Ionic model, failure

The acquisition of such an extensive set of properties for this class of molecules has prompted a number of authors to explore the use of ionic models for systematically characterizing these properties. We have recently reviewed some of the successes and failures of these models,(2.) Including references to the various authors. 

The fact that radius ratio arguments do not always predict the correct structure is sometimes regarded as a serious failure of the ionic model, and an indication that nonionic forces must be involved in bonding. Given the uncertainties in definition of ionic radii, however, and the fact that they are known to vary with CN, it is hardly surprising that predictions based on the assumption of hard spheres are unreliable. It also appears that for some compounds the difference in energy between different structure types is very small, and the observed structure may change with temperature or pressure. 

The most important deficiency in the models developed so far concerns the failure to take account of interactions between the mobile ions. As the ionic concentration in polymer electrolytes is frequently greater than 1.0moldm and the mean distance between ions of the order of 0.5-0.7 nm, then relatively stong coulombic interactions exist which must affect ion motion. Ratner and Nitzan have begun to address this problem from a theoretical viewpoint (Ratner and Nitzan, 1989) although it has not been fully developed yet to give a complete description of conduction in ion associated polymer electrolytes. The interactions between ions which lead to ion association are discussed further in the following section. 

From the theoretical perspective, the need to assess the nature of the Coulom-bic phase transition has led to many activities. Thus, most theories have relied on the RPM as a generic model for the ionic phase transition. From the various theoretical tools for deriving the EOS, only MSA- and DH-based approaches have found wide application. Applications of the HNC, which is a standard theory in general electrolyte thermodynamics, have remained scarce because of numerical problems when approaching phase transitions. However, pure DH and MSA theory are linear theories that fail at low T. It is known for a long time that, at least in parts, this failure can be remedied by accounting for ion pair formation. More recently, it has become clear that at near- and subcritical temperatures, free-ion-ion-pair and ion-pair-ion-pair interactions play a crucial role. Just in this regard, DH theory seems to provide a particularly flexible and transparent scheme for such theoretical extensions. 

An alternative approach is to prepare a reactive-ion surfactant for which the counterion is itself the reactant and inert counterions and interionic competition are absent (21-23). In principle, this method simplifies estimation of the concentration of an ionic nucleophile, for example, in the micellar pseudophase. Both these treatments of ionic reactions involve assumptions and approximations that seem to be satisfactory, provided that ionic concentrations are low, e.g., <0.1 M. These assumptions and approximations fail when electrolyte concentrations are high (24-25). A more rigorous treatment is based on application of the Poisson-Boltzmann equation in spherical symmetry (26-28), and this treatment accounts for some of the failures of the simpler models (29, 30). 

Perez-Hemandez and Blum" have recently obtained essentially analytic expressions for in the MSA, and quantitative results are given by Veri-cat et al. The MSA results are found to be qualitatively similar to those described above, with decreasing as the ionic concentration is increased. Vericat et al. also compare the MSA results for with experimental values of figoL foi" aqueous solutions. They show that if one is willing to treat the dipole moment of water as an adjustable parameter, rough agreement can be obtained. However, in view of the simplicity of the model, the likely inaccuracy of the MSA (cf. Section III.D), and the failure to account for the dynamic contributions to Esol> it is difficult to reach any conclusions from such comparisons. 

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