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Structural and Mechanical Properties of Nanopowders

Subject Area Mechanical Process Engineering
Term from 2011 to 2014
Project identifier Deutsche Forschungsgemeinschaft (DFG) - Project number 184017420
 
Final Report Year 2018

Final Report Abstract

Cohesive powders are in general not freshly synthesized every time they are needed. Instead, before they are being processed, they already have undergone a history of transport, storage, and distribution into batches. This history is in general not well controlled, but it can be assumed that it changes the packing structure of the powder in a fairly reproducable way, at least statistically. In this project we developed a statistical model to capture the essence of this phenomenon: We consider the structural evolution, when a powder undergoes many cycles of fragmentation (e.g. by shaking, or suspension in a turbulent fluid) and subsequent settling (sedimentation). The model assumes that there is a characteristic length scale for the fragmentation process. Such a model had previous been investigated by us in two dimensions. Here, we explored the three-dimensional case, which is closer to applications. To model sedimentation of complex shaped flakes realistically turned out to require a completely new algorithm, because of different topological properties of a three-dimensional packing compared to a two-dimensional one. The solution of this problem enabled us to study sediment structures in unprecedented detail. Combining this sedimentation model with repeated fragmentation led to the result that after a while the structure becomes statistically robust. The approach of this final structure takes a time that increases linearly with the characteristic fragmentation length. Up to this length the final structure is fractal, i.e. all pore sizes occur in a self-similar way. The relation of this finding to the fragment size statistics has been investigated. The abundance of fragments decreases as a power lao of their size. We found that the same scaling relation between the exponent and the fractal dimension holds as in two dimensions, although their values are different. We showed that the scaling properties do not depend on the way, the sedimentation is modeled. If fragments stick upon first contact instead of rolling down, the scaling properties remain the same. We also investigated the rˆle of the dust for the formation of a fractal substructure. The fragmentation was modified such that the dust was filtered out before settling sets in. This resulted in a sediment structure with increased porosity, as expected. However, the fractal dimension changes very little, only by about 5% in two dimensions. This led to the conclusion that the fractal dimension is not very sensitive to the details of the fragmentation process either. For the cohesion between particles the surface roughness is essential. It evolves in time, if the particles deform plastically in collisions. This has also been modeled in this project, as another example of a cyclic process that evolves into a steady state. It turns out that this process is also characterized by scaling laws, however the phenomenology and exponents differ from the case of cyclic fragmentation and sedimentation. Obviously, there are different universality classes of cyclic processes, and their exploration remains an interesting task for the future.

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