Dependence of fractal dimension of DLCA clusters on size of primary particles

• We review and analyze fractal dimensions (Df) of DLCA clusters.
• Literature Df values decrease as the particle size increases.
• Our designed experiments confirm such Df dependence on the particle size.
• Intracluster multiple scattering does not change Df from static light scattering.

It is well known that clusters generated from colloidal aggregation driven by Brownian motion are typical fractal objects with the fractal dimension in the range of 1.75–1.85 under the diffusion-limited cluster aggregation (DLCA) conditions. In this work, we review and analyze the values of the fractal dimension for DLCA clusters experimentally determined in the literature. It is found that the value of the fractal dimension decreases significantly as the primary particle radius increases. Then, we have properly designed the DLCA experiments, using different radii of the primary particles, and determined the fractal dimensions of the generated clusters. Our results have well confirmed that the fractal dimension indeed decreases as the particle radius increases. To explore the mechanism leading to such dependence, we have performed intense computations through the full T-Matrix theory, and we conclude that this is not related to the effect of the intra-cluster multiple scattering on the slope of the scattering structure factor. The large fractal dimensions of the clusters generated by very small nanoparticles could be explained by thermal restructuring due to their low bonding energies, but no clear explanation can be given for the small fractal dimensions of the clusters made of large particles.

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