Temperature dependence of micelle shape transitions in copolymer solutions: the role of inter-block incompatibility

Abstract

The nature of the transition between worm-like and spherical micelles in block copolymer dispersions varies between systems. In some formulations, heating drives a transition from worms to spheres, while in other systems the same transition is induced by cooling. In addition, a sphere-worm interconversion can be accompanied either by an increase or a decrease in the solvation of the core, even if the direction of the temperature dependence is the same. Here, self-consistent field theory is used to provide a potential explanation of this range of behaviour. Specifically, we show that, within this model, the dependence of the transition on the incompatibility $\chi_{BS}$ of the solvophobic block B and the solvent S (the parameter most closely related to the temperature) is strongly influenced by the incompatibility $\chi_{AB}$ between B and the solvophilic block A. When $\chi_{AB}$ is small ($\chi_{AB}\le 0.1$), it is found that increasing $\chi_{BS}$ produces a transition from worm-like micelles to spheres (or, more generally, from less curved to more curved structures). When $\chi_{AB}$ is above 0.1, increasing $\chi_{BS}$ drives the system from spheres to worm-like micelles. Whether a transition is observed within a realistic range of $\chi_{BS}$ is also found to depend on the fraction of solvophilic material in the copolymer. The relevance of our calculations to experimental results is discussed, and we suggest that the direction of the temperature dependence may be controlled not only by the solution behaviour of the solvophobic block (upper critical solution temperature versus lower critical solution temperature) but also by $\chi_{AB}$.