Aggregation in dense solutions of rods

Abstract

The growth of clusters formed by reacting rigid rods of axial ratio x with linkers of functionality z in a dense reaction mixture is modelled. Compact clusters of a volume fraction ϕ∼[ln (z– 1)]/x result, independently of the reaction mixture density so long as this is high. Cluster–cluster aggregation is neglected in this model. Fluctuations in growth are examined and, for the model introduced, yield fractal paths of connection in the clusters. Groups of strands emanating from a common root coarsen at the expense of other groups. Thus elasticity should be unusual for a compact object and stresses greatly concentrated by the competition in growth between the descendants of roots.