Flux of cations

The analysis of oxidation processes to which diffusion control and interfacial equilibrium applied has been analysed by Wagner (1933) who used the Einstein mobility equation as a starting point. To describe the oxidation for example of nickel to the monoxide NiO, consideration must be given to tire respective fluxes of cations, anions and positive holes. These fluxes must be balanced to preserve local electroneutrality tliroughout the growing oxide. The flux equation for each species includes a term due to a chemical potential gradient plus a term due to the elecuic potential gradient... 

We denote by x the distance from the metal surface, and by n x) and rip x) the concentrations of cation vancancies and positive holes in the oxide. Let and Vp be their mobilities, and and Dp their diffusion coefficients. Let F x) be the electrostatic field in the oxide. J, the flux of cation vacancies (number crossing unit area per second), will be expressed by... 

The most serious toxicological effect of endrin is central neurotoxicity (Klaasen et al. 1986). Organo-chlorines interfere with the normal flux of cations across the axon, disrupting central nervous system homeostasis (Finkel 1983 Klaasen et al. 1986). Endrin is one of the most toxic cyclodienes, and seizure activity may develop rapidly after exposure (Proctor et al. 1988). In most cases, recovery is rapid. However, headaches, dizziness, weakness, and anorexia may persist for 2-4 weeks. 

For thick carrier membranes we may usually apply the assumption of a thermodynamic equilibrium at the phase boundaries as a good approximation (see above). On the other hand, it should be considered that a positive flux of cationic complexes within the membrane (as induced by an applied voltage E< 0) leads to a certain accumulation of free carriers at x = d, respectively to a depletion at x = 0 (see Fig. 1). For practical purposes the carriers are confined to the membrane phase in the case of ideal bulk membranes (in contrast, a supply of carriers from the outside solutions is stipulated for transport studies on bilayers45,51). 

Figure 1-3. The flux of cation vacancies in a transition metal oxide AX exposed to an oxygen potential gradient. Note that only the cation sublattice is depicted schematically.

According to the Danesi model, the flux of cations through the membrane is equal to ... 

The flux of cations is governed by the following two relations. At high cesium concentrations (C > EID) (where E denotes the concentration of carrier in the membrane),... 

Toxicity The acute oral LD50 and dermal LD50 toxicity of toxaphene in rats are 40 and 600 mg/kg, respectively. Toxaphene is an active nerve poison and interferes with fluxes of cations across nerve cell membranes, which increases neuronal irritability and results in convulsions and seizures. Toxaphene also has been found to damage the lungs, liver, and kidney of animals and humans. Although the dermal adsorption efficiency of toxaphene is less than that of other organochlorines, its absorption is enhanced by fat and fat solvents. Toxaphene has been shown to cause cancer in pregnant animals and to induce birth defects.68... 

The magnitude of the spike potential is around a hundred millivolts, (a) Following the spirit of the H-H theory, use the Goldman equation to calculate the change in ionic concentration between the outside and inside of the axon that is needed to explain this spike, (b) From this result, calculate the flux of cations per square centimeter of membrane that would have to pass across the membrane to bring about the concentration change. 

It is possible that the rate-determining process in the kinetics of ion exchange is the film diffusion. Consider a spherical particle encircled by an aqueous solution sphere (see Figure 7.8), in which the zeolite is homoionic at t = 0, the electrolytic solution has a very high volume (i.e., C2A == constant), and the diffusion is stationary and one-dimensional in a direction perpendicular to the zeolite surface [44], Then, under the conditions discussed above, it is possible to calculate the exchange flux of cation B, that is,. 7 , as follows [23] ... 

Charge balance requires that the outward flux of cations from the silicate be balanced by the inward flux of hydrogen ions. For example, the apparent sodium diffusion coefficient in equation 5 is therefore really the interdiffusion coefficient, +,... 

The chief toxic action of the organochlorine pesticides is on the nervous system, where these compounds interfere with fluxes of cations across nerve cell membranes, increasing neuronal irritability. This effect is manifest mainly as convulsions, sometimes limited to myoclonic jerking, but often... 

