Divalent cation radii

As the ratio is >0.732 the Cs should be 8-fold coordinated. It is clear from Figure 6.1 that the coordination number is indeed 8. This structure does not appear to occur for oxides since the (divalent) cation radius would need to be >102.5pm (0 is 140pm). It is not directional bonding that causes the structure to be adopted, just the packing requirements. This structure is the model B2 structure found in some important intermetallics like NiAl. It is also adopted by a number of halides having useful optical properties as shown in Figure 6.2, CsBr, Csl, TlCl, and TlBr transmit in part of the ultraviolet (UV), all of the visible (the shaded region), and the near infrared (IR). 

The type of catalyst influences the rate and reaction mechanism. Reactions catalyzed with both monovalent and divalent metal hydroxides, KOH, NaOH, LiOH and Ba(OH)2, Ca(OH)2, and Mg(OH)2, showed that both valence and ionic radius of hydrated cations affect the formation rate and final concentrations of various reaction intermediates and products.61 For the same valence, a linear relationship was observed between the formaldehyde disappearance rate and ionic radius of hydrated cations where larger cation radii gave rise to higher rate constants. In addition, irrespective of the ionic radii, divalent cations lead to faster formaldehyde disappearance rates titan monovalent cations. For the proposed mechanism where an intermediate chelate participates in the reaction (Fig. 7.30), an increase in positive charge density in smaller cations was suggested to improve the stability of the chelate complex and, therefore, decrease the rate of the reaction. The radii and valence also affect the formation and disappearance of various hydrox-ymethylated phenolic compounds which dictate the composition of final products. 

The effect of the nature of the divalent cation is very pronounced as illustrated in Figure 2 on sample A30. Pectins were found to be much more sensitive to copper than to calcium. A scale of affinity towards divalent cations can be easily obtained this way [18]. This result corroborates what has been measured by pH titration upon addition of increasing amount of cations [28,29], where the order of decreasing selectivity was Pb = Cu Zn > Cd = Ni > Ca. This scale does not follow the size of the radius of the cations but is in agreement with the sequence of complex stability of Irving-Williams [30]. 

In such systems as (M, Mj (i/2))X (M, monovalent cation Mj, divalent cation X, common anion), the much stronger interaction of M2 with X leads to restricted internal mobility of Mi. This is called the tranquilization effect by M2 on the internal mobility of Mi. This effect is clear when Mj is a divalent or trivalent cation. However, it also occurs in binary alkali systems such as (Na, K)OH. The isotherms belong to type II (Fig. 2) % decreases with increasing concentration of Na. Since the ionic radius of OH-is as small as F", the Coulombic attraction of Na-OH is considerably stronger than that of K-OH. 

This Group IIA (or Group 2) element (atomic symbol, Ca atomic number, 20 atomic weight, 40.078 electronic configuration = ls 2s 2p 3s 3p 4s ) loses both As electrons to form a divalent cation of 0.99A ionic radius. Ionic calcium combines readily with oxygen ligands (chiefly water, phosphates, polyphosphates, and carbox-ylates) to form stable metal ion complexes. Ca under-... 

Ionic strength influences are well known with respect to the rate and energetics of nucleic acid hybridization [17]. Charge and ionic radius are both important in terms of stabilizing the structure of the duplex as well as stabilizing the stem portion of the molecular beacon [17]. The stem structure stability was increased when a divalent cation was incorporated into the hybridization buffer solution [17]. It was reported that cations were best at stabilizing the duplex formed upon hybridization in the order Ca2+ > Mg2+ K+ > Na+. The ultimate detection limit of the sensor configuration was calculated to be 1.1 nM [17]. 

Cations of the first transition series do not conform to the smooth pattern for the lanthanide elements shown in fig. 6.1. This is illustrated in fig. 6.2a by the radii of divalent cations in oxides containing transition metal ions in high-spin states. There is an overall decrease of octahedral ionic radius from Ca2+to Zn2+, but values first decrease to V2+, then rise to Mn2+, decrease to Ni2+, and rise again to Zn2+. The characteristic double-humped curve shown in fig. 6.2a has... 

In fact, the site occupancy of a normal spinel is abnormal. According to the radius ratio concept, larger divalent cations should occupy octahedral sites and smaller trivalent cations might be expected to favour the tetrahedral sites. The mineral spinel, Mg A1204 which is predominantly normal, does not conform with radius ratio criteria. 

In ferromagnesian silicates, therefore, Ni2+ ions are expected to be enriched over Mg2+ in smallest octahedral sites, with the other divalent transition metal ions favouring larger sites in the crystal structures. Thus, based on the ionic radius criterion alone, the olivine Ml and pyroxene Ml sites would be expected be enriched in Ni2+, with the other divalent cations showing preferences for the larger olivine M2 and pyroxene M2 sites. Similarly, in aluminosilicates, all trivalent transition metal ions are predicted to show preferences for the largest [A106] octahedron. 

