Nature of Disordered Micelles in Sphere-Forming Block Copolymer Melts

Taking a nucleation perspective, we study the nature of the disordered micelles in highly asymmetric, sphere-forming diblock copolymer melts using the self-consistent-field theory. The micelles are shown to correspond to strong, activated, localized composition fluctuations in the disordered state due to finite molecular weights. By taking into account the translational entropy of the micelles, we obtain the concentration and the free energy of the disordered micelles. The critical micelle temperature (in terms of the familiar combination χN), operationally defined to correspond to the onset of sufficient number of micelles in the system, is identified by invoking a criterion involving the concentration of micelles. The disordered micelles are part of the disordered phase, and the only phase transition between the disordered state and the ordered phase is the order−disorder transition (ODT). However, there exists a sharply defined temperature (higher than the critical micelle temperature), which we term the micelle dissociation temperature, beyond which micelles with finite lifetimes become impossible. The range of χN for the disordered micelles to be observable shrinks as N-1/2 with increasing degrees of polymerization N of the copolymers. In the infinite molecular weight limit, the window vanishes and the mean-field phase diagram calculated by Matsen and Bates is recovered. The disordered micelles, as a part of the disordered phase, contribute to the increased scattering intensity and the low-q shift of the structure factor in diblock copolymer melts near the ODT