Fractal geometry of colloidal aggregates

TLDR: In this article, the fractal dimension of colloidal aggregates of small silica particles is measured by both light and x-ray scattering, showing that the aggregates are fractal.

Abstract: Measurement of the fractal dimension, $D$, of colloidal aggregates of small silica particles is reported. We observe power-law decay of the structure factor $[S(k)\ensuremath{\sim}{k}^{\ensuremath{-}D}]$ by both light and x-ray scattering showing that the aggregates are fractal. $D$ is found to be 2.12\ifmmode\pm\else\textpm\fi{}0.05, which is intermediate between recent numerical results for the kinetic models of diffusion-limited aggregation ($D=2.5$) and cluster aggregation ($D=1.75$), but is rather close to the value for lattice animals ($D=2.0$), which are equilibrium structures.