165 A.12 Conductivity for type A systems as a function of system size,L/r(continued)166 A.13 Ni phase fraction and particle number for type B systems as a function of. Particles in the range 85-169 nm showed the highest coordination with particles of the same size.
Background
A detailed explanation of the thermodynamics, chemical kinetics and operation of fuel cells can be found in the Fuel Cell Handbook by Appleby and Foulkes [2]. The most important part of the fuel cell is the membrane electrode assembly (MEA). a) Anode, an electrode that absorbs fuel molecules, and in the case of more complex fuels allows complex fuels to be catalytically converted to simpler fuels such as H2 and CO2. b) Cathode, an electrode where oxidizing agents, usually O2 as a component of an air-based flow stream, can be absorbed and reduced.
Organization
This model will be used to demonstrate and calculate the influence of transport and kinetic limitations on the performance of composite anodes. In this chapter, we will develop numerical models that will be used in this work to evaluate the physical, electrical, and chemical properties of composite electrodes.
Background
The second section of the chapter will present a summary of the relevant theory on percolation and solution of resistance networks. The use of sphere-based resistor network models to build a model of the anode of an SOFC was first introduced by Svein Sunde in a series of papers published in 1995 and.
Theory
In terms of electron flow, the simplest view of the anode is as a pair of resistors in parallel between the electrolyte boundary and the current collector. The no-flow condition across ∂Ω3 and ∂Ω4 allows the boundary conditions of the problem to be determined.
Model Description
The radius of the intersection can be used to calculate both the area and the perimeter of the intersection. Surface areas of solid phases will be used in the calculation of heterogeneous chemistry.
Network Model
This process repeats for a certain time or number of steps (ideally large enough so that molecules have sampled representative areas of the pore structure). Intersecting particles of the same type are treated as nodes connected by a resistor, where the resistance between particles is calculated using geometry and material properties. Intersections between particles of different types are treated as nodes connected by a current source, with the current determined by the local three-phase boundary electrochemistry.
Ns is the number of intersecting particles of the same type, NTPB is the number of heterogeneous intersecting particles, Rk is the resistance between particles, and Φ is the potential. In this case, the network model uses the CVODES solver [9], a numerical backward-difference method, to integrate the following charge conservation equation in time until the steady-state criteria are met. Since only the steady-state solution is of interest, terms associated with the capacitive current have been omitted from the charge transfer equation;.
Introduction
Monodispersed and Simple Polydispersed Systems
We assume that the change in particle packing is mainly due to particle interactions at the boundary, and we recognize that for this geometry (see Section 3.2.1 ) the ratio of boundary particles to interior particles is very close. One difference is the difference in the variance of the phase proportions for Ni and YSZ. To review B-type systems, the standard deviation of the number of YSZ particles is about half the standard deviation of the number of Ni particles.
There was significantly less variation in the conductance of the phase composed of larger particles. The total number of configurations is the product of the number of configurations for each of the 3 groups. All internal particles in the conducting chain have a coordination number of 2 with respect to the other conducting particles.
In this case, the percentage of particles that permeate is the number of particles that permeate, L/2r, divided by the total number of particles (L/r)3. For cases with a proportion of the nickel phase between 0.20 and 0.27—cases during which the transition to percolation occurs—65 cases were performed.
TPB Length and Connectivity
One approach to try to improve this situation is to drop the assumption that the particles in the model obey simple distributions. For the monodisperse system, TPB is a symmetric function of both the Ni and YSZ phase fractions, with the maximum occurring at φNi=φYSZ. If these values are compared with the percolation from Figure 3.15, it can be seen that for the type A system, percolation is largely achieved when φNi≥0.27.
To highlight the symmetry of these results with respect to the relative phase concentration. The transition behavior shown in Figure 3.22 coincides with the percolation threshold for the type A system as described in section 3.2.2.2. For the type B system, the symmetry with respect to the relative phase concentration of Ni versus YSZ is not present.
Experimental Distributions
The nominal performance of NY-1 and NY-2 systems is very similar to that of monodisperse and simple polydisperse systems. The percolation behavior of the NY-1 and NY-2 distributions is also similar, as the percolation threshold occurs near Zi−i = 2.2. We did not perform more detailed calculations in the area of the percolation threshold, as was the case for type A systems, but for both NY-1 and NY-2 systems, no infiltration of the Ni phase occurred until Zi−i >2.2.
