Interaction and percolation in theL64 triblock copolymer micellar system

We present results of analyses of an extensive set of static light scattering (SLS), small angle neutron scattering (SANS), and viscoelastic (frequency dependent complex moduli) measurements of aqueous solutions of a triblock copolymer micellar system. We investigate Pluronic L64 $\left({\mathrm{PEO}}_{13}{\mathrm{PPO}}_{30}{\mathrm{PEO}}_{13}\right)$-water system in a wide range of composition and temperature. We determine phase diagram of the disordered micellar phase, including a cmc-cmt curve, a cloud point curve, the critical concentration, and the critical temperature by means of SLS and SANS. The microstructure and interaction between micelles are determined by analyses of SANS intensities. SANS intensity distributions are well described by combining the cap-and-gown model for the polymer segmental distribution within a micelle and the sticky hard sphere model for the intermicellar structure factor. The existence of percolation loci at well defined poins in the temperature-concentration plane is inferred from an abrupt increase of the stickiness parameter extracted from SANS data and from two order of magnitude jump of the complex moduli at the percolation point. Study of temperature dependence of real (storage) and imaginary (loss) part of the complex modulus at fixed concentration and frequency lends further support to the existence of a percolation line. We observe an increase of some order of magnitude of the real and imaginary part of viscosity at certain temperature and composition, a phenomenon usually ascribed to a gelation process in a polymer solution. The definitive confirmation of the percolation process is obtained by frequency dependent complex viscosity measured in a frequency range 0–160 (rad/sec). From these measurements we clearly observe a well defined frequency scaling behavior of the complex moduli and a loss angle (δ) independent of the frequency. Scaling exponents, determined for frequency-dependent complex moduli satisfy the scaling relations predicted by the scalar elasticity percolation theory.