Resistance overpotential

The impedance is dependent on temperature, as can be seen in Figure 4, which shows the area specific resistance (ASR) of a cell as a function of cell temperature for different gas flow rates. For the same cell temperatures, lower ASR was observed for increasing gas flow rates due to the increased gas diffusion near the electrodes that effectively reduced the overpotential resistances [4], Because the anode and cathode are often conductive, the impedance of the cell is dependent largely on the thickness of the electrolyte. Using an anode supported cell structure, a YSZ electrolyte can be used as thin as 10-20 pm or even 1-2 pm [32, 33] as compared to 0.5 mm for a typical electrolyte supported cell [26],... 

The distribution of current (local rate of reaction) on an electrode surface is important in many appHcations. When surface overpotentials can also be neglected, the resulting current distribution is called primary. Primary current distributions depend on geometry only and are often highly nonuniform. If electrode kinetics is also considered, Laplace s equation stiU appHes but is subject to different boundary conditions. The resulting current distribution is called a secondary current distribution. Here, for linear kinetics the current distribution is characterized by the Wagner number, Wa, a dimensionless ratio of kinetic to ohmic resistance. 

Tertiay Current Distribution. The current distribution is again impacted when the overpotential influence is that of concentration. As the limiting current density takes effect, this impact occurs. The result is that the higher current density is distorted toward the entrance of the cell. Because of the nonuniform electrolyte resistance, secondary and tertiary current distribution are further compHcated when there is gas evolution along the cell track. Examples of iavestigations ia this area are available (50—52). 

Resistance overpotential i/r Since in corrosion the resistance of the metallic path for charge transfer is negligible, resistance overpotential ijr is determined by factors associated with the solution or with the metal surface. Thus resistance overpotential may be defined as... 

The importance of the method in corrosion testing and research has stimulated other work, and since Stern s papers appeared there have been a number of publications many of which question the validity of the concept of linear polarisation. The derivation of linearity polarisation is based on an approximation involving the difference of two exponential terms, and a number of papers have appeared that have attempted to define the range of validity of polarisation resistance measurements. Barnartt" derived an analytical expression for the deviations from linearity and concluded that it varied widely between different systems. Leroy", using mathematical and graphical methods, concluded that linearity was sufficient for the technique to be valid in many practical corrosion systems. Most authors emphasise the importance of making polarisation resistance measurements at both positive and negative overpotentials. 

Polarisation Resistance slope of the linear plot of overpotential versus current density measured at potentials close to the corrosion potential, or the tangent of such a curve at the corrosion potential if the plot is not linear. If a small change in potential, A , gives rise to a change in current density. A/, then the polarisation resistance is / p(Q m ) = AE/Ai. 

For the electrolysis of a solution to be maintained, the potential applied to the electrodes of the cell (Eapp ) must overcome the decomposition potential of the electrolyte (ED) (which as shown above includes the back e.m.f. and also any overpotential effects), as well as the electrical resistance of the solution. Thus, Eapp must be equal to or greater than (ED + IR), where / is the electrolysis current, and R the cell resistance. As electrolysis proceeds, the concentration of the cation which is being deposited decreases, and consequently the cathode potential changes. 

Corresponding to the charge in the potential of single electrodes which is related to their different overpotentials, a shift in the overall cell voltage is observed. Moreover, an increasing cell temperature can be noticed. Besides Joule-effect heat losses Wj, caused by voltage drops due to the internal resistance Rt (electrolyte, contact to the electrodes, etc.) of the cell, thermal losses WK (related to overpotentials) are the reason for this phenomenon. 

The latter equals IRwc where RWc is the ohmic resistance between the working and counter electrode. Experimentally it is rather easy to measure the riohmic.wc term using the current interruption technique as shown in Figure 4.9. Upon current interruption the ohmic overpotential r 0i,mjCtwc vanishes within less than 1 ps and the remaining part of the overpotential which vanishes much slower is t w+T c (Eq. 4.9). 

Figure 8.32. PEMFC potential as a function of current density for different CO contents in the hydrogen supply. Note the rapid drop in potential as soon as current is drawn, even for pure hydrogen. This is due to overpotentials in the system, while the monotonic decrease at higher current is attributed to the internal resistance of the PEM. [Adapted from H.F. Oetjen,...

In practice the situation is less favorable due to losses associated with overpotentials in the cell and the resistance of the membrane. Overpotential is an electrochemical term that, basically, can be seen as the usual potential energy barriers for the various steps of the reactions. Therefore, the practical efficiency of a fuel cell is around 40-60 %. For comparison, the Carnot efficiency of a modern turbine used to generate electricity is of order of 50 %. It is important to realize, though, that the efficiency of Carnot engines is in practice limited by thermodynamics, while that of fuel cells is largely set by material properties, which may be improved. 

However, under working conditions, with a current density j, the cell voltage E(j) decreases greatly as the result of three limiting factors the charge transfer overpotentials r]a,act and Pc,act at the two electrodes due to slow kinetics of the electrochemical processes (p, is defined as the difference between the working electrode potential ( j), and the equilibrium potential eq,i). the ohmic drop Rf. j, with the ohmic resistance of the electrolyte and interface, and the mass transfer limitations for reactants and products. The cell voltage can thus be expressed as... 

In general, the physical state of the electrodes used in electrochemical processes is the solid state (monolithic or particulate). The material of which the electrode is composed may actually participate in the electrochemical reactions, being consumed by or deposited from the solution, or it may be inert and merely provide an interface at which the reactions may occur. There are three properties which all types of electrodes must possess if the power requirements of the process are to be minimized (i) the electrodes should be able to conduct electricity well, i.e., they should be made of good conductors (ii) the overpotentials at the electrodes should be low and (iii) the electrodes should not become passivated, by which it is meant that they should not react to form on their surfaces any compound that inhibits the desired electrochemical reaction. Some additional desirable requirements for a satisfactory performance of the cell are that the electrodes should be amenable to being manufactured or prepared easily that they should be resistant to corrosion by the elements within the cell that they should be mechanically strong and that they should be of low cost. Electrodes are usually mounted vertically, and in some cases horizontally only in some rare special cases are they mounted in an inclined manner. 

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 convenient to distinguish three components of the overpotential, r. Two of these are associated respectively with mass-transfer restrictions in the electrolyte near the electrode (concentration overpotential, f/c), and with kinetic limitations of the reaction taking place at the electrode surface (surface overpotential, rjs) the third one is related to ohmic resistance. 

The second bracket contains the aspect ratio. The group in the first bracket is a measure of the approach to the limiting current modified by a total overpotential. The authors describe this group as a ratio of mass-transfer resistance to kinetic resistance. 

At higher overpotentials the second-order terms become important, and Eq. (6.9) is no longer valid. At very large overpotentials, when eorj > A, Eq. (6.8) even predicts a decrease of the current with increasing overpotential, i.e., a negative resistance. However, better versions of this theory to be presented in the following section do not show this behavior. 

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