Block copolymer micelles: Viscoelasticity and interaction potential of soft spheres

Block copolymer micelles in the size range between 10 and 100 nm are investigated as model systems for soft spheres. The zero shear viscosity η0 and complex modulus G* of micellar solutions are studied via dynamic mechanical spectroscopy and shear viscosity measurements over a wide range of concentrations. Depending on their structure, block copolymer micelles exhibit the characteristic rheological behavior of hard spheres, soft spheres, or polymers. With increasing concentration, hard-sphere and most soft-sphere samples exhibit a sharp liquid–solid transi-tion as apparent by a divergence of zero shear viscosity η0 and the development of a fre-quency-independent elastic modulus. The transition occurs at a certain volume fraction which can be related to the softness of the particles. In the solid regime the elastic modulus G exhibits a characteristic concentration dependence which is related to the spatial variation of the soft sphere repulsive potential. We observe a G∝Z1.48r−2.46 relation between modulus, aggregation number Z and intermicellar distance r which is close to the theoretical prediction G∼Z3/2r−2 of Witten and Pincus derived for polymerically stabilized colloidal particles.