Electrode, overpotential currents

Using this two-step model, which can be expanded to include other intermediate steps as well, a simple formulation for the electrode overpotential current relationship at a given electrode can be developed. If we assume that the reaction rate constants involved are independent of the surface coverage of reactant R, then we can derive the Langmuir kinetics model solution. With constant rate constants in Eq. (4.62), at steady state we can... 

In many cases mass transfer is not the sole cause of unsteady-state limiting currents, observed when a fast current ramp is imposed on an elongated electrode. In copper deposition, in particular, as a result of the appreciable surface overpotential (see Section III,C) and the ohmic potential drop between electrodes, the current distribution below the limiting current is very different from that at the true steady-state limiting current. 

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.)...

If a cell is operated potentiometrically, then only two electrodes are required. However, if closed-circuit operation is to be employed it is necessary to measure electrode overpotentials. To measure electrode overpotentials it is necessary to use a three-electrode DC system. The system consists of a working electrode which is exposed to reaction conditions, a counter electrode (which is exposed to a constant partial pressure of oxygen in the case of an oxygen-ion conducting electrolyte), and a reference electrode. The reference electrode remains unpolarized during the measurements and may be exposed to either reaction conditions or the constant conditions of the counter electrode. A power supply is used to polarise the working and counter electrodes while the current is recorded (see Figure 3). 

Arrhenius plots of conductivity for the four components of the elementary cell are shown in Fig. 34. They indicate that electrolyte and interconnection materials are responsible of the main part of ohmic losses. Furthermore, both must be gas tight. Therefore, it is necessary to use them as thin and dense layers with a minimum of microcracks. It has to be said that in the literature not much attention has been paid to electrode overpotentials in evaluating polarization losses. These parameters greatly depend on composition, porosity and current density. Their study must be developed in parallel with the physical properties such as electrical conductivity, thermal expansion coefficient, density, atomic diffusion, etc. 

Here / is the current density with the subscript representing a specific electrode reaction, capacitive current density at an electrode, or current density for the power source or the load. The surface overpotential (defined as the difference between the solid and electrolyte phase potentials) drives the electrochemical reactions and determines the capacitive current. Therefore, the three Eqs. (34), (35), and (3) can be solved for the three unknowns the electrolyte phase potential in the H2/air cell (e,Power), electrolyte phase potential in the air/air cell (e,Load), and cathode solid phase potential (s,cath), with anode solid phase potential (Sjan) being set to be zero as a reference. The carbon corrosion current is then determined using the calculated phase potential difference across the cathode/membrane interface in the air/air cell. The model couples carbon corrosion with the oxygen evolution reaction, other normal electrode reactions (HOR and ORR), and the capacitive current in the fuel cell during start-stop. 

Figure 13 shows the potential and concentration distributions for different values of dimensionless potential under conditions when internal pore diffusion (s = 0.1) and local mass transport (y = 10) are a factor. As expected the concentration and relative overpotential decrease further away from the free electrolyte (or membrane) due to the combined effect of diffusion mass transport and the poor penetration of current into the electrode due to ionic conductivity limitations. The major difference in the data is with respect to the variation in reactant concentrations. In the case when an internal mass transport resistance occurs (y = 10) the fall in concentration, at a fixed value of electrode overpotential, is not as great as the case when no internal mass transport resistance occurs. This is due to the resistance causing a reduction in the consumption of reactant locally, and thereby increasing available reactant concentration the effect of which is more significant at higher electrode overpotentials. 

To make Tafel plots (Figure 8.15) [124,125] subsequent to the subtraction of the ohmic losses (iR), the electrode overpotential, p, is plotted versus ln(.//./0). For systems controlled by standard electrochemical kinetics, the slope at a high overpotential gives the anodic and the cathodic transference coefficients, aA and ac, respectively, and the intercept gives the exchange current density, J0. 

Since only the working electrode overpotential and current reveal, respectively, the thermodynamic and kinetic information of a... 

The PEVD reaction current, 60 s after changing the working electrode overpotential at each step, from a stage n PEVD sample is recorded. The results were repeatable. Two kinds of plots are commonly used to show the dependence of the current on overpotentials at various temperatures. One is a current vs. overpotenlial plot as shown in Figure 39 the other is aln(current) vs. overpotenlial plot (Tafel plot) in Figure 40. 

Figure 45 shows a three-dimensional SECV spectrum for a stage II PEVD system at 550°C. This spectrum can be projected to three planes, i.e., the working electrode overpotential - PEVD current plane, the PEVD current - time... 

The total cell activation overpotential is the sum of the activation overpotentials at the anode and cathode, as shown in Fig. 13 for the case of H2O electrolysis using Pt electrodes in alkaline solutions. The two overpotentials can be separated by the use of a reference electrode. Thus, the use of reference electrodes is essential for the study of electrocatalysis, since in this case one can individually study the dependence of each electrode overpotential on the current and thus assess the elec-trocatalytic performance of each electrode. The best electrocatalyst, for each charge-transfer reaction is, obviously, the one that minimizes the activation overpotential. 

Additional parameters specified in the numerical model include the electrode exchange current densities and several gap electrical contact resistances. These quantities were determined empirically by comparing FLUENT predictions with stack performance data. The FLUENT model uses the electrode exchange current densities to quantify the magnitude of the activation overpotentials via a Butler-Volmer equation [1], A radiation heat transfer boundary condition was applied around the periphery of the model to simulate the thermal conditions of our experimental stack, situated in a high-temperature electrically heated radiant furnace. The edges ofthe numerical model are treated as a small surface in a large enclosure with an effective emissivity of 1.0, subjected to a radiant temperature of 1 103 K, equal to the gas-inlet temperatures. 

The current at the electrode where oxidation a —r b takes place is referred to as the anodic current. If the density Ca of the reduced species a is kept constant near the electrode, the current is = ekb aCa- The result (17.16) predicts that under the specified conditions (large Er, small z/) a logarithmic plot of the current with respect to erf/iksT increases linearly with the overpotential z , with a slope 1/2. This behavior is known in electrochemistry as TafeTs law, and the corresponding slope is related to the so called TafeTs slope. An example where this law is quantitatively observed is shown in Fig. 17.2. In fact, a linear dependence of log(/) on the overpotential is often seen, however the observed slope can considerably deviate from and is sometimes temperature-dependent. Observed deviations are usually associated with the approximations made in deriving (17.16) from (17.15) and may be also related to the assumption made above that all the overpotential is realized as a potential drop between the molecule and the metal, an assumption that is better satisfied when the ionic strength of the solution increases. 

Figure 1 is a cross-section of an electrolytic cell with a resistive electrode and a terminal for contact at one end of the electrode. The current lines in the cell are shown along with the corresponding potential drop. Within the electrolyte (point C-D) the potential drop is linear at the electrolyte/seed layer interface there is a sudden drop in potential, on one side there is the charge transfer and concentration overpotential while on the other side is the metal potential. Finally there is a non-linear drop through the seed layer (A-B). The current lines are closely spaced near the contact terminal both on the electrolyte side and within the seed layer. This effectively means that the local current density will be high next to the contact terminal where the current lines are closely spaced. 

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