Valence activity factor

The equivalent salinity (to replace In S in Eq. (3.3)) of a sodium salt different from chloride has been fully established from the experimental point of view, thanks to the introduction of the valency activity factor VAF [29]. In S (wt.% NaCl) has to be replaced by 1.766 + In SNe in Eq. (3.3) to take into account the change in salinity unit (from wt.% NaCl to normality of sodium ion). Sne is the equivalent salinity of the sodium salt (in mole of sodium ion per litre) defined by... 

These results indicate that the higher the anion valence the less the ionic strength as far as equivalent salinity is concerned. This was readily translated by defining the valence activity factor (VAF) as follows, for both single sodium electrolyte and mixtures ... 

The charge of the critical complex AB naturally is equal to the algebraic sum of the charges of A and B. If, for example, A is a univalent ion and B is a neutral molecule, the critical complex will have a valence of 1. The kinetic activity factor therefore will be independent of the electrolyte content between rather wide limits since /a and fx will vary approximately in the same manner. At larger ionic strengths a more distinct salt effect will be observed since individual differences between A and AB will enter and because /b will no longer be equal to unity. 

Under polymerisation conditions, the active center of the transition-metal haHde is reduced to a lower valence state, ultimately to which is unable to polymerise monomers other than ethylene. The ratio /V +, in particular, under reactor conditions is the determining factor for catalyst activity to produce EPM and EPDM species. This ratio /V + can be upgraded by adding to the reaction mixture a promoter, which causes oxidation of to Examples of promoters in the eadier Hterature were carbon tetrachloride, hexachlorocyclopentadiene, trichloroacetic ester, and hensotrichloride (8). Later, butyl perchlorocrotonate and other proprietary compounds were introduced (9,10). 

No completely general and quantitative theory of the stereochemical activity of the lone-pair of electrons in complex halides of tervalent As, Sb and Bi has been developed but certain trends are discernible. The lone-pair becomes less decisive in modifying the stereochemistry (a) with increase in the coordination number of the central atom from 4 through 5 to 6, (b) with increase in the atomic weight of the central atom (As > Sb > Bi), and (c) with increa.se in the atomic weight of the halogen (F > Cl > Br > 1). The relative energies of the various valence-Ievel orbitals may also be an important factor the F(a) orbital of F lies well below both the s and the p valence... 

The difference in catalytic activity between the La- and the Ba-based hexa-aluminates results from the following reasons the first difference is the valence of cation in the mirror pleuie between tri-valent lanthanum ion and di-valent barium ion. The second is the crystal structure between magnetoplumbite and P-alumina, which are different in the coordination of ions and concentration of Frenkel-type defect in mirror plane. The redox cycle of transition metal in hexa-aluminate lattice, which closely related with catalytic activity, is affected sensitively with these two factors. 

Trends in the electronic structure of the chalcogenide catalysts have proved to be helpful in the design and understanding of the catalyst clusters. During ORR, the molecular oxygen has been found to react with the cluster as a whole, rather than individual metal atoms.177 The overall number of electrons per cluster unit (NEC) in the valence bond has been shown to have a factor in the activity and stability of the cluster catalysts.177,181 The unsubstituted Chevrel phases have a NEC of 20.177,181 Substituting or intercalating other transition metals into the crystal lattice to make ternary or pseudo-binary Chevrel phases allows for the increase of NEC. It has been found that as the NEC approaches 24, the catalytic activity improves.181 Alonso-Vante compiled the results from his previous studies to show the effect of NEC in... 

A recently proposed semiclassical model, in which an electronic transmission coefficient and a nuclear tunneling factor are introduced as corrections to the classical activated-complex expression, is described. The nuclear tunneling corrections are shown to be important only at low temperatures or when the electron transfer is very exothermic. By contrast, corrections for nonadiabaticity may be significant for most outer-sphere reactions of metal complexes. The rate constants for the Fe(H20)6 +-Fe(H20)6 +> Ru(NH3)62+-Ru(NH3)63+ and Ru(bpy)32+-Ru(bpy)33+ electron exchange reactions predicted by the semiclassical model are in very good agreement with the observed values. The implications of the model for optically-induced electron transfer in mixed-valence systems are noted. 

It appears that for the layered Mn and Co oxides considered, ionic size effects do not play a significant role in the preference for octahedral or tetrahedral sites nor in the activation barrier to hops between the two. Consequently, size effects probably do not play a significant role in determining the mobility of Mn or Co through a ccp oxide framework. In contrast, the results indicate that valence and electronic structure are more decisive factors in the site preference of Mn or Co and hence in their propensity to migrate through a ccp oxide framework. This is consistent with the work of Goodenough that found valence to be an important determinant of the site preference of 3d TM ions in oxides. 

Some of these factors contain metal ions as redox-active components. In these cases, it is usually single electrons that are transferred, with the metal ion changing its valency. Unpaired electrons often occur in this process, but these are located in d orbitals (see p.2) and are therefore less dangerous than single electrons in non-metal atoms ( free radicals see below). 

Symmetry restrictions may also be placed on the active orbitals in order to determine the nature of the resulting modern valence bond solution. This is exemplified by the common use of o - n separation for planar molecules (c/ Section 5). In earlier applications to ozone and diborane [2,4] it was also seen that the distribution of active orbitals among the irreducible representations was the deciding factor for the types of VB solution possible. It should also be borne in mind here that the nature of the lowest-lying CASSCF solution may not always coincide with that of the optimal fully-variational modem VB wavefunction. 

Up to this point we have discussed the formation of polarons in ionic crystals. Polarons of another type can also form in elements and other systems, such as the valence bands of alkali and silver halides, where the polarizability is not the relevant factor. In fact Holstein s (1959) original discussion of the small polaron was of this form. This kind of polaron is sometimes called a molecular polaron, and is illustrated in Fig, 2.3(a), and in Fig. 2.3(b) in the activated configuration of the atoms when the electron can move from one site to another. There is nothing analogous to the large polaron in this case in three-dimensional systems either a small polaron is formed or there is little effect on the effective mass from interaction with phonons. 

Two factors combine to lend a greater diversity in the stereochemistries exhibited by bivalent germanium, tin and lead compounds, the increased radius of Mn compared with that of Mw and the presence of a non-bonding pair of electrons. When the non-bonding pair of electrons occupies the isotropic valence level s orbital, as in, for example, the complex cations Pb[SC(NH2)2]6+ and Pb[antipyrine]6+, or when they are donated to conductance band levels, as in the binary tin and lead selenides or tellurides or the perovskite ternary phases CsMX3 (M = Sn, Pb X = Cl, Br, I), then the metal coordination is regular. However, in the majority of compounds an apparent vacancy in the coordination sphere of the metal is observed, which is usually ascribed to the presence of the non-bonding pair of electrons in a hybrid orbital and cited as evidence for a stereochemically active lone pair . 

---