Ionic transport number

Various methods are available for determining the solvation number hj and (or) the radius of the primary solvation sheath (1) by comparing the values of the true and apparent ionic transport numbers, (2) by determining the Stokes radii of the ions, or (3) by measuring the compressibility of the solution [the compressibility decreases... 

During electrolysis there is no change in composition of an individual melt close to the electrode surfaces only its quantity (volume) will change. The resulting void space is filled again by flow of the entire liquid melt mass. This flow replaces the diffusional transport of ions customarily associated with aqueous solutions. This has particular consequences for the method used to measure ionic transport numbers ... 

The resolution of this apparent contradiction to the thermodynamic expectations for this transfer is that the ionic membrane will always contain a small electron/positive hole component in the otherwise predominantly ionic conductivity. Thus in an experiment of very long duration, depending on the ionic transport number of the membrane, the eventual transfer would be of both oxygen and sulphur to the manganese side of the membrane. The transfer can be shown schematically as... 

Figure 6.2 Ionic transport number for oxide ion conductivity in the pyrochlore phases Lu2Ti207, Lu2.096Tii.904O6.952> and Lu2286Tii.7i406.857- [Data adapted from A. V. Shlyakhtina, J. C. C. Abrantes, A. V. Levchenko, A. V. Knot ko, O. K. Karyagina, and L. G. Shcherbakova, Solid State Ionics, 177, 1149-1155 (2006).]...

Permselectivity of a nonideal membrane system is characterized by ionic transport numbers t , defined as... 

Here t is the ionic transport number, a is the electrolyte activity, and the subscripts 1 and 2 refer to the left and right sides of the junction. For Omxi = mx2. Ej(i)=0. If the experimental (actual) variations in component (i), obtained by changing the ratio C /c2, are plotted against the values calculated by Eq. (6.16), lin-... 

As described in Section 5.8, the conductivity of electrolyte solutions is a result of the transport of ions. Thus, conductimetry is the most straightforward method for studying the behavior of ions and electrolytes in solutions. The problems of electrolytic conductivity and ionic transport number in non-aqueous solutions have been dealt with in several books [1-7]. However, even now, our knowledge of ionic conductivity is increasing, especially in relation to the role of dynamical solvent properties. In this chapter, fundamental aspects of conductimetry in non-aqueous solutions are outlined. 

The steady-state result (Eq. (77)) can be directly used to separate ionic and electronic conductivities the disadvantage of the technique is that it presupposes gas-separation. If not special measures are taken, it becomes unreliable for the ionic transport number less than 1%. Thus, this method well complements the Wagner-Hebb method which is very sensitive to small transference numbers. The partial conductivities of PbO shown in Figure 48 have been de-convoluted by the emf technique just described.3... 

The second component, Eu (s), is independent of the electrolyte concentration, but it depends on the ionic transport numbers in both solvents and on the difference between the standard chemical potentials of ions in both solvents. In this case also, an equation which describes Eu (s) was given [47] however, it has only a qualitative significance. 

The phenomenological coefficients may be related to the diffusion coefficients or to the mobility of the ions (equation (6.7.21). In the present case, they can be related to the ionic transport numbers because... 

One promising group of solid electrolytes are the apatite-type silicates Aio x (SiO4)6O2 8 (where A = rare- and alkaline-earth cations). These exhibit a high ionic transport number, a moderate thermal expansion, and show no chemical reactivity with the cathode materials [41]. 

Air, O2, N2 and H2 were used as gas 1 or gas 2, in wet or dry states. The relevant ionic transport number is then obtained by comparing the measured emf with the predicted emf from the Nernst equation. 

In a recent reinvestigation with a-Tel as a solid electrolyte the theoretical e.m.f. of the difference cell E3 was found to be shifted to higher values, which implies a decrease in the partial iodine ionic conductivity from the ionic transport number 0.8-0.9 to 0.05-0.1. 

In electroanalysis, Eq. (23) forms the basis of highly sensitive techniques of potentiometric titration. The practical apphcations are presented by numerous potentiometric sensors, particularly biosensors [71-74]. The potential measurements in microheterogeneous media (microemulsions anionic, cationic and nonionic micelles) were worked out recently [75]. A separate field is the potentiometric studies of liquid/liquid junctions directed to the determination of ionic transport numbers. 

In this electrolyte with only two ions with identical concentrations, the equation for the junction voltage gets even simpler if one can assume that the ionic transport numbers are identical at all points throughout the system ... 

Fig. 4.2. (a) Schematic representation of electrolytic domain, i.e. relative electronic (for instance n and p type for ZrOj Ca) and ionic conductivity as a function of partial pressure pXj of the more volatile element (e.g. Oj or Ij). Dotted zone corresponds to a mixed conduction domain where the ionic transport number (tj) goes from 0 to 1 (with permission). The Agl area is limited by the a-p transition and by melting on the low and high temperature sides, respectively, (b) Schematic defect structure of an oxide M2O3 as a function of the water pressure. The oxide is dominated by anti-Frenkel defects and protons ([H ]) and doped with cations, concentration of which is assumed to be constant ([MI ]). Metal vacancies are shown as examples of minority defects. 

The hydrogen bond and protonic species by the ionic transport number ti. ... 

The ionic transport number is directly related to the utilization of the given material as electrolyte or insertion electrode. The + <7 ) ratio is usually of the order of 10" to 10" if the material is supposed to be used as electrolyte. Its measurement is not straightforward and generally has not been made for protonic conductors. 

The similarity in the ionic transport mechanism in organic liquid electrolytes and solid polymer electrolytes is reflected in the ionic transport numbers measured in the two media. Table 3.5 lists the transport numbers for Li in LiC104 solutions in propylene carbonate (PC) and propylene carbonate/dimethoxy ethane (PC/DME) mixtures [26]. The t+ in PC/LiC104 is 0.28 which increases to between 0.40 and 0.50 with the addition of DME. This increase in t+ in PC/DME mixtures may reflect a change in the solvation characteristics of Li, and/or ionic species present, with the addition of DME. It is then possible that a range of cation transference numbers between 0.2 and 0.6 measured in polymer electrolytes is a reflection of the coordination properties of the particular polymer host with Li" and the nature of the ionic species present. 

The ionic transport numbers for alkaline PVA-based SPE are very important because the high anionic transport number of SPE can limit the carbonation problems [56]. The anionic transport number (f) was measured by the dynamic Hittorf s method [57]. A test cell, as shown in Fig. 11, with two Pt electrodes was made for electrolysis and the electrolysis current was imposed by a power supply. All PVA-based polymer electrolyte membranes were located and fixed at two separated compartments with the same 1 M KOH solution. The reaction occurred at the Pt-cathode, producing O2, H2 and OH while consuming water and OH . The balance of OH ions in each compartment led to OH transport number after a fixed amount of charge was passed through the polymer membranes. 

Figure 12. The alkali metal salt effect on ionic transport number for alkaline PVA solid polymer electrolyte.

The mobility of the electronic charge carriers is much greater than that of the ions. Therefore, despite the low concentration of electrons, when the oxygen partial pressure is very low the electronic partial conductivity will be of the order of the ionic partial conductivity. The following equation may then be written for the ionic transport number [29] ... 

If the predominant migrating species, cation or anion, is known, e.g. from marker movement studies, the ionic transport number can... 

We can also deduce from it the ionic transport number t ... 

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