Ohmic Resistance of the Cell

The current density distribution in a rectangular electrolytic cell in which parallel electrodes cover only part of the wall of the cell is illustrated in Fig. 3.4. The linear approximation of the current density distribution in the cell with plane parallel electrodes shown in Fig. 3.4a is presented schematically in Fig. 3.4b. 

The analysis performed here for the current density distribution between the edges of electrode and the side walls of cell is also valid for the case where there is the distance between the upper edges of the electrodes and free surface of solution. 

The resistance of the whole electrolyte is then given by Popov et al. [4]  

The side screens enabled that the distance Lh between the edges of the electrodes and the side walls of the cell to be varied for given values Ah and 2Ch- The resistance of the system for various adjusted values Lh was measured by the bridge method using the platinum electrodes in a 0.020 M KCl solution. The electrodes were 2 cm long and 1 cm wide. The inter-electrode distance was 2 cm. Hence, in this case Ah = Ch- The back sides of the electrodes were insulated. The upper edges of the electrode touch the free surface of the solution and the lower edges of the electrode touch the bottom of the cell. 

The dependence of the total resistance of a system with plane parallel electrodes on the distance between the electrode edges and the cell side walls is shown in Fig. 3.6. 

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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... 

A low ohmic resistance of the cell is desired from several points of view this may be achieved by having a small distance between anode and cathode, a large electrode surface, a compact cell, and a low-resistance diaphragm. A distance between anode and cathode as small as 0.1-0.2 mm has been reported [9], although usually larger distances are employed. A large electrode area may involve the use of many electrodes a further development in this direction is the fluidized bed electrode (Chapter 31). 

In a practical device, the cell geometry must allow for the illumination of the semiconductor/solution interface, and the ohmic resistance of the cell should be minimised to avoid internal power loss. This is best achieved in a thin-layer device in which the semiconductor electrode faces the Sun and is illuminated throngh the electrolyte and the counter electrode. The counter electrode should therefore either be translucent or coarsely gridded. 

With increase of formation current density the polarization (voltage) of the cell increases, i.e. the potentials of the two types of plates rise. They may reach values higher than the evolution potentials of the H H2 and H2OIO2 electrodes. Consequently, flie rates of O2 and H2 evolution increase, i.e. greater volumes of gas are evolved per unit time. Adsorbed gas layers form on the surface of the lead and lead dioxide active materials, which increase the ohmic resistance of the cell and its polarization, and hence, the energy consumption for battery formation increases, too. The formed gas phase should be carried out of the cell, which can also be achieved by electrolyte re-circulation. 

Ohmic resistance of the cell Current efficiency Anodic, cathodic overpotential (V) Electrolyte conductivity (S m ) Reagent conversion Space-time yield... 

Despite the ionic resistance of the electrolyte plays an important role in the cell ohmic resistance, it is the contribution of the anode and cathode resistance which determines the high ohmic resistance of the cell this is due to the long path of the electrons in the electrodes [29] (high in-plane resistance). The equivalent electrical circuit has been assumed by the current literature [30,31] and the ohmic overpotential has been evaluated according to the equations (42) and (43) ... 

The ohmic polarization in Eq. (26.12) represents the total area specific ohmic resistance of the cell. Ri is the sum of the anode, cathode, electrolyte, interconnect, and contact ohmic resistances. Typically, the ohmic resistance is dominated by the electrolyte resistance and decreases with increasing operating temperature. The reduction in ohmic polarization is part of the reason why anode-supported cells have become the standard design in current high-performance SOFCs. 

The choice of the electrolyte is one of the most important tasks in designing a cell for a battery. The electrolyte electronically separates the electrodes from reacting directly in a chemical reaction, it transports electrochemically active species to/from the electrodes, and it is responsible for the Ohmic resistance of the cell that determines Joule s heating and the loss in power and usable electrical energy. In several cell types, the electrolyte takes even its own part in the main electrochemical reactions of the cell. Then, the electrolyte is defined by the specific cell reaction. In other cases, only concentrations of the electrolyte components can be varied within a limited range. Even if the electrolyte does not take part in the main electrochemical reactions, it still has a strong impact on the performance of the cell. Its chemical and electrochemical properties including... 

