Fuoss theory

Another defect problem to which the ion-pair theory of electrolyte solutions has been applied is that of interactions to acceptor and donor impurities in solid solution in germanium and silicon. Reiss73>74 pointed out certain difficulties in the Fuoss formulation. His kinetic approach to the problem gave results numerically very similar to that of the Fuoss theory. A novel aspect of this method was that the negative ions were treated as randomly distributed but immobile while the positive ions could move freely. 

The two curves in Fig. 2.14 are the relationships between log KA and log er for a 1 1 electrolyte. The solid curve was obtained by Bjerrum s theory [Eq. (2.17)] and the dotted curve by Fuoss theory [Eq. (2.19)], both assuming a=0.5 nm. The big difference between the two theories is that, according to Bjerrum s theory, ion association does not occur if r exceeds a certain value ( 50 in Fig. 2.14), although the value depends on the value of a. Both theories are not perfect and could be improved. In recent treatments of ion association, non-coulombic short-range interactions between ions are also taken into account [40]. By introducing non-coulombic interactions, W (r), Eq. (2.17) is modified to a form as in Eq. (2.20) ... 

Fig. 2.14 Comparison of the log /

Fuoss theory for ion association I.S.2d Galvani potential see potential galvanic cells 1.5.Se gases. 

Studies on ion-pair formation initiated by N. BJerrum were extended theoretically by Onsager and Fuoss, and the theory of ion-pair formation almost completed in the 1960 s. Since they were in US A, the studies on ion-pair formation were more actively carried out in USA than other pans of the world. Since the study does not need expensive tools, the work could be done in Japan by using the Onsager-Fuoss theory. 

In these equations the interionic and ion-solvent frictional effects have been separated. The former effect affects both kinds of ions equally and represents the electrophoretic and relaxation effects of the Onsager-Fuoss theory. The ion-solvent friction is unperturbed by these interactions and thus represents the free ion friction against a solvent at rest. 

The theoretical basis of his calculation is less secure than Bjerrum s, but his work had the merit of inspiring high precision work on the behaviour of electrolyte solutions over a range of relative permittivities. Bjenum s and Fuoss theories predicted different dependencies of association (sce Section 12.16). 

Consequently, Kq refers to particular configurations of encounter complexes with assigned equilibrium constant Kos (see Section 2.3.1). For small ligands, Ko has frequently been approximated by Kqs as estimated by the Fuoss theory. However, if L = H2P, it would be more appropriate to write... 

In spite of their limitations, the Onsager-Fuoss theory appears to be useful to theo-retioally estimate the diffusion eoefificients, of these electrolytes in aqueous solutions and thus, to contribute to a better understanding of the stracture of those systems. Because slight variations in this a parameter have little effect on the final results of the ionic-size values used in Eqs. (1) to (4) were obtained as average ones from those in the literature and ours calculated from MM methods. In addition, for all systems, the variation in the diffusion coefficient, D, is mainly due to the variation of the ZCj. contribution (attributed to the nonideal thermodynamic behavior) and, to a lesser extent, to the electro phoretic effect in the mobility factor,... 

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