Anion minimum distance between

The equation can then be used to calculate lattice energies, providing the Madelung constant is known and the minimum distance between cation and anion can be calculated. 

The experimentally measured anion-cation distances in highly ionic solids can be interpreted on the assumption that each ion has a nearly fixed radius. For example, the difference in anion-cation distance between the halides NaX and KX is close to 36 pm irrespective of the anion X, and it is natural to attribute this to the difference in radii between Na+ and K+. To separate the observed distances into the sum of two ionic radii is, however, difficult to do in an entirely satisfactory way. One procedure is to look for the minimum value in the electron density distribution between neighboring ions, but apart from the experimental difficulties involved such measurements do not really support the assumption of constant radius. Sets of ionic radii are therefore all based ultimately on somewhat arbitrary assumptions. Several different sets have been derived, the most widely used being those of Shannon and Prewitt, based on the assumed radius of 140 pm for O in six-coordination. Values for a selection of ions are shown in Table 1. 

Figure 18 schematically displays parts of CPK packing model for [Pt(en)2][PtCl2(en)2](20)4 in the yz plane (direction of coordination) and in the jny plane, respectively [95]. A minimum distance between aligned anionic head groups of double-chained amphiphiles is estimated as 5 A from CPK molecular model, and this value matches well with the Pt -Cl-Pt distance d) in the onedimensional complex. Therefore, it is reasonable that the halogen-bridged mixed-valence complex can be well preserved in polyion complexes. 

K is the inverse radius of the ionic atmosphere d is the minimum distance between the anion and cation 8, is the solvent relative permittivity (dielectric constant)... 

Minimum distance between the anion and the cation [m] Activity of anions, A"(aq) [dimensionless]... 

J. Bjerrum (1926) first developed the theory of ion association. He introduced the concept of a certain critical distance between the cation and the anion at which the electrostatic attractive force is balanced by the mean force corresponding to thermal motion. The energy of the ion is at a minimum at this distance. The method of calculation is analogous to that of Debye and Hiickel in the theory of activity coefficients (see Section 1.3.1). The probability Pt dr has to be found for the ith ion species to be present in a volume element in the shape of a spherical shell with thickness dr at a sufficiently small distance r from the central ion (index k). 

From a qualitative point of view, a minimum difference in ionization constants is to be expected, because even though a molecule contains two equivalent ionizable protons, once one proton has been lost, the second is retained more strongly by an energy amounting to e jOr (where e is the electronic charge, D is the dielectric constant, and r is the distance between the proton and the charge on the add anion). Thus, for oxalic acid, Ky is about 1000 21 for adipic add, Ky is only about SK2 (nearly the factor of 4). The titration curve of an add in which Ky = 415 2 can be shown to be-identical in every respect to the titration curve of a monobasic acid of one-half its molecular wdght and with dissodation constant Kyjl. 

EPR signals for both the flavosemiquinone radical and the low-spin ferric heme have been reported (65, 78-82). The flavosemiquinone signal, which is easily observed at 123 K, shows a typical g value of 2.0039 0.002 (65). The bandwidth, which is around 15 G, is very like that of an anionic, or red, semiquinone (65). The EPR signal of the low-spin ferric heme can be observed at low temperatures ( 28 K) and shows g values of 2.99, 2.22, and 1,47 (65), which are similar to those found for cytochrome 65 (81). EPR rapid freezing studies have allowed the amounts of semiquinone and ferric heme to be monitored during reduction of the enzyme by L-lactate (66). This has proved to be extremely useful in the development of kinetic schemes to describe the flow of electrons in the enzyme. The distance between the prosthetic groups in H. anomala flavocytochrome 62 has been estimated from EPR experiments and spin-lattice relaxation measurements (82). Pyruvate was used to stablize the flavosemiquinone and the effect on the signal of this species from oxidized and reduced heme was measured. The results indicated a minimum intercenter distance of 18-20 A (82). 

An ionic solid should achieve maximum electrostatic stability when (i) each ion is surrounded by as many as possible ions of opposite charge, and (ii) the anioncation distance is as short as possible. There is, however, a play-off between these two factors. Consider an octahedral hole in a close-packed array of anions (see Topic D3) The minimum radius of the hole, obtained when the anions are in contact, is 0.414 times the anion radius. A cation smaller than this will not be able achieve the minimum possible anion-cation distance in octahedral coordination, and a structure with lower coordination (e.g. tetrahedral) may be preferred. These considerations lead to the radius ratio rules, which predict the likely CN for the smaller ion (usually the cation) in terms of the ratio r where... 

As long as we use the spherical ion model, the Coulomb interaction energy will obviously be at a minimum, and the molecule most stable, if the distance between the anions is as large as possible, i.e. if the molecule is linear. Would this stiU be so if we allow the ions to become polarized ... 

We suppose that the electrolyte contains n cations (or anions) per m, that the minimum possible distance between ions is d (hard sphere model) and that is the average distance between two ions 1 and 2. In a volume F= 1 m we then have (r,2> = (VI2ny ... 

The shortest cation-anion distance in an ionic compound corresponds to the sum of the ionic radii. This distance can be determined experimentally. However, there is no straightforward way to obtain values for the radii themselves. Data taken from carefully performed X-ray diffraction experiments allow the calculation of the electron density in the crystal the point having the minimum electron density along the connection line between a cation and an adjacent anion can be taken as the contact point of the ions. As shown in the example of sodium fluoride in Fig. 6.1, the ions in the crystal show certain deviations from spherical shape, i.e. the electron shell is polarized. This indicates the presence of some degree of covalent bonding, which can be interpreted as a partial backflow of electron density from the anion to the cation. The electron density minimum therefore does not necessarily represent the ideal place for the limit between cation and anion. 

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