"Diblock copolymer micelle structure and dynamics near the order-disorder transition"
At high temperatures, the blocks of an AB-diblock copolymer melt mix on a molecular level, to form the homogeneous disordered phase (DIS). As the melt is cooled, the blocks microphase segregate, forming ordered structures, such as BCC-ordered micelles (BCC). We study the order-disorder transition (ODT) in AB-diblock copolymer melts as described by the Landau-Brazovskii model. We start with the simple, direct DIS to BCC transition via nucleation in the mean-field limit, and then modify our approach to include disordered micelles (DM) and physically realistic random compositional fluctuations (noise) with an amplitude that depends on the invariant polymerization index, N¯ , and varies as N¯ -1/4. In the direct DIS to BCC transition via nucleation in the mean-field limit we find spherical nuclei, the behavior of which are consistent with classical nucleation theory close to coexistence but become diffuse at deeper undercoolings and we observe the crossover to spinodal decomposition. We also examine the dynamics of the ODT and derive an expression for the motion of a planar interfaces between two phases. Our result can be thought of as a generalization of the result by Goveas and Milner (1997). When noise is included the ODT is suppressed and disordered micelles appear as stable structures between DIS and BCC. We systematically examine the structural and dynamic properties of disordered micelles by directly analyzingmonomer densities and by calculating the scattering function, to mimic experimental techniques. Our results are consistent between analysis methods and show a general agreement with experiments on DM, suggesting that the DM that we have found in the Landau-Brazovskii model are physically realistic and that our analysis methods are valid. On cooling, there is a continuous crossover from DIS to DM for polymers of experimentally relevant values of N¯ . Once micelles have been established they diffuse through the melt by hopping between energetic minima. For large noise amplitudes the melt appears to explore configuration space during our simulations, however, for low noise amplitudes the melt evolves more slowly and can become trapped in a configuration that is liquid-ordered but has a relaxation time that is long on the scale of our simulations.