turbulent diffusion is usually anisotropic (i.e., much larger in the horizontal than vertical direction). There are two main reasons for that observation (1) the extension of natural systems in the horizontal is usually much larger than in the vertical. Thus, the turbulent structures (often called eddies) that correspond to the mean free paths of random motions often look like pancakes that is, they are flat along the vertical axis and mainly extended along the horizontal axes. (2) Often the atmosphere or the water body in a lake or ocean is density stratified (i.e., the density increases with depth). This compresses the eddies even further in the vertical. Gravitational forces keep the water parcels from moving too far away from the depth where they are neutrally buoyant, that is, where they have the same density as their environment. Thus, the anisotropic shape of the eddies results in turbulent diffusivities which differ in size along different spatial directions. 

Nematic phases are characterized by an unordered statistical distribution of the centers of gravity of molecules and the long range orientational order of the anisotropically shaped molecules. This orientational order can be described by the Hermans orientation function 44>, introduced for l.c. s as order parameter S by Maier and Saupe 12),... 

An extended, structurally rigid, highly anisotropic shape seems to be the main criterion for liquid crystalline behaviour, and, as a result, many liquid crystalline materials are based on substituted... 

Recent studies showed that amphiphilic properties have to be taken into account for most water-soluble monomer units when their behavior in water solutions is considered. The amphiphilic properties of monomer units lead to an anisotropic shape of the polymer structures formed under appropriate conditions, which is confirmed both by computer simulation and experimental investigations. The concept of amphiphilicity applied to the monomer units leads to a new classification based on the interfacial and partitioning properties of the monomers. The classification in question opens a broad prospective for predicting properties of polymer systems with developed interfaces (i.e., micelles, polymer globules, fine dispersions of polymer aggregates). The relation between the standard free energy of adsorption and partition makes it possible to estimate semiquantitatively the distribution between the bulk and the interface of monomers and monomer units in complex polymer systems. 

The origin of this relaxation is in heterogeneity of the ceramic, in which anisotropically shaped grains exhibit strong variation in their piezoelectric and dielectric properties in different directions. As discussed in [17], in such heterogeneous materials Maxwell-Wagner like processes may lead to a behavior shown in Figure 13.6. 

Table 1.3 Ratios of the averaged principal moments of the radius of gyration tensor, asphericity, acylindricity, and anisotropic shape factor for model dendrimers (1, Fig. l.l)a).

As a ferroelectric perovskite in ceramic form cools through its Curie point it contracts isotropically since the orientations of its component crystals are random. However, the individual crystals will have a tendency to assume the anisotropic shapes required by the orientation of their crystal axes. This tendency will be counteracted by the isotropic contraction of the cavities they occupy. As a consequence a complex system of differently oriented domains that minimizes the elastic strain energy within the crystals will become established. 

Under a different growth regime, one that promotes fast, kinetic growth, more highly anisotropic shapes, such as rods and wires, can be obtained. In semiconductor nanoparticle... 

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