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

Abstract

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.

Surface‐Reactive Patchy Nanoparticles and Nanodiscs Prepared by Tandem Nanoprecipitation and Internal Phase Separation

“…A constant observation is that in all cases where onion‐like structures are encountered (Figure , C2, A4, and rows D–F), the outermost layer always consists of PS, as discerned by the light region that is unstained by osmium. Strikingly, this observation contradicts the fact that the lower interfacial surface tension between PI and water (55.8 mN m −1 ) compared to that of PS and water (58 mN m −1 ) would lead to formation of nanoparticles with PI as the outermost layer . The current observation is indeed the opposite of previously reported SORP results for PS‐ b ‐PI BCPs.…”

Fabrication of Nanostructured Composite Microspheres Based on the Self‐Assembly of Polymers and Functional Nanomaterials

“…However, the associated interface is rigid and so it is difficult to include interface fluctuations in such simulations. The modeling of deformable microsphere interfaces has been examined, based on dynamic self‐consistent field theory (SCFT) . Pinna and co‐workers also reported the simulation of the interfacial structures of block copolymer shells fixed on colloidal particles based on the Ginzburg–Landau approach in association with the cell dynamics simulation (CDS) method .…”

“…More recently, simulations of block copolymer phase separation under 3D confinement was precisely reproduced by numerical calculations employing the coupled Cahn–Hilliard equation ( Figure ). This technique modeled the dynamic processes associated with phase transformation in 3D confinement structures due to thermal annealing . These simulation methods assist in developing approaches to controlling the formation of phase separated structures in polymer blends and block copolymer microspheres.…”

Solution landscapes of the diblock copolymer-homopolymer model under two-dimensional confinement

“…The diblock copolymers under different confinements have been well studied, such as two-dimensional (2D) cylindrical confinement [9][10][11][12], three-dimensional (3D) cylindrical confinement [13][14][15], and 3D spherical or polyhedral confinement [16][17][18]. Many morphologies have been discovered [8,11,19,20], for example, the onion-like and layered structures for symmetric copolymers under spherical confinement in experiments [21,22]. These resulting morphologies are often distinctly different from those in the bulk phase [23] and thus defined as the "frustrated phases" [24].…”