Nernst-Einstein deviations from

Note The values in the parentheses are experimental results.A j is the deviation from the Nernst-Einstein equation expressed by K= (F2/VmRTXz+D+ 1 - A ). 

W. Nernst and F. A. Lindemann, Berl. Ber., 1911, p. 494, discuss the deviations from Einstein s result. P. Ehrenfest, Welche Rolle spielt die Lichtquantenhypothese in der Theorie der W rme-strahlung Ann. d. Phys., 36 (1911), 91, studies the possibility of a generalization of Planck s assumption in the field of black-body radiation. 

The above argument brings out an important point about the limitations of the Nernst-Einstein equation. It does not matter whether the diffusion coefficient and the equivalent conductivity vary with concentration to introduce deviations into the Nernst-Einstein equation, D and A must have different concentration dependencies. The concentration dependence of the diffusion coefficient has been shown to be due to nonideality (f 1), i.e., due to ion-ion interactions, and it will be shown later that the concentration dependence of the equivalent conductivity is also due to ion-ion interactions. It is not the existence of interactions perse that underlies deviations from the Nernst-Einstein equation otherwise, molten salts and ionic crystals, in which there are strong interionic forces, would show far more than the observed few percent deviation of experimental data from values calculated by the Nernst-Einstein equation. The essential point is that the interactions must affect the diffusion coefficient and the equivalent conductivity by different mechanism and thus to different extents. How this comes about for diffusion and conduction in solution will be seen later. 

This explanation is all very well for the liquid sodium chloride type of case, but deviations from the predictions of the Nernst-Einstein equation occur in dilute aqueous solutions also, and here the + and - ions are separated by stretches of water, and ion pairs do not form significantly until about 0.1 M. 

Because deviations from the Nernst-Einstein equation are so widespread, and because the reasoning that gives rise to the equation is phenomenological, it is better to work out a general kind of noncommittal response—one that is free of a specific model such as that suggested in the molten salt case (see Section 5.2). The response... 

The Nernst-Einstein reiation can be tested by using the experimentally determined tracer-diffusion coefficients D,. to calcuiate the equivalent conductivity A and then comparing this theoreticai vaiue with the experimentally observed A. It is found that the vaiues of A caicuiated by Eq. (5.61) are distinctly greater (by 10 to 50%) than the measured values (see Table 5.27 and Fig. 5.33). Thus there are deviations from the Nernst-Einstein equation and this is strange because its deduction is phenomenological. ... 

In deviations from the Nernst-Einstein equation in a molten salt, one hypothesis involved paired-vacancy diffusion. Such a model implies that holes of about twice the average size are available at about one-fifth the frequency of averagesized holes. Use the equation in the text for the distribution of hole size to test this model. 

The deviation of the actual molar conductivity measured through electrochemical techniques to that obtained from the diffusion coefficients (PFG-NMR measurements) and Nernst-Einstein equation quantifies the extent of interactions between the ions and is defined as the ionicity ratio (Ajinp/A MR). It must also be noted that the theory does not implicitly define the origins of any deviation or allow for the treatment of any concentration dependence. 

Kubo type relations ( ). By expansion it may be separated into terms containing only the autocorrelation function of a given particle and terms contain crosscorrelation functions. The latter can be identified as being the source of deviations from the Nernst-Einstein equation.(2)... 

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