A historical introduction to computer models for fractal aggregates

It has been known for a century that small particles dispersed in liquids and gases can form aggregates with extraordinarily low densities, and a variety of studies in the 1960s and 1970s, based on conceptual models and computer models, suggested that "anomalous" scaling relationships were associated with the structures of these aggregates. However, the lack of a suitable theoretical framework and the limits of computer technology inhibited the development of a coherent understanding of the structures of these aggregates and the kinetics of their formation. In the 1980s, the popularization of fractal geometry and rapid advances in computer technology removed these barriers to progress. In this review, the early work on fractal aggregates is discussed and the basic particle-cluster and cluster-cluster aggregation models introduced in the 1980s are described. During the 1990s, interest has been focused on the subtle relationships between aggregation, gelation and spinodal decomposition and on the physical behavior of systems containing fractal aggregates. The following papers in this special issue of the Journal of Sol-Gel Science and Technology on "Computer simulations of aggregation and sol-gel processes" describe recent advances in these directions. They are previewed in this introductory contribution.