Diffusivity ionic conductivity

Like diffusion, ionic conduction is a thermally activated process. Low activation barriers are, therefore, achieved in the same manner. Geometric features, such as open channels, result in larger diffusivities (easier ion movement) because this lowers the magnitude of the AH terms in Eqs. 6.38 and 6.39. For example, in /3 alumina, the sodium ions are located in sparsely populated layers positioned between spinel blocks. Accordingly, they diffuse through these channels easily owing to the large number of vacancies present. 

In the present study, we have examined other transport properties of 0/W microemulsions containing the nonionic surfactant Tween 60 whose dielectric and conductivity properties have been previously characterized. We have chosen properties (water self-diffusion, ionic conductivity at low frequencies, and thermal conductivity) that can be analyzed using the same mixture theory, and which therefore can be compared in a consistent way. Limited transport data are presented from other microemulsions as well. 

Very little is known about the oxygen diffusivity (ionic conductivity) and surface exchange of oxygen under reducing conditions in any of these materials. Such studies have proved valuable in understanding the behavior of cathodes and now need to be applied to anode materials. So far, only Lai jcSr. Feo.8Cro.203 has been studied in this way [80]. 

If at least one site occupation in the list of atomic coordinates is less than one and this site is not filled by other atoms, there is atomic disorder or even a defect structure. This conforms the basis for several physical properties of the material, e.g., diffusion, ionic conductivity, chemical reactivity. Superconductivity is a special phenomenon. ... 

The most direct effect of defects on tire properties of a material usually derive from altered ionic conductivity and diffusion properties. So-called superionic conductors materials which have an ionic conductivity comparable to that of molten salts. This h conductivity is due to the presence of defects, which can be introduced thermally or the presence of impurities. Diffusion affects important processes such as corrosion z catalysis. The specific heat capacity is also affected near the melting temperature the h capacity of a defective material is higher than for the equivalent ideal crystal. This refle the fact that the creation of defects is enthalpically unfavourable but is more than comp sated for by the increase in entropy, so leading to an overall decrease in the free energy... 

For an ion to move through the lattice, there must be an empty equivalent vacancy or interstitial site available, and it must possess sufficient energy to overcome the potential barrier between the two sites. Ionic conductivity, or the transport of charge by mobile ions, is a diffusion and activated process. From Fick s Law, J = —D dn/dx), for diffusion of a species in a concentration gradient, the diffusion coefficient D is given by... 

In polycrystalline materials, ion transport within the grain boundary must also be considered. For oxides with close-packed oxygens, the O-ion almost always diffuses much faster in the boundary region than in the bulk. In general, second phases at grain boundaries are less close packed and provide a pathway for more rapid diffusion of ionic species. Thus the simplified picture of bulk ionic conduction is made more complex by these additional effects. 

The previous definitions can be interpreted in terms of ionic-species diffusivities and conductivities. The latter are easily measured and depend on temperature and composition. For example, the equivalent conductance A is commonly tabulated in chemistry handbooks as the limiting (infinite dilution) conductance and at standard concentrations, typically at 25°C. A = 1000 K/C = ) + ) = +... 

Basic Equations AU of the processes described in this sec tion depend to some extent on the following background theory. Substances move through membranes by several meoianisms. For porous membranes, such as are used in microfiltration, viscous flow dominates the process. For electrodialytic membranes, the mass transfer is caused by an elec trical potential resulting in ionic conduction. For aU membranes, Ficldan diffusion is of some importance, and it is of dom-... 

It is unclear at this time whether this difference is due to the different anions present in the non-haloaluminate ionic liquids or due to differences in the two types of transport number measurements. The apparent greater importance of the cation to the movement of charge demonstrated by the transport numbers (Table 3.6-7) is consistent with the observations made from the diffusion and conductivity data above. Indeed, these data taken in total may indicate that the cation tends to be the majority charge carrier for all ionic liquids, especially the allcylimidazoliums. However, a greater quantity of transport number measurements, performed on a wider variety of ionic liquids, will be needed to ascertain whether this is indeed the case. 

