Group radius ratios

Hyperbranched polymers have also been prepared via living anionic polymerization. The reaction of poly(4-methylstyrene)-fo-polystyrene lithium with a small amount of divinylbenzene, afforded a star-block copolymer with 4-methylstyrene units in the periphery [200]. The methyl groups were subsequently metalated with s-butyllithium/tetramethylethylenediamine. The produced anions initiated the polymerization of a-methylstyrene (Scheme 109). From the radius of gyration to hydrodynamic radius ratio (0.96-1.1) it was concluded that the second generation polymers behaved like soft spheres. 

The atomization energies were linearly related to the effective radius ratios Similar relations held among Group IIIB mono-... 

For those ionic compounds (such as cesium chloride) in which the radius ratio rc/r exceeds 0.73 it is possible to group eight anions tightly around each cation. The anions may be considered to occupy the comers of a cube with the cation in the center, or alternately, an anion may be regarded as the center of a cube with eight cations grouped around it the... 

The Group 12 elements differ markedly from those in Group 2 in nearly all respects except having II as their only important oxidation state. Thus, while the Zn2+ and Mg2+ ions are very similar in their 6-coordinate radii (0.88 A and 0.86 A, respectively), Zn2+ has a relatively polarizable 3d10 shell whereas the neon core of Mg2+ is very hard. This special combination of softness and a high charge-to-radius ratio appears to be responsible for the unique role played by zinc in biochemistry (see Section 15-17). 

Extended structures of (at least) binary compounds EX most frequently involve covalent bonding between the simplest formula units EiX via E and X atoms or groups that are bridging (two-coordinate or higher), rather than terminal (one-coordinate). Moderately accurate predictions of periodic trends in structural types for EX can be made using stoichiometry and radius-ratio calculations (starting with the premise that the compound can be formed, at least conceptually, from cations of E and anions of X). (1) If the radius ratio of the ions in the compound EX lies between 0.225 and 0.414, E is predicted to have a total coordination number of 4 if the ratio lies between 0.414 and 0.732, E should have a total coordination number of 6 if the ratio is above 0.732, E should have a total coordination number of 8. (2) Once the coordination number of E is predicted, the average coordination number of the anionic element X can be predicted ... 

Coordination to metals follows the usual trends. The transition metals try to achieve octahedral coordination (with a few exceptions), but the cations of the electropositive group 1-3 elements exhibit a rich variety. The coordination polyhedra are determined by radius ratios more than by topological preferences. For polyphosphides in general, all P atoms are involved in M-P interactions according to the number of lone pairs present. The anionic (lb)P and (2b)P as well as the neutral (3b)P° species adopt quasi-tetrahedral coordination, especially if main-group cations are involved. Only a few exceptions are known, for example Li3P7. With more covalent M-P bonds, the number (m + n) of available lone pairs of a polyanion P " is strongly related to the metal coordination number that is, CN(M) < m + n). If CN(M) > m + n), ion-ion and ion-dipole interactions dominate. The relation <7[M-(2b)P] > <7[M-(3b)P] is true in most cases. 

Unlike ionic structures where co-ordination numbers are determined by the radius ratio rule and the bonds are not directed, homopolar structures have directed bonds. An element in the group of the Periodic Table can form 8—N bonds per atom and co-ordination numbers are small, usually four or less. 

An. nnalysis of 227 compounds indicated that the radius ratio rule worked about two-thirds of the time. Particularly troublesome were Group IB (I I) and IIB (12) chalcogenides like HgS. Nathan, L. C. J. Chem. i/uc. 1985, 62, 215-218. 

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