Diffusion coefficients, molten salts

In the data compiled by Janz and Bansal, various methods for measuring diffusion coefficients in molten salts are mentioned. The methods may be broadly classified as electrochemical and analytical. However, some other methods have occasionally been employed. Various electrochemical methods were reviewed by Lesko. Tracer diffusion in molten salts was reviewed by Spedding in 1971, where some other methods were also mentioned. 

In experiments involving radiotracer measurements of diffusion in molten salt, the Stokes-Einstein equation has been found to be roughly applicable. For a series of ions, in molten salts it was found that the product D /T = 10 dyn mol . From this information, find whether the best form of the coefficient in this expression for this case is nearer to 6 or 4. 

Diffusivities in molten salts and metals are even more difficult to predict, and here one often resorts to an Arrhenius-type relation to express the strong temperature dependence of the diffusion coefficient, which is concealed in the viscosity of Equation 3.3a and Equation 3.3b ... 

The mobilities of ions in molten salts, as reflected in their electrical conductivities, are an order of magnitude larger than Arose in Are conesponding solids. A typical value for diffusion coefficient of cations in molten salts is about 5 X lO cm s which is about one hundred times higher Aran in the solid near the melting point. The diffusion coefficients of cation and anion appear to be about the same in Are alkali halides, wiAr the cation being about 30% higher tlrair Are anion in the carbonates and nitrates. 

Typical values of self-diffusion coefficients and mutual diffusion coefficients in aqueous solutions and in molten salt systems such as (K,Ag)N03 are of the order... 

A few more similar data compilations have been issued by Janz s group and also include diffusion coefficients.They have regarded KNO3 and NaCl as the standard molten salts at middle and high temperature ranges, respectively, and compiled data on various properties, together with their recommended values, in one volume. ... 

Some 30 years ago, transport properties of molten salts were reviewed by Janz and Reeves, who described classical experimental techniques for measuring density, electrical conductance, viscosity, transport number, and self-diffusion coefficient. 

Methods Used to Measure Diffusion Coefficients in Molten Salts ... 

Chronopotentiometry has been widely used to determine diffusion coefficients in molten salts. Chronopotentiometry is an experimental procedure in which the potential of an electrode is observed as a function of time during the passage of a constant current sufficiently large to produce concentration polarization with respect to the species undergoing electrochemical reaction. 

G. J. Janz and N. P. Bansal, J. Phys. Chem. Ref 11 (1982) 505 Molten Salts Diffusion Coefficients in Single and Multi-Component Salt Systems, American Chemical Society-American Institute of Physics-National Bureau of Standards, Washington, DC, 1982. 

Typical values of self-diffusion coefficients and mutual diffusion coefficients in aqueous solutions and in molten salt systems such as (K,Ag)N03 are of the order of 10 m s and the coefficients do not usually vary by more than a factor of 10 over the whole composition range [1, 2, 15]. From measurements in pure ionic liquids we have learned that their self-diffusion coefficients are only of the order of 10 m s From this point of view it is interesting to investigate systems of ordinary and ionic liquids. Figure 4.4-3 shows the results of first measurements in the methanol/[BMIM][PF6] system, which can be seen as a prototype for a system in which an organic and an ionic liquid are mixed. 

The Nernst-Einstein relation shows the dependence between the self-diffusion coefficient Dt and the equivalent conductivity A of molten salts ... 

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. 

In a molten salt solution of CdClj in KCl, radiotracer measurements of the diffusion coefficient of Cd at 470 °C showed the heat of activation to be 23.0 kJ moC. A rough calculation of the entropy of activation showed this to be small, about 41.8 J mol K ... 

Thus, T is the residence time, the time between hops, the time the two reactant particles have to decide whether to react. Near the melting point of a molten salt, the diffusion coefficient in solutes is on the order of 10" cm s". With I chosen as 3 x 10" cm (a typical value of the distance between sites within the molten salt structure), one obtains 10" s for the residence time, which is about 100 times longer than that in the gas phase at the same temperature and hence there is a hundredfold greater chance to react. 

Calculate the transport numbers of the cation and the anion in molten CsCl at 943 K. The experimental equivalent conductivity of the fused salt is 67.7 ohms cm equiv. The observed diffusion coefficients of Cs" and Cl ions in molten CsCl are 3.5 x 10 - and 3.8 x 10" cm s", respectively. (Contractor)... 

Assume one takes a 1 1 molten salt for which the increase of volume on melting is 20%, while the intemuclear distance shrinks by 5%. Calculate on the basis of simple statistics the fraction of paired vacancies. For simplicity, assume the radii of the cation and the anion are equal (as in KF) and use the Stokes-Einstein equation to calculate the diffusion coefficient of the ions and that of the paired vacancies. (The viscosity of KE at 1000 K is 1.41 centipoise the mean radius... 

In a number of articles, the Nernst-Einstein equation was used to correlate values of the electrical conductivity and the diffusion coefficients. The application of this equation to molten salts did not bring expected results as the electrical conductivity values calculated from the diffusion data are always higher than the experimental conductivity data. As a main reason for this difference, the presence of cavities in the melt is mentioned, which are sufficiently large so that both the cations and the anions could be placed in them. Such cavities are regarded as pair vacancies. If a pair jump of both kinds of ions using the pair vacancy takes place, both the atoms participate in the mass transfer and thus in the diffusion process, but not in the charge transfer. 

This is of course not the case when working with room temperature ionic liquid systems. Electrochemical and spectroscopic studies of cobalt, copper, and nickel, have been carried out in the AlClj-butylpyridinium chloride molten salt system. The direct current and pulsed current electrodeposition of Ni-Al alloys has also been shown in acidic AlCls-butylpyridinium chloride ionic liquids. This particular alloy has also been shown to be successful in AlCl3-[C2-mim]Cl ashave Co-Al andCu-Al. Electrochemical techniques can also be used to calculate the diffusion coefficients of metal ions. Table 21.2.6 shows the calculated diffusion coefficients and stokes-Einstein products of cobalt(II), copper(I), nickel(II) and zinc(II) in the 40-60 mol% [Cj-mimlCl-AlClj ionic liquid. 

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