Conduction, ionic

Ionic conduction depends on the presence of vacant sites into which ions can move. In the absence of a field, thermal vibrations proportional to kT may cause 

NaCl is a suitable material for further discussion since it has been extensively investigated. The lattice contains Schottky defects but the VNa (Na+ has r6 = 102 pm) moves more readily than the Va (Cl- has r6 = 181pm) so that charge transport can be taken as almost wholly due to movement of V Na. 

In the absence of an electric field the charged vacancy migrates randomly, and its mobility depends on temperature since this determines the ease with which the Na+ surmounts the energy barrier to movement. Because the crystal is highly ionic in character the barrier is electrostatic in origin, and the ion in its normal lattice position is in an electrostatic potential energy well (Fig. 2.17). 

Since we know the bias in jump probability in one direction, it is not difficult to arrive at the following expression for the current density  

Because the temperature dependence of a is dominated by the exponential term, the expression for conductivity is frequently written 

Ions can move through an ionic compoimd by vacancy diffusion driven by an electric field rather than by a concentration gradient. The current density is ji = riiZiepbiE, where rii is the ion concentration, Z C is the charge on the ion, and /a is the ion mobility. The ion mobility is 

The phenomenological equation for electrical conduction in an ionic solid is the same as that for electronic conduction, as shown in Eq. 6.21. However, the universal expression for electrical conductivity (Eq. 6.23) must be modified to include the transport contribution by all the species, including cations, anions, and electrons  

In this expression, qi is the charge of the migrating species i. Materials in which both ionic and electronic conduction occur are termed mixed conductors. Examples include LiNi02 and LiCo02. In most ceramics, however, tZei is negligible at normal temperatures. 

A more general expression for the ionic conductivity term in Eq. 6.40 is  

In physical chemistry, it is customary to speak in terms of the fraction of the conductivity carried by a particular species. The fraction of the total current carried by the rth species is called the transference number, or transfer number The total of all the transference numbers, including that of the electrons in the case of mixed conductors, must equal one. In many ceramics, the conduction occurs predominantly via the movement of one type of ion. For example, in the alkali halides, tcation whereas in Ce02, 

For any particular solid, the relative activation barriers for the available mechanisms determine whether the anions or cations are responsible for the ionic conduction. For example, in a yttria-stabilized Zr02, with the formula Zri Y ,.02-(x/2). aliovalent substitution of Zr by Y generates a large number of oxygen vacancies, giving rise to a mechanism for oxide ion conduction. Indeed, it is found that the anions diffuse about six orders of magnitude faster than the cations. 

Assuming that, to a first approximation, U+ and U are equal to U, and dj and d are equal to d, substitution of the resulting expression for the drift velocities into equation (9.33) leads to 

In the limit of small fields, sinh[eEd/(2kT)]f eEd/(2kT) and normal ohmic conductivity is observed, with j proportional to E. As the temperature rises the conductivity a =j/E falls rapidly. The exponential factor 

The temperature dependence of the conductivity of a glassy polymer generally changes significantly when its temperature is raised above the glass-transition temperature Tg. In the treatment just given the change 

Polymers designed for use as electrolytes in batteries are used at temperatures well above Tg. In this region a different model for conduction is more applicable, namely one based on the fluctuations in the distribution of free volume that occur above Tg due to the localised movements of the polymer chain segments. It is assumed that any ion sits in a region of free volume and can move into an adjacent space only when a sufficiently large element of free volume becomes available immediately adjacent to it. 

Let Uq be the average size of an element of free volume and v the minimum size of the element of free volume required for movement. The probability that an element of free volume permitting movement arises in unit time is then proportional to exp(—u /uq). At each opportunity to move the ion is accelerated in the direction of the applied electrical field and picks up a component of velocity qEx in the direction of the field, where x is the time taken for the move and q is the charge on the ion. The mean drift velocity in the field direction is thus proportional to qExnex —v /vQ), where n is the number of ions per unit volume. For given n the conductivity is thus proportional to exp(—u /Uq). Strictly speaking the constant of proportionality depends on T, but this dependence is small compared with the dependence on T contained in the exponential. The quantity must clearly be proportional to the total fractional free volume Ff, so that the conductivity is proportional to exp(—c/Ff), where c is a constant for the particular polymer and ion. Substitution for Ff from equation (7.33) and rearranging leads finally to the temperature dependence of the conductivity  

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The most familiar type of electrokinetic experiment consists of setting up a potential gradient in a solution containing charged particles and determining their rate of motion. If the particles are small molecular ions, the phenomenon is called ionic conductance, if they are larger units, such as protein molecules, or colloidal particles, it is called electrophoresis. 

Ionic conductors arise whenever there are mobile ions present. In electrolyte solutions, such ions are nonually fonued by the dissolution of an ionic solid. Provided the dissolution leads to the complete separation of the ionic components to fonu essentially independent anions and cations, the electrolyte is tenued strong. By contrast, weak electrolytes, such as organic carboxylic acids, are present mainly in the undissociated fonu in solution, with the total ionic concentration orders of magnitude lower than the fonual concentration of the solute. Ionic conductivity will be treated in some detail below, but we initially concentrate on the equilibrium stmcture of liquids and ionic solutions. 

We know from equation A2.4.32 and equation A2.4.34 that the limiting ionic conductivities are directly proportional to the limiting ionic mobilities in fact... 

Anions are usually less strongly hydrated, as indicated above, and from equation A2.4.38 this would suggest that increasing the charge on the anion should lead unequivocally to an increase in mobility and hence to an increase in limitmg ionic conductivity. An inspection of table A2.4.2 shows this to be home out to some extent by the limited data... 

