Measuring Transport Numbers in Mixtures

Internal or external mobilities in additive binary systems provide more heuristic information than in pure salts. For pure salts, the only parameter that can be obtained easily is the temperature, while detecting a change in pressure needs a difficult technique as well as specialized apparatus. However, in additive binary systems, where the composition can be easily varied, two mobilities can be compared under the same condition. 

For obtaining internal or external mobilities, the corresponding transport numbers are usually measured. There are several methods for determining transport numbers in molten salts that is, the Kleimn method (countercurrent electromigration method or column method), the Hittorf method (disk method), the zone electromigration method (layer method), the emf method, and the moving boundary method. These are described in a comprehensive review.  

There is difficulty in defining the absolute mobilities of the constituent ions in a molten salt, since it does not contain fixed particles that could serve as a coordinate reference. Experimental means for measuring external transport numbers or external mobilities are scarce, although the zone electromigration method (layer method) and the improved Hittorf method may be used. In addition, external mobilities in molten salts cannot be easily calculated, even from molecular dynamics simulation. 

Klemm has proposed defining internal mobility by reference to one defined ion of the system, such as the anion. In the case of pure salt, the internal transport number of the cation is then unity. In the case of a mixture, the internal mobility Uj is related to the internal transport number 

The internal transport numbers may be measured most accurately and precisely by the Klemm method, which was developed for the purpose of isotope separation. This method has the following merits (1) It is insensitive to a small amount of impurities, such as water. (2) Even in the region of very small concentration of an ion of interest, 12 can be measured accurately. (3) It can be applied to additive ternary systems. An apparatus for the Klemm method of measuring 12 in nitrate mixtures is shown in Fig. I. This cell developed for nitrates by Okada s group has the following advantages compared with other electromigration cells  

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