Anion transference number

Figure 3. Anion transference number as a function of concentration for sodium in NH% 0 calculated from the e.m.f. data of Kraus assuming activity coefficients of unity A from moving boundary experiments of Dye et al. (12).

The formula (VI-29) is valid for any uni-univalent electrolyte. It is evident from this formula that the sign of the liquid junction potential and also the orientation of the diffusion double layer, in respect to the double layer at the electrodes, depends on the relative magnitude of the anion and cation transference numbers. Should the anion transference number exceed that of cation... 

The ionic conductivity is due to both cation and anion species. The cationic transference number = (o / o. ). The anionic transference number x = 1 - x. Different ionic and electronic contributions to the total conductivity can be measured by an electrolysis experiment with the use of selective blocking electrodes which is for blocking all the conducting ion species but the desired one [16, 22].This is a direct current (d.c.) experiment. 

The range of the oxygen partial pressure where the rare earth doped ceria exhibits oxide anion conduction is limited over 10" Pa in P02 at 800°C (The oxide anion transference number decreased to 0.5 at this condition.), whereas the well-known stabilized zirconia shows the stable ion conduction between 10" and 10 Pa. This low stability against reducing atmosphere observed in the rare earth doped ceria is a fatal problem for applications. 

Because charged ion clusters can contribute to the conduction process, it becomes not only helpful but necessary to distinguish between the transport number of an individual species (e.g. t(M ), t(M2X ), etc.) and the cationic or anionic transference number, or t" which is the sum of the contributions of all the species with the same charge. Methods for measuring transport and transference numbers are discussed in detailed elsewhere [2, 20, 30, 50, 54, 108] and summarized in Table 1.2. 

The concentration cell techniques involve the use of concentration cells. Bouridah et aL (1986) measured the electromotive force (EMF) of suitable cells under conditions where no current was passed, and obtained the anion transference number from... 

Table 1. Transference Number of Cations, Anions t, and Electrons or Holes in Several Compounds...

Current flow through the frits is supported by ions. Cations and anions both support the virtual current by flowing in opposite directions, and the transference number of a particular ion is defined as the fraction of the total current it carries. The sum of all transference numbers then is necessarily unity. If the fraction of the virtual current carried by the cations equals the fraction carried by the anions then the solution is said to be equitransferent. 

Both the anions and cations can contribute to the current. In the absence of concentration gradients, the transference number relates the fraction of current carried by each species... 

It is worth mentioning that single-ion conductivities of lithium ions and anions at infinite dilution, and transference numbers of ligand-solvated lithium ions estimated therefrom, increase due to the replacement of more than one (generally four) solvent molecules. Table 6 demonstrates this beneficial feature. 

The synthesis of a variety of lithium ion conducting borosiloxane polymers have been reported.51 The incorporation of the Lewis acidic boron and silicon into the polymer backbone was expected to facilitate their interaction with anions and thereby increase the T+ (transference numbers) of the resulting polymers.52... 

The lithium transference number (l,) of these organoboron polymer electrolytes was evaluated by combination of dc polarization and ac impedance methods, as reported by Evans et al44 (Table 1). The observed t+ at 30°C was 0.50-0.35, indicating that anions were significantly trapped in these systems. Owing to the stronger Lewis acidity of the alkylborane unit, alkylborane-type polymers showed relatively higher t+. 

The lithium transference number (t+) of a polymer bearing PEO550 side chain/LiCF3S03 was found to be 0.38 at 30°C. This value implies that anions were effectively trapped by organoboron units, similar to linear organoboron polymer electrolytes. 

The lithium transference number calculated for 7/LiTFSI was 0.47 at 30°C, showing that anions were effectively trapped by methoxyboron unit. 

To immobilize such anions as borate, organoboron polymers were reacted with aryllithium reagents.31,32 The reaction of alkylborane polymers with n-BuLi was examined first however, the ionic conductivity of the resulting material was very low. Moreover, complicated peaks were observed in the H-NMR spectrum. Conversely, selective lithium borate formation was observed in the nB-NMR spectrum when PhLi was employed (scheme 6). An ionic conductivity of 9.45 X 10 7Scm 1 was observed at 50°C. The observed ionic conductivity was relatively low because of the decreased number of carrier ions compared with dissolved salt systems. However, the lithium transference number of this polymer was markedly high (0.82 at 30°C). 

A variety of organoboron polymer electrolytes were successfully prepared by hydroboration polymerization or dehydrocoupling polymerization. Investigations of the ion conductive properties of these polymers are summarized in Table 7. From this systematic study using defined organoboron polymers, it was clearly demonstrated that incorporation of organoboron anion receptors or lithium borate structures are fruitful approaches to improve the lithium transference number of an ion conductive matrix. 

Interestingly, the nonpolyether-type polymer electrolyte 7 showed a relatively high lithium transference number of 0.47 in the presence of LiTFSI. This is possibly due to the absence of strong binding of ether oxygen to the lithium cation. Moreover, anion trapping of the boron atom is not retarded by coordination of oxygen to the... 

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