Figure 9.7 Transition pressures at 1,000 °C for various olivines transforming to the P-phase ( modified spinel or wadsleyite) or Y-phase (spinel or ringwoodite) as a function of the ionic radius ratio divalent cation (Fr+) to Si4 or Ge4 (M4 ) (from Syono et al., 1971). Note that the cations acquiring excess CFSE in spinel over olivine (e.g., Fe2+, Co2+, Ni2+) deviate from a linear trend.

Besides, the interaction of divalent cations with the zeolite framework and water is stronger on account of the higher charge and lower cationic radius exhibited by Ca2+ (Ca2+ 0.99 A) in contrast with Na+ and K+ (Na+ 0.95 A and K+ 1.33 A). This effect induces a lower mobility of divalent cations, on account of the fact that divalent cations are more intimately linked with the zeolite framework. Hence, the lower cationic mobility is an additional reason for the decrement in the permittivity of tested samples, and this effect is also detected by the thermodielectric analyzer as a decrease in V0 [110,119],... 

Figure 4.53 shows the dispersion spectra of hydrated Ca-HC, K-HC, and Na-HC at 300K [120], They are plotted in the x-axis, and the natural logarithm of the frequency (Hz) versus the natural logarithm of the real part of the relative permittivity in the y-axis. This experiment shows once more the higher mobility of monovalent cations in comparison with divalent cations and the higher mobility of Na+ with respect to K+. The cause of this effect is due to the inferior cationic radius of Na+ in comparison with that of K+. 

Hydration Enthalpies (-HJ vs. Cationic Radius (R) for Some Divalent Cations... 

TfR-mediated endocytosis is a well-known uptake system Tf binds one or two Fe atoms, but only diferric Tf (Fe2Tf) has a high affinity for TfR to be taken up by the receptor-mediated endocytosis. This system uses a mobilization pathway that involves endosomal acidification, reduction of ferric Fe, and ferrous Fe transport [8]. Recently, it was clarified that divalent cation/ metal ion transporter (DCT1) or Nramp2 involves iron transport from the endosome to the cytosol [9, 10]. Al resembles Fe in chemical characteristics ionic radius, charge density, and coordination number [11]. Therefore, Al binds with Tf to form di—Al—Tf. Al bound to Tf even passes through the blood-brain barrier to enter the neuronal cells via Tf receptor-mediated endocytosis [12]. 

Clearly, this is the direction in which further fundamental studies should be oriented. For example, it will be interesting to find out whether much higher surface coverages can be accomplished on a carbon whose maximum number of (cation-exchangeable) adsorption sites, e.g., 3 mmol COO /g C, is not only created but made electrostatically accessible by adjusting the solution chemistry. Under these conditions, for example, the theoretical uptake of a divalent cation is 1.5 mmol/g, which translates into 450 mVg, which in turn is a large fraction of the total surface area. This is obtained by assuming a radius of 0.4 nm for a hydrated divalent cation, which is usual for heavy metals [309], Indeed, in the study of Cr(IlI) adsorption by activated carbon MO (see Table 3), the surface covered by a monolayer of the adsorbed eations was 196 mVg on a sample whose Nt and CO2 surface areas were 164 and 537 mVg, respectively. 

Empirical calculations carried out for cations show that vacancy compensation is clearly the preferred route, at least for large dopant cations (radius >0.8A). Formation of interstitials is also ruled out by measurements of true density and comparison with calculated values . For the smaller cations (i.e. Al ), some compensation via dopant interstitial may occur. The reactions described in Eq. 2.18 and 2.21 (for a divalent cation) therefore summarise the main route to defect formation in solid solutions of the type Ce. jMj02,o.5x and Ce, xMx02.x respectively. 

An enzymic counterpart of these complex base-catalysed rearrangements of sugars may be the reaction catalysed by 4-phospho-3,4-dihydroxy-2-butanone synthetase. The enzyme catalyses the formation of the eponymous intermediate in secondary metabolism from ribulose 5-phosphate. Labelling studies indicated that C1-C3 of the substrate became C1-C3 of the product, that H3 of the substrate derived from solvent and that C4 was lost as formate. X-ray crystal structures of the native enzyme and a partly active mutant in complex with the substrate are available. The active site of the enzyme from Met ha-nococcus jannaschii contains two metals, which can be any divalent cations of the approximate radius of Mg " or Mn ", the two usually observed. Their disposition is very reminiscent of those in the hydride transfer aldose-ketose isomerases, but also to ribulose-5-phosphate carboxylase, which works by an enolisation mechanism, so the enolisation route suggested by Steinbacher et al. is repeated in Figure 6.14, as is the Bilik-type alkyl group shift, for which an equivalent reverse aldol-aldol mechanism cannot be written. 

Figure 7. Log D vs. ionic radius for typical divalent cations in the HDEHP-aqueous nitrate system (21)...

---