Transformation of Block Copolymer Nanoparticles from Ellipsoids with Striped Lamellae into Onionlike Spheres and Dynamical Control via Coupled Cahn-Hilliard Equations.

Annealing of block copolymers has become a tool of great importance for the reconfiguration of nanoparticles. Here, we present the experimental results of annealing block copolymer nanoparticles and a theoretical model to describe the morphological transformation of ellipsoids with striped lamellae into onionlike spheres. A good correspondence between the experimental findings and predictions of the model was observed. The model based on finding the steepest direction of descent of an appropriate free energy leads to a set of Cahn-Hilliard equations that correctly describe the dynamical transformation of striped ellipsoids into onionlike spheres and reverse onionlike particles, regardless of the nature of the annealing process. This universality makes it possible to describe a variety of experimental conditions involving nanoparticles underlying a heating process. A notable advantage of the proposed approach is that it enables selective control of the interaction between the confined block copolymer and the surrounding medium. This feature endows the model with a great versatility to enable the reproduction of several combined effects of surfactants in diverse conditions, including cases with reverse affinities for the block copolymer segments. A phase diagram to describe a variety of morphologies is presented. We employ the relationship between the temperature-dependent Flory-Huggins parameter and the width of the interfaces to account for changes in temperature due to the heating process. Simulation results correctly show how the transformation evolves as the temperature increases. This increment in temperature corresponds to progressively smaller values of the interfacial width. We anticipate that the proposed approach will facilitate the design and more precise control of experiments involving various kinds of annealing processes.