Polarization ohmic resistance

Tafel slope (Napieran loop) transfer coefficient diffusion layer thickness dielectric constant, relative electric field constant = 8.85 x 10 F cm overvoltage, polarization ohmic voltage drop, resistance polarization specific conductance, conductivity electrochemical potential of material X,... 

In an analysis of an electrode process, it is useful to obtain the impedance spectrum —the dependence of the impedance on the frequency in the complex plane, or the dependence of Z" on Z, and to analyse it by using suitable equivalent circuits for the given electrode system and electrode process. Figure 5.21 depicts four basic types of impedance spectra and the corresponding equivalent circuits for the capacity of the electrical double layer alone (A), for the capacity of the electrical double layer when the electrolytic cell has an ohmic resistance RB (B), for an electrode with a double-layer capacity CD and simultaneous electrode reaction with polarization resistance Rp(C) and for the same case as C where the ohmic resistance of the cell RB is also included (D). It is obvious from the diagram that the impedance for case A is... 

FIGURE 2.13 (a) Maximum power and (b) cell total ohmic resistance (labeled as IR resistance ) and interfacial resistance (labeled as polarization ) at constant current density of 0.3 A/cm2 versus the volume percent of Ni in the Ni-YSZ cermet for electrolyte-supported cells with an active area of 2 cm2 operated at 1000°C. (From Koide, H. et al., Solid State Ionics, 132 253-260, 2000. Copyright by Elsevier, reproduced with permission.)... 

Effects from polarization of electrodes should be eliminated or properly treated to obtain the true ohmic resistance of the solution. 

Ohmic Polarization Ohmic losses occur because of resistance to the flow of ions in the electrolyte and resistance to flow of electrons through the electrode materials. The dominant ohmic losses, through the electrolyte, are reduced by decreasing the electrode separation and enhancing the ionic conductivity of the electrolyte. Because both the electrolyte and fuel cell electrodes obey Ohm s law, the ohmic losses can be expressed by the equation... 

To determine actual cell performance, three losses must be deducted from the Nernst potential activation polarization, ohmic polarization, and concentration polarization. Definition of the ohmic polarization is simply the product of cell current and cell resistance. Both activation polarization and concentration polarization required additional description for basic understanding. 

The tape casting and electrophoretic deposition processes are amenable to scaleup, and thin electrolyte structures (0.25-0.5 mm) can be produced. The ohmic resistance of an electrolyte structure and the resulting ohmic polarization have a large influence on the operating voltage of MCFCs (14). FCE has stated that the electrolyte matrix encompasses 70% of the ohmic loss (15). At a current density of 160 mA/cm, the voltage drop (AVohm) of an 0.18 cm thick electrolyte structure, with a specific conductivity of -0.3 ohm cm at 650°C, was found to obey the relationship (13). 

Ohmic polarization arises from the resistance of the electrolyte, the conductive diluent, and materials of construction of the electrodes, current collectors, terminals, and contact between particles of the active mass and conductive diluent or from a resistive film on the surface of the electrode. Ohmic polarization appears and disappears instantaneously (<10 s) when current flows and ceases. Under the effect of ohmic resistance, R, there is a linear Ohm s Law relationship between /and rj. 

It should be understood that even for micro surface features the potential is uniform and the ohmic resistance through the bath to peaks and valleys is about the same. Also, electrode potential against SCE will be uniform. What is different is that over micro patterns the boundary of the diffusion layer does not quite follow the pattern contour (Fig. 12.3). Rather, it thus lies farther from depth or vias than from bump peaks. The effective thickness, 8N, of the diffusion layer shows greater variations. This variation of 8N over a micro profile therefore produces a variation in the amount of concentration polarization locally. Since the potential is virtually uniform, differences in the local rate of metal deposition result if it is controlled by the diffusion rate of either the depositing ions or the inhibiting addition (leveling) agents. 

When j0 is very small, the region corresponding to linear polarization may not be accessible because residual currents due to the oxidation and reduction of impurities may be larger than the currents due to the electrode reaction under consideration. In addition, the ohmic resistance at the electrode—electrolyte interface can only be neglected if it is much less than the polarization resistance. 

Ohmic polarization takes place on account of resistance to the flow of ions and electrons in the battery. More precisely, ohmic polarization results from the resistance that arises as a result of the presence of such components in the battery as the electrolyte, electrodes, current collectors, and terminals. The overpotential generated is expressed by the term IE, in which R is the specific area resistance [6,8,66] and I is the flowing current. This type of polarization emerges and vanishes instantly, when the current flows and ceases, respectively. This is given by the Ohm s law relationship, t n = IE, between the current, I, and the overpotential, i)Q, due to the ohmic resistance in the cell. 

The Wagner parameter, W, is the ratio of the kinetic resistance to the ohmic resistance. The Wagner parameter is the ratio of the true polarization slope given by the partial derivative, dE /di, evaluated at the overpotential of interest at constant pressure, temperature, and concentration, divided by the characteristic length and the solution resistance (2,40). 

In analyzing the polarization data, it can be seen that the cathodic reaction on the copper (oxygen reduction) quickly becomes diffusion controlled. However, at potentials below -0.4 V, hydrogen evolution begins to become the dominant reaction, as seen by the Tafel behavior at those potentials. At the higher anodic potentials applied to the steel specimen, the effect of uncompensated ohmic resistance (IRohmk) can be seen as a curving up of the anodic portion of the curve. 

In this experiment, corrosion rates will be estimated via the Stern-Geary relationship by measuring the polarization resistance, Rp. This parameter will be measured in two ways via conventional polarization resistance (PR) measurements and via electrochemical impedance spectroscopy (EIS). In addition, the errors in corrosion rate estimation introduced by the use of a finite scan rate and the presence of uncompensated ohmic resistance will be demonstrated. 

This set of experiments has focused on the use of two nondestructive electrochemical techniques to measure polarization resistance and thereby estimate the corrosion rate. In addition, the effects of scan rate and uncompensated ohmic resistance were studied. Three main points should have been made by this lab (1) Uncompensated ohmic resistance is always present and must be measured and taken into account before Rp values can be converted into corrosion rates, otherwise an overestimation of Rv will result. This overestimate of Rp leads to an underestimate of corrosion rate, with the severity of this effect dependent upon the ratio Rp/Ra. (2) Finite scan rates result in current shunted through the interfacial capacitance, thereby decreasing the observed impedance and overestimating the corrosion rate. (3) Both of these errors can be taken into account by measuring Ra via EIS or current interruption and by using a low enough scan rate as indicated by an EIS measurement in order to force the interfacial capacitance to take on very large impedance values in comparison to Rp. 

Only under such small signal conditions does the polarization overpotential assume linear correlation with the current density, and resembles an ohmic resistance. 

At the mid-point of the polarization curve (Figure 1.20), the cell voltage drop is dominated by the drop caused by internal resistance. This internal resistance is also called ohmic resistance. The drop can be calculated as AEohmic = IceuRei-... 

As shown in Figure 3.13, the voltage losses can be analyzed from the polarization curve. Generally, the voltage losses consist of four parts (1) loss due to gas crossover this is represented by the open circuit voltage (OCV), which is lower than the thermodynamic voltage (2) loss due to activation resistance (3) loss due to ohmic resistance and (4) loss due to mass transport limitation. 

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