Of spherical motifs

MELTING TEMPERATURES AND ENTROPIES OF FUSION OF CRYSTALS OF SPHERICAL MOTIFS... 

As will be shown, model systems for cells employing lipids or composed of polymers have been in existence for some time. Model systems for coccolith-type structures are well known on the nanoscale in inorganic and materials chemistry. Indeed, many complex metal oxides crystallize into approximations of spherical networks. Often, though, the spherical motif interpenetrates other spheres making the formation of discrete spheres rare. Inorganic clusters such as quantum dots may appear as microscopic spheres, particularly when visualized by scanning electron microscopy, but they are not hollow, nor do they contain voids that would be of value as sites for molecular recognition. All these examples have the outward appearance of cells but not all function as capsules for host molecules. 

Matter is composed of spherical-like atoms. No two atomic cores—the nuclei plus inner shell electrons—can occupy the same volume of space, and it is impossible for spheres to fill all space completely. Consequently, spherical atoms coalesce into a solid with void spaces called interstices. A mathematical construct known as a space lattice may be envisioned, which is comprised of equidistant lattice points representing the geometric centers of structural motifs. The lattice points are equidistant since a lattice possesses translational invariance. A motif may be a single atom, a collection of atoms, an entire molecule, some fraction of a molecule, or an assembly of molecules. The motif is also referred to as the basis or, sometimes, the asymmetric unit, since it has no symmetry of its own. For example, in rock salt a sodium and chloride ion pair constitutes the asymmetric unit. This ion pair is repeated systematically, using point symmetry and translational symmetry operations, to form the space lattice of the crystal. 

Another example of the existence of condis crystalline polymorphs between liquid crystal and crystal phase is OOBPD. Table 5.4 contains a listing of the observed transitions Again, the combined entropies of transition from the condis crystal K1 to the melt [41.6 J/(K mol)] are what is expected for fusion of a single, rigid, non-spherical motif (see Sect. 1). 

Figure 5.119 extends the list of almost spherical motifs to much larger, organic molecules with a molecular stmcture which is still close to spherical. Again, these molecules are plastic crystals and have gained orientational mobihty before ultimate... 

Melting Temperatures and Entropies of Melting of Crystals with Spherical Motifs... 

A more detailed empirical rule for the entropy of melting is listed at the bottom of Fig. 3.7. Three types of disorder make up the change on fusion positional (pos), orientational (or), and conformational (conf). The approximate contributions to AS are listed in brackets. The first term represents Richards s rule. It is the only contribution for spherical motifs. Irregular motifs can, in addition, show orientational disorder, and thus gain an extra 20-50 J/(K mol) on fusion. Flexible molecules, finally, have a third contribution to the entropy of fusion of 7 -12 J/(K mol) for each flexible bead within the molecule. 

Table 5.2 illustrates a collection of entropies of fusion for crystals with spherical motifs. Motifs are the building blocks, such as atoms, ions, molecules, or parts of molecules, which, by repetition, make up the crystal. One recognizes immediately that all data fit into the limit of Richards s rule (see Sect. 3.4.2). It is thus not the monatomic nature of the motifs, as initially thought by Richards, that is of importance, but rather their spherical nature. Crystals of noble gases and metals are listed in the top portion of the table and fit Richards s rule well. The more complicated inorganic and organic molecules in the two bottom portions are similarly described by Richards s rule. The entropy contribution of 7-14 J/(K mol) seems only a little dependent on the chemical nature of the motif. Size is also not of importance,... 

Disclosing the binding motif of multiblock RAFT polymers on AuNPs from citrate reduction raises the questimi of whether the polymer binding can vary for different types of AuNPs. It is known that AuNPs from the two-phase Brust-Schiffrin synthesis can assemble into spherical particle networks when treated with low molecular weight crosslinking agent [106, 107]. When tetraocty-lammonium bromide-capped AuNPs from this two-phase method are functionalized in toluene dispersion with multiblock RAFT polymers of styrene, the formation of spherical AuNP assemblies can be observed by TEM (Fig. 9) [108]. It can be concluded from these TEM images that the particle density inside... 

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