Cation diameters

Cation Cation diameter, E Crown ether Cavity diameter, E... 

The match between crown cavity diameter and cation diameter is obvious from Table 3 showing that, eg, and 12-crown-4 (la) or, respectively and 18-crown-6 (Ic) correspond. Similar are the cryptands of gradually increasing cavity size [2.1.1], [2.2.1] and [2.2.2] for and... 

Table 2.1. Relationship between crown hole sizes and cation diameters...

Cavity size and cation diameter 283 Spatial arrangement of binding sites 289 Additional binding sites 293 Electron density at the binding sites 299 Nitrogen and sulfur donor sites 302 Solvent effects 304 Anion effects 308... 

The stability of crown-ether complexes depends on several factors these include cavity size of the ligand, cation diameter, spatial distribution of ring binding sites, the character of the hetero-atoms, the presence of additional binding sites and the type of solvent used. In apolar solutions it also depends on the nature of the anion. The effects of these parameters will be illustrated in the next sections. 

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)... 

Cation Cation Diameter Polyether Ring Hole Diameter (A)... 

Figure 3.2. Dependence of the stability constant K on the cation diameters for alkali metal complexes with three crown ethers,...

Figure 10 (a) Relation between log Ks and the ratio of cation diameter to cavity size for dicyclohexyl[18]crown-6 in water at 25 °C (b) log K, values of several crown ether-alkali cation complexes... 

The structure of ionic crystals usually corresponds to the maximum possible coordination number. If the ions are assumed to be hard spheres, there must be contact between ions of opposite signs and no contact between ions of like sign. The coordination depends on the ratio of anion-to-cation diameters. Figure 13.5 shows that the critical condition for threefold coordination is R/(R + r) = cos 30° = /3/2. Therefore, to prevent contact between like ions,... 

Metal salt Cation diameter n = 4 p- t-butylcalix [n] arene n = 6 n = 8... 

In the mean spherical approximation (MSA) treatment of the ion association in aqueous solutions, the linearity of the relative permittivity and of the hydrated cation diameters with the electrolyte concentration was taken into account and a good fit of the experimental activity and osmotic coefficient was obtained [72-75]. The MSA model was elaborated on the basis of cluster expansion considerations involving the direct correlation function the treatment can deal with the many-body interaction term and with a screening parameter and proved expedient for the interpretation of experimental results concerning inorganic electrolyte solutions [67,75-77]. 

The hole-size relationship between cations and crown ethers has been a part of the lore in the cation binding area for nearly two decades. Although, to our knowledge, no formal definition of this principle has ever been offered, the general concept seems to be that cation binding will be optimized when the cation diameter and macrocycle cavity size are identical. A simple consequence of this concept is the notion that 15-crown-5 is selective (binds more strongly) for Na+ over K+. We have measured the homogeneous (equilibrium) stability constants for the reaction... 

PolyeThef cavity Slameters for these crown ethers as estimated from Corey-Pauling-Kortun (CPK) space-filling models or determined from X-ray crystal data are compared with the alkali metal cation diameters in Table I (6,13). In general, strongest complexation is expected when the ratio of metal ion to polyether cavity diameters... 

Table I. Comparison of Polyether Cavity and Cation Diameters...

The complexing abilities of thiacrown ethers and related macrocycles depend on several factors that have not been fully investigated. These factors include ligand cavity size, spatial distribution of binding sites within the ring, types of donor atoms, hard and soft acid-base rule , cation diameter, solvent, macrocycle conformation, and other factors . 

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