Nanotechnology

Mass fractal dimension from 2D microscopy images via an aggregation model with variable compactness

“…The morphological aggregation model 20 builds clusters consisting of a number of non-overlapping elementary objects arranged according to a given statistical average fractal dimension 3 . Clusters are built by sequential addition, assigning a different sticking probability to the points on the cluster.…”

“…The Eq. ( 5) is valid within limits, in terms of projected log( )∕ log( 0 ), for a given 3 . The lower and the upper limit (respectively ,min and ,max ) are reported as reachable limit ranges by the aggregation model.…”

“…Image-analysis is frequently used to characterize colloidal particles of silica 1 , alumina 2 , soot or carbon. These particles can exist as a powder or within liquid suspensions, and they find applications in different domains like electronics, pharmaceutic and catalysis 3 . Such applications depend on particles size and structure.…”

“…The mass fractal dimension is close to unity for linear clusters, near to 2 for planar clusters and around 3 for isotropic 3D clusters. 3 can be measured by experimental scattering techniques such as Small Angle X-Ray 8 or Neutron 9 Scattering. A change in 3 of a colloidal aggregate/agglomerate modifies its density, involving different dispersibility and settling behaviour 10 .…”

“…Microscopy-image analysis provides precious information on size and structure of colloidal aggregates and agglomerates. The structure of colloids is often characterized using the three-dimensional mass fractal dimension 3 , which is different from the twodimensional fractal dimension 2 that can be computed from microscopy-images. In this work we propose to use a recent morphological aggregation model to find a relationship between 2D image fractal dimension and 3D mass fractal dimension of aggregates and agglomerates.…”