Fig. 31, Schematic of physicochemical processes that cwcur within a passive film according to the point defect model m = metal atom Mm = metal cation in cation site Oo = oxygen ion in anion site VjjJ = cation vacancy Vq = anion vaccancy Vm = vacancy in metal phase. During film growth, cation vacancies are produced at the film/solution interface, but are consumed at the metal/film interface. Likewise, anion vacancies are formed at the metal/film interface, but are consumed at the film/solution interface. Consequently, the fluxes of cation vacancies and anion vacancies are in the directions indicated. Note that reactions (i), (iii), and (iv) are lattice-conservative processes, whereas reactions (ii) and (v) are not. Reproduced from J. Electrochem, Sec. 139, 3434 (1992) by permission of the Electrochemical Society.

A-sec/eq. Since t = 1 in the ideal case, one equivalent of cations is removed through the membrane for every faraday of current flowing through the region of interest. Now in the aqueous phase near the membrane, the flux of cations transported electrically is ... 

Assuming that cationic transport across the growing oxide layer controls the rate of scaling and that thermodynamic equilibrium is established at each interface, the process can be analyzed as follows. The outward cation flux, is equal and opposite to the inward flux of cation defects (here taken to be vacancies). This model is shown in Figure 3.9. 

Equation (3.32) can be used to describe the flux of cations, anions, or electrons through the oxide layer. Due to their different mobilities, different species would tend to move at different rates, however, this would set up electric fields tending to oppose this independence. In fact, the three species migrate at rates that are defined by the necessity of maintaining electroneutrality throughout the scale, i.e, such that there is no net charge across the oxide scale. This condition is usually achieved due to the very high mobility of electrons or electronic defects. 

The theory of multi-layered scale growth on pure metals has been treated by Yurek et al The hypothetical system treated is shown in Figure 4.9. It is assumed that the growth of both scales is diffusion controlled with the outward migration of cations large relative to the inward migration of anions. The flux of cations in each oxide is assumed to be independent of distance. Each oxide exhibits predominantly... 

Transition from Linear to Parabolic Kinetics When thermodynamic equilibrium is nearly estabhshed at the surface and also at the oxide/metal interface, oxidation is virtually controlled by diffusion in the solid oxide. For oxides such as FeO, NiO, CoO, CU2O, and so on with cation vacancies Vm as the prevailing defects, the growth occurs by outward flux of cations and inward flux of vacancies, both fluxes are equal and given by... 

A polyion in the form of a thin membrane is used as ion-exchange membrane in another application of the ion-exchange phenomenon. When exposed to an electrolyte, an ion-exchange membrane will allow counterions to pass through it, but will act as a barrier to the complementary ion, and is therefore said to be permselective. Thus a polyanionic membrane will allow passage of cations and a polycationic membrane that of anions, so that under the influence of an electric current, continuous fluxes of cations and anions, respectively, can be set up across these membranes. This principle is exploited in electrodialysis and in chlor-alkali cells as described later. 

The flux of cations is coupled with the flux of anions. The total current density is given by Faraday s law ... 

The last fundamental frequency scale is related to the fact that on the right-hand side of the particle, normal outward fluxes of cations from the double layer find inward fluxes of anions brought normally from the bulk by the field. As a consequence, an increase in neutral electrolyte concentration is produced, and, for the same reasoning, a decrease will occur at the left side. A gradient of neutral electrolyte concentration (concentration polarization) is thus produced, with... 

At long times, on the other hand, the flux of the blocked anion falls to zero, and a constant flux of cations passes through the system. In order to maintain electroneutrality there must also be a gradient in anion concentration and hence in electric potential, which just balances the gradient in anion chanical potential. 

The effect of the electric field allows us to neglect cation movement in the reverse direction. The flux of cations in the oxide, N+, is then given by (6.21), where v corresponds to a frequency factor. The quantity c+ represents the concentration of mobile charge carriers, typically point defects, assumed constant within the film. 

The transport (flux) of cations through the membrane caused by an electrical potential difference is given by ... 

Equations (19.13) to (19.15) follow from the condition that steady-state fluxes of cation vacancies, cation interstitials, and oxygen vacancies, are the same at the two interfaces. Finally, it is possible to calculate the values of... 

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