PREDICTING DISORDER-ORDER PHASE-TRANSITIONS IN POLYMERIC MICELLES

The structure observed in concentrated polymeric micelles results from interactions between coronal chains that develop as micelles are brou ght to approach distances where the chains either compress or interdig itate. One powerful model for polymeric micelles comprises spherical p articles with chains tethered to their core at a specified surface den sity. This treatment combined with self-consistent field theory provid es an estimate of the pair interaction potential between micelles. The se pair interaction potentials allow modeling of the structure and the rmodynamic properties that depend on the overall micelle concentration . We perform neutron scattering experiments to measure the short-range correlations in the liquid, through the static structure factor S(q), and compare these results with models that rely on a solution of the Ornstein-Zernike equation subject to a Rogers-Young closure. A descrip tion of the homogeneous liquid serves as the basis for employing densi ty functional theory (DFT) to estimate the free energy of the solid. I n this investigation, we use the modified weighted density approximati on of Denton and Ashcroft [Phys. Rev. A 39, 4701 (1989)] to estimate t he free energy of the solid for each of our micellar systems to predic t the liquid-solid phase transition. Although we experimentally observ e transitions to face-centered-cubic (fcc) and body-centered-cubic (bc c) crystals depending on the length of the corona relative to the core , we only predict a simple liquid-fcc transition with the DFT method. The nature of the transition suggests a simple perturbation result usi ng the hard sphere as the reference system. Despite the inability to p redict the bcc lattice type, both DFT and hard-sphere models accuratel y predict coexistence over the entire range of our experiments.