Model of Polydisperse Wormlike Stars and Its Application to Dyestuff Aggregates

A description of the scattering behavior of combinatorial wormlike stars, based on Koyama's approximation for linear wormlike chains, was extended to polydisperse star samples. The number of arms per star was constant. All arms within a single star-branched particle had the same length. Polydispersity was accounted for by merely using a Schulz−Zimm type of distribution for the overall contour length of the branched wormlike particles. Applicability of this model was tested on aggregates of anionic azo dyestuffs. The aggregation process was induced by the addition of low amounts of MgSO4 to aqueous dyestuff solutions and recorded on-line by means of time-resolved multiangle static light scattering. Each aggregation run resulted in a large number of scattering curves as a function of the aggregation time. A first interpretation of the scattering curves with the model of linear wormlike chains led to acceptable parametrization with an averaged persistence length of 180 nm. However, application of the combinatorial wormlike star model indicated a likelihood for slight branching. Thereby, a reliability limit of the linear wormlike chain model was revealed if branching of the growing linear aggregates sets in.