Aggregate shape determination via light scattering by aligned and randomly oriented polydisperse aggregates

Highlights: • Calculations of structure factor and A₃₁ for DLCA-like aggregates. • Linear correlation for small q between slope ratio and A₃₁ for aggregates (d_f= 1.78). • Correlation between the maximum structure factor and A₃₁ (for shape information). • Application of previous methods to broad aggregate size distributions. • Detailed shape information obtained by using both aligned and random orientations. We present calculations of light scattered by simulated aligned and randomly oriented fractal aggregates of touching spheres. The alignment by an applied electric field is in the direction yielding the minimum energy associated with the polarizability of the aggregate. This direction is also within a few degrees of the direction associated with the smallest inertial eigenvalue. Aggregates were generated to have a fractal dimension of 1.78 (characteristic of diffusion–limited cluster-cluster aggregation) and to simulate the range of aggregate sizes (30 to 2000) and size distributions for post-flame generated soot by a range of hydrocarbon fuels. More nearly monodisperse aggregates were also generated to simulate the size distributions obtained via mobility or mass classification. We show that a ratio of slopes computed from small angle light scattering intensities (Guinier plots) is related to the shape parameter A₃₁, which is the ratio of the largest to the smallest principle radii of gyration of the inertia tensor. A geometric interpretation of the overall shape is presented based on the semi-axes of an ellipsoid. Results on the correlation between the maximum structure factor ratio {S(q)}_a/ {S(q)}_r for the monodisperse and polydisperse clusters and the average value of A₃₁ indicate that light scattering measurements in the q range of fractal behavior would also be feasible for shape characterization. Our calculations indicate that light scattering measurements have a good potential for characterizing aggregate shape with an advantage of being more sensitive to shape than mobility measurements.