Multiphase Polymer- Based Materials: An Atlas of Phase Morphology at the Nano and Micro Scale

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Similarly, the full curve is not expected to occur because the high permeability of traditional gas-diffusion layers means that once breakthrough and a dominant pore pathway has formed, it is sufficient for removing the liquid water assuming that the ribs do not block too much of the exit pathway. Also shown in the figure is a curve for a catalyst layer, which, due to its small pores, has a wider range of pressures.

It is also measured to be more hydrophilic than a GDL, especially if it contains cracks.

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For use in models, the measured capillary-pressure — saturation relationship is often fit to a function e. The above discussion is based on assuming that one can weight the liquid and vapor transport through the phase volume fractions. In addition, when used in macroscopic models, the underlying assumption is that the capillary-pressure — saturation relationship can be applied locally although it is measured or typically predicted for the entire layer.

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The validity of this assumption still remains an open question, especially since it is known that DM structures are not spatially homogeneous. Although the liquid and gas phases are related through transport properties, they also have an effect on each other's fluxes through heat transport and phase-change-induced PCI flow.

The water is transported along that gradient and condenses and gives off heat at the gas channel or cooler flowfield rib as shown in Figure 5. Thus, PCI flow is the dominant mode of water removal at higher temperatures, and may even cause the cell water content to decrease at higher current densities because the heat generated outpaces the water generation. However, while the water-removal characteristics are a benefit of PCI flow, the net flux of water vapor is now out of the cell, which can results in the gas-phase velocity also being out of the cell see equation In either case, the movement of the water vapor from the catalyst layer to the gas channel due to PCI flow represents a mass-transfer limitation in terms of getting oxygen to the catalyst layer since it now must diffuse against that flux.

Finally, PCI flow also results in substantial heat removal from the hotter catalyst layer, thereby flattening the temperature gradients. In the preceding section, we focused on multiphase aspects in terms of liquid and vapor. However, in both automotive and stationary applications, PEFCs must permit rapid startup with minimal energy from subfreezing temperatures i. This freezing can severely inhibit cell performance and often results in cell failure.

Over the past decade, several numerical continuum cold-start models have been developed. For example, Balliet et al. Numerous studies have also examined the stack-level thermal response during cold-start. More recently, Jiao et al. The amount of freezing-point depression in a given pore is primarily a function of pore radius — smaller pores tend to freeze at a lower temperature due to the shift in w chemical potential.

This thermodynamic-based freezing circumvents the use of ice-crystallization rate expressions, since at the time, none were available for PEFC-porous media. Furthermore, in recent years, in-situ visualization and detection of ice formation within PEFC-porous media has progressed. Although water did not freeze immediately, the mechanisms and kinetics of ice crystallization were not investigated. Recently, Dursch et al. The values of J T can be measured by repeated experimental freezing studies.

Solid and dashed lines correspond to the kinetic-based approach and thermodynamic-based approach equation 90 , respectively. Accordingly, these controlling parameters can be adjusted to significantly delay or even prevent ice formation.

The impact of the nucleation-limited regime is also shown to agree better with experimental isothermal cold-start data, and the other experimental findings mentioned above. In addition to freeze kinetics, Dursch et al. It was shown that ice-melting times decrease nonlinearly with increasing heating rate, although the melting temperatures remain at the thermodynamic-based values consistent with Gibbs-Thomson, equation 89 but are rate limited by heat transfer.

This melting time should be incorporated into cold-start simulations. Within the area of numerical simulation for the performance and durability of PEFCs, there has always been a great interest and need to understand the linkage between the properties of the component materials in the MEA and the performance of the unit cell and stack. As research progressed and an increasing level of detail was paid to the fabrication, engineering, and effect of the individual component properties on the overall PEFC performance and durability, there began to emerge attempts to resolve the morphology of the components with ever increasing levels of resolution and detail.

These morphology-based simulations are typically ascribed with the label of being microstructural simulations and are related significantly to transport and multiphase aspects. For each component within a PEFC, a relevant length scale can be considered dependent on the physical process being considered and the morphology of the component itself.

In regards to this, one typically finds that the analysis of the PEFC porous media i. While the latter is outside the scope of this review, some remarks should be made on the former. Morphological-based models offer the potential to investigate explicitly the relationship between the porous media and the specific transport property generally with consideration given for the constituent material properties, spatial distributions, and statistical variations that may originate within manufacturing processes.

In order to make these linkages, however, a virtual method of representation of the component structure is required. Porous media within PEFCs are generally accepted to fall into the category of random, heterogeneous porous media. It was from the aerospace, metallurgy, and energy industries that some of the earliest attempts at morphological analysis and numerical reconstructions are found. The second method, image-based reconstruction, employs experimental diagnostic imaging, such as SEM, TEM, or X-ray computed tomography XCT , combined with a numerical processing step that converts the images to a virtual structure thus translating the original experimental images into a morphology that can be used for numerical analysis.

For the latter approach, this can be accomplished, for example, by extracting images from the center lines of single fiber from the resultant images of GDLs. These center lines are then used in conjunction with a stochastic algorithm to reconnect parts of the center lines in an attempt to preserve the curvature of the fibers.

For stochastic reconstruction, the virtual generation of the microstructures relies on the use of a random number generator, statistical distribution of geometric information relating to the constituent materials that comprise the media, and a series of rule-sets. However, the main criteria in deciding this aspect should relate primarily to the size of the morphological domain relative to the transport coefficient of interest, wherein the transport coefficient does not vary if the domain size changes i.

