Nernst diffusion impedance

Figure 3.51 shows the impedance spectra for a Pt/FTO sandwich cell at different bias potentials reported by Hauch and Georg.The impedance element on the left of the spectrum (high frequencies) is the Pt/ electrolyte interface (charge-transfer resistance and double layer capacitance) on the right (low frequencies) there is the Nernst diffusion impedance. The diameter of the high frequency semicircle in the impedance... 

If concentration relaxation occurs in a diffusion layer with a thickness 5N (Nernst diffusion layer), the impedance ZF is then [5,10]... 

An important example of the system with an ideally permeable external interface is the diffusion of an electroactive species across the boundary layer in solution near the solid electrode surface, described within the framework of the Nernst diffusion layer model. Mathematically, an equivalent problem appears for the diffusion of a solute electroactive species to the electrode surface across a passive membrane layer. The non-stationary distribution of this species inside the layer corresponds to a finite - diffusion problem. Its solution for the film with an ideally permeable external boundary and with the concentration modulation at the electrode film contact in the course of the passage of an alternating current results in one of two expressions for finite-Warburg impedance for the contribution of the layer Ziayer = H(0) tanh(icard)1/2/(iwrd)1/2 containing the characteristic - diffusion time, Td = L2/D (L, layer thickness, D, - diffusion coefficient), and the low-frequency resistance of the layer, R(0) = dE/dl, this derivative corresponding to -> direct current conditions. 

Nernst applied the electrical bridge invented by Wheatstone to the measurement of the dielectric constants for aqueous electrolytes and different organic fluids. Nemst s approach was soon employed by others for measurement of dielectric properties and the resistance of galvanic cells. Finkelstein applied the technique to the analysis of the dielectric response of oxides. Warburg developed expressions for the impedance response associated with the laws of diffusion, developed almost 50 years earlier by Fick, and introduced the electrical circuit analogue for electrolytic systems in which the capacitance and resistance were functions of frequency. The concept of diffusion impedance was applied by Kruger to the capacitive response of mercury electrodes. ... 

The kinetic impedance Zj represents the faradaie impedance in the absence of a concentration overpotential. In the simplest case, the kinetie impedance corresponds to the transfer resistance Rt, but in more complicated situations it may include several circuit elements. The diffusion impedance Z describes the contribution of the concentration overpotential to the faradaic impedance and therefore depends on the transport phenomena in solution. In the absence of convection, it is referred to as the Warburg impedance and, in the opposite case, as the Nernst impedance Z. ... 

A derivation analogous to the previous yields the Nernst impedance, once the boundary conditions are modified to include the effects of convection y= S, Ac = 0, where represents the thickness of the Nernst diffusion layer. The solution of (5.153) gives, in this case ... 

Plot, on an impedance plane format, the impedance obtained for a Nernst stagnant diffusion layer and the impedance obtained for a rotating disk electrode under assumption of an infinite Schmidt number. Show that, while the behaviors of the two models at high and low frequencies are in agreement, the two models do not agree at intermediate frequencies. Explain. 

C. Deslouis, I. Epelboin, M. Keddam, and J. C. Lestrade, "Impedance de Diffusion d un Disque Tournant en Regime Hydrodynamique Laminaire. Etude Experimentale et Comparaison avec le Module de Nernst," Journal of Electro-... 

Figure 4.5.60. (a) Equivalent circuit (EC) of the PEFC with O2/H2 gas supply, for low current densities, (b) Equivalent circuit of the PEEC with O2/H2 gas supply, for high current densities with an additional diffusion step (Nernst-impedance), (c) Equivalent circuit of the PEFC with O2/H2 gas supply with Nernst-impedance and porous electrode model. 

Though in the general case, mathematical expressions of the Nernst model are more complicated than of those semi-infinite diffusion, stationary mass transport is described by a rather simple Eq. (3.12). In this connection, there occurs an interesting possibility to use superposition of both models, which is convenient to apply when i is the periodic time function. Perturbation signals of this type are considered in the theory of electrochemical impedance spectroscopy. In this case, i(t)... 

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