THE aggregation of colloidal particles is of fundamental importance in colloid science and its applications. The recent application of scaling concepts1,2 has resulted in a much deeper understanding of the structure of colloidal aggregates and the kinetics of their formation. Two distinct, limiting regimes of irreversible colloid aggregation have been identified3. Diffusion-limited colloid aggregation occurs when there is negligible repulsive force between the colloidal particles, so that the aggregation rate is limited solely by the time taken for clusters to encounter each other by diffusion. Reaction-limited colloid aggregation occurs when there is still a substantial, but not insurmountable, repulsive force beween the particles, so that the aggregation rate is limited by the time taken for two clusters to overcome this repulsive barrier by thermal activation. These regimes correspond to the limiting cases of rapid and slow colloid aggregation that have long been recognized in colloid science4. An intriguing possibility suggested by recent work is that each of these limiting regimes of colloid aggregation is universal, independent of the chemical details of the particular colloid system. Here we investigate the aggregation of three chemically different colloidal systems under both diffusion-limited and reaction-limited aggregation conditions. A scaling analysis of light-scattering data is used to compare the behaviour and provides convincing experimental evidence that the two regimes of aggregation are indeed universal.

Universality in colloid aggregation

On techniques for the measurement of the mass fractal dimension of aggregates.

This article describes the advances that have been made over the past ten years on the problem of fracton excitations in fractal structures. The relevant systems to this subject are so numerous that focus is limited to a specific structure, the percolating network. Recent progress has followed three directions: scaling, numerical simulations, and experiment. In a happy coincidence, large-scale computations, especially those involving array processors, have become possible in recent years. Experimental techniques such as light- and neutron-scattering experiments have also been developed. Together, they form the basis for a review article useful as a guide to understanding these developments and for charting future research directions. In addition, new numerical simulation results for the dynamical properties of diluted antiferromagnets are presented and interpreted in terms of scaling arguments. The authors hope this article will bring the major advances and future issues facing this field into clearer focus, and will stimulate further research on the dynamical properties of random systems.

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Dynamical properties of fractal networks: Scaling, numerical simulations, and physical realizations

The authors study the process of diffusion-limited colloid aggregation (DLCA) using both static and dynamic light scattering. Static light scattering is used to measure the fractal dimension of the clusters as well as their structure factor, which is found to be in good agreement with that obtained from calculation using computer-generated clusters. Dynamic light scattering is used to probe both translational and rotational diffusion motion of the clusters. A method to separate their respective contributions is developed, allowing a quantitative determination of the average hydrodynamic radius. In addition, they determine the ratio of the hydrodynamic radius to the radius of gyration for individual aggregates, and find beta =0.93. A method is developed to scale all the dynamic light scattering data onto a single master curve, whose shape is sensitive to key features of the DLCA process. Good agreement is found between the prediction of the shape of the master curve and that obtained from experiments. Using several completely different colloids, they find that the shape of their master curves are identical, their fractal dimensions are identical and their aggregation kinetics are identical. This provides strong evidence of the universality of the DLCA regime of colloid aggregation.

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Universal diffusion-limited colloid aggregation

In this paper an assessment of the processing and properties of interpenetrating phase composites is presented. Such materials, defined as multiphase composites in which each phase is topologically interconnected throughout the microstructure, were the subject of a DOE Basic Energy Sciences sponsored workshop on research needs and opportunities held in July 1989 in Snowmass, Colorado. In place of a report representing the proceedings of the workshop, this paper provides a review of the field in its present, nascent state and identifies some of the critical scientific and technological issues posed by development of this class of material. The emphasis is on processing approaches and properties of interpenetrating phase composites. A list of the participants contributing to the workshop is given.

Interpenetrating Phase Composites

We present experimental results showing that colloidal silica spheres can be induced to aggregate either slowly or very rapidly. The slow process always yields clusters with a fractal dimensionality ${\mathrm{d}}_{\mathrm{f}}$=2.08\ifmmode\pm\else\textpm\fi{}0.05, but the rapid process can produce clusters with either ${\mathrm{d}}_{\mathrm{f}}$=1.75\ifmmode\pm\else\textpm\fi{}0.05 or ${\mathrm{d}}_{\mathrm{f}}$=2.08\ifmmode\pm\else\textpm\fi{}0.05. However, clusters with ${\mathrm{d}}_{\mathrm{f}}$=1.75 are always observed to restructure so as to yield ${\mathrm{d}}_{\mathrm{f}}$=2.08\ifmmode\pm\else\textpm\fi{}0.05.

Restructuring of colloidal silica aggregates.

Classical light-scattering studies of colloidal silica gels show that they have a fractal structure for length scales shorter than a concentration-dependent crossover length $\ensuremath{\xi}$, and behave like a collection of nearly randomly distributed scattering centers for length scales greater than $\ensuremath{\xi}$. Our data show that $\ensuremath{\xi}$ has a power-law concentration dependence, $\ensuremath{\xi}\ensuremath{\propto}{c}^{\ensuremath{-}1.17\ifmmode\pm\else\textpm\fi{}0.1}$.

Gelation of colloidal silica

Spherical colloidal silica particles of ~ 7nm diameter may easily be induced to aggregate into “large” (≳5µm) structures even in dilute solution, by the addition of sufficient salt. The resulting aggregates appear to be fractal, scale invariant objects, as determined by classical light scattering. Studies carried out in 0.5M NaCl show that the fractal exponent characterizing the clusters is 2.08±0.04 over a wide range of pH, and that the aggregation kinetics are slow and exponential in time. Studies in 1M NaCl reveal a transition to very rapid aggregation at high pH or very low particle concentration. This rapid aggregation regime results in a fractal dimension of either 2.08 or 1.77 depending upon conditions.

Claude Aubert

Papers

Restructuring of colloidal silica aggregates.

Gelation of colloidal silica

Aggregation of Colloidal Silica