Idealized ion pair

Fig. 4.19 Polarization effects (a) idealized ion pair with no polarization, (b) mutually polarized ton psir, (c) polarization sufficient to form covalent bond. Dashed lines represent hypothetical unpdarized tons...

The latter approach was championed by Fajans and is embodied in Fajans rules, whose basic premise is summarized in Fig. 4.2. In Fig. 4.2a an idealized ion pair is shown for which the covalent character is nonexistent (i.e., the ions are assumed to be hard spheres). In Fig. 4.2 > some covalent character is imparted by shifting the electron cloud of the more polarizable anion toward the polarizing cation. In the extreme case that the cation is totally embedded in the electron cloud of the anion (Fig. 4.2c) a strong covalent bond is formed. The extent to which the electron cloud is distorted and shared between the two ions is thus a measure of the covalent character of that bond. The covalent character thus defined depends on three factors ... 

Here d is the disparity between the free energy per ion pair added to the non-ideal solution and the free energy per ion pair added to the corresponding ideal solution. It is the disparity between the communal term in the free energy and the cratic term in the free energy. In the solution... 

Therefore, an ideal polymer electrolyte must be flexible (associated with a low Tg), completely amorphous, and must have a high number of cation-coordination sites to assist in the process of salt solvatation and ion pair separation (see Table 11). A review on this subject has been recently published by Inoue [594]. 

All these methods give similar results but their sensitivities and resolutions are different. For example, UV-Vis spectrophotometry gives good results if a single colorant or mixture of colorants (with different absorption spectra) were previously separated by SPE, ion pair formation, and a good previous extraction. Due to their added-value capability, HPLC and CE became the ideal techniques for the analysis of multicomponent mixtures of natural and synthetic colorants found in drinks. To make correct evaluations in complex dye mixtures, a chemometric multicomponent analysis (PLS, nonlinear regression) is necessary to discriminate colorant contributions from other food constituents (sugars, phenolics, etc.). 

Yakov Frenkel showed in 1926 that ideal crystals could not exist at temperatures above the absolute zero. Part of the ions leave their sites under the effect of thermaf vibrations and are accommodated in the interstitial space, leaving vacancies at the sites formerly taken up. Such point defects have been named Frenkel defects. These ideas were developed further by Walter Schottky in 1929, who pointed out that defects will also arise when individual ions or ion pairs are removed from the bulk... 

Therefore the lattice-gas model has proved most useful for the study of those processes in which the ionic double layer plays a major role, and there are quite a few. So it has been used to investigate the interfacial capacity, electron and ion-transfer reactions, and even such complex processes as ion pairing and assisted ion transfer. Because of its simplicity we carmot expect this model to give quantitative results for particular systems, but it is ideally suited to qualitative investigations such as the prediction of trends and orders of magnitude for various effects. 

Eqs. (15), (17), and (21) can be used to define other observable quantities, such as relative surface excess concentrations of ions, which also comprise the contributions from the free ionic and ion-pair surface excesses, e.g., for the ideally polarized ITIES,... 

The popularity of reversed-phase liquid chromatography (RPC) is easily explained by its unmatched simplicity, versatility and scope [15,22,50,52,71,149,288-290]. Neutral and ionic solutes can be separated simultaneously and the rapid equilibration of the stationary phase with changes in mobile phase composition allows gradient elution techniques to be used routinely. Secondary chemical equilibria, such as ion suppression, ion-pair formation, metal complexatlon, and micelle formation are easily exploited in RPC to optimize separation selectivity and to augment changes availaple from varying the mobile phase solvent composition. Retention in RPC, at least in the accepted ideal sense, occurs by non-specific hydrophobic interactions of the solute with the... 

The subscripts i and x label the ionic constituents of the ion pair and aixm refers to the activity of the ion pair in the membrane phase. At a constant counter-ion activity, axw, and for the ideal case that yiw and yix = 1, equation (25) can be converted to the commonly defined distribution ratio Dixmw ... 

In the o.s. reaction, the ion pair A+ - B is formed in a first step. The corresponding equilibrium constant can usually be obtained from simple electrostatic models. In this "ideal" case specific chemical interactions can be neglected and the rate constant of the E.T. step follows the theory of R.A. Marcus (see for example Marcus, 1975, or Cannon, 1980). In the i.s. reaction each of the three steps in reaction (9.2) may determine the reaction rates. The lability of the coordinated ligands at the... 

The theory proposed by Debye and Huckel dominated the study of aqueous electrolytes from around 1920 to near the end of the 1950 s. The Debye-Huckel theory was based on a model of electrolyte solutions in which the ions were treated as point charges (later as charged spheres), and the solvent was considered to be a homogeneous dielectric. Deviations from ideal behaviors were assumed to be due only to the long range electrostatic forces between ions. Refinements to include ion-ion pairing and ion... 

When solvated ions migrate within the electrolyte, the drag force applied by the surrounding solvent molecules is measured by solvent viscosity rj. Thus, in a solvent of lower viscosity, the solvated ions would move more easily in response to an applied electric field, as expressed by the Einstein—Stokes relation (eq 3). Solvents of low viscosity have always been considered the ideal candidates for electrolyte application however, their actual use was restricted because most of these solvents have low dielectric constants (Tables 1 and 2) and cannot dissociate ions effectively enough to prevent ion pairing. 

A simple mathematical treatment based on this model successfully reproduced the variation in ion conductivity with solvent composition as observed in experiments on numerous different systems. It also proposed that, in an ideal situation where no ion pair formation is present, the change in ion conductivity should follow a linear relation as predicted by the semiempirical Walden s law ... 

Numerous X-ray investigations have unravelled the solid state structure of contact and solvent-separated ion pairs. It was therefore considered to be of interest to evaluate also the potential of solid state NMR as a tool for the investigation of this structural problem. In addition to the study of chemical shifts discussed above (Section II.B), the quadrupole coupling constant of the nuclide Li, x( Li), was expected to be an ideal sensor for the bonding situation around the lithium cation because, due to its dependence on the electric field gradient, the quadrupolar interaction for this spin-3/2 nucleus is strongly influenced by local symmetry, as exemplified in Section II.C.3. This is also shown with some model calculations in Section ILF. 

When ions of valence 2 or higher are used as an electrolyte in the mobile phase and if this ion is a counter ion to the analyte or pairing ion in ion-pair chromatography. E.g., if tetrabutylammonium ion is used as a pairing ion at pH=9 in the presence of PO in the electrolyte, it will probably not behave as ideally as at pH=2 where phosphate will be in the H2PO4 form. 

The nature of the active species in the anionic polymerization of non-polar monomers, e. g. styrene, has been disclosed to a high degree. The kinetic measurements showed, that the polymerization proceeds in an ideal way, without side-reactions, and that the active species exist in the form of free ions, solvent-sparated and contact ion pairs, which are in a dynamic equilibrium (l -4). For these three species the rate constants and activation parameters (including the activation volumes), as well as the rate constants and equilibrium constants of interconversion have been determined (4-7.) Moreover, it could be shown by many different methods (e. g. conductivity and spectroscopic methods) that the concept of solvent-separated ion pairs can be applied to many ionic compounds in non-aqueous polar solvents (8). 

---