Fractal substructure of a nanopowder generated by repeated fragmentation and sedimentation: the rôle of the dust
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Packings of cohesive nanoparticles, that is nanopowders, may be obtained as the result of repeated fragmentation–reagglomeration cycles (Schwager et al. in Phys Rev Lett 100:218002, 2008) such that the resulting sediment reveals a fractal structure. The size distribution of the fragments after a fragmentation step is a superposition of a narrow distribution of large particles (chunks) whose size is determined by the cutting length and a power-law distribution for small particles, representing scale invariant dust. It was shown that the exponent of the power-law, \(\tau \), is in non-trivial relation to the fractal dimension, \(d_f\), via \(d_f(2-\tau )=1\). This poses the question for the structure of the sediment created by repeated fragmentation–reagglomeration cycles when the dust particles are excluded from the reagglomeration step. We found that even in this case, repeated fragmentation–reagglomeration cycles yield a sediment of fractal structure with slightly reduced fractal dimension while the dust exponent, \(\tau \), remains unchanged.
KeywordsNanomaterials Fractal structure Granular material Sequential deposition
We thank the German Research Foundation (DFG) for funding through its Cluster of Excellence “Engineering of Advanced Materials” at the University of Erlangen-Nuremberg and through Grants WO 577/9 and PO 472/22-1.
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Conflict of interest
None of the authors received honoraria for speaking at symposia in relation to this paper. None of the authors received financial support for attending symposia in relation to this paper. None of the authors received financial support for educational programs in relation to this paper. All authors are employed and had consultation with various other parties, also related to the material presented in the current paper. The authors received support from project sponsors as given above. Two of the authors (DEW and TP) are members of the editorial board of “Granular Matter”. None of the authors has multiple affiliations. None of the authors has financial relationships, for example equity ownership or investment interest in relation to the current paper. None of the authors holds intellectual property rights (e.g. patents, copyrights and royalties from such rights) in relation to the current paper. There are no holdings of spouse and/or children of any of the authors that may have financial interest in the work, relating to the current paper. None of the authors has interests that go beyond financial interests and compensation (non-financial interests) that may be important to readers of the current paper.
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