Activation overpotential dependence

Since both OCV and activation overpotential depend on some gas species concentration, and since in a PEN lumped structure the mass transport cannot be directly modeled within the domain thickness, the so-called concentration losses are introduced. They represent the voltage reduction due to the fact that the gas species concentration reacting in the reaction zone is different from that used in the calculation (i.e. the concentration relative to the gas channel, also referred to as the bulk ). 

Charge Transport. Side reactions can occur if the current distribution (electrode potential) along an electrode is not uniform. The side reactions can take the form of unwanted by-product formation or localized corrosion of the electrode. The problem of current distribution is addressed by the analysis of charge transport ia cell design. The path of current flow ia a cell is dependent on cell geometry, activation overpotential, concentration overpotential, and conductivity of the electrolyte and electrodes. Three types of current distribution can be described (48) when these factors are analyzed, a nontrivial exercise even for simple geometries (11). 

The physical mechanism described allows one to answer two basic questions (1) Why does the electrochemical process usually require activation and (2) Why is there no inverted region in the current-overpotential dependence ... 

The dimensionless limiting current density N represents the ratio of ohmic potential drop to the concentration overpotential at the electrode. A large value of N implies that the ohmic resistance tends to be the controlling factor for the current distribution. For small values of N, the concentration overpotential is large and the mass transfer tends to be the rate-limiting step of the overall process. The dimensionless exchange current density J represents the ratio of the ohmic potential drop to the activation overpotential. When both N and J approach infinity, one obtains the geometrically dependent primary current distribution. 

It is important to note that as early as 1931, the density of electronic states in metals, the distribution of electronic states of ions in solution, and the effect of adsorption of species on metal electrode surfaces on activation barriers were adequately taken into account in the seminal Gurney-Butler nonquadratic quantum mechanical treatments, which provide excellent agreement with the observed current-overpotential dependence. 

The activation overpotentials for both electrodes are high therefore, the electrochemical kinetics of the both electrodes can be approximated by Tafel kinetics. The concentration dependence of exchange current density was given by Costamagna and Honegger.The open-circuit potential of a SOFC is calculated via the Nernst equation.The conductivity of the electrolyte, i.e., YSZ, is a strong function of temperature and increases with temperature. The temperature dependence of the electrolyte conductivity is expressed by the Arrhenius equation. 

The form of the I vs. V relation (7.317) for a cell, which has just been derived, depends upon the assumption that the activation overpotentials Tij and ti2 at the two interfaces have pushed the i vs. T) curves into the exponential region. If, instead, the two interfaces are showing ohmic behavior, then one has from Eq. (7.308) and linear i vs. T) relations (7.25) ... 

Note how, even in the region in which there is linear behavior of V with respect to /, the actual value of the potential that the generator could put out depends on the value of the so-called constant, i.e., on the activation overpotential and thus on the exchange current densities and the catalytic power of the electrodes. 

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. 

The dependence of the activation overpotential on current in generally described... 

Chemical reactions can happen before or after the charge-transfer step. Any step can be rate determining, that is, the slowest one determines the total reaction rate. As the electrode polarizes, the resulting overpotential consists of several factors. The most important ones are activation, concentration, and resistance overpotentials. The activation overpotential results from the limited rate of a charge-transfer step, concentration overpotential from the mass-transfer step, and resistance overpotential is the result of ohmic resistances such as solution resistance. Depending on the nature of the slowest step, the reaction is activation, mass transfer, or resistance controlled. 

The thickness distribution of electrodeposits depends on the current distribution over the cathode, which determines the local current density on the surface. The current distribution is determined by the geometrical characteristics of the electrodes and the cell, the polarization at the electrode surface, and the mass transfer in the electrolyte. The primary current distribution depends only on the current and resistance of the electrolyte on the path from anode to cathode. The reaction overpotential (activation overpotential) and the concentration overpotential (diffusion overpotential) are neglected. The secondary... 

The activation overpotential mainly depends on the kinetic parameters of processes under consideration on the given substrate... 

When an ion is on the surface of the electrode, electrons must transfer from the electrode to the ion. How easily this takes place depends on the electrode metal and the nature of its surface. You must build up a charge first until the potential difference is such that a transfer will take place. This is called activation overpotential. Figure 26-6 shows how this varies as the current density changes. 

The calculated value E° = +1.23 V for the O2, 4H /2H20 electrode implies that electrolysis of water using this applied potential difference at pH 0 should be possible. Even with a platinum electrode, however, no O2 is produced. The minimum potential for O2 evolution to occur is about 1.8V. The excess potential required ( 0.6V) is the overpotential of O2 on platinum. For electrolytic production of H2 at a Pt electrode, there is no overpotential. For other metals as electrodes, overpotentials are observed, e.g. 0.8 V for Hg. In general, the overpotential depends on the gas evolved, the electrode material and the current density. It may be thought of as the activation energy for conversion of the species discharged at the electrode into that liberated from the electrolytic cell, and an example is given in worked example 16.3. Some metals do not liberate H2 from water or acids because of the overpotential of H2 on them. 

V/hen only activation overpotentials are important, the obtained current distribution is called the secondary distribution. The potential difference across the interface depends on the local current density. Therefore, the solution near the electrodes is no longer an equi-potential surface. Since higher current densities involve larger overpotentials (passivation excluded), the activation overpotentials will tend to make the current distribution more uniform. Also the total current will decrease. This can easily be understood by means of fig. 1.16. 

Primary current distribution depends only on cell geometry if the potential is uniform over the electrode, when the activation overpotential is assumed to be zero and mass-transfer effects are considered to be absent. This can be determined generally by solving the Laplace equation (1) in the bulk using either Neumann or Dirichlet boundary conditions. The Dirichlet boundary condition specifies the potential on the electrode, whereas the... 

Randles analysis was based on the fact that, for transient responses to electrical perturbation, the electrical properties of electrodes at which the simple activation-controlled charge transfer is the rate-determining step (rds) can be represented by the equivalent circuit shown in Figure 6, where is a nonlinear and overpotential-dependent Faradaic resistance, which can be derived from Eq. (23). At very small values of 17 for which the exponential terms can be linearized (17 < 10 mV), this is obtained as... 

The sensitivity of the cell voltage to the fuel utilization depends on several contributions (1) the Nemst potential (2) the activation overpotential (3) the diffusion overpotential (4) eventually, the effect of leakages of air at the anode side. Conversely, a modification of the fuel utilization does not cause any effect on the ohmic overpotential inside the cell layers, and therefore the ohmic overpotential is not affected by the fuel utilization term. 

Anyway, from both these models it is possible to express the anode activation overpotential as a function of the local partial pressures of fuel and products, expressing thus the dependence of the activation overpotential on the fuel utilization factor. 

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