Electrode thin-film models

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. 

The methods for solving Equation 16.48 are found in the literature [5,7], We are not going to discuss further since we are especially interested in the case of wetting porous gas-diffusion electrodes with respect to the thin-film model. 

Sensor fabrication has been accomplished in various ways. One method [29] combines the phthalocyanine compound with stearic acid to form a bonded substance which is then dissolved in an organic solvent. The mixture is deposited by one of several possible methods onto a substrate and subsequently fired to remove the vehicle. A thin-film model, manufactured by vacuum sublimation over interdigited electrodes on 3 mm x 3 mm alumina substrates [28], exhibited sensitivity to CI2, F2, and BCI3, but not to common reducing species. The films operating continuously did not survive longer than 6 months. 

A theoretical analysis of the current distribution and overpotential-current density relations for two models of porous gas diffusion electrodes—the simple pore and thin film models—has been carried out (108,109). The results of the analysis for the simple pore model will be summarized here. The reactant gas diffuses through the pore to the gas-electrolyte interface at 2 = 0, where it dissolves in the electrolyte and the dissolved gas diffuses through the electrolyte to the various electrocatalytic sites along the pore at which the reaction occurs (Fig. 25). It is assumed that the first and second steps of diffusion of reactant gas through the electrolyte-free part of the pore (z < 0) and of dissolution of gas at the gas-electrolyte interface are fast. 

Four categories of electrode models can be identified from Table 28.3 the spatially lumped model, the thin-film model, the agglomerate model, and the volume-averaged model. Schemes of the basic concepts of these four model categories are depicted in Figure 28.4. Each of the schemes shows an electrode pore, with the gas channels located at the top and the liquid electrolyte, depicted in gray, at the bottom. In some models, electrolyte is also present in the pore. The reaction zones are indicated by a black face (spot, line, or grid structure). Fluxes of mass and ions are indicated by arrows. 

The model of Wilemski and co-workers [2, 3,26] is one of the first molten carbonate fuel-cell electrode models. Together with the models of Jewulsld and Suski [28,34], they form the basis for the class of thin-film electrode models (Figure 28.4). The following general assumptions are made in thin-film models ... 

Srinivasan D, Hurwitz HD. Theory of a thin film model of porous gas-diffusion electrodes. Electrochim Acta 1967 12(5) 495-512. 

If the electrochemical processes occur mainly in the region of the thin film, the interface gas/electrolyte may be represented by Fig. 98 b. The real profile [50, 51] of the thin film has been approximated in the thin film model by a film of constant thickness, ignoring the slight increase of film thickness with distance from the upper edge. The thin film model is discussed in this section. The other case where the electrochemical processes take place largely in the region of the meniscus (see Fig. 98 c) is treated in section 6 as the meniscus model of the gas-diffusion electrode. 

The simplest and most widely used model to explain the response of organic photovoltaic devices under illumination is a metal-insulaior-metal (MIM) tunnel diode [55] with asymmetrical work-function metal electrodes (see Fig. 15-10). In forward bias, holes from the high work-function metal and electrons from the low work-function metal are injected into the organic semiconductor thin film. Because of the asymmetry of the work-functions for the two different metals, forward bias currents are orders of magnitude larger than reverse bias currents at low voltages. The expansion of the current transport model described above to a carrier generation term was not taken into account until now. 

Fig. 3. Diagrams of electrochemical cells used in flow systems for thin film deposition by EC-ALE. A) First small thin layer flow cell (modeled after electrochemical liquid chromatography detectors). A gasket defined the area where the deposition was performed, and solutions were pumped in and out though the top plate. Reproduced by permission from ref. [ 110]. B) H-cell design where the samples were suspended in the solutions, and solutions were filled and drained from below. Reproduced by permission from ref. [111]. C) Larger thin layer flow cell. This is very similar to that shown in 3A, except that the deposition area is larger and laminar flow is easier to develop because of the solution inlet and outlet designs. In addition, the opposite wall of the cell is a piece of ITO, used as the auxiliary electrode. It is transparent so the deposit can be monitored visually, and it provides an excellent current distribution. The reference electrode is incorporated right in the cell, as well. Adapted from ref. [113],...