Since both H2 oxidation and reduction encounter low overpotentials, the voltage required for the pumping process is low. The I-V curve is typically linear and the slope of the line is mainly the Ohmic resistance of the cell. However, in the presence of CO, the anode is poisoned and the pumping voltage can increase significantly with the pumping current density, (Figure 11.33)... 

Halseid et al. [24] have tested the ohmic resistance of the cell while introducing 1 and 10 ppm NH3 into the anode stream. It was foimd that the increase in cell resistance after the cell was exposed to NH3 was about 20% in most cases, and made just 5% (1 ppm) and 15% (10 ppm) contribution to the performance losses. Ton exchange" may provide a reasonable explanation for the quick and severe impact of NH3, i.e., NHj would react with protons in the membrane, thus staying in the membrane and causing the decrease in the protonic conductivity of the membrane. In addition, the water content in the membrane phase decreases linearly with increasing NH4 fraction [22]. For PFSA membrane, dehydration will cause catastrophic consequences to the fuel cell performance. 

The obtained results showed that the cell performance was influenced by the interfacial resistances, especially at temperatures below 550 °C, where the cell performance is essentially limited by the electrolyte-cathode interfacial resistances. The ohmic resistance of the cell is usually taken as the overall electrolyte... 

The working voltage of an operating fuel cell (/, is even lower because of the internal ohmic resistance of the cell and the shift of potential of the electrodes occurring when current flows, also called electrode polarization, and caused by... 

The main advantage of the coplanar fuel cell design is the possibility of considerably reducing the internal ohmic resistance of the cell, which is due primarily to the ohmic resistauce of the electrolyte. To decrease the ohmic resistance of conventional MEAs it is necessary to reduce the thickness of the electrolyte. An excessive reduction of this thickness can have detrimental consequences the formation of cracks and pinholes and the loss of stability and gas-tighmess. In strip cells the ohmic resistance is determined by the width of the gap between cathodes and anodes and can be decreased simply by narrowing this gap. If the electrodes are micropattemed to be close together, the cell s power density can be increased considerably. 

Fig. 9.8 Schematic diagram showing the domain of possible ccnnbinations of the reftaence electrode width (Lre), distance between working and reference electrodes ( ), and solid-electrolyte thickness (d) in the planar cells with symmetric WE and CE, illustrated in the inset [8]. Solid line corresponds to the condition A.Uj / Ra 1) = 10 where A /re is the potential differtaice along the RE, Rci is the total ohmic resistance of the cell, and I is the total electrical cumait. Bine area corresponds to the region where normalized A17re does not introduce any significant error in the measurements...

The recovery time depends on the impedance at the electrode-electrolyte interface. Depending on the time constant associated with the resistance and capacitance (RC constant) of the interface, the voltage exponentially recovers. By measuring the jump (or drop) at zero time (or realistically within 10 s), one can obtain the value of the ohmic resistance of the cell. The ohmic resistance of the cell Rohm (il-cm ) is determined as the quotient of the instantaneous change in voltage and the cell current density i (A cm" ) just prior to the interrupt event, Rohm = 5(V)/i. If the cell is operating far below mass transfer limits, then the voltage recovery corresponds to the activation loss in the cell. 

AC impedance studies have indicated that DMFC performance loss due to interfacial failure can be linked to (1) increased ohmic resistance of the cell, (2) enhanced electrode overpotential, and (3) electrode flooding. Ohmic loss due to the interfacial resistance buildup can contribute several tens of milliohm square centimeters to the total ceU resistance. An increase in the overpotential is caused by the loss of contact between the membrane and the catalyst, which renders part of the catalyst layer unusable (a possible major performance loss). Electrode flooding can be attributed to the nonuniform current distribution, which is more significant when membrane-cathode delamination occurs. 

An increase in operating temperature lowers the internal resistance (mainly ohmic resistance) of the cell. The experimental data suggest an increase of voltage... 

The impedance spectra of Figs. B.13, B.14, B.15, and B.16 further clarify the previous points. By way of an example, at 650 C the ohmic resistance of the cell is around 10 mQ and clearly independent of the fuel composition, but total cell polarization increases as the N2-content increases with 20% nitrogen content in the fuel stream, total cell polarization is around 19 mQ, rising to around 24 mQ with 80% molar content. Moreover, as the N2 content increases, it is mass transport processes rather than electrochemical processes that clearly hmit fuel cell operation. 

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