There is a significant difference in the conductivity performance of the NY-1 and NY-2 systems, which is not evident in the monodisperse and simple polydisperse models. The variance in the conductivity of the experimentally based ensembles is significantly larger than for the monodisperse case. The type B system is not shown for clarity, but the variance in the reduced conductivity of the type B system is similar to that of the monodisperse type A systems.
TPB Length
Moreover, these values do not have a significant difference with respect to the percolation state of the system. In addition to the increased variability in measurements, there is a significant difference in the calculated values for TPB density for the NY-1 and NY-2 systems. The TPB density of the NY-2 system is approximately two orders of magnitude lower than both the A-type and B-type systems.
The TPB density of the NY-1 systems is approximately three orders of magnitude lower than both the Type A and Type B systems. They measured a TPB density of 4.28×1012m/m3, which is slightly lower than the TPB density for cases of type A and B, but significantly higher than case NY-1 or NY-2. This result is not captured by any of the configurations we evaluated in this chapter.
Conclusions
A nearly continuous TPB indicates that the Ni and YSZ phases are themselves nearly continuous, a result that, in the models evaluated here, occurs only near the point whereφNi =φYSZ. We cannot know from the information we have whether this increase in variability is a feature that improves or degrades the performance of the model in terms of reflecting the performance of the physical system. We expect that both the extent and geometry of the TPB will strongly influence the electrochemical performance of Ni-YSZ anode systems.
For this reason, the large variation in TPB density based solely on particle size distribution is troubling. It is necessary to have a better understanding of the true geometry of the TPB in Ni-YSZ anodes. It is important to consider the possibility that for a more complex model that takes into account TPB electrochemistry, the TPB density values to be used will need to be estimated from factors outside the geometry.
Introduction
Section 4.3 examines the experimentally determined structure of a particular composite anode section to determine the critical differences in the structure of an actual composite anode versus an essentially random particle assembly.
Pulsed Laser Deposition (PLD)
Low temperature: the substrate was not heated except for the cloud caused by the laser ablation of the Ni target. Drops applied to the substrate form particles on the surface of the substrate. Apart from these imperfections, Ni leaves a fine-grained surface that uniformly covers the YSZ surface.
Most of the Ni coating formed into a network, leaving parts of the YSZ surface visible. Analysis of these reconstructions can provide confirmation of the expected structure of the Ni phase. In the original voxel-based reconstruction by Wilson et al., the connectivity of the TPB is greater than 90%.
Creating Cermet Data from Ion Beam Data
Reconstructions of the three separate phases of the cermet: YSZ, Ni and the void phase. Considering that the YSZ phase represents more than half of the volume of the cermet, this is an expected result. The connection between particles is detailed in terms of coordination numbers of particles of different sizes i.
The coordination numbers show that these particles are mainly in contact with particles of the same phase. The Ni phase is almost completely connected despite its very low fraction of the total volume. This is also consistent with the behavior of Ni in the PLD experiments shown in Section 4.2.
Conclusions
This analysis determined that the structure was indeed not random, and that the connectivity of the phases, especially the Ni phase, is much greater than might be expected given the assumption of an essentially random structure. In the case of the FIB-SEM reconstruction, percolation is achieved at 21% Ni phase fraction. Without more data focused on percolation when the Ni phase is between 20–25%, it is not possible to draw a strong conclusion that the onset of Ni percolation in real composite anodes occurs at lower levels.
This is because the conductivity of the Ni phase is six orders of magnitude higher than that of the oxide phase. This means that the Ni potential in a Ni-YSZ anode is constant compared to the potential of the YSZ phase. In this situation, improving the conductivity of the Ni phase by increasing the Ni phase fractions does not result in any significant gain in electrochemical performance.
Model Details
A species model that resolves the gas and surface phase species concentrations in the void phase and on the surface phases of the cermet, respectively. For each of the surface phases, the coverage of the k-th surface phase species satisfies. For Table 5.2 and Figure 5.2, the faradaic currents generated within a given z region of the electrode are summarized.
The magnitude of the rate of change in both the electronic and ionic currents in the is equal to the Faradic current at the point inside the anode. In fact, the electronic current density can and should be seen as the cumulative sum of the Faradic current in the z-direction. Of particular interest here are those models of the Ni-YSZ system based on the random packing of particles within the cermet.
Monodispersed Systems (Type A)
System with a Fixed Ratio Between Ni and YSZ Par- ticles (Type B)ticles (Type B)
