Micellar solutions of associative triblock copolymers: The relationship between structure and rheology

We report the rheology of the micellar solutions formed from narrow-molecular-weight poly(ethylene oxide) chains fully endcapped with C-16 or C-18 alkanes and correlate the viscoelasticity, characterized by the high-frequency modulus G(infinity)' and a single relaxation time lambda, with the measured characteristics of the micellar solutions. Scaling G(infinity)' by p(3/2)kT/tau R-H(3) (p = aggregation number, R-H = hydrodynamic radius, 1/tau = attractive virial coefficient, k = Boltzmann's constant, and T = temperature) and plotting against the hydrodynamic volume fraction of micelles collapses the two sets of data. The relaxation time scales as the diffusion time, mu R-c(3)/kT, for a free hydrophobe escaping from a micellar core of radius R-c times a Boltzmann factor accounting for an association energy that increases linearly with hydrophobe length. The low shear viscosity follows as eta(o) = lambda G(infinity)'.