Algorithms and methods for analysis of the optical structure factor of fractal aggregates

Abstract

We introduce numerical methods and algorithms to estimate the main parameters of fractal-like particle aggregates from their optical structure factor (i.e. light scattering diagrams). The first algorithm is based on a direct and simple method, but its applicability is limited to aggregates with large size parameter and intermediate fractal dimension. The second algorithm requires to build calibration curves based on accurate particle agglomeration and particle light scattering models. It allows analyzing the optical structure factor of much smaller aggregates, regardless of their fractal dimension and the size of the single particles. Therefore, this algorithm as well as the introduction of a criterial curve to detect the different scattering regimes, are thought to be powerful tools to perform reliable and reproducible analysis.

Using the DDA (Discrete Dipole Approximation) Method in Determining the Extinction Cross Section of Black Carbon

“…TEM (Transmission Electron Microscopy), but they were not considered in this work. More information about them can be found elsewhere [24][25][26]. Furthermore, light based techniques can be used to study different structures, like erythrocytes or fibres [27][28][29][30][31][32].…”

Absorption and scattering by fractal aggregates and by their equivalent coated spheres

“…This method launches a spherical particle of radius a on a random walk. A collision between the marching particle and the aggregate leads to adherence of the two if the new aggregate structure satisfies the prescribed prefactor k f and fractal dimension D f [40]. This procedure is repeated until the aggregate contains the desired number of monomers N s .…”

“…Sorensen [2] and Lapuerta [39] assumed a value of k f for aggregates of soot particles to be 1.593 corresponding to the most compact packing of monodisperse monomers. Fractal aggregate formation can be numerically simulated using particle cluster aggregation algorithm [2,40,41]. This method launches a spherical particle of radius a on a random walk.…”

Measurement of Agglomerates Shape Parameters with Threedimensional Reconstruction Based on a Laser Displacement Sensor

“…Perspectives for our work mainly are that the method presented could be use in combination with more complex morphological analyses [16] o to validate other optical particle characterization methods [17].…”