Nernst impedance

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. 

Figure 4.5.69. Time elapsed of the Warburg parameter W from the Nernst impedance (Eq. 82) for the ( ) Pt/C and ( ) PtRu/C anodes after evaluation of the time dependent impedance spectra with the equivalent circuit from Figure 4.5.67.

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 ... 

At high frequency, the Nernst impedance becomes equal to the Warburg impedance since for A = °° B = 1, C = 0. Figure 5.29 represents Zw and Zpj in the complex plane. The Nernst impedance goes through a maximum then drops back down to the real axis at low frequencies. 

The Warburg and Nernst impedances were derived under the assumption that the potential obeys the Nernst equation. The more realistic Randles model takes into account the kinetics of charge transfer as described by the Butler-Volmer equation. For the electrode reaction (5.147) this is written as... 

Potentiometry is a method of obtaining chemical information by measuring the potential of an indicator electrode under zero current flow. It is based on the Nernst equation, which expresses the electrode potential as a function of the activity (or activities) of the chemical species in solution. The information obtained varies with indicator electrode, from the activity (concentration) of a chemical species to the redox potential in the solution. The potential of the indicator electrode is measured against a reference electrode using a high inptit-impedance mV/pH me-... 

From (6.44), we see that in order to obtain a selective membrane, the value of the ion-exchange constant must be small and the sodium ion mobility in the hydrated layer relative to that of the hydrogen ion must also be small. The expansion of the selectivity coefficient to include selectivity to other ions involves inclusion of more complex ion-exchange equilibria, and the use of a more complex form of the Nernst-Planck equation. This rapidly leads to intractable algebra that requires numerical solution (Franceschetti et al 1991 Kucza et al 2006). Nevertheless, the concept of the physical origin of the selectivity coefficient remains the same. Electrochemical impedance spectroscopy has been successfully used in analysis of the ISE function (Gabrielli et al 2004). 

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

With the switch open, the potential measured by the high-impedence voltmeter would be -0.118 V. This value can be calculated from the Nernst equation. The reversible potential of the Pt wire in chamber A would be zero relative to NHE as it is itself an NHE, the reversible potential of the WE in chamber B would be... 

The type and concentration of defects in solids determine or, at least, affect the transport properties. For instance, the -> ion conductivity in a crystal bulk is usually proportional to the -> concentration of -> ionic charge carriers, namely vacancies or interstitials (see also -> Nernst-Einstein equation). Clustering of the point defects may impede transport. The concentration and -> mobility of ionic charge carriers in the vicinity of extended defects may differ from ideal due to space-charge effects (see also - space charge region). 

Open-circuit potential (OCP) — This is the - potential of the - working electrode relative to the - reference electrode when no potential or - current is being applied to the - cell [i]. In case of a reversible electrode system (- reversibility) the OCP is also referred to as the - equilibrium potential. Otherwise it is called the - rest potential, or the - corrosion potential, depending on the studied system. The OCP is measured using high-input - impedance voltmeters, or potentiometers, as in - potentiometry. OCP s of - electrodes of the first, the second, and the third kind, of - redox electrodes and of - ion-selective membrane electrodes are defined by the - Nernst equation. The - corrosion po-... 

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. 

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-... 

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. ... 

To understand better what is occurring, let us examine in more detail the modeled impedance in Figure 8.26. Figure 8.27 shows the same impedance in a Bode plot of real and imaginary parfs plotted as a function of frequency. We saw in equation (8.64) that there are four major components to the total measurable impedance The components are the anode and cathode overpotentials, the membrane ionic potential difference and the Nernst... 

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)... 

Actually, Ion analyzer, as a high input impedance millivoltmeter, is widely used in measuring the EMF of the battery which is composed by ion selective electrode, reference electrode, and solution. The concentration of the unknown solution is acquired through measuring the EMF margin between standard solution and tested solution under the same electrode system. By the Nernst equation the authors have inferred... 

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... 

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