Fractal Geometry of Colloidal Aggregates

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