The effects of mercury film electrode morphology in the anodic stripping SWV of electrochemically reversible and quasi-reversible processes were investigated experimentally [47-51], Mercury electroplated onto solid electrodes can take the form of either a uniform thin film or an assembly of microdroplets, which depends on the substrate [51 ]. At low sqtrare-wave frequencies the relationship between the net peak crrrrent and the frequency can be described by the theory developed for the thin-film electrode because the diffusion layers at the snrface of microdroplets are overlapped and the mass transfer can be approximated by the planar diffusion model [47,48],... 

In the modeling of the electrode reaction (2.230) proceeding in a thin-layer cell or within a thin film on the electrode surface, the differential equation (1.2) and (1.3), together with the following boundary conditions (2.231) to (2.233) have to be considered ... 

The applicability of the foregoing procednre has been tested by modeling simple reaction under semi-infinite diffusion conditions (reaction 1.1) and EC mechanism coupled to adsorption of the redox couple (reaction (2.177)) [2]. The solutions derived by the original and modified step-function method have been compared in order to evaluate the error involved by the proposed modification. As expected, the precision of the modified step-function method depends solely on the value of p, i.e., the number of time subintervals. For instance, for the complex EC mechanism, the error was less than 2% for p>20. This slight modification of the mathematical procedure has opened the gate toward modeling of very complex electrode mechanisms such as those coupled to adsorption equilibria and regenerative catalytic reactions [2] and various mechanisms in thin-film voltammetry [5-7]. 

Figure 24. Models illustrating the source of chemical capacitance for thin film mixed conducting electrodes, (a) Oxygen reduction/oxidation is limited by absorption/de-sorption at the gas-exposed surface, (b) Oxygen reduction/ oxidation is limited by ambipolar diffusion of 0 through the mixed conducting film. The characteristic time constant for these two physical situations is different (as shown) but involves the same chemical capacitance Cl, as explained in the text.

Figure 48. Kenjo s ID macrohomogeneous model for polarization and ohmic losses in a composite electrode, (a) Sketch of the composite microstructure, (b) Description of ionic conduction in the ionic subphase and reaction at the TPB s in terms of interpenetrating thin films following the approach of ref 302. (c) Predicted overpotential profile in the electrode near the electrode/electrolyte interface, (d) Predicted admittance as a function of the electrode thickness as used to fit the data in Figure 47. (Reprinted with permission from refs 300 and 301. Copyright 1991 and 1992 Electrochemical Society, Inc. and Elsevier, reepectively.)...

A model of such structures has been proposed that captures transport phenomena of both substrates and redox cosubstrate species within a composite biocatalytic electrode.The model is based on macrohomo-geneous and thin-film theories for porous electrodes and accounts for Michaelis—Menton enzyme kinetics and one-dimensional diffusion of multiple species through a porous structure defined as a mesh of tubular fibers. In addition to the solid and aqueous phases, the model also allows for the presence of a gas phase (of uniformly contiguous morphology), as shown in Figure 11, allowing the treatment of high-rate gas-phase reactant transport into the electrode. 

In electrode kinetics, interface reactions have been extensively modeled by electrochemists [K.J. Vetter (1967)]. Adsorption, chemisorption, dissociation, electron transfer, and tunneling may all be rate determining steps. At crystal/crystal interfaces, one expects the kinetic parameters of these steps to depend on the energy levels of the electrons (Fig. 7-4) and the particular conformation of the interface, and thus on the crystal s relative orientation. It follows then that a polycrystalline, that is, a (structurally) inhomogeneous thin film, cannot be characterized by a single rate law. 

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