(172a) Multidimensionality in Fluidized Nanopowder Agglomerates

Fluidization is a promising but challenging technique for processing of nanoparticles, e.g. to produce coated nanoparticles [1]. Due to van der Waals forces, dominant at the nano-scale, nanoparticles do not fluidize individually but form agglomerates [2]. These agglomerates are usually described with fractal geometry and by a fractal dimension around 2.5 [3, 4]. However, this dimension is typically obtained with settling experiments [3], which include multiple assumptions [5] and can only focus on the macro-scale of the agglomerates, since the smallest scales are not visible. The characterization of the whole agglomerate structure with only one fractal dimension seems in contradiction with the –also broadly accepted– fact that the agglomerates have a hierarchical structure [2, 6]. If the mechanism of formation of the different hierarchical levels is different, one would expect to find different fractal dimensions in each level, reflecting the mechanism that governed its formation.

We aim to clarify this contradiction measuring in-situ the structure of the fluidized nanoparticles agglomerates with spin-echo small-angle neutron scattering (SESANS) [7]. The SESANS outcome is polarization as a function of length scale, which can be related to the autocorrelation function of the sample.

We investigate two models to describe the autocorrelation function γ(r) of the agglomerates structure. One of them is the classical fractal description on the mono-dimensional form γ(r) ∝r^Df-3. The other model includes two fractal dimensions, one describing the smallest scales γ(r) ∝r^Df1-3 and another one describing the largest scales γ(r) ∝r^Df2-3.

The mono-dimensional form fails to predict the experimental polarization. Contrary, the agreement between the experimental and the modeled polarizations is excellent for the bi-dimensional γ(r), indicating that fluidized TiO₂ P25 agglomerates have at least two fractal dimensions. One of them is approximately 2.1 and characterizes the primary strong chain-like aggregates that the particles typically form in the production process. The second one is about 2.8 and characterizes the secondary agglomerates formed by the primary agglomerates.

The results are in line with the hierarchical levels proposed by Yao et al. [2]. The fractal dimension changes between these levels as a result of the different mechanisms that govern their formation. This is opposite to the classical description that uses only one fractal dimension to characterize the scaling in the whole structure. The bi-fractal characterization can help to unravel the mechanisms that form each hierarchical level, and to explain diffusion processes inside the agglomerates.

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2.            Yao, W., G. Guangsheng, W. Fei, and W. Jun, Powder Technology, 2002. 124(1–2): p. 152-159.

3.            Castellanos, A., J.M. Valverde, and M.A.S. Quintanilla, Physical Review E, 2001. 64(4): p. 041304.

4.            Nam, C.H., R. Pfeffer, R.N. Dave, and S. Sundaresan, AIChE Journal, 2004. 50(8): p. 1776-1785.

5.            Tang, P. and J.A. Raper, Powder Technology, 2002. 123(2–3): p. 114-125.

6.            Valverde, J.M. and A. Castellanos, AIChE Journal, 2006. 52(2): p. 838-842.

7.            Andersson, R., L.F. van Heijkamp, I.M. de Schepper, and W.G. Bouwman, Journal of Applied Crystallography, 2008. 41(5): p. 868-885.