Interpretation of light scattering and turbidity measurements in aggregated systems: effect of intra-cluster...

In this work we studied the effect of intracluster multiple-light scattering on the scattering properties of a population of fractal aggregates. To do so, experimental data of diffusion-limited aggregation for three polystyrene latexes with similar surface properties but different primary particle diameters (equal to 118, 420, and 810 nm) were obtained by static light scattering and by means of a spectrophotometer. In parallel, a population balance equation (PBE) model, which takes into account the effect of intracluster multiple-light scattering by solving the T-matrix and the mean-field version of T-matrix, was formulated and validated against time evolution of the root mean radius of gyration, , of the zero angle intensity of scattered light, I(0), and of the turbidity, tau. It was found that the mean-field version of the T-matrix theory is able to correctly predict the time evolution of all measured light scattering quantities for all sizes of primary particles without any adjustable parameter. The structure of the aggregates, characterized by fractal dimension, d(f), was independent of the primary particle size and equal to 1.7, which is in agreement with values found in literature. Since the mean-field version of the T-matrix theory used is rather complicated and requires advanced knowledge of cluster structure (i.e., the particle-particle correlation function), a simplified version of the light scattering model was proposed and tested. It was found that within the range of operating conditions investigated, the simplified version of the light scattering model was able to describe with reasonable accuracy the time evolution of all measured light scattering quantities of the cluster mass distribution (CMD) for all three sizes of primary particles and two values of the laser wavelength.