Molecules quasi-spherical

Except for Ceo, lack of sufficient quantities of pure material has prevented more detailed structural characterization of the fullerenes by X-ray diffraction analysis, and even for Ceo problems of orientational disorder of the quasi-spherical molecules in the lattice have exacerbated the situation. At room temperature Cgo crystallizes in a face-centred cubic lattice (Fm3) but below 249 K the molecules become orientationally ordered and a simple cubic lattice (Po3) results. A neutron diffraction analysis of the ordered phase at 5K led to the structure shown in Fig. 8.7a this reveals that the ordering results from the fact that... 

In Og (Figure 8.1.5b), xmlike in the Ig case, the fuel jet momentum dispersed and the centerline velocity decayed rapidly owing to the lack of buoyancy. As a result, the fuel molecules diffused in every direction and formed a quasi-spherical flame. The slow diffusion processes (1) limited the transport rates of the fuel and oxygen into the flame zone and (2) decreased... 

This rule works best for apolar, quasi-spherical molecules. Large deviations occur when chemical association is involved (e.g., carboxylic acids), from molecular dipolarity (e.g., dimethyl sulfoxide), and from molecular asphericity (e.g., neopentane/ -pentane). Strongly associating solvents (e.g., HF, H2, NH3, alcohols, carboxylic acids) have Trouton constants which are higher than the average value of 88 J mol K" found for nonassociating solvents such as diethyl ether and benzene. 

The nematic phase has unquestionably been the go-to phase to study and understand the major driving forces that govern interactions between suspended, quasi-spherical nanoparticles and liquid crystal molecules or mixtures. We credit this to three important factors (1) early experimental studies [288, 289] based on the foundation of de Gennes very early work on ferronematics [121], (2) the availability of nematic liquid crystals including room temperature and wide temperature... 

Fig. 16 2D-cartoons of quasi-spherical nanoparticles protected with mesogenic or pro-mesogenic capping agents giving rise to liquid crystalline quasi-spherical nanoparticles. The three major approaches include the decoration with calamitic molecules in an end-on fashion (7), with dendrons featuring calamitic or polycatenar moieties at the termini (8), and with laterally substituted calamitic molecules in a side-on fashion (9). The concept shown for the quasi-spherical nanoparticle 7 was also successfully used for spindle-like nanoparticles [533, 534]... 

FIG. 2 The force between two curved mica surfaces in octamethylcyclotetrasiloxane (OMCTS), an inert nonpolar liquid whose molecules are quasi-spherical with a diameter (7 = 9 nm. The solid curve in the main figure gives the experimental results [37] whereas the solid curve in the inset gives the theoretical results of Henderson and Lozada-Cassou [38]. In both parts, the broken curve gives the results of the DLVO theory. Reproduced with permission from Israelachvili [37], Fig. 13.4. 

Quasi-spherical molecular range, [aq, amjn) both aq and amjn are defined above. For any threshold value within the quasi-spherical range the density domain representing the molecule is convex. If amjn is small enough, then in the strict mathematical sense, for very low density thresholds all molecules have convex density domains. 

A properly folded chain molecule can form a cavity with a shape globally complementing the shape of an enclosed, quasi-spherical molecule. If, however, the enclosed molecule has a toroidal or more complicated topology, where the hole of the torus is small so the surrounding chain molecule cannot enter this hole, then an approximate global complementarity by a chain molecule is unlikely to reflect the correct topology of the enclosed molecule. 

In a surprising recent development, Kratschmer et al. have shown that certain all-carbon molecules are produced in large quantities in the evaporation of graphite and can be isolated as soluble, well-defined solids. The major species was identiHed as molecular C ) through mass spectrometry and by comparison of the infrared spectrum with theoretical predictions for the celebrated truncated-icosahedron structure, which had earlier been proposed to account for cluster beam observations. The solid material, described as a new form of elemental carbon in a nearly pure state, has a disordered hep lattice of packed quasi-spherical molecules, but determination of the precise molecular structure awaits diffraction from well-ordered crystals. 

The formation mechanism of the material was also studied by fluorescence techniques, and more particularly by time-resolved fluorescence [24]. In these experiments, the synthesis temperature was lowered down to 60 °C in order to slow down the kinetics of precipitation. The value of the aggregation number (N = 104) at the beginning of the experiment indicates that the micelles in the precursor solution have a quasi-spherical shape (axial ratio equal to 1.8) and interact with urea molecules. The pyrene fluorescence lifetime decreases when aluminum nitrate is added to a solution containing SDS and urea. Consequently, nitrate anions, which are fluorescence quenchers, are at the micelle surface. 

It is generally believed that the polarizabilities of monatomic ions and molecules are independent of field direction. For undistorted quasi-spherical molecules (e.g. CH4, CC14, etc.) the same is usually assumed. When two such atoms are held together, as in a diatomic molecule, the new system is not isotropically polarizable. The model discussed by Silberstein (1917) makes this understandable. If a unit field acts along the line of centres A-B it will induce primary moments parallel to itself in both A and B, and likewise if it acts at 90° to A-B. Each primary moment will induce a secondary moment in its neighbour in the first case the secondary moments will add to the primary moments, but in the second they will subtract. Hence b along the line of centres exceeds that across it, and the polarizability of A-B is an anisotropic property. A similar situation is to be expected with the majority of polyatomic ions or molecules (see Table 21). 

Apparent Molar Kerr Constants of Some Quasi-spherical Molecules... 

Solid fullerene displays interesting properties. After condensation, the Cgo molecules forms a face centered cubic (f.c.c.) structure fullerite. This is the only material which consists of quasi-spherical molecules, all atoms of which are of one kind. X-ray dispersion experiments show that fullerite forms a closely packed f.c.c. crystal in which the distance between the nearest molecules is 10.04 A [2]. The least distance between two molecular surfaces is 2.9 A, and the distance between the nearest atoms in a crystal is 1.42 A. Thus, the experiments specify that the molecular structure of Ceo is preserved in the solid. Strong orientational disorder is observed at room temperature [64] and this disorder decreases as the temperatures decreases. 

It has been pointed out that Trouton s rule is not a strict law, but a remarkable good approximation [13]. The rule works best for nonpolar, quasi-spherical molecules. 

The molecule is a quasi-spherical top with C2, symmetiy. The correspondence between Motet formahsm and that according to Watson is outlined in [06Bou]. Watson s notation is used here. 

A cubic phase of space group laid (which was the first cubic structure to be solved [161] and is among the most commonly observed [162]). The structure of laid belongs to a body-centered space group of rods (which are essentially a surfactant bilayer with a circular cross section) connected 3 x 3 to generate two interwoven but unconnected 3D networks [162]. A chiral cubic phase of space group PA Il has been observed so far in only one lipid-protein-water system [163]. Its proposed structure is similar to that of laid. It has one water-lipid network interwoven with one network of quasi-spherical inverse micelles that encloses the protein molecules. 

HIGH TEMPERATURE VISCOSITIES AND INTERMOLECULAR FORCES OF QUASI-SPHERICAL MOLECULES. 

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