The relationship between the ionic conductivity oi and the temperature T can either be derived from the diffusivity D or the mobility u assuming Arrhenius-type behavior ... 

Figure 48. Evolution of the apparent diffusion coefficient (V as a function of solution ionic conductivity (x ) (Reprinted from H.-J. Grande, T. F. Otero, and 1. Cantero, Conformational relaxation in conducting polymers Effect of the polymer-solvent interactions. J. Non-Cryst. Sol. 235-237, 619, 1998. Figs. 1-3, Copyright 1998. Reproduced with kind permission of Elsevier Science-NL, Sara Burgerhartstraat 25, 1055 KV Amsterdam, The Netherlands.)...

The above methods measure ion transport rates as ionic conductivities. By varying the parameters of the experiment, it is often possible to indirectly identify the mobile ion(s),173 and in some cases to estimate individual ion mobilities or diffusion coefficients.144 Because of the uncertainty in identifying and quantifying mobile ions in this way, EQCM studies that provide the (net) mass change accompanying an electrochemical process36 have played an important complementary role. 

Other refractory oxides that can be deposited by CVD have excellent thermal stability and oxidation resistance. Some, like alumina and yttria, are also good barriers to oxygen diffusion providing that they are free of pores and cracks. Many however are not, such as zirconia, hafnia, thoria, and ceria. These oxides have a fluorite structure, which is a simple open cubic structure and is particularly susceptible to oxygen diffusion through ionic conductivity. The diffusion rate of oxygen in these materials can be considerable. 

In an ideal ionic crystal, all ions are held rigidly in the lattice sites, where they perform only thermal vibratory motion. Transfer of an ion between sites under the effect of electrostatic fields (migration) or concentration gradients (diffusion) is not possible in such a crystal. Initially, therefore, the phenomenon of ionic conduction in solid ionic crystals was not understood. 

The diffusive and convective terms in Eq. (20-10) are the same as in nonelectrolytic mass transfer. The ionic mobility Uj, (g mol cm )/(J-s), can be related to the ionic-diffusion coefficient D, cmVs, and the ionic conductance of the ith species X, cmV(f2-g equivalent) ... 

Experimental methods for determining diffusion coefficients are described in the following section. The diffusion coefficients of the individual ions at infinite dilution can be calculated from the ionic conductivities by using Eqs (2.3.22), (2.4.2) and (2.4.3). The individual diffusion coefficients of the ions in the presence of an excess of indifferent electrolyte are usually found by electrochemical methods such as polarography or chronopotentiometry (see Section 5.4). Examples of diffusion coefficients determined in this way are listed in Table 2.4. Table 2.5 gives examples of the diffusion coefficients of various salts in aqueous solutions in dependence on the concentration. 

Using Eq. (2.6.18) the temperature dependence of various transport properties of polymers, such as diffusion coefficient D, ionic conductivity a and fluidity (reciprocal viscosity) 1/rj are described, since all these quantities are proportional to p. Except for fluidity, the proportionality constant (pre-exponential factor) also depends, however, on temperature,... 

Having established the validity of the force field for such a wide range of properties the authors go on to extend and apply the force field to electrolyte systems [141]. In particular the diffusion of Li+ in the polymer medium is treated, which is one of the key properties for understanding ionic conduction in the... 

Some values for the enthalpy of formation of Schottky defects in alkali halides of formula MX that adopt the sodium chloride structure are given in Table 2.1. The experimental determination of these values (obtained mostly from diffusion or ionic conductivity data (Chapters 5 and 6) is not easy, and there is a large scatter of values in the literature. The most reliable data are for the easily purified alkali halides. Currently, values for defect formation energies are more often obtained from calculations (Section 2.10). 

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