Application of cascade theory to light scattering from a coagulating dispersion of random aggregates

Abstract

As first demonstrated by Stockmayer, statistical theories of random polycondensation can provide equivalent results to those of kinetic treatments, e.g. Smoluchowski theory. Classical diffusion-limited coagulation is mathematically conformal to an RA₂ statistical process. This analogy has been exploited to provide an alternative model, rooted in statistical formalism, for the scattering from coagulating dispersions of spherical particles. Cascade theory is utilised. With random-flight configurational statistics of the aggregates, the model provides predictions in surprising agreement with experimental data. With ‘blob’ configurational statistics to allow for short-range excluded volume effects the model can represent recent computer simulations of random aggregation by Clague and Dickinson (J. Chem. Soc., Faraday Trans. 2, 1984, 80, 1985). When applied to extensively aggregated systems the model is consistent with self-similar structural behaviour on long length scales. The inferred fractal dimension D= 1.9 ± 0.1 is not obviously sensitive to the range of configurational statistics considered here.