Heterogeneity of the Segmental Dynamics in Cylindrical and Spherical Phases of Diblock Copolymers

We have performed simulations of a simple bead-spring model for cylindrical and spherical phases of diblock copolymers. We have analyzed in detail the dynamic heterogeneity of the structural alpha-relaxation of the component confined in the minority domains. In analogy with previous investigations on the lamellar phase of the same bead-spring model, the analysis reveals moderate gradients of mobility in the investigated temperature range, which qualitatively probes time scales up to 100 ns. Thus, alpha-relaxation times measured at different distances from the domain center spread Over less than one decade. The spatial extension of the gradients of mobility is apparently consistent with that previously observed in the lamellar phase of the same model Gradients of mobility do not seem to be related to gradients of density within the domains, which are indeed. absent. We have performed an analysis of self- and effective concentrations, a concept usually invoked to explain the alpha-relaxation in Polymer mixtures and that ha,been recently adapted to the analysis of experimental data of diblock copolymers in ordered phases. The simulation results reveal a strong disagreement with the proposed empirical relation between self- and effective concentration, as well as with the Flory-Fox mixing rule for the dynamics. This suggests that the use of these relations may bias the analysis of experimental data.