Electrodes electrode-level modelling

The electrochemistry of the SOFC can be modeled at the mesoscale in cell- and electrode-level models. In these models, the electrochemistry is calculated based on the local conditions within the SOFC tri-layer and the local Faradaic current density is resolved through the thickness of the cell. In mesoscale electrochemistry, both the local electrochemistry and the global electrochemistry are considered. The local electrochemistry is the local reactions within the electrodes which produce a local Faradaic current density the global electrochemistry is the integral of the local electrochemistry over the tri-layer and produces the common I-Vcurves that are used to describe the performance of the SOFC. 

The parameter a is specific for a given electrode microstructure and may be estimated from known or estimated microstructural parameters, physicochemical surface area measurements (e.g., by the BET technique, yielding total pore volume), or special-purpose electrochemical measurements (which yield the product iofl). However, a is rarely known accurately and may vary significantly with current load. Electrode-level models may be used to determine this variation and calculate polarisation without recourse to Eq. (1 Ob) (see Section 11.8). 

Using an approximate electrochemical performance model, as discussed in Section 11.2, or a more detailed electrode-level model, as will be discussed in Section 11.8, the polarisation components can be estimated and the heat... 

Electrode-level models describe the performance of SOFC electrodes in detail. They take into account the distribution of species concentrations, electric potential, current, and even temperature in the electrode. Their purpose is to (i) interpret the performance (polarisation curve) of electrodes in terms of rate-limiting resistances such as kinetic (activation), mass transfer, and ohmic resistance and (ii) predict the local polarisation in full-scale cell and stack models. 

Fig. 10 Electrochemical energy level model for orbital mediated tunneling. Ap and Ac are the gas-and crystalline-phase electron affinities, 1/2(SCE) is the electrochemical potential referenced to the saturated calomel electrode, and provides the solution-phase electron affinity. Ev, is the Fermi level of the substrate (Au here). The corresponding positions in the OMT spectrum are shown by Ar and A0 and correspond to the electron affinity and ionization potential of the adsorbate film modified by interaction with the supporting metal, At. The spectrum is that of nickel(II) tetraphenyl-porphyrin on Au (111). (Reprinted with permission from [26])...

Detailed CFD models of fuel cells (see Chapters 3 and 4), on the other hand, use continuum assumption to predict the 3-D distributions of the physical quantities inside the fuel cells. These models are more complex and computationally expensive compared to reduced order models especially due to the disparity between the smallest and largest length scales in a fuel cell. The thickness of the electrodes and electrolyte is usually tens of microns whereas the overall dimensions of a fuel cell or stack could be tens of centimeters. Though some authors used detailed 3-D models for cell or stack level modeling, they are mostly confined to component level modeling. In what follows, we present the governing equations for some of these models. 

Modelling of the IP-SOFC tube involves different levels of detail, such as the electrode, the single cell, the stack, and the system level. At the electrode level, the main... 

Use an ammonia electrode (Orion Model 95-10, Beckman Model 39565 or equivalent) along with a readout device, such as a pH meter with expanded millivolt scale between -700 mV and +700 mV or a specific ion meter. The electrode assembly consists of a sensor glass electrode and a reference electrode mounted behind a hydrophobic gas-permeable membrane. The membrane separates the aqueous sample from an ammonium chloride internal solution. Before analysis, the sample is treated with caustic soda to convert any NH4+ ion present in the sample into NH3. The dissolved NH3 in the sample diffuses through the membrane until the partial pressure of NH3 in the sample becomes equal to that in the internal solution. The partial pressure of ammonia is proportional to its concentration in the sample. The diffusion of NH3 into the internal solution increases its pH, which is measured by a pH electrode. The chloride level in the internal standard solution remains constant. It is sensed by a chloride ion-selective electrode which serves as the reference electrode. 

Molecular-Level Modeling of the Structure and Proton Transport within the Membrane Electrode Assembly of Hydrogen Proton Exchange Membrane Fuel Cells... 

Molecular level modelling of the catalyst reactions are made in the manner described in section 3.1.4. Such quantum chemical modelling can also be performed for CO adsorbing to the Pt or Pt-Ru catalyst surface at the negative electrode, where a number of reactions may take place in addition to (3.15), describing the competition between splitting of hydrogen molecules and the conversion of CO and any water present to CO2 and protons. 

Figure 2.12 Surface coverage of coumarin inhibitor as a function of the potential for various coumarin concentrations and electrode rotation rates. The dashed lines correspond toafit to the leveling model outlined in the text (source Ref. [58]).

