Characterization of Fractal Structures by Spray Flame Synthesis Using X-ray Scattering

Abstract

In this work, we take on an in-depth characterization of the complex particle structures made by spray flame synthesis. Because of the resulting hierarchical aggregates, very few measurement techniques are available to analyze their primary particle and fractal properties. Therefore, we use small-angle X-ray scattering (SAXS) and transmission electron microscopy (TEM) to investigate the influence of the precursor concentration on the fractal structures of zirconia nanoparticles. The combination of information gained from these measurement results leads to a detailed description of the particle system, including the polydispersity and size distribution of the primary particles. Based on our findings, unstable process conditions could be identified at low precursor concentrations resulting in the broadest size distribution of primary particles with rough surfaces. Higher precursor concentrations lead to reproducible primary particle sizes almost independent of the initial precursor concentration. Regarding the fractal properties, the typical shape of aggregates for aerosols is present for the investigated range of precursor concentrations. In conclusion, the consistent results for SAXS and TEM show a conclusive characterization of a complex particle system, allowing for the identification of the underlying particle formation mechanism.

Lattice models for ballistic aggregation: cluster-shape dependent exponents

“…While close, it is not clear whether the fractal dimension is different for the diffusive and ballistic models. The value 1.49 is very close to that observed in sprays (1.54) [45], and cells (1.5) [44]. It would be interesting to explore this connection further as well as understand the dependence of the fractal dimension on different mass dependent velocities, especially the limit where larger masses move faster.…”

“…The fractal dimension of clusters formed by aggregation is of interest in many experiments (for example, see [5,[42][43][44][45]). While it is to be expected that the exponents θ n and θ e will depend on the nature of transport and the shapes of the clusters, it is not clear whether the fractal dimension depends on transport.…”

“…The scaling theory leads to hyperscaling relations between the different exponents independent of the mean field assumptions. Fractal shapes are of particular importance in the case of the experiments on aggregates of soot [5,42], mammary epithelial cells [43,44], spray flames [45], etc., where the aggregates have a fractal dimension different from those of compact structures (d f = 2, 3). While the fractal dimensions seen in experiments [5,43] are sometimes close to that for diffusion limited aggregation (d f ≈ 1.7), there are many examples for which it is very different (for instance 1.54 for sprays [45], 1.5 for cells [44] or 2.4 for soot [42]).…”

Spray Flame Synthesis and Multiscale Characterization of Carbon Black–Silica Hetero-Aggregates

“…In order to obtain comprehensive information about primary particles, as well as aggregate and mixing properties, a combination of ultra-small-angle X-ray scattering (USAXS), high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) with energy-dispersive X-ray spectroscopy (EDXS) and analytical disc centrifugation (ADC) is used. USAXS provides integral information about the aggregates and is routinely used for aggregates of carbon and silica, as well as products obtained via spray flame synthesis [ 29 , 30 , 31 , 32 ]. The results include fractal dimensions of the aggregates as well as the mean primary particle sizes of both materials.…”