Matthew H. Helgeson, University of Delaware, Newark, DE 19711, Florian Nettesheim, Chemical Engineering, University of Delaware, 150 Academy Street, Newark, DE 19711, Norman J. Wagner, Department of Chemical Engineering, University of Delaware, 150 Academy St., Newark, DE 19716, and Eric Kaler, Stony Brook University, Stony Brook, NY 11794.
Recent work has shown that addition of colloidal nanoparticles to wormlike micellar (WLM) solutions allows unique tunability of the structure and rheology of WLM networks, resulting from structuring of the surfactant at the particle surface, including direct association of micelles and nanoparticles. However, this association leads to micelle-mediated attractive interactions between particles, which result in thermoreversible aggregation and phase separation of the particles at sufficient concentrations. To describe this new class of colloidal interactions, we have extended a statistical thermodynamic model for colloids bridged by telechelic polymers [Bhatia and Russel, Macromolecules, 2000] to include the statistics of reversible chain scission developed for WLMs. The model predicts a long-range attraction with a deeper minimum than that predicted for telechelic polymers due to changes in the equilibrium distribution of chain lengths at sufficiently small separation. The model is validated by comparing thermodynamic predictions to experimentally observed phase equilibria and measurements of the static structure factor using small-angle neutron scattering (SANS) with contrast variation. By mapping of the potential onto a square well fluid, SANS results can be fit to obtain model parameters, which are in quantitative agreement with independently measured values of the micellar contour length and adsorption energy using rheology and isothermal titration calorimetry measurements. The results suggest that the micelle-mediated interaction model is a more realistic description of the structure and thermodynamics of colloids dispersed in WLM media than more generic potentials.