Mobile ions

Electrochemistry is concerned with the study of the interface between an electronic and an ionic conductor and, traditionally, has concentrated on (i) the nature of the ionic conductor, which is usually an aqueous or (more rarely) a non-aqueous solution, polymer or superionic solid containing mobile ions (ii) the structure of the electrified interface that fonns on inunersion of an electronic conductor into an ionic conductor and (iii) the electron-transfer processes that can take place at this interface and the limitations on the rates of such processes. 

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. 

Assign A value of 1 or 0 to each grid point to identify points that are or are not accessible to mobile ions, respectively. 

At lower frequencies, orientational polarization may occur if the glass contains permanent ionic or molecular dipoles, such as H2O or an Si—OH group, that can rotate or oscillate in the presence of an appHed electric field. Another source of orientational polarization at even lower frequencies is the oscillatory movement of mobile ions such as Na". The higher the amount of alkaH oxide in the glass, the higher the dielectric constant. When the movement of mobile charge carriers is obstmcted by a barrier, the accumulation of carriers at the interface leads to interfacial polarization. Interfacial polarization can occur in phase-separated glasses if the phases have different dielectric constants. 

In contrast to triaxial porcelains, packaging materials such as 99% AI2O2 prepared by a soHd-state sintering process, display significantly lower dielectric loss. In these materials, there is no residual glassy phase with its associated mobile ion content, and therefore, conduction losses are minimized. 

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... 

Electrical conduction ia glasses is mainly attributed to the migration of mobile ions such as LE, Na", K", and OH under the influence of an appHed field. At higher temperatures, >250° C, divalent ions, eg, Ca " and Mg ", contribute to conduction, although their mobiUty is much less (14). Conduction ia glass is an activated process and thus the number of conducting ions iacreases with both temperature and field. The temperature—resistivity dependence is given... 

The ion transport number is defined as the fraction of current carried through the membrane by counterions. If the concentration of fixed charges in the membrane is high compared to the concentration of the ambient solution, then the mobile ions in the IX membrane are mosdy counterions, co-ions are effectively excluded, and the ion transport number then approaches 1. Commercial membranes have ion transport numbers in dilute solutions of ca 0.85—0.95. The relationship between ion transport number and current efficiency is shown in Figure 3 where is the fraction of current carried by the counterions (anions) through the AX membrane and is the fraction of current carried by the counterions (cations) through the CX membrane. The remainder of the current (1 — in the case of the AX membranes and (1 — in the case of the CX membranes is carried by co-ions and... 

Mobile ions, such as sodium or potassium, tend to migrate to thep-n junction of the IC device where they acquire an electron, and deposit as the corresponding metal on the p-n junction this consequendy destroys the device. Furthermore, mobile ions also support leakage currents between biased device features, which degrade device performance and ultimately destroy the devices by electrochemical processes such as metal conductor dissolution. 

For example, chloride and duoride ions, even in trace amounts (ppm), could cause the dissolution of aluminum metallization of complimentary metal oxide semiconductor (CMOS) devices. CMOS is likely to be the trend of VLSI technology and sodium chloride is a common contaminant. The protection of these devices from the effects of these mobile ions is an absolute requirement. The use of an ultrahigh purity encapsulant to encapsulate the passivated IC is the answer to some mobile ion contaminant problems. 

The abiHty of a given material to perform as an electronic embedding encapsulant depends largely on its properties. Ultrapure chemical properties with a low level of mobile ions such as sodium, potassium, and chloride are essential. Furthermore, the material s electrical, mechanical, and rheological properties are critical. 

The concentration of salt in physiological systems is on the order of 150 mM, which corresponds to approximately 350 water molecules for each cation-anion pair. Eor this reason, investigations of salt effects in biological systems using detailed atomic models and molecular dynamic simulations become rapidly prohibitive, and mean-field treatments based on continuum electrostatics are advantageous. Such approximations, which were pioneered by Debye and Huckel [11], are valid at moderately low ionic concentration when core-core interactions between the mobile ions can be neglected. Briefly, the spatial density throughout the solvent is assumed to depend only on the local electrostatic poten-... 

It is applicable to plastic packaging materials, where purities with respect to mobile ions, such as Cl and Na, can be checked. In addition, a-particle precursors, such as U and Th, can be determined in solid plastics with sub-ppb detection limits. 

In practice the cathodic protection current will be carried in the corrosive environment by more mobile ions, e.g. OH, Na, etc. 

