Ionic solution theory

Friedman H L 1962 Ionic Solution Theory (New York Interscience)... 

Allnatt A 1964 Integral equations in ionic solution theory Mol. Phys. 8 533... 

Optimized convergence and application to ionic solution theory J. Chem. Phys. 55 1497... 

Conway, B. E., Ionic interactions and activity behaviour, CTE, 5, Chap. 2 (1982). Friedman, H. L., Ionic Solution Theory, Wiley-Interscience, New York, 1962. Harned, H. S., and B. B. Owen, The Physical Chemistry of Electrolytic Solutions, Reinhold, New York, 1950. 

Ionic Solution Theory, H. L. Friedman, Wiley, New York, 1953, is a standard work in the held, but is a bit mathematical and can be difficult to follow. An easier book to follow is Ions, Electrodes and Membranes (second edition) by Jin Koryta, Wiley, Chichester, 1992, and is an altogether more readable introduction to the topic. It can also be trusted with details of pH electrodes and cells. Its examples are well chosen, many being biological, such as nerves, synapses, and cell membranes. It is probably the only book of its kind to contain cartoons. 

The remainder of Section I is devoted to a rather brief review of earlier work in the field in order to gain a little perspective. In Sections II to IV the basic results of the cluster method are derived. In Section V a very brief account of the application of the formal equations to some systems with short-range forces is given. Section VI is devoted to a review of the application to systems with Coulomb forces between defects, where the cluster formalism is particularly advantageous for bringing the discussion to the level of modern ionic-solution theory.86 Finally, in Section VII a brief account is given of Mayer s formalism for lattice defects69 since it is in certain respects complementary to that principally discussed here. We would like to emphasize that the material in Sections V and VI is illustrative of the method. This is not meant to be an exhaustive review of results obtainable. 

For ionic defects the individual terms in the formal virial expansions diverge just as they do in ionic solution theory. The essence of the Mayer theory is a formal diagram classification followed by summation to yield new expansions in which individual terms are finite. The recent book by Friedman25 contains excellent discussions of the solution theory. We give here only an outline emphasizing the points at which defect and solution theories diverge. Fuller treatment can be found in Ref. 4. 

For simplicity we consider only the continuum limit (i.e. Mayer ionic solution theory). The last equation allows us to calculate the value of p which the association theory should predict in order to be compatible with the true value, which we assume to be given by the Mayer theory in the range considered. It is... 

Friedman, H. L., Ionic Solution Theory Based on Cluster Expansion Methods, Interscience Publishers, New York, 1962. 

Conformal ionic solution theory was the first theory applied to molten salts which rigorously took coulomb interactions into... 

Fig. 4. Comparison of activity coefficients of LiF obtained from liquidus temperatures of LiF in the LiF-KCl system with those calculated from the conformal ionic solution theory (CIS).

The proper treatment of ionic fluids at low T by appropriate pairing theories is a long-standing concern in standard ionic solution theory which, in the light of theories for ionic criticality, has received considerable new impetus. Pairing theories combine statistical-mechanical theory with a chemical model of ion pair association. The statistical-mechanical treatment is restricted to terms of the Mayer/-functions which are linear in / , while the higher terms are taken care by the mass action law... 

Manning, G. (1969c). Limiting laws and counterion condensation in polyelectrolyte solutions III. An analysis based on Mayer ionic solution theory. J. Chem. Phys. 51(8), 3249-3252. 

Note. The Debye length (LD), although not introduced into the present simplified discussion, is a parameter frequently referred to in the gas-sensor literature. It was originally introduced into ionic solution theory and later applied to semiconductor theory where it is especially applicable to semi con -ductor/metal and semiconductor/semiconductor junctions. It is a measure of the distance beyond which the disturbance at the junction has effectively no influence on the electron distribution and therefore closely related to d (see Eq. (4.49)). It is a material parameter given by LD = (j kl /e2(, )12 where cQ is the undisturbed electron concentration, essentially the extrinsic electron concentration in the case of doped n-type tin oxide, and the other symbols have their usual meaning.)... 

This position of ionic solution theory has, however, a challenger, " and, during the 1970s and 1980s, it was this radically different approach to ionic solution theory... 

What is the significance of these results on dimer and trimer formation for ionic solution theory In the post-Debye and HUckel world, particularly between about 1950 and 1980 (applications of the Mayer theory), some theorists made calculations in which it was assumed that aU electrolytes were completely dissociated at least up to 3 mol dm. The present work shows that the degree of association, even for 1 1 salts, is -10% at only 0.1 mol dm . One sees that these results are higher than those of the primitive Bjerrum theory. 

IONIC SOLUTION THEORY IN THE TWENTY-FIRST CENTURY... 

However, there is no doubt that from the 1980s on, a very hopeful type of development has been taking place in ionic solution theories. It is the correlation function approach, not a theory or a model, but an open-ended way to obtain a realistic idea of how an ionic solution works (Fig. 3.58). In this approach, pair correlation functions that are experimentally determined from neutron diffraction measurements represent the truth, without the obstructions sometimes introduced by a model. From a knowledge of the pair correlation function, it is possible to calculate properties (osmotic pressure, activities). The pair correlation function acts as an ever-ready test for new models, for the models no longer have to be asked to re-replicate specific properties of solutions, but can be asked to what degree they can replicate the known pair correlation functions. 

It is rather easy to make a list of milestones in ionic solution theory ... 

There is yet a further stage for ionic solution theory that will not be presented here beeause it is still fragmentary in achievement and densely complex in the physical theory that underlies it. This final stage is the quantum mechanieal one, in which an attempt is made to deseribe a solution at the Sehrodinger equation level. Such work has been pioneered by Clementi and his colleagues since the mid-1980s. 

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