Overpotential impedence

Cathode overpotential impedance with and without the double layer capacitance. 

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. 

D.Y. Wang, and A.S. Nowick, Cathodic and anodic polarization phenomena at platinum electrodes with doped Ce02 as electrolyte. II. Transient overpotential and A-C Impedance, /. Electrochem. Soc. 126(7), 1166-1172(1979). 

The Warburg impedance is related to the concentration overpotential and applied AC by... 

To further understand and characterise the oxide deactivation process, a.c. impedance studies were carried out, primarily with a 30 at.% Ru/Ti electrode, at various stages during deactivation. These data were compared to those obtained for freshly formed Ru/Ti oxide films, ranging in Ru content from 5 to 40 at.%. Impedance data were collected at the oxide OCP (approximately 0.9 V versus SCE) in fresh NaCI solutions. Under these conditions, no chlorine reactions can occur and the OCP is defined by the equilibria of the redox states on the Ru oxide surface. Deactivation was generally accomplished by square-wave potential cycling, using overpotentials versus the chlorine/chloride potential of 1.59 to — 0.08 V (60 s cycle-1) in 5 M NaCI + 0.1 M HC1 solutions at room temperature. 

Thus, the polarisation data, cyclic voltammetric results and the a.c. impedance measurements all suggest that, when an Ru02/TiC>2 anode exhibits a high overpotential, this is a direct consequence of the surface depletion of Ru. This is also consistent with the estimated Re values of approximately 20 Q for the failed electrodes, in contrast to the known, much higher specific resistivity of Ti02 of... 

In general it will be necessary to measure via impedance measurements using a four electrode cell. A schematic diagram of the cell which would be used for such measurements is shown in Fig. 10.15. The expected behaviour will be as described in Eqn (10.3) except that Warburg impedances can arise from either or both phases. An example of an impedance spectrum of the H2O/PVC interface is shown in Fig. 10.16. The application of a constant overpotential will, in general, lead to a slowly decaying current with time due to the concentration changes which occur in both phases, so that steady state current potential measurements will be of limited use. 

Figure 5. Measurement and analysis of steady-state i— V characteristics, (a) Following subtraction of ohmic losses (determined from impedance or current-interrupt measurements), the electrode overpotential rj is plotted vs ln(i). For systems governed by classic electrochemical kinetics, the slope at high overpotential yields anodic and cathodic transfer coefficients (Ua and aj while the intercept yields the exchange current density (i o). These parameters can be used in an empirical rate expression for the kinetics (Butler—Volmer equation) or related to more specific parameters associated with individual reaction steps.(b) Example of Mn(IV) reduction to Mn(III) at a Pt electrode in 7.5 M H2SO4 solution at 25 Below limiting current the system obeys Tafel kinetics with Ua 1/4. Data are from ref 363. (Reprinted with permission from ref 362. Copyright 2001 John Wiley Sons.)...

However, as mentioned previously, gas-diffusion electrodes usually deviate substantially from traditional electrochemical—kinetic behavior, often being limited by multiple rate-determining factors and/or changes in those factors with overpotential or other conditions. In attempting to analyze this type of electrode, one of the most influential experimental techniques to take hold in the solid-state electrochemical literature in the last 35 years is electrochemical impedance spectroscopy (EIS)—also know as a.c. impedance. As illustrated in Figure 6, by measuring the sinusoidal i— response as a function... 

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... 

However, as we saw in section 3.3 for platinum on YSZ, the fact that i—rj data fits a Butler—Volmer expression does not necessarily indicate that the electrode is limited by interfacial electrochemical kinetics. Supporting this point is a series of papers published by Svensson et al., who modeled the current—overpotential i—rj) characteristics of porous mixed-conducting electrodes. As shown in Figure 28a, these models take a similar mechanistic approach as the Adler model but consider additional physics (surface adsorption and transport) and forego time dependence (required to predict impedance) in order to solve for the full nonlinear i—rj characteristics at steady state. 

Sensitivity of interfacial resistance to various factors. For perovskite mixed conductors on some ceria-based electrolytes, workers have reported virtually zero interfacial resistance such that the electrode overpotential is dominated entirely by dissociation of O2 and transport of intermediates to the electrode/ electrolyte interface. As we will see in section 6, this conclusion is not universally true of all materials additional impedance arcs have been observed for perovskites on YSZ and with ceria at lower temperatures or with certain electrolyte dopants. 

What this calculation shows is that the rate of bulk transport observed in a thin film of LSM is at least 3 orders of magnitude too low to explain the performance of porous LSM at low overpotential, assuming an entirely bulk transport path. This calculation echoes prior estimates of Adler and co-workers, who showed that the zero-bias impedance of porous LSM cannot be explained in terms of a bulk path. In addition, estimates of the chemical capacitance based on loroi s impedance for porous LSM yield values of 10 —10 F/cm , which as mentioned previously in section 5.2 are more consistent with a surface process... 

Surface path at low overpotential. Qualitative and quantitative analysis of impedance data, tracer studies, as well as various studies of thin-film electrodes suggest that under low-overpotential LSM operates primarily via a surface-mediated mechanism (like Pt). This conclusion appears to be consistent with the properties of LSM, which is fully oxygen stoichiometric under ambient Pq. However, little is known about how far the active region of reduction extends beyond the solid/solid interface (via surface diffusion) or the relative importance of chemical steps (on the LSM surface) vs electrochemical kinetics at the solid/solid interface. 

Bulk path at moderate to high overpotential. Studies of impedance time scales, tracer diffusion profiles, and electrode microstructure suggest that at moderate to high cathodic over potential, LSM becomes sufficiently reduced to open up a parallel bulk transport path near the three-phase boundary (like the perovskite mixed conductors). This effect may explain the complex dependence of electrode performance on electrode geometry and length scale. To date, no quantitative measurements or models have provided a means to determine the degree to which surface and bulk paths contribute under an arbitrary set of conditions. 

Very high impedance (>10 kf2cm ) of reversible Mg electrode systems studied also indicated" adsorption processes. However, overpotentials of only several tens of millivolts are sufficient to break down the adsorbed layers, resulting in a much lower impedance (< 100 cm ) during the electrochemical processes. 

Chronopotentiometry, galvanostatic transients, 1411 as analytical technique, 1411 activation overpotential, 1411 Clavilier, and single crystals, 1095 Cluster formation energy of, 1304 and Frumkin isotherm, 1197 Cobalt-nickel plating, 1375 Cold combustion, definition, 1041 Cole-Cole plot, impedance, 1129, 1135 Colloidal particles, 880, 882 and differential capacity, 880 Complex impedance, 1135 Computer simulation, 1160 of adsorption processes, 965 and overall reaction, 1259 and rate determining step, 1260... 

Rate determining step (cont.) electrocatalysis and, 1276 methanol oxidation, 1270 in multistep reactions, 1180 overpotential and, 1175 places where it can occur, 1260 pseudo-equilibrium, 1260 quasi equilibrium and, 1176 reaction mechanism and, 1260 steady state and, 1176 surface chemical reactions and, 1261 Real impedance, 1128, 1135 Reciprocal relation, the, 1250 Recombination reaction, 1168 Receiver states, 1494 Reddy, 1163... 

Calculating Exchange Current Densities and Rate Constants from Impedance Plots. If one takes the Butler-Volmer equation (7.24) under the reversible condition, i.e that in which the overpotential, rj, tends to zero, then,... 

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