Conductance theories 1957, Fuoss

Other workers have also discussed this concept of a contact ion pair , but detailed analysis indicates that there is a considerable degree of latitude in what physically is meant by a contact ion pair . Fuoss revisited this dilemma in his 1978 conductance theory (see Section... 

Section 12.9 on post 1950 modem conductance theories for symmetrical electrolytes and Section 12.10 on Fuoss-Onsager s 1957 conductance equation for symmetrical electrolytes can be omitted until earlier sections are assimilated. These two sections deal with more up to date work which is able to be formulated in a straightforward analytical equation. The development behind these theories is complex and only a brief overview of the ideas behind these theories is given. Nonetheless the Fuoss-Onsager 1957 equation has been much used to analyse experimental data. How this is carried out in practice is given in Sections 12.10.1 to... 

The early conductance theories given by Debye and Hiickel in 1926, Onsager in 1927 and Fuoss and Onsager in 1932 used a model which assumed all the postulates of the Debye-Hiickel theory (see Section 10.3). The factors which have to be considered in addition are the effects of the asymmetric ionic atmosphere, i.e. relaxation and electrophoresis, and viscous drag due to the frictional effects of the solvent on the movement of an ion under an applied external field. These effects result in a decreased ionic velocity and decreased ionic molar conductivity and become greater as the concentration increases. 

In aU of these modifications no account was taken of the need to consider cross terms arising from the effect of relaxation on the electrophoretic effect, and from the effect of electrophoresis on relaxation, but they did hint at the form of the conductance theory put forward later by Fuoss and Onsager. 

The first chapter of the book sets the stage for many of the topics dealt with later, and, in particular, is a prelude to the development of the two major theoretical topics described in the book, namely the theory of non-ideality and conductance theory. The conventional giants of these fields are Debye and Hiickel with their theory of non-ideality and Debye, Huckel, Fuoss and Onsager with their various conductance equations. These topics are dealt with in Chapters 10 and 12. In addition, the author has included for both topics a qualitative account of modern work in these fields. There is much exciting work being done at present in these fields, especially in the use of statistical mechanics and computer simulations for the theory of nonideality. Likewise some of the advances in conductance theory are indicated. 

Both treatments make use of the same general equations for transport processes in fluids and of the same model to represent the electrolyte solution. However, they lead to somewhat different results due to the manner in which the problem is approached and because of the different boundary conditions employed to evaluate the constants which appear upon integration of the differential equations. We shall give here an account of the conductance theory based on the mathematical approach used by Pitts and shall point out the differences and agreements between his treatment and that of Fuoss and Onsager. The mathematical technique used by the latter authors has been given in detail by Fuoss... 

The Fuoss-Onsager-Skinner equation satisfactorily describes the electrolytic conductance of lithium bromide in acetone. Values of 198.1 0.9 Q l cm2 eq l and (3.3 0.1) X I03 are established for A0 and KA, respectively, at 25°C furthermore, a value of 2.53 A is obtained for the sum of the ionic radii ( ). When bromosuccinic acid is added to 10 5 N lithium bromide in acetone, there is a decrease in the specific conductance of lithium bromide rather than the increase that is observed at higher concentrations. As the concentration of bromosuccinic acid is increased, the values obtained for A0 and KA decrease, while those for a increase when the bromosuccinic acid and acetone are considered to constitute a mixed solvent. These results do not permit any simple explanation. When bromosuccinic acid and acetone are considered a mixed solvent, the Fuoss-Onsager-Skinner theory does not describe the system. 

A test of equation (79), based on the theory of ion association, is provided by the measurements of Fuoss and Kraus of the conductance of tetraisoamylammonium nitrate in a series of dioxane-water mixtures of dielectric constant ranging from 2.2 to 78.6 (cf. Fig. 21) at 25 . From the results in dilute solution the dissociation constants were calculated by the method described on page 158. 

The interpretation of the branch, where the WP increases, more sophisticated. A minimum of WP implies a redissociation of the pairs and/or the formation of charged ion clusters. Fuoss and Kraus [41] assumed the formation of charged ion triplets. Recent theory attributes the increase of the conductivity to redissociation, resulting from the interactions of the free ions with the ion pairs and the increase of the dielectric permittivity due to the formation of ion pairs that causes a decrease of the association constant [38],... 

Fuoss developed a new theory of ion association in 1958 [27] which overcame some of the difficulties associated with the Bjerrum approach. The cations in the solution were assumed to be conducting spheres of radius a and the anions to be point charges. The ions are assumed to be immersed in a dielectric continuum of permittivity Sj. Only oppositely charged ions separated by the distance a are assumed to form ion pairs. The resulting expression for the association constant is... 

However, this must be seen in the context of the considerable impetus and stimulus which the Fuoss-Onsager treatment of conductance has given to the experimentalist who has striven to find more and more precise methods with which to test the various theories outlined. This has resulted in very considerable improvements being made to conductance apparatus. It has also placed a very detailed emphasis on obtaining precision and accuracy of the measurements themselves. This has been of considerable import when making measurements at very low concentrations where the experimental difficulties are greatest, but where it is important to test the theory in regions where it is expected to be valid. Such expectations have been vindicated by precision low concentration work where confidence can be placed in the accuracy of the conductance equation. This is reminiscent of the impetus to experimentalists after the Debye-Hiickel equation had been put forward. 

Solid electrolytes are not usually solutions of a conducting solute in a solvent matrix. Liquid electrolyte solutions are often sufficiently dilute (1-10 millimolar) to be described by the textbook theories of Debye-Hiickel or Onsager and oppositely charged ions are sufficiently dispersed for interaction between anions and cations to be minimized. By contrast, molten salts are very concentrated (typically 2-20 molar), ion-ion interactions are pronounced, and alternative theories such as that of Fuoss [105] are required. Polymer electrolytes typically have [repeat unit] [cation] ratios, n, in the range 8 to 30, corresponding to 0.7 to 2.5 molar for PEOn LiC104 [106], and ion clustering is an important feature of their behaviour. To account for both the ion-polymer and ion-cluster interactions, Ratner and Nitzan have developed dynamic percolation theory [107]. 

Several extensions and modifications of the electrolyte theory in the first half of the twentieth century should be mentioned Bjeiium [14] introduced the concept of limited electrostatic dissociation (ion pair formation), Onsager and Fuoss extended the DH approach and the ideas of Debye about the electrophoretic and the relaxation effect on transport properties such as electrical conductivity and diffusion coefficients [15]. As already mentioned, the DH description is also the basis of one of the two constituting parts of the DLVO theory in colloidal chemistry. 

Fuoss RM (1978) Review of the theory of electrolytic conductance. J Soln Chem 7 771-782. doi 10.1007/ BF00643581... 

---