We determine the effective mobility radius for fractal aggregate particles. Our method is to use static light scattering to measure the radius of gyration $R_g$ of the aggregates, and dynamic light scattering to measure the diffusion coefficient hence the mobility radius $R_m.$ The range of our results can be specified by the Knudsen number Kn, which is the mean free path of the medium molecules divided by the radius of the aggregate. Our results apply to the entire range of Kn from the continuum limit (Kn=0) to the free molecular limit $\left(\mathrm{Kn}\gg 1\right).$ In the continuum regime we find $R_m{/R}_g=0.97\mathrm{}\pm 0.05$ when the aggregate fractal dimension is $D_f\simeq 2.15,$ and $0.70\pm 0.05$ when $D_f\simeq \mathrm{1.75.}$ The latter result is independent of Kn for $\mathrm{Kn}\lesssim \mathrm{1.3.}$ The free molecular mobility goes as $R_m{=aN}^{0.44\pm 0.03},$ where a is the monomer radius and N is the number of monomers per aggregate. Since $R_g\sim {\mathrm{aN}}^{{1/D}_f},$ $R_m{/R}_g$ is not a constant when Kn is large. We find for all Kn that the functionality of $R_m{/R}_g$ must always begin with the correct $\overrightarrow{N}1$ limit, and this affects experimental observation.

• Received 24 March 1999

DOI:https://doi.org/10.1103/PhysRevE.60.3036