3D-Positioning of Nanoparticles in High-Curvature Block Copolymer Domains

Abstract

The defined assembly of nanoparticles in polymer matrices is an important precondition for next-generation functional materials. Here we demonstrate that a defined three-dimensional nanoparticle assembly within the unit cells can be realized by directly linking the nanoparticles to block copolymers. We show that for a range of nearly symmetric to unsymmetric block copolymers there are only two formed structures, a hexagonal lattice of P6/mmm-symmetry, where the nanoparticles are located in 1D-arrays within the cylindrical domains, and a cubic lattice of Im3m-symmetry, where the nanoparticles are located in the octahedral voids of a BCC-lattice, corresponding to the structure of ferrite steel. We observe the block length ratio and thus the interfacial curvature to be the most important parameter determining the lattice type. This is rationalized in terms of minimal chain extension such that domain topologies with large positive curvature are highly preferred. Already volume fractions of only one percent are sufficient to destabilize a lamellar structure and favor the formation of highly curved interfaces. The study thus demonstrates how nanoparticles can be located on well-defined positions in three-dimensional unit cells of block copolymer nanocomposites. This opens the way to functional 3D-nanocomposites where the nanoparticles need to be located on defined matrix positions.

Keywords: SAXS; TEM; block copolymers; nanocomposites; polymers.

Figure 1

1D‐SAXS curves of the nanocomposites Fe₂O₃@PS₁₇₁‐PI₁₃₈ (a) and Fe₂O₃@PS₁₂₆‐PI₁₈₄ (b). Peaks are indexed as (hkl). For the nanocomposites the highest order is observed for the highest grafting densities where the first 9 reflections can be indexed on a hexagonal P6/mmm lattice.

Figure 2

a) TEM‐image of a monolayer of Fe₂O₃@PS₁₂₆‐PI₁₈₄ showing the localization of the nanoparticles in PS cylindrical domains. b) STEM image of ultrathin section of a bulk Fe₂O₃@PS₁₇₁‐PI₁₃₈ nanocomposite showing the arrangement of the nanoparticles in the parallel assembled cylindrical microdomains. Also shown are calculations of the [100]‐projection (a) and the [210]‐projection (b) of nanoparticle arrays based on the P6/mmm unit cell with a=2c and a statistical mean deviations from the lattice points of δ=2.5 nm. Also shown are sets of unit cells visualizing the orientation for each particular projection.

Figure 3

a) Representation of the P6/mmm lattice with the nanoparticles (blue) arranged in a linear array within the PS‐cylinders (red) in the PI‐matrix (green). The structure represent a relative cylinder radius R _cyl/a=0.37 and a relative nanoparticle radius of R _NP/a=0.12 to agree with the relative sizes and the volume fractions of the nanocomposite Fe₂O₃@PS₁₇₁‐PI₁₃₈. b) Representation of the Im3m lattice with the nanoparticles (blue) arranged in the octahedral voids of a BCC lattice consisting of PI‐spheres (green) in a PS‐matrix (red). The structure represents a relative PI sphere radius of R _sph/a=0.30 and a relative nanoparticle radius of R _NP/a=0.11 to agree with the relative sizes and the volume fractions of the nanocomposite Fe₂O₃@PS₂₄₈‐PI₁₀₂.

Figure 4

a) 1D‐SAXS curves of the nanocomposites Fe₂O₃@PS₂₄₈‐PI₁₀₂. Peaks are indexed as (hkl). For the nanocomposites the highest order is observed for the highest grafting densities where the first 8 reflections on a cubic Im3m lattice can be detected. b) shows the measured 2D‐SAXS‐pattern of an oriented section of Fe₂O₃@PS₂₄₈‐PI₁₀₂, together with a 2D‐image calculated assuming the X‐ray beam to be parallel to the [100]‐direction of the Im3m crystal lattice (insert).

Figure 5

a) TEM‐image of monolayers showing the arrangement of the nanoparticles in the cubic microdomains of Fe₂O₃@PS₂₄₈‐PI₁₀₂ nanocomposite. b), c), d) STEM‐images at 20 kV showing arrangements of nanoparticles in ultrathin sections of the nanocomposites in [110] b), [111] c), and an oblique [x10] direction d). Simulated images based on a BCC lattice with the nanoparticles located within the octahedral voids are shown, together with the unit cell to visualize the corresponding orientation. The statistical mean deviations from the lattice points is δ=3.0 nm. The red circles indicate the positions of the PI‐spheres. White rectangles indicate characteristic projections in the electron microscopy images.

Figure 6

Scheme of a) the linear array → honeycomb lattice transition observed in 2D and the c) P6/mmm → BCC_void transition observed in 3D. The honeycomb lattice features Y‐connected nanoparticles in a planar surface. The BCC_void lattice features X‐connected nanoparticles on the planar surface of the BCC unit cell. b) and d) specify the geometrical parameters that determine the stretching of the polymer chains to connect the nanoparticle surface to the interface.