  Co-assembly of inorganic nanoparticles (NPs) and nanostructured polymer
matrix represents an intricate interplay of enthalpic or entropic forces.
Particle size largely affects the phase behavior of the nanocomposite.
Theoretical studies indicate that new morphologies would emerge when the
particles become comparable to the soft matrix's size, but this has rarely been
supported experimentally. By designing a multicomponent blend composed of NPs,
block copolymer-based supramolecules, and small molecules, a 3-D ordered
lattice beyond the native BCP's morphology was recently reported when the
particle is larger than the microdomain of BCP. The blend can accommodate
various formulation variables. In this contribution, when the particle size
equals the microdomain size, a symmetry-broken phase appears in a narrow range
of particle sizes and compositions, which we named the "train track" structure.
In this phase, the NPs aligned into a 3-D hexagonal lattice and packed
asymmetrically along the c axis, making the projection of the ac and the bc
plane resemble train tracks. Computation studies show that the broken symmetry
reduces the polymer chain deformation and stabilizes the metastable hexagonally
perforated lamellar morphology. Given the mobility of the multicomponent blend,
the system shows a self-sorting behavior: segregating into two macroscopic
phases with different nanostructures based on only a few nanometers NP size
differences. Smaller NPs form "train track" morphology, while larger NPs form
"simple hexagon" structure, where the NPs take a symmetric hexagonal
arrangement. Detailed structural evolution and simulation studies confirm the
systematic-wide cooperativity across different components, indicating the
strong self-regulation of the multicomponent system.
