Combined study of coagulation kinetics and close-range aggregate structure

Abstract

The kinetics of coagulation of model polystyrene latex spheres under both reaction and diffusion control have been studied. The zeroth moment of the aggregate distribution has been measured by an automated laser particle-counting method, and the second moment by time-resolved low-angle light scattering. Emphasis has been both on dimer formation and the longer-time kinetics of cluster–cluster aggregation. Extension of the light scattering method of Giles and Lips (J. Chem. Soc., Faraday Trans. 1, 1974, 74, 733) has yielded information on the close-range structure in growing aggregates. The moments of the aggregate distribution can deviate from the predictions of the simple Smoluchowski constant-kernel equation. Acceleration in rate from reaction to diffusion control can occur in so-called rapid coagulation and in an intermediate regime of slow coagulation. In very slow coagulation, the rate decelerates, suggesting transition from reaction to equilibrium control. Interpretation on kinetic random polycondensation theory for an RA_f process has yielded effective functionalities f which increase with particle density and decrease with increasing reaction control. The potential of spherical particles for high functional reactivity is not in general realised because aggregates can rearrange within the timescale of collisions, and spheres can form cycles (ring-closed structures) as early as the trimer stage, with consequent wastage of functionalities. The close-range structure of aggregates increases in compactness with increasing reaction control and decreasing particle concentration. The kinetics in the regime of the very slow coagulation are consistent with an initial reversible step of dimerisation followed by the irreversible formation of higher-order aggregates with ring-closed bonding. Application of reversible polycondensation theory to the dimer step has enabled the strength of attraction, a finite primary minimum, to be quantified. The observed deviations from constant-kernel Smoluchowski kinetics have important implications for the measurement of classical colloid stability plots and may be the origin of the discrepancies between the predictions of DLVO theory and kinetic measurements of colloid stability.