It will be recalled that in Fig. 28 we found that for the most mobile ions the mobility has the smallest temperature coefficient. If any species of ion in aqueous solution at room temperature causes a local loosening of the water structure, the solvent in the co-sphere of each ion will have a viscosity smaller than that of the normal solvent. A solute in which both anions and cations are of this type will have in (160) a negative viscosity //-coefficient. At the same time the local loosening of the water structure will permit a more lively Brownian motion than the ion would otherwise have at this temperature. Normally a certain rise of temperature would be needed to produce an equal loosening of the water structure. If, in the co-sphere of any species of ion, there exists already at a low temperature a certain loosening of the water structure, the mobility of this ion is likely to have an abnormally small temperature coefficient, as pointed out in Sec. 34. 

Electro-conductivity of molten salts is a kinetic property that depends on the nature of the mobile ions and ionic interactions. The interaction that leads to the formation of complex ions has a varying influence on the electroconductivity of the melts, depending on the nature of the initial components. When the initial components are purely ionic, forming of complexes leads to a decrease in conductivity, whereas associated initial compounds result in an increase in conductivity compared to the behavior of an ideal system. Since electro-conductivity is never an additive property, the calculation of the conductivity for an ideal system is performed using the well-known equation proposed by Markov and Shumina (Markov s Equation) [315]. 

Assume the following compounds dissolve in water to form separate, mobile ions in solution. Write the formulas and names for the ions that can be expected. 

This relationship makes it possible to calculate the maximum ionic conductivity of solid electrolytes. Assuming that the mobile ions are moving with thermal velocity v without resting and oscillating at any lattice site, this results in a jump frequency... 

Figure 8. Arrhenius diagram for various fast ion conductors. For each indicated monovalent mobile ion, the given ionic conductors are the fastest ones known (Na Na 1 - / "-Al203 Cu+, CulflRb4I7Cll3 K+, K+-/T-A120, H H3Moi2P04(, -30H2O Ag, Ag Rbls F, La0 95Sr005F295 Li, ...

In most cases of practically useful ionic conductors one may assume a very large concentration of mobile ionic defects. As a result, the chemical potential of the mobile ions may be regarded as being essentially constant within the material. Thus, any ionic transport in such a material must be predominantly due to the influence of an internal electrostatic potential gradient,... 

Equation (3.7) describes the equality of the chemical potentials of the mobile ions on both sides of the gel boundary expressed through the Donnan ratio KD and the ion charges z, Eq. (3.8) concerns the dissociation equilibrium of ionizable (carboxyl) groups of the network a is the degree of dissociation, eg is the concentration of the hydrogen ions in the gel Eq. (3.9) represents the gel electroneutrality condition. 

Other useful solid-state electrodes are based on silver compounds (particularly silver sulfide). Silver sulfide is an ionic conductor, in which silver ions are the mobile ions. Mixed pellets containing Ag2S-AgX (where X = Cl, Br, I, SCN) have been successfiilly used for the determination of one of these particular anions. The behavior of these electrodes is determined primarily by the solubility products involved. The relative solubility products of various ions with Ag+ thus dictate the selectivity (i.e., kt] = KSp(Agf)/KSP(Aw)). Consequently, the iodide electrode (membrane of Ag2S/AgI) displays high selectivity over Br- and Cl-. In contrast, die chloride electrode suffers from severe interference from Br- and I-. Similarly, mixtures of silver sulfide with CdS, CuS, or PbS provide membranes that are responsive to Cd2+, Cu2+, or Pb2+, respectively. A limitation of these mixed-salt electrodes is tiiat the solubility of die second salt must be much larger than that of silver sulfide. A silver sulfide membrane by itself responds to either S2- or Ag+ ions, down to die 10-8M level. 

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. 

On the other hand, Doblhofer218 has pointed out that since conducting polymer films are solvated and contain mobile ions, the potential drop occurs primarily at the metal/polymer interface. As with a redox polymer, electrons move across the film because of concentration gradients of oxidized and reduced sites, and redox processes involving solution species occur as bimolecular reactions with polymer redox sites at the polymer/solution interface. This model was found to be consistent with data for the reduction and oxidation of a variety of species at poly(7V-methylpyrrole). This polymer has a relatively low maximum conductivity (10-6 - 10 5 S cm"1) and was only partially oxidized in the mediation experiments, which may explain why it behaved more like a redox polymer than a typical conducting polymer. 

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