At low currents, the rate of change of die electrode potential with current is associated with the limiting rate of electron transfer across the phase boundary between the electronically conducting electrode and the ionically conducting solution, and is temied the electron transfer overpotential. The electron transfer rate at a given overpotential has been found to depend on the nature of the species participating in the reaction, and the properties of the electrolyte and the electrode itself (such as, for example, the chemical nature of the metal). 

One of the most important advances in electrochemistry in the last decade was tlie application of STM and AFM to structural problems at the electrified solid/liquid interface [108. 109]. Sonnenfield and Hansma [110] were the first to use STM to study a surface innnersed in a liquid, thus extending STM beyond the gas/solid interfaces without a significant loss in resolution. In situ local-probe investigations at solid/liquid interfaces can be perfomied under electrochemical conditions if both phases are electronic and ionic conducting and this... 

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... 

Magnetic field strength H Molar ionic conductivity A, A... 

Table 8.32 Limiting Equivalent Ionic Conductances in Aqueous Solutions 8.157...

The equivalent conductivity of an electrolyte is the sum of contributions of the individual ions. At infinite dilution A° = A° -f A, where A° and A are the ionic conductances of cations and anions, respectively, at infinite dilution (Table 8.35). 

In Section 8, the material on solubility constants has been doubled to 550 entries. Sections on proton transfer reactions, including some at various temperatures, formation constants of metal complexes with organic and inorganic ligands, buffer solutions of all types, reference electrodes, indicators, and electrode potentials are retained with some revisions. The material on conductances has been revised and expanded, particularly in the table on limiting equivalent ionic conductances. 

Fig. 3. An overview of atomistic mechanisms involved in electroceramic components and the corresponding uses (a) ferroelectric domains capacitors and piezoelectrics, PTC thermistors (b) electronic conduction NTC thermistor (c) insulators and substrates (d) surface conduction humidity sensors (e) ferrimagnetic domains ferrite hard and soft magnets, magnetic tape (f) metal—semiconductor transition critical temperature NTC thermistor (g) ionic conduction gas sensors and batteries and (h) grain boundary phenomena varistors, boundary layer capacitors, PTC thermistors.

Ionic conductivity is used in oxygen sensors and in batteries (qv). Stabilized zirconia, Zr Ca 02 has a very large number of oxygen vacancies and very high conductivity. P-Alurnina/72(9(9j5 -4< -(y, NaAl O y, is an excellent cation conductor because of the high mobiUty of Na" ions. Ceramics of P-alurnina are used as the electrolyte in sodium-sulfur batteries. 

Molten Carbonate Fuel Cell. The electrolyte ia the MCFC is usually a combiaation of alkah (Li, Na, K) carbonates retaiaed ia a ceramic matrix of LiA102 particles. The fuel cell operates at 600 to 700°C where the alkah carbonates form a highly conductive molten salt and carbonate ions provide ionic conduction. At the operating temperatures ia MCFCs, Ni-based materials containing chromium (anode) and nickel oxide (cathode) can function as electrode materials, and noble metals are not required. 

Phosphazene polymers are inherently good electrical insulators unless side-group stmctures allow ionic conduction in the presence of salts. This insulating property forms the basis for appHcations as wire and cable jackets and coatings. Polyphosphazenes also exhibit excellent visible and uv radiation transparency when chromophoric substituents are absent. 

Applications. Polymers with small alkyl substituents, particularly (13), are ideal candidates for elastomer formulation because of quite low temperature flexibiUty, hydrolytic and chemical stabiUty, and high temperature stabiUty. The abiUty to readily incorporate other substituents (ia addition to methyl), particularly vinyl groups, should provide for conventional cure sites. In light of the biocompatibiUty of polysdoxanes and P—O- and P—N-substituted polyphosphazenes, poly(alkyl/arylphosphazenes) are also likely to be biocompatible polymers. Therefore, biomedical appHcations can also be envisaged for (3). A third potential appHcation is ia the area of soHd-state batteries. The first steps toward ionic conductivity have been observed with polymers (13) and (15) using lithium and silver salts (78). 

Lithium Nitride. Lithium nitride [26134-62-3], Li N, is prepared from the strongly exothermic direct reaction of lithium and nitrogen. The reaction proceeds to completion even when the temperature is kept below the melting point of lithium metal. The lithium ion is extremely mobile in the hexagonal lattice resulting in one of the highest known soHd ionic conductivities. Lithium nitride in combination with other compounds is used as a catalyst for the conversion of hexagonal boron nitride to the cubic form. The properties of lithium nitride have been extensively reviewed (66). 

Static electrification may not be a property of the basic stmcture, but of a new surface formed by a monomolecular layer of water (82). All textile fibers at a relative humidity, at which a continuous monomolecular layer is formed, actually do have the same charge density. This is attributed to the absence of ionic transport which caimot occur in a monomolecular layer. At higher moisture levels than required to form a monomolecular layer, ionic conductivity can occur because of excess water molecules and by hydration of the ions. At very low moisture-regain levels, all materials acquire the same charge (83). 

E/ectro te is a material that provides ionic conductivity between the positive and negative electrodes of a cell. 

Silver—Zinc Separators. The basic separator material is a regenerated cellulose (unplastici2ed cellophane) which acts as a semipermeable membrane aHowiag ionic conduction through the separator and preventing the migration of active materials from one electrode to the other. 

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