Sintering Undermines Fuel Cell Performance, Yet the Mechanism is Not Well-known
Fuel cells, specifically polymer electrolyte fuel cells, see plenty of coverage in the media because they offer the caveat to renewable energy – a car engine which runs on abundant natural gases, yet releases nothing more than water. However, one large issue that remains is the expected lifetime. Due to the design of the catalyst, fuel cells are prone to sintering effects which ultimately reduce the performance of the engine. Sintering is the process by which nanoscale particles, or nanoparticles for short, combine to form larger particles (something like watching chocolate chips melt in a bowl); and despite its original study in the 1900’s, there does not yet exist a unified model to apply sintering to fuel cells. Instead of investigating sintering applied to fuel cells, most publications state end particle sizes and maybe contribute the process to one of two models, Ostwald ripening or Smoluchowski ripening, also called coalescence. Although the two models vary in experimental results, the two are similar in ideology which may imply that the two can be unified to a single equation. However, to understand how each mechanism works requires an understanding of why sintering is thermodynamically favored.
Why do nanoparticles grow?
In general, atoms on the surface of a particle are higher in energy than atoms in the center, also called bulk atoms. If you imagine a perfect crystal lattice, this would be true because the atoms found on the surface are bound to fewer neighbors than atoms in the bulk. Therefore, because sintering promotes the growth of larger particles, which have a lower ratio of surface area to volume, sintering is thermodynamically favored.
Another important result of surface atoms having higher energy is that they can be manipulated by temperature fluctuations. Since surface atoms are bound to only a few neighbors, energy fluctuations make it possible for the atoms to be kicked off from the particle. Once kicked off, the free atom can move between particles and eventually deposit elsewhere. This result is important because this movement of atoms between nanoparticles drives both Ostwald ripening and Smoluchowski ripening. To elaborate further on the two mechanisms, Ostwald ripening is understood as the dissolution of single atoms from smaller particles and deposition onto larger particles. Smoluchowski ripening is the gradual migration and merging of single particles into larger particles.
Ostwald ripening is based on the idea that each particle is stationary and nanoparticles form by freely moving atoms depositing onto larger particles, at the expense of smaller particles. Since the growth phase is carried by single atom movement, Ostwald ripening becomes more prominent when the particles are submerged in liquid. If the particles are surrounded by liquid, the surface atoms are removed more readily as they dissolve into the solution. When dissolved, the liquid then encourages Ostwald ripening by carrying each atom along the catalyst surface until it deposits onto a larger particle. In other terms, Ostwald ripening occurs due to single atom movement, which can be facilitated by a liquid environment. Since Ostwald ripening encourages particle growth at the expense of smaller particles, it tends to display a particle size distribution that tails towards smaller particles. In mathematical language, the particle size distribution is log-normal tailing towards smaller particle sizes.
As opposed to Ostwald ripening, Smoluchowski ripening is based on the idea of individual particles migrating and coalescing into larger particles, where particle movement is modeled by Brownian motion. In other words, through the continual gain and loss of surface atoms, each particle has the potential to move a net distance if the coordinate for that particle is taken as the center of mass, and not the point of highest density. By this motion, each individual particle has the potential to collide with a nearby particle where they then coalesce to form larger particles. Since Smoluchowski ripening fully consumes particles as growth occurs, the particle size distribution tails towards larger sizes. In mathematical language, Smoluchowski ripening is log-normal tailing towards larger particle sizes.
Is it possible to unify the two models?
Despite the fact that the two models differ, in that Ostwald ripening assumes that each particle is stationary whereas Smoluchowski ripening assumes that each particle is moving some net distance, the two models are actually quite similar. For instance, both rely on single atom movement between particles and they both demonstrate log-normal particle size distributions. Therefore, it seems that it may be possible to unify a set of equations to describe sintering.
Since Ostwald ripening is more prominent when the material is in solution, the presence of solvent systems may be a large factor in unifying the two models. However, even if there is a single equation to describe sintering, it is very difficult to apply. For example, current fuel cell catalysts are moving away from single elements and instead are consisting of alloys which use cheap and rare earth elements. Now that there are different elements, it will become problematic to predict which atoms will move faster between particles and if lattice structures will prevent atom deposition. Of course applying a theoretical model of sintering will be difficult, but because it will allow for strong stability predictions, understanding sintering will be worth the efforts. Therefore, until that day, we can only hope that testing fuel cell performance will not hinder development too greatly.
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