Percolation modeling investigation of TPB formation in a solid oxide fuel cell electrode–electrolyte interface

Abstract

A Monte Carlo percolation model has been developed and utilized to characterize the factors controlling triple phase boundary (TPB) formation in an SOFC electrode. The model accounts for (1) electronic conductor, ionic conductor, and gas phase percolation, (2) competition between percolation of gas and electronically conducting phases, and (3) determination of continuous, though not necessarily fully percolating, paths from TPBs to the bulk phases. The model results show that physical processes near the TPB, such as sorbate transport, significantly affect TPB formation in a composite electrode. Active TPB formation is found to be most significantly dependent upon continuous and competing percolation of multiple phases. Simultaneously requiring continuous paths and accounting for non-continuous boundary conditions results in lower active TPB formation levels (up to 8% of possible sites) than presented in the literature (75% of possible sites). In addition, the varying ratio of active to potential TPB sites predicted by the current model (up to 80%) differs significantly from the constant reported in the literature (80%), which lacks analyses of three-phase percolation, gas phase paths, and gas/current collector boundary conditions. This dependence of active TPB formation on percolation of all three phases is important to understand as a basis for determining SOFC performance and optimization.

Modeling and comparison to literature data of composite solid oxide fuel cell electrode–electrolyte interface conductivity

“…The current work augments the model to simulate conductive performance measurements by development and application of a method to calculate the conductivity of an arbitrary, randomly organized conductivity network. The previous work with this model [21] has supported the understanding that the high energy conversion efficiency often attributed to fuel cell operation is critically dependent upon the morphology of the microstructure of the fuel cell electrode-electrolyte interface. It was particularly demonstrated that in this interfacial region, and within the structure of the electrode itself for composite electrodes, the necessary phases (gas, ionic conductor, and electronic conductor) form intertwining pathways and structures, with TPBs forming at the locations where these pathways all come into contact.…”

“…Not only is the number of TPBs formed important, but also location within the electrode, interconnectivity, and the length of conducting paths leading to and from each TPB are also important. The formation and location of TPBs, including their dependence upon interconnectivity of phases and interaction with the current collector geometry, have previously been investigated [21]; these observations can now be extended to the overall conductance (akin to the inverse of area specific resistance, ASR) of the electrode-electrolyte interface.…”

“…The current work is built upon a previously developed twodimensional Monte Carlo model that was used to investigate some of these phenomena [21]. The model differs from those presented above in that it includes novel consideration of the gas phase as a percolating network with just as much impact on performance as the percolation of the ionic and electronic phases.…”

“…In particular, the percolation of the gas phase through the electrode has been investigated and shown to have a marked impact on the formation of active TPBs in the electrode. The effects of the gas phase physically extend beyond the gaseous pathways in the electrodes themselves, as the gaseous reactant and product phases are subject to surface exchange and transport phenomena, as discussed in [22] and modeled in [21], and shown in Fig. 1.…”

“…Models have also contributed novel observations about electrode performance and its relationship to interfacial microstructure. In particular, the dependence of performance on the physical size of particles and the entire electrode have been recreated through simulation by researchers such as Costamagna et al, Deseure et al and others [15][16][17][18][19]; the dependence on electrode composition has been repeatedly found to be of particular importance [15][16][17][19][20][21]; the dependence of likelihood of TPB formation on location within the electrode has been characterized by the work of Costamagna et al as well as through the current model [21,15]; the dependence on the ratio of electronic-to-ionic conductivity has been identified [16]; the effect of functional and compositional grading in the electrode has been characterized by Deseure et al and Schneider et al [17,19]; the dependence of TPB formation on the geometry of the current collector and the intermixing of gaseous and electronically conducting phases in this boundary has been noted to be of particular importance through the previous use of the current model [21]; and the approximation that a TPB length is roughly three times the radius of a representative particle has been calculated [20].…”