On the measurement of the fractal dimension of aggregated particles by electron microscopy : experimental method, corrections and comparison with numerical models

Abstract

Des images digitalisées en fond noir annulaire d'agrégats polydispersés de billes de fer sont obtenues avec un microscope électronique piloté par ordinateur. On discute des différentes méthodes capables d'extraire la dimension fractale des agrégats et on analyse les différentes sources d'erreur. Les résultats sont comparés avec des simulations à l'ordinateur utilisant une version polydisperse du modèle d' agrégation par collage d'amas. Les simulations montrent que la polydispersité n'affecte pas la valeur de la dimension fractale. Le résultat expérimental (D =1,9 ± 0,1) est consistant avec un modèle d'agrégation par collage d'amas avec trajectoires linéaires. Abstract.-Digital annular dark-field images of aggregated iron polydisperse particles are obtained using a computer-controlled STEM. Different methods are discussed on how to extract the fractal dimension of the aggregates, and the sources of error are analysed. The results are compared with computer simulations on a polydisperse version of the cluster-cluster aggregation model. Simulations show that polydispersity does not affect the fractal dimension. The experimental result for the fractal dimension (D =1.9 ± 0.1) is consistent with the cluster-cluster model with linear trajectories.

Fractal-like structures in colloid science

“…Note that the typical d f for DLCA, DLA, and BPCA are considerably larger (i.e., 1.8, 2.25 and 2.81, respectively), underlining the strong impact of polydispersity on d f . Interestingly, such low d f values arise only for large enough polydispersities, whereas for rather monodisperse systems (σ g ≈ 1 − 1.5), "standard" values for d f were found, as already observed in the Monte Carlo studies of Bushell and Amal [52] for DLCA and by Tence et al in BPCA [53]. It should be stressed though that this interesting dependency of d f from the particles polydispersity has been observed only in simulations, and that it would be of great interest to seek for an experimental confirmation.…”

Fractal Dimension Analysis of Single, In-Situ, Restructured Carbonaceous Aggregates

“…Although the spherule size commonly exhibits a Gaussian distribution, Tence et al (1986) found that D was not significantly influenced by a polydispersion in d,, hence allowing the average diameter to be used.…”

Measurement of Nanoparticle Agglomerates by Combined Measurement of Electrical Mobility and Unipolar Charging Properties

“…In addition, interpretation of the 2D images for 3D results may rely on assumptions and cause inaccuracy. Deriving the fractal dimension of 3D particles from 2D images is limited by the inability to distinguish 3D agglomerates with a fractal dimension between 2 and 3 (Katrinak et al 1993;Tence et al 1986). Fast and online measurement for agglomerates is required in many scenarios including measuring fast changing agglomerates, quality control for material manufacturing, monitoring toxic air-borne agglomerates, and so on.…”