Transport number of ion

It must be pointed out that in a diffusion layer where the ions are transported not only by migration but also by diffusion, the effective transport numbers t of the ions (the ratios between partial currents ij and total current t) will differ from the parameter tj [defined by Eq. (1.13)], which is the transport number of ion j in the bulk electrolyte, where concentration gradients and diffusional transport of substances are absent. In fact, in our case the effective transport number of the reacting ions in the diffusion layer is unity and that of the nonreacting ions is zero. 

To estimate and /iD, it is necessary to estimate the electrolyte concentrations at the membrane surfaces. On the assumption that the boundary layers established are invariant, such concentrations can be calculated on the basis of the bulk concentrations, current density, transport number of ions, and mass transfer coefficient (km), via Eq. 15. 

The limiting current density is determined by concentration-polarization effects at the membrane surface in the diluate containing compartment that in turn is determined by the diluate concentration, the compartment design, and the feed-flow velocity. Concentration polarization in electrodialysis is also the result of differences in the transport number of ions in the solution and in the membrane. The transport number of a counterion in an ion-exchange membrane is generally close to 1 and that of the co ion close to 0, while in the solution the transport numbers of anion and cations are not very different. 

Tubandt was a pioneer of - solid state electrochemistry. He introduced a methodology to determine the - transport numbers of ions in -> solid electrolytes [i], which is now referred to as -> Tubandt method. Together with his co-workers he performed seminal studies of conductivities and transport numbers of solid electrolytes, e.g., of silver, lead, and copper halides, and silver sulfide. He showed for the first time that the entire dark current of silver bromide is transported by silver ions, and also that slightly below the melting point silver iodide has a higher conductivity than the melt. 

In foams with charged gas/liquid interfaces, as in other disperse systems, various electrokinetic phenomena are possible to occur. Such are the change in the transport numbers of ions, electroosmosis, streaming potential and surface conductivity. While these phenomena are largely studied in disperse systems with solid disperse phase, the first electrokinetic observations in foams have been reported only recently. 

Fig. 32.—Tubandt s method for measurement of transport numbers of ions in a-Agl.

R. Yamane, T. Sata, Y. Mizutani and Y. Onoue, Concentration polarization phenomena in ion-exchange membrane electrodialysis. II. The effect of the condition of the diffusion-boundary layer on the limiting current density and on the relative transport numbers of ions, Bull. Chem. Soc. Jpn., 1969, 42, 2741. 

Outline two important methods for determining transport numbers of ions. 

The measurements of ion transport numbers made by method of EMF and by sign of thermo-electric force reveal, that in all studied materials at Po2 > 10 Pa and in air the electronic conductivity of p-type (hole conductiviy) predominates, and at P02 < 10-1 Pa the electrical conductivity is predominantly ionic. The transport number of ions f alters depending on oxygen partial pressure, temperature and doping from 0,9 down to 0,1. 

Transport numbers of ions composing some commonly used solutions are suimnarized in Table 4. Finally, Table 5 provides the results of the evaluation of thermodiffusion potentials by Eq. (98), and using the parameters in Tables 3 and 4. 

It is also important to note that the distribution of the common ion(s) accounts for the potential difference established at the liquid/liquid interface. Diffusion potentials can also play a part, but the potential differences derived in the above expressions are equilibrium values arising because of the differences in solvation of the participating ions. As a historical note, some of the earliest experiments on immiscible electrolyte phases were performed with the aim of establishing transport numbers of ions, using a variant of the concentration cell, with an immiscible liquid separating the two aqueous phases (33). 

Subsequently, Ezis et al. studied the dependence of the transport number of ions on composition x in Pb(ZrxTii x)03 in detail using an electrochemical oxygen concentration cell [8]. Their experiment showed that the transport... 

The Electrolyte material must possess high ionic conductivity and no electronic conductivity. The transport number of ions should be close to unity whereas it should be zero (ideally) for the electrons. The oxide ion conductivity is >10 S/cm for the cell operating temperamre. 

---