Formation of diblock copolymer nanoparticles: Theoretical aspects

We explore the shape and internal structure of diblock copolymer (di-BCP) nanoparticles (NPs) by using the Ginzburg-Landau free-energy expansion and the dynamic self-consistent field theory (DSCFT). The self-assembly of di-BCP lamellae confined in emulsion droplets can form either ellipsoidal or onion-like NPs. The corresponding inner structure is a lamellar phase that is either perpendicular to the ellipsoid long axis (L_⊥) or forms a multi-layer concentric shell (C_∥), respectively. We focus on the effects of the interaction parameters between the A and B monomers χ, and polymer/solvent χ_PS, as well as the NP size on the nanoparticle shape and internal morphology. The aspect ratio (l_AR), defined as the length ratio between the long and short axes, is used to characterize the overall NP shape. Our results show that when the solvent is neutral towards the two blocks, the ratio l_AR increases as χ increases, indicating that the NP becomes more elongated. Likewise, decreasing χ_PS or increasing the NP size also results in a more elongated NP. Furthermore, as the solvent preference towards one of the A or B blocks increases, the NP undergoes a shape transition from a striped ellipsoid (L_⊥) to onion-like sphere (C_∥). Our results are in good agreement with previous experiments, and some of the predictions could be tested in future experiments.