Nonadditive Effective Interactions and Entropy-Driven Non-Close-Packed Self-Assembly Cluster of Nanoparticle in Ordered Block Copolymer Structure

In general, nanoparticles with additive interactions tend to aggregate into a close-packed cluster, which minimizes surface area. Within the ordered structures formed by block copolymers, the effective interactions between nanoparticles exhibit nonadditive characteristics induced by the depletion effect with the block chains as depletant. Especially when the size of the nanoparticles is comparable to that of the polymer, the structure of the cluster formed by nanoparticles significantly influences the conformation of block chains in the phase domain, and the changes of chain conformation affect the mutual interactions between nanoparticles as well. Driven by these nonadditive attractive interactions, novel self-assembly behaviors of nanoparticles will be observed, which differ from those of nanoparticles with additive interactions. This review employs self-consistent field theory to quantitatively investigate the additivity of the effective two-body interactions between spherical nanoparticles in lamellar structures formed by block copolymers. The self-assembly behaviors of nanoparticles with these nonadditive attractive interactions are well addressed. It has been observed that the three-dimensional (3D) or two-dimensional (2D) close-packed structure with minimal surface area is stable only when the nanoparticles are relatively small compared to the block chain length. For large-sized nanoparticles, a non-close-packed structure, ring-like cluster, is formed. By comparing the conformational characteristics of polymers in the system with different aggregation structures of nanoparticles, this article reveals the entropy-driven mechanism that the relative sizes of polymers and nanoparticles can be used to tune the competition between the depletion effect and polymer conformational entropy and then regulate the directed self-assembly of nanoparticles (NPs) in block copolymer (BCP) behaviors. When nanoparticles are relatively small, the aggregates have a negligible impact on the polymer conformations. At this stage, the depletion effect dominates the self-assembly of the nanoparticles, and close-packed structures can be obtained. When the size of nanoparticles is comparable to that of the block chains, the competition between the attractive interactions induced by the depletion effect and the conformational entropy loss caused by exclusion due to cluster results in the formation of non-close-packed ring-like clusters. However, when nanoparticles are slightly larger than the block chains, they cause deformation of the interface of the phase domain, and at this point, interfacial tension-induced interactions begin to dominate the assembly of nanoparticles. This novel mechanism can be applied to the directed assembly of nanoparticles in various periodic structures formed by block copolymers and can also be used in the design of novel self-assembly structures for isotropic nanoparticles.