Electrode modeling

In the previous sections we have seen that the electrodes of an IPMC are not bulk metal. Rather, the electrode structure depends largely on the electroless plating procedure and the deposition conditions. As was also seen, the electrode characteristics affect the performance of the actuation considerably. Here an electrode model accommodating various characteristics is proposed. The model assumes that the electrode is composed of particles and voids between the particles. The model can be used to imder-stand the influence of the parameters, such as electrode thickness, particle size, particle gap, etc., on the electrical properties of IPMCs [Kim et al. (2007b)]. 

Coagulation of the platinum particles takes place during the electroplating process. Particles with diameter less than 10 nm coagulate during the reduction and eventually grow to 50-100 nm as illustrated in Fig. 2.17. In this model it is assumed that the coagulated platinum particles are spherical and conserve the electrical properties of platinum. Also, the particles are assumed to have the same size. Illustration on Fig. 2.18 shows the piled particles model and how the particles are in contact with each other. 

In order to calculate the height of the layers of the particles, a regular tetrahedron created by connecting the centers of the particles is used (see Fig. 2.19). The height of the tetrahedron (ho) and the two layers composed 

The effective diameter D of the particle changes with the contact (see Fig. 2.18 (c)). The new diameter is denoted with D. As the numbers of layers in all the directions are considered with the contact area, the number of particles in the electrode can be determined using the following equations  

The voids model along with the variable and direction descriptions is illustrated in Fig. 2.21. 

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Various pc electrode models have been tested.827 Using the independent diffuse layer electrode model74,262 the value of E n = -0.88 V (SCE) can be simulated for Cd + Pb alloys with 63% Pb if bulk and surface compositions coincide. However, large deviations of calculated and experimental C,E curves are observed at a 0. Better correspondence between experimental and calculated C,E curves was obtained with the common diffuse-layer electrode model,262 if the Pb percentage in the solid phase is taken as 20%. However, the calculated C, at a Ois noticeably lower than the experimental one. It has been concluded that Pb is the surface-active component in Cd + Pb alloys, but there are noticeable deviations from electrical double-layer models for composite electrodes.827... 

Polyanaline, oxidation of, 563 Polycrystine electrodes, models of the double layer for, 49 Polypyrrole... 

Fig. 11-1. Mixed electrode model (local cell model) for corrosion of metals i = anodic current for transfer of iron ions i = cathodic current of electron transfer for reduction of hydrogen ions.

Porous-Electrode Models. The porous-electrode models are based on the single-pore models above, except that, instead of a single pore, the exact geometric details are not considered. Euler and Nonnenmacher and Newman and Tobias were some of the first to describe porous-electrode theory. Newman and Tiedemann review porous-electrode theory for battery applications, wherein they had only solid and solution phases. The equations for when a gas phase also exists have been reviewed by Bockris and Srinivasan and DeVidts and White,and porous-electrode theory is also discussed by New-man in more detail. 

The next set of models treats the catalyst layers using the complete simple porous-electrode modeling approach described above. Thus, the catalyst layers have a finite thickness, and all of the variables are determined as per Table 1 with a length scale of the catalyst layer. While some of these models assume that the gas-phase reactant concentration is uniform in the catalyst layers,most allow for diffusion to occur in the gas phase. 

The final simple macrohomogeneous porous-electrode models are the ones that are more akin to thin-film models. In these models, the same approach is taken, but instead of gas diffusion in the catalyst layer, the reactant gas dissolves in the electrolyte and moves by diffusion and reaction. The... 

The rest of the comparisons were done for the cathode. The results all showed that the agglomerate model fits the data better than the porous-electrode model. However, it should be noted that the porous-electrode model used was usually a thin-film model and so was not very robust. Furthermore, the agglomerate model has more parameters that can be used to fit experimental data. Finally, some of the agglomerate models compared were actually embedded models that account for both length scales, and therefore, they normally agree better with the experimental data. 

Platinum auxiliary electrode (model 52-67 1, Crison, Spain) double junction Ag/AgCl reference electrode (Orion 900200) with 0.1M KC1 as external reference solution and GECE as working electrode. 

The three-electrode system consisted of disposable working electrode (PGE), an Ag/AgCl reference electrode (Model RE-1, BAS, West Lafayette, IN, USA) and a platinum wire as the auxiliary electrode. 

Orion Research (1978) Instruction Manual for Nitrate Ion Electrode, Model 93-07, Orion Research, Cambridge, MA, USA. 

By using the expanding sphere electrode model for the DME, Koutecky obtained the following expression for the instantaneous limiting current [35-37] ... 

For this three-dimensional electrode model, with or without decoupling of the two coupled equations, the approximate solutions can be obtained by using the Mathematica codes of the ADM given in the Appendix.17 The algebraic expressions of dimensionless potential and concentration are in a series form with even orders as... 

The derivation of the model is similar to that derived for the porous electrode model. We have very similar model equations to Eqs. (115) and (116) for an anodic current, given by... 

PAMC for coupled ODE s of tree-dimentional electrode model ... 

Instruction Manual, Nitrogen Oxide Electrode, Model 95-46. Orion Research, Inc., Boston, MA, 1987. 

Figure 4.11 Effect of SAM formation on the cyclic voltammetry of ferrocenylmethyltrimethylam-monium on a polycrystalline gold electrode the supporting electrolyte is 0.5 M H2SO4, with a scan rate of 0.1 V s-1. Curve (a) is the reversible cyclic voltammogram obtained on bare gold, while curves (b)-(d) are obtained on the same electrode with different monolayers (for details see text). The symbols represent theoretical fits to a microarray electrode model. Reprinted with permission from H.O. Finklea, D.A. Snider, J. Fedyk, E. Sabatani, Y. Gafni and I. Rubinstein, Langmuir, 9,3660 (1993). Copyright (1993) American Chemical Society...

The electrochemical behavior of poly(pyrrole) films prepared and cycled in an AICI3 [C2mim][Cl] melt was investigated in detail and improvements in reproducibility and the rate of oxidation and reduction of these films were observed compared to films prepared under similar conditions in acetonitrile [49]. This was postulated to be a result of an increase in the porosity of poly(pyrrole) films deposited from the melt compared to those from acetonitrile, although attempts to describe this porosity using porous electrode models were not totally conclusive. 

Hamano et al. [112a] extended their electrode model to include superadditivity and the effects of halide ions and quaternary salts on development. 

Fig. 42. Schematic of regions considered in PEFC air electrode modeling, including (from left to right) gas flow channel, gas-diffusion backing, and cathode catalyst layer. Oxygen is transported in the backing through the gas-phase component of a porous/tortuous medium and through the catalyst layer by diffusion through a condensed medium. The catalyst layer also transports protons and is assumed to have evenly distributed catalyst particles within its volume [100]. (Reprinted by permission of the Electrochemic Society).

Instruction Manual, Chloride Electrode Model 94-17B, Combination Chlo-... 

Fluoride was determined mainly by using an Orion fluoride electrode (model 90-01) with a Coming model 10 expanded pH meter. The procedures described earlier (9,11,12) were modified as follows. To a 10 ml sample of water in a plastic beaker was added 40 ml of stock seawater (30%o), followed by 10 ml of total ionic strength buffer (TISB, pH = 5.5, ionic strength 1.9) (13). Initial reading (=Ex) was recorded after... 

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