Diffusion of fractal aggregates in the free molecular regime

We use static and dynamic light scattering to determine how the diffusion coefficient of a fractal aggregate in the free molecular regime depends on its morphological properties. Our system is a carbonaceous flame soot aerosol containing fractal aggregates with ${\mathit{D}}_{\mathit{f}}$=1.8. We find that the Epstein equation for the diffusion coefficient holds with an effective mobility radius given by ${\mathit{R}}_{\mathit{m}}$=0.99${\mathit{aN}}^{0.43}$, where N is the number of monomers per aggregate and a is the monomer radius. This result is quantitatively explained as due to the projectional area of the aggregate which includes monomer-monomer screening.