Model point electrode

The preceding sections have discussed what occurs inside the membrane. The potential has been that in the ionomer. Our goal here is to develop an analytic model of the potential from the metal on each side into and through the ionomer. As this chapter is concerned with membrane modeling, we will only consider a hydrogen pump cell with hydrogen electrodes on the anode and cathode sides. We will treat point electrodes on the boundaries of the one-dimensional membrane. The point electrode model will supply the necessary interface equations to use in a distributed electrode model, which one would need in order to expect the model to match experimental data. However, this chapter focuses on the membrane, not the electrode. We will assume we can maintain equal H2 gas pressure on each side so that the gas contribution to any Nemst potential will be zero. 

In order to predict absolute dielectric strengths we need to have more detailed information than is yet available about electronic states and mobilities in polymers. For the present we can only conclude that there is satisfactory agreement between the form of the theoretical results, based on a rather general electronic model, and the best experimental results. To the extent that the model is a very reasonable one, we can say that we can understand intrinsic breakdown behaviour. Measurement of pre-breakdown currents, especially with pointed electrodes which impose regions of very high field strength at their tips when embedded in the material, suggests that electronic carrier production either by injection from the electrodes (Schottky emission) or from impurities (Poole-Frenkel effect) may play a part in the breakdown process. More work is required, however, before this can be fully understood. 

In the following, a short overview of the most important assumptions and equations of the four electrode model categories is given. In addition, it is pointed out how the electrode models comply with the input/output scheme in Figure 28.3. The equations presented in this chapter are formulated in a general notation, which does not discriminate between anode and cathode models. 

Usually, the starting point of model derivation is either a physical description along the channel or across the membrane electrode assembly (MEA). For HT-PEFCs, the interaction of product water and electrolyte deserves special attention. Water is produced on the cathode side of the fuel cell and will either be released to the gas phase or become adsorbed in the electrolyte. As can be derived from electrochemical impedance spectroscopy (EIS) measurements [14], water production and removal are not equally fast Water uptake of the membrane is very fast because the water production takes place inside the electrolyte, whereas the transport of water vapor to the gas channels is difiusion limited. It takes several minutes before a stationary state is reached for a single cell. The electrolyte, which consists of phosphoric add, water, and the membrane polymer, changes composition as a function of temperature and water content [15-18]. As a consequence, the proton conductivity changes as a function of current density [14, 19, 20). 

Passive electrodes with a nearly constant corrosion current over an appreciable potential range. They are generally dealt widi in terms of high field migration. Passive electrodes with a potential-dependent current, most commonly exhibiting a minimum. Less advanced models are available they involve the contribution of defects (e.g., point defect model). 

The objective of an electrode model is to analyse the point-to-point distribution of the reaction in an SOFC electrode, leading to current, potential, and species concentration distributions. The result of the analysis is a prediction of the polarisation of the electrode due to (i) kinetic resistance, (ii) mass transfer resistance, and (iii) ohmic resistance. 

There are two types of fluoride lon-selective electrodes available [27] Onon model 96-09-00, a combination fluoride electrode, and model 94-09-00, which requires a reference electrode The author prefers to use Onon model 94-09-00 because it has a longer operational life and is less expensive When an electrode fails, the reference electrode is usually less expensive to replace The Fisher Accumet pH meter, model 825 MP, automatically computes and corrects the electrode slope It gives a direct reading for pH, electrode potential, and concentra tion in parts per million The fluoride lon-specific electrode can be used for direct measurement [2S, 29] or for potenPometric titration with Th" or nitrate solutions, with the electrode as an end point indicator... 

The inner layer (closest to the electrode), known as the inner Helmholtz plane (IHP), contains solvent molecules and specifically adsorbed ions (which are not hilly solvated). It is defined by the locus of points for the specifically adsorbed ions. The next layer, the outer Helmholtz plane (OHP), reflects the imaginary plane passing through the center of solvated ions at then closest approach to the surface. The solvated ions are nonspecifically adsorbed and are attracted to the surface by long-range coulombic forces. Both Helmholtz layers represent the compact layer. Such a compact layer of charges is strongly held by the electrode and can survive even when the electrode is pulled out of the solution. The Helmholtz model does not take into account the thermal motion of ions, which loosens them from the compact layer. 

Before the pH electrode is used, it should be calibrated using two (or more) buffers of known pH. Many standard buffers are commercially available, with an accuracy of 0.01 pH unit. Calibration must be performed at the same temperature at which the measurement will be made care must be taken to match the temperature of samples and standards. The exact procedure depends on the model of pH meter used. Modem pH meters, such as the one shown in Figure 5-8, are microcomputer controlled, and allow double-point calibration, slope calculation, temperature adjustment, and accuracy to 0.001 pH unit, all with few basic steps. The electrode must... 

According to a theoretical analysis,262,267 the CDL model is valid for pc electrodes with very small grains (y < 5 to 10 nm) with a moderate difference of Eas0 for the different faces (A ff=0 = 0.1 to 0.15 V) and for dilute electrolyte solutions (c < 0.01 M) near the point of total zero charge. For the other cases, the IDL model should be valid. 

Carnie and Chan and Blum and Henderson have calculated the capacitance for an idealized model of an electrified interface using the mean spherical approximation (MSA). The interface is considered to consist of a solution of charged hard spheres in a solvent of hard spheres with embedded point dipoles, while the electrode is considered to be a uniformly charged hard wall whose dielectric constant is equal to that of the electrolyte (so that image forces need not be considered). 

Empirical kinetics are useful if they allow us to develop chemical models of interfacial reactions from which we can design experimental conditions of synthesis to obtain thick films of conducting polymers having properties tailored for specific applications. Even when those properties are electrochemical, the coated electrode has to be extracted from the solution of synthesis, rinsed, and then immersed in a new solution in which the electrochemical properties are studied. So only the polymer attached to the electrode after it is rinsed is useful for applications. Only this polymer has to be considered as the final product of the electrochemical reaction of synthesis from the point of view of polymeric applications. 

Our laboratory has planned the theoretical approach to those systems and their technological applications from the point of view that as electrochemical systems they have to follow electrochemical theories, but as polymeric materials they have to respond to the models of polymer science. The solution has been to integrate electrochemistry and polymer science.178 This task required the inclusion of the electrode structure inside electrochemical models. Apparently the task would be easier if regular and crystallographic structures were involved, but most of the electrogenerated conducting polymers have an amorphous and cross-linked structure. 

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