Nernst ionic transfer

This passage of ions may be conveniently called the Nernst ionic transfer. 

Because the ionic transference number for zirconia material is taken as being unity, then this equation reduces to the Nernst equation " ... 

In the lattice-gas model, as treated in Section IV.D above, ion transfer is viewed as an activated process. In an alternative view it is considered as a transport governed by the Nernst-Planck or the Langevin equation. These two models are not necessarily contra-dictive for high ionic concentrations the space-charge regions and the interface have similar widths, and then the barrier for ion transfer may vanish. So the activated mechanism may operate at low and the transport mechanism at high ionic concentrations. 

The Nernst-Planck equation constitutes the starting point for the electrotransport models [55-57], The overall flux of the ionic species i (/,) comprises the diffusion term driven by the chemical potential gradient (dc,/dx) and the electric transference term due to the electrical potential gradient (d /dx) ... 

The static - double-layer effect has been accounted for by assuming an equilibrium ionic distribution up to the positions located close to the interface in phases w and o, respectively, presumably at the corresponding outer Helmholtz plane (-> Frumkin correction) [iii], see also -> Verwey-Niessen model. Significance of the Frumkin correction was discussed critically to show that it applies only at equilibrium, that is, in the absence of faradaic current [vi]. Instead, the dynamic Levich correction should be used if the system is not at equilibrium [vi, vii]. Theoretical description of the ion transfer has remained a matter of continuing discussion. It has not been clear whether ion transfer across ITIES is better described as an activated (Butler-Volmer) process [viii], as a mass transport (Nernst-Planck) phenomenon [ix, x], or as a combination of both [xi]. Evidence has been also provided that the Frumkin correction overestimates the effect of electric double layer [xii]. Molecular dynamics (MD) computer simulations highlighted the dynamic role of the water protrusions (fingers) and friction effects [xiii, xiv], which has been further studied theoretically [xv,xvi]. 

Distribution (Nernst) potential — Multi-ion partition equilibria at the -> interface between two immiscible electrolyte solutions give rise to a -> Galvanipotential difference, Af(j> = (j>w- 0°, where 0wand cj>°are the -> inner potentials of phases w and o. This potential difference is called the distribution potential [i]. The theory was developed for the system of N ionic species i (i = 1,2..N) in each phase on the basis of the -> Nernst equation, the -> electroneutrality condition, and the mass-conservation law [ii]. At equilibrium, the equality of the - electrochemical potentials of the ions in the adjacent phases yields the Nernst equation for the ion-transfer potential,... 

Hung derived a general expression for calculating the distribution potential from the initial concentrations of ionic species, their standard ion transfer potentials, and the volumes of the two phases [19]. When all ionic species in W and O are completely dissociated, and the condition of electroneutrality holds in both phases, the combination of Nernst equations for all ionic species with the conservation of mass leads to... 

In the experimental application of these equations, we must remember that c refers to the ionic concentration and not to the total concentration. AVe cannot therefore expect our equations to be in exact agreement with experiment as long as we are ignorant of the exact value of the degree of ionisation. Conversely, however, we may use an experimental determination of the e. m.f. to calculate the degree of ionisation or the transference number. The validity of the Nernst equations has been placed beyond doubt by the results of numerous measurements. 

The Nernst-Planck Equation Obviously, a full formulation of governing equations should also include the mass transfer equation for each type of ions in the system. The ionic concentration distribution, ,(r), is generally... 

Similar results, as with surfactants, can be obtained when applying DC fields. The mass transfer of ionic species in an electric field, when there is no current applied, is according to the Nernst-Planck equation [19] ... 

To conclude on the physical meaning of the activation energy, or the lack of it, is not very easy yet. The only safe conclusion is to state that the local driving force at the interface is much higher than that involved in ionic diffusion or ionic conductivity, as soon as we depart from the equilibrium Galvani potential difference. Consequently, linearized equations such as the Nernst-Planck equation do not apply outside the narrow potential range, where the charge transfer resistance can be measured. 

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