Comparison of methods to derive morphological parameters of multi-fractal samples of particle aggregates from TEM images

We investigate two main methods for detecting correlations between the size and fractal dimension of small particle aggregates from two-dimension Transmission Electron Microscopy (TEM) images. The first method is based on a multi-scale analysis of an entire aggregate sample, whereas the second method (modified Box-Counting algorithm, MBC) is based on the analysis the self-similarity properties of each aggregate within a sample. Both methods were tested on a sample of soot aggregates as well as synthetic TEM images produced with a tuneable Diffusion Limited Aggregation code. We have found that the MBC method provides a less noisy estimation for the evolution of the fractal dimension with the size of aggregates, giving at the same time a criterion to reject the aggregates with insufficient self-similarity properties. So that with this method, the mean fractal dimension of the soot sample was found to be much lower (1.66±0.02) than that derived with the classical multi-scale analysis (1.88±0.02).

► Detecting correlations between the morphological parameters of particle aggregates. ► Calibration curves are derived from a tunable diffusion limited aggregation code. ► A multi-scale method estimates the mean fractal dimension of an entire sample. ► A Box-Counting method estimates self-similarity properties of each aggregate. ► Box-Counting method successfully detects multi-fractal samples.