Nemst impedance

So far unlimited diffusion has been assumed. When the diffusion layer has finite dimension, with a boundary of constant concentration of the diffusing species and permeable for these species, however, a different expression for the diffusion impedance is derived which is the so-called Nemst impedance. This impedance is given by the equation... 

The Nemst impedance is shown in the Nyquist and Bode diagrams in Figure 5.11. The ratio D/Sj (D diffusion coefficient, diffusion layer thickness) has the dimension of a... 

The evolution of the charge transfer resistance of the anodes is shown in Figure 4.5.68 as a function of the elapsed time. The Nemst impedance (Zjv) represented in Figure 4.5.69 shows the greatest difference between the two anodes. The Nemst... 

This diffnsion overvoltage leads to the Nemst impedance. Operating the fuel cell with oxygen (po, = 1), no diffusion overvoltage for X = 0.5 occnrs. Therefore, the open cell voltage, given by Eq. (86), is very sensitive to the water vapor content in the fuel gas and can be nsed to determine the water vapor in the fnel gas quantitatively. 

Figure 5.29 Nyqnist diagram showing Warbnrg and Nemst impedances calcnlated for a= 1 Q s and X =...

An example of a transfer function based on a physical model is the Nemst impedance of a transport controlled electrode reaction. The impedance spectra in Fig. 7-14, which were obtained on a rotating platinum disk electrode at the equilibrium potential of the iron hexacyanoferrate redox system, exhibit the typical shape of a transport-controlled process. The transfer function cannot be described by a limited number of electrical circuit elements but must be derived from the differential equations of Fick s 2nd law and the appropriate boundary conditions. For finite linear diffusion, the so-called Nemst impedance Z can be derived theoretically... 

NADHj, redox potentials 182 natrium chloride solutions 234 natural gas, multiphase flow 267 natural materials, microbial corrosion 193 Nemst diffusion layer 17 Nemst equation 10 f, 22 ff, 38,45,62 Nemst impedance 308 neutral solutions... 

Smaller values of necessitate the appHcation of voltages greater than those calculated from the Nemst equation to obtain a corresponding set of surface concentrations of electroactive species. These voltages are called overpotentials and iadicate chemically related difficulties with the electrolysis. In other words, electron exchange between the electrode and the electroactive species is impeded by the chemistry of the process itself. 

Since the solid—solid interface and bulk of the mixed conductor remain in chemical and electrical equilibrium, the measured overpotential t] is related directly to the spatially uniform oxidation state of the film through the Nemst equation 4Ft] = RTf d — (3o). Solving for d( and recognizing that the impedance Z = rjU, one obtains... 

In general, the reference electrode should be (1) a reversible electrode that obeys the Nemst equation, (2) stable, and (3) able to respond quickly to changes in environmental conditions [63], The most commonly used reference electrodes for measuring the AC impedance spectra for fuel cells are the DHE (dynamic hydrogen electrode) and the RHE (reversible hydrogen electrode) [64, 65],... 

Process models Nemst dielectrics (1894) Warburg diffusion (1901) Finkelstein Solid film (1902) Randles double layer and diffusion impedance (1947) Gerischer two heterogeneous steps with adsorbed intermediate (1955) De Levie porous electrodes (1967) Schuhmann homogeneous reactions and diffusion (1964) Gabrielli generalized impedance (1977) Isaacs LEIS (1992)... 

Within the Nemst hypothesis, the diffusion impedance is assumed to be that for a stagnant film of effective thickness that is related to velocity by... 

Remember 11.4 The formula pr impedance obtained under the Nemst hypothesis, as given by equation (11.70), provides a poor model for convective-diffusion impedance. 

A Nemst stagnant-diffusion-layer model was used to accovmt for the diffusion impedance. This model is often used to account for mass transfer in convective systems, even though it is well known that this model caimot ac-coimt accurately for the convective diffusion associated with a rotating disk electrode. 

By his application of Laplace transforms to the transient response of electrical circuits, Oliver Heaviside created the foimdation for impedance spectroscopy. Heaviside coined the words inductance, capacitance, and impedance and introduced these concepts to the treatment of electrical circuits. His papers on the subject, published in The Electrician beginning in 1872, were compiled by Heaviside in book form in 1894.6/7 pj-om the perspective of the application to physical systems, however, the history of impedance spectroscopy begins in 1894 with the work of Nemst. ... 

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. ... 

Approbation of the proposed impedance method has been done on the oxygen probes with the structure described above as (4.5) in the temperature range of 380-480°C. Initially, the emf of the probe was allowed to attain a stable value. Me-MeO/molten metal emfs were within 1 mV of their theoretical values. The thermodynamic emf (Nemst equation) for an oxygen probe with a Bi-Bi203 RE is... 

Fig. 11 Faradaic impedance Zp(co) plotted for a finite thickness of the diffusion layer (Nemst hypothesis) (frequency in Hz), For comparison, the impedance is also plotted (dotted lines) for an infinite thickness of the diffusion layer...

In Fig. 11, the oscillation above the Warburg straight hne (at frequencies from 0.4 to 0.14 Hz)) is related to the Nemst hypothesis. A numerical calculation taking into account the convection term in the transport equation showed that the impedance diagram is below the Warburg straight line. 

Figure 5.11 Representation of diffusion impedance spectra of diffusion processes limited by a Nemst diffusion layer, 182 D, D/S = 30 s . (a) Nyquist plot and (b) Bode plot.

The eeU voltage ( ) between an ion-seleetive electrode and a reference electrode, measured by a high-impedance voltmeter, bears a linear relationship to the negative logarithm of the activity of ions examined over a range eovering several (4-5) orders of magnitude of the concentration (Nemst relationship) ... 

Chemical applications of impedance spectroscopy began with the work of Nemst [5], followed by many others, including those applications to the distribution of relaxation time constants by Cole and Cole [6] and Davidson and Cole [7]. Warburg [8] developed the impedance of mass transfer (the so-called Warburg impedance), which allowed further applications of EIS to redox reactions. 

Equations of the faradaic impedance can be simplified assuming that the surface concentrations follow the Nemst law that is they correspond to the electro-chemical equilibrium after staying at a constant potential for a certain time while the ac concentrations corresponding to higher frequencies or shorter times are out of equilibrium. Using the Nemst equation ... 

Macdonald and coworkers [158-164] obtained an exact solution of the finite-length diffusion impedance in unsupported conditions where the Nemst-Planck and continuity equations for both negative and positive mobile charges were solved and involved full satisfaction of Poisson s equation. One can expect such conditions in diluted electrolytic solutions and in poorly conductive solids. 

Self-diffusion coefficients of distinct mobile species measured using PFG-NMR are based on spectral selectivity. In the context of IL selfdiffusion, PFG-NMR measures the time-averaged (miUisecond timescale) diffusion coefficients. Since ion-pair (cation-anion) interactions take place on a timescale faster than that, the measured diffusion coefficients are a weighted average over charged and neutral species. This is the reason for the variation between conductivity calculated from diffiasion coefficients determined by the Nemst-Einstein equation [15] (Eq. 1) and conductivity measured using impedance analysis ... 

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