An example of a reconstruction of a GDL is shown in Figure 7 , where one clearly observes the fibrous structure. Schematic of a computationally reconstructed carbon-fiber paper reprinted from Ref. For all of these simulations, it should be noted that predicting a volume-averaged coefficient for use in macroscopic models necessitates conducting simulations enough times to get representative structures and values. Thus, the use of a quality random number generator is paramount in generating an appropriate numerical representation, where it has been suggested that the use of 25 samples is sufficient to represent an appropriate sample set given the stochastic nature of the experimental geometry data.

Ultimately, it is best to compare aspects that relate directly to the distribution of material through the sample but on a statistical or probabilistic basis, thus the use of both imaging and measurable characteristics are ideal. Due to the increasing amount of structural characterization and the virtual microstructures, it is now possible to model transport through the DM using direct simulations. In addition, they are still numerically intense especially for the statistical number of simulations required. For example, Zamel et al. A large amount of research and analysis has been done to improve the capability in the morphological modeling area in the last decade.

Domain generation has become sufficiently more sophisticated with techniques being developed to generate stochastically not just fiber arrangements but full DM structures including Teflon, binder, and MPLs. In addition, experimental techniques in terms of characterization of the various effective properties are also increasing in scope and complexity as discussed in a later section.

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However, as mentioned in the previous section, most of these experiments remain valid for only the entire layer, and not as a function of DM thickness. Thus, to be used in situations where there are gradients and flow, one needs to assume local equilibrium and that a given volume element is representative of the entire domain; such an assumption remains unproven. Overall, there is a need to understand the physics within the DM but without necessitating the determination of a substantial set of unknown parameters.

A promising treatment that satisfies those requirements is that of pore-network modeling. However, it is still too computationally costly to account for all of the coupled physics along with the rest of cell components. Therefore, it is valuable for use in a multiscaling approach wherein the pore-scale models yield the functional relationships required for the more macroscopic complete-cell models e. Pore-network modeling allows for consideration of more physical and chemical properties than the macroscopic approaches described in the preceding section.

A pore-network model utilizes a simplified description of the pore space within the DM.

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Thus, one idealizes the geometry in terms of pores and interconnections nodes as shown in Figure 8. It should be noted that although the network implicitly assumes cylindrical pores, in reality it is a resistor network wherein the actual non-cylindrical pores are casted in terms of effective cylindrical ones that have the same resulting resistance toward transport, and a similar effective resistance can also account for changes in surface interactions e. The generated network is validated by comparison of calculated and measured parameters including the pore- and throat-size distribution data as well as measurements such as the capillary pressure — saturation relationship.

Water flow and distribution within the generated network Figure 8 is solved by a stepwise fashion from one point to another, and thus is independent of the real-space discretization grid i. Schematic of a pore-network-model solution figure reprinted from Ref. For modeling transport, the same governing equation and multi-phase phenomena described in the above sections remain valid. For example, for liquid-water imbibition, the model examines each intersection or node where the water travels based on the local pressure and pore properties.

The effective viscosity is modeled to provide a smooth transition between the wetting and non-wetting viscosities while a pore is neither completely filled nor empty. The capillary pressure is also modeled as a function of the fluid position within each pore. In addition to the pore sizes and lengths, one also needs the pore contact angle and fluid properties. A sample output of a pore-network model is shown in Figure 9. The simulations are stochastic, similar to the transport of water in the DM, and thus enough realizations are required for understanding as discussed above.

Such distributions can also provide direct insight and help in terms of understanding the impact of the water network on the exterior interfaces as discussed in sections below. The distributions can then be used in other transport simulations to predict the gas-phase tortuosity and effective diffusion coefficients, which are needed for the macroscopic modeling of the gas phase.

Currently, the pore-network models do not yet contain all of the physics, although advancements such as including phase change and coupled thermal effects are providing promising results. Work is also needed in understanding and incorporating thickness-dependent structural heterogeneities and in linking these models with boundary conditions defined by interfacial interactions with the other PEFC components.

Water distributions at the time a capillary finger reaches the gas flow channel for two pore networks generated from the same pore-size distribution figure reprinted from Ref. The impact of interfacial regions in the PEFC has so far been commonly neglected in classical full-cell multiphase modeling efforts. Traditionally, the interface between two layers or the channel wall and DM has been neglected or simply treated as an infinitely thin barrier with discrete property values on either side and no co-mingling of surfaces and properties.

However, more recent modeling and experimental work has demonstrated the importance of these interfaces in water storage, transport, and durability. Also, the interfacial conditions typically drive the transport phenomena and are key in determining the boundary conditions for the various models.

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The specific interfaces of interest discussed in this section include the DM with the catalyst layer, the boundary between the MPL and GDL, and the interactions and interface between the GDL and flowfield, which could be critical in terms of setting the lower value of the liquid pressure and thus holdup within the cell. Classical macroscopic models only consider a bulk contact angle, pore size, tortuosity, porosity, and thermal conductivity in calculation of liquid transport with bulk capillary-transport functions, and neglect any interfacial regions, or capillary action formed by the channel wall interface with the diffusion medium.

However, one expects that the performance is quite different when the interfacial conditions above are changed, even if the normal multiphase parameters listed are identical. Clearly, there is much more to study in order to develop the next-generation of optimized materials and designs with advanced multiphase models incorporating these effects.

In fact, only a few models assume non-equilibrium 95 — 97 even though, as mentioned there is thought to be an interfacial resistance toward at least water-vapor transport 51 — 68 , 92 , 93 and assumingly transport of other species as well.

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Through-plane conductivity results are inconclusive since those done in vapor normally require a correction for interfacial contact resistance which can mask any interfacial resistance , and in liquid one does not observe an interfacial resistance. Thus, the question then is how to treat such a complex interface.