Some authors have asserted that the quasi-Fermi level model requires a threshold with respect to light intensity. This problem has been discussed for photoconversion systems such as photoelectrolysis of FI2O (Gregg and Nozik, 1993 Shreve and Lewis, 1995). Since the discussion on the threshold problem has frequently led to misinterpretations, we want to clarify the situation by considering a simple charge-transfer between an n-type semiconductor and redox system, as illustrated in Fig. 2.23. The system is at equilibrium (i = 0) if the overvoltage is zero (rj = 0). Flere the quasi-Fermi levels of electrons and holes are both equal to Ap,redox (not shown). Assuming that the redox process occurs entirely via the valence band, then only the quasi-Fermi level of holes at the surface, Sp, is of interest. Anodic polarisation of the electrode in the dark produces a very small anodic current (lower i-rj curve in the centre of Fig. 2.23). As mentioned in the previous section, is practically pinned close to fip,redox (Fig. 2.23A) whereas p, differs from Ap,redox by qr]. On illumination, the anodic... 

Surgical technique under general anesthesia, electrodes (Medtronic Model 3387 DBS lead Medtronic, Inc., Minneapolis, MN) are stereotactically placed in both left and right CM nuclei through a coronal incision and bifrontal burr holes made at a distance of 10 to 15 mm at each side of the midline at the level of the coronal suture. The CM localization is accomplished by air ventriculography. This method allows us to demonstrate the anterior commissure (AC) and posterior commissure (PC) of the third ventricle with remarkable precision. Two lines are drawn, the AOPC line and the vertical line perpendicular to the PC (VPC). The target point for the electrode tip was a distance 10 mm from the midline and the intersection of the AC-PC line with the VPC [Velasco et al, 1989,2000b]. 

Most of the theoretical work has been restricted to perfect single-crystal electrodes. However, in practical applications such as fuel cells, in which the electrode acts as a catalyst, it is desirable to maximize the surface area by using rough electrodes. Very rough electrodes can be modeled as fractals [68], but a double-layer theory for such electrodes has remained elusive. The opposite limit of small roughness has been treated by Daikhin and coworkers [69] at the GC level. 

Following this work, the authors of reference [24] proposed a methodology whereby 2D and 3D thermal models have been coupled for examination of lithium-ion technology in HEVs and PHEVs. In this work, the temperature evolution of each battery cell can be evaluated and analyzed. However, such approach needs considerably complicated characterization tests at the electrode level. 

Mathematical models of SOFCs have been developed at scales from the molec-ular/atomic level through the system level. At the nanoscale, molecular dynamics and density functional theory (DFT) models have been developed to investigate the transport of species on the surfaces of the electrodes [6] while at the macroscale, system-level models are used to consider the controls of an SOFC system [7j. The... 

CeU-level macroscale models consider the heat transfer, species transport, chemical reactions, and electrochemistry within the SOFC cell [27, 31, 51, 52]. In cell-level models, the detailed transport of gas in the fuel and air channels and in the porous electrodes are simulated on a macroscale. This requires a rigorous CFD simulation and commercial codes, such as FLUENT, COMSOL, and Star-CD, are used for cell-level models. Cell-level models consider the electrodes and electrolyte on a continuum scale, which means that the models do not explicitly resolve... 

In an effective properties model, the porous microstructures of the SOFC electrodes are treated as continua and microstructural properties such as porosity, tortuosity, grain size, and composition are used to calculate the effective transport and reaction parameters for the model. The microstmctural properties are determined by a number of methods, including fabrication data such as composition and mass fractions of the solid species, characteristic features extracted from micrographs such as particle sizes, pore size, and porosity, experimental measurements, and smaller meso- and nanoscale modeling. Effective transport and reaction parameters are calculated from the measured properties of the porous electrodes and used in the governing equations of the ceU-level model. For example, the effective diffusion coefficients of the porous electrodes are typically calculated from the diffusion coefficient of Eq. (26.4), and the porosity ( gas) and tortuosity I of the electrode ... 

Cell-level models solve the species [Eq. (26.1)], momentum [Eq. (26.5)], and energy [Eq. (26.7)] conservation equations using the effective properties of the electrodes and can include the electrochemistry using a continuum-scale (Section 26.2.4.1) or a mesoscale (Section 26.2.4.2) approach. Traditionally, cell-level models use a continuum-scale electrochemistry approach, which includes the electrochemistry as a boundary condition at the electrode-electrolyte interface [17, 51, 54] or over a specified reaction zone near the interface. The electrochemistry is modeled via the Nernst equation [Eq. (26.12)] using a prescribed current density and assumptions for the polarizations in the cell. The continuum-scale electrochemistry is then coupled to the species conservation equation [Eq. (26.1)] using Faraday s law ... 

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