Aggregation of colloidal silica: Reaction-limited kernel, stability ratio and distribution moments

Abstract

The kinetics of aggregation of colloidal silica, with a single-sphere diameter of 12 nm, under reaction-limited conditions, have been studied over a range of particle number concentrations and ionic strengths. Second-order rate coefficients in the initial stages of the reaction were found to vary from 3 × 10 ⁻¹⁸ to 2 × 10 ⁻¹⁵ cm ³ s ⁻¹ . The coagulation kernel can be expressed in the form K _ij ∝(ij) ^A/2 , where A lies between 0.99 and 0.72. This agrees well with a theoretical prediction for the collision frequency of (ij) ^0.52 , for d _f = 2.1. The stability ratio, W, was found to be dependent on ionic concentration, c, according to log W = −α log c + β, where α is dependent on cluster size. The second moment of the distribution, M ₂ , deviates in the earlier stages of the reaction from its predicted value of ca. 2M ₀ ⁻¹ , but at large cluster masses (m > 10 ⁴ ) M ₂ behaves as for diffusion-limited aggregation. At low ionic strengths, the reaction is initially limited by the repulsive, electrostatic, potential; at large cluster masses steric effects begin to dominate. With high ionic strengths, there is an increased probability of reaction between larger clusters, up to some limiting size above which diffusional effects dominate.