Ionic diameters

One of the prime tenets of the template effect is that a cation of appropriate size coordinates with the heteroatom binding sites in the incipient ring system. Evidence to be discussed below indicates that there is a clear relationship between the size of the coordinating cation and the size of the ring formed. Before presenting this evidence, it is useful to note the approximate ring sizes of common crowns and the known ionic diameters of sundry metal cations. This is done in Table 2.1. 

Crown Ether (hole size, A) Favored Cation (ionic diameter, A) ... 

Table 4.4 Comparison of ionic diameters and crown ether hole sizes ...

MiNbC F compounds have a NaC 1-type structure, and are stable only in the case of lithium due to the steric similarity between the lithium ion and Nb3. In the case of other alkali metal cations with larger ionic diameters, the M4Nb04F compounds decompose yielding orthoniobates and simple fluorides of alkali metals, as follows ... 

The derivation of the equations of the Debye-Huckel theory did not require differentiation between a solution of a single electrolyte and an electrolyte mixture provided that the limiting law approximation Eq. (1.3.24), was used, which does not contain any specific ionic parameter. If, however, approximation (1.3.29) is to be used, containing the effective ionic diameter ay it must be recalled that this quantity was introduced as the minimal mean distance of approach of both positive and negative ions to the central ion. Thus, this quantity a is in a certain sense an average of effects of all the ions but, at the same time, a characteristic value for the given central... 

Solubilities are calculated from a variety of sources compiled by the author. The mean ionic diameter is calculated by Eq. (6.13) using molar volumes in CRC Handbook of Chemistry and Physics. The value of a for OCPp is calculated from the crystallographic data on OCP in Brown et al. (1962). 

Fio. 1 Relation between log K and the ratio of cation diameter to cavity size for (cfa-syn-c r)-dicyclohexyl-18-crown-6 [20] in water at 2S°C. Ionic diameters taken from Pedersen (1967a), and log K values from Izatt et al. (1976a) and Frensforf (197 la)... 

Tab. 10.3. Ionic diameter, charge density and coordination number of some cations...

Cation Ionic diameter Charge density Coordination number... 

Stevenson et al. (2006) estimated the height of the cavity between the fluorenyl and methylbenzyl fragments in the anion-radical of Scheme 3.54 to be 0.35 nm. According to Marcus (1994) table, the ionic diameters are equal to 0.28 nm for K+ and 0.34 nm for Cs. It is lucid that K+ is too small to physically fill the gap between the two isolated n systems. On the contrary, Cs+ is about perfect to bridge the gap over and complete an effective overlap of the unoccupied s orbital of the cation with the JT orbitals of both the moieties of the anion-radical. 

Helgeson and Kirkham, 1974). In equations 8.32.1 and 8.32.2, p is solvent density, e is the dielectric constant of the solvent, and a, is the effective diameter of ion i in solution. The latter parameter must not be confused with the ionic diameter of the ion in a condensed aggregation state, but represents the range of electrostatic interaction with the solvent molecules (see section 8.11.3). 

For an aqueous suspension of crystals to grow, the solute must (a) make its way to the surface by diffusion, (b) undergo desolvation, and (c) insert itself into the lattice structure. The first step involves establishment of a stationary diffusional concentration field around each particle. The elementary step for diffusion has an activation energy (AG ), and a molecule or ion changes its position with a frequency of (kBT/h)exp[-AGl,/kBT]. Einstein s treatment of Brownian motion indicates that a displacement of A will occur within a time t if A equals the square root of 2Dt. Thus, the rate constant for change of position equal to one ionic diameter d will be... 

On the size of the cavity in the crown ether which can be tailored to allow for the selective binding of only certain cations, i.e., whose ionic radius is best accommodated by the poly ether. Thus 18-crown-6 shows a high affinity for K (ionic diameter 2.66 A) and 15-crown-5 for Na+ (ionic diameter 1.80A). 

The above-mentioned metallorganic compounds must have the property of forming complexes with the halides of transitions metals. It is required, in order to get catalytic complexes, that the metal of metallorganic compounds be able to create a strong localized electric field therefore, metals having a very small ionic diameter (below 1 A.) jointly with a very electropositive character are to be used. For such reasons, metals such as Ca,... 

Table 3.5 Comparison of the diameters of different crown ethers with the ionic diameter of various metal cations.

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