Studying the concentration dependence of the aggregation number of a micellar model system by SANS

We present a small-angle neutron scattering (SANS) structural characterization of n-alkyl-PEO polymer micelles in aqueous solution with special focus on the dependence of the micellar aggregation number on increasing concentration. The single micellar properties in the dilute region up to the overlap concentration phi* are determined by exploiting the well characterized unimer exchange kinetics of the model system in a freezing and diluting experiment. The micellar solutions are brought to thermodynamic equilibrium at high temperatures, where unimer exchange is fast, and are then cooled to low temperatures and diluted to concentrations in the limit of infinite dilution. At low temperatures the kinetics, and therefore the key mechanism for micellar rearrangement, is frozen on the experimental time scale, thus preserving the micellar structure in the dilution process. Information about the single micellar structure in the semidilute and concentrated region are extracted from structure factor analysis at high concentrations where the micelles order into fcc and bcc close packed lattices and the aggregation number can be calculated by geometrical arguments. This approach enables us to investigate the aggregation behavior in a wide concentration regime from dilute to 6.phi*, showing a constant aggregation number with concentration over a large concentration regime up to a critical concentration about three times phi*. When exceeding this critical concentration, the aggregation number was found to increase with increasing concentration. This behavior is compared to scaling theories for star-like polymer micelles.