Entropically Driven Formation of Hierarchically Ordered Nanocomposites

Abstract

Using theoretical models, we undertake the first investigation into the rich behavior that emerges when binary particle mixtures are blended with microphase-separating copolymers. We isolate an example of coupled self-assembly in such materials, where the system undergoes a nanoscale ordering of the particles along with a phase transformation in the copolymer matrix. Furthermore, the selfassembly is driven by entropic effects involving all the different components. The results reveal that entropy can be exploited to create highly ordered nanocomposites with potentially unique electronic and photonic properties. DOI: 10.1103/PhysRevLett.89.155503 PACS numbers: 81.07.Pr, 61.46.+w, 83.80.Uv The self-assembly of hard and soft components into nanostructured composites can facilitate the development of novel biomimetic [1], photonic [2], and electronic [3,4] materials. By themselves, binary mixtures of hard particles that differ in size or shape can self-assemble into a startling array of ordered structures [5,6]. Soft block copolymers can ''microphase separate'' into spatially periodic lamellar, cylindrical, spherical, or more complicated mesophases [7]. Using theoretical methods, in this Letter we conduct the first investigations into the cooperative behavior and novel structures that can potentially emerge when these two disparate ordering phenomena are coupled. Focusing on a small volume fraction of bidisperse spheres in AB diblocks, we isolate a system that simultaneously exhibits a structural change in the system of particles and a transformation in the microstructure of the copolymer matrix, creating in a single process a nanocomposite that potentially exhibits unique optoelectronic properties. Furthermore, these morphological changes are driven entirely by entropic effects involving all of the species. Our results indicate that the blending of particle mixtures and block copolymers can be exploited to create materials with new morphologies and functions.To characterize the diblocks in our system, we let f denote the fraction of A segments per chain. The enthalpic interaction between an A segment and a B segment is described by the dimensionless Flory-Huggins parameter, AB . Both the larger (referred to as p 1 ) and smaller (p 2 ) spheres are preferentially wetted by the A blocks. That is, the Flory-Huggins interaction parameter between the particles and A is taken as p1A p2A 0, and the interaction parameter between the different particles and the B species is set equal to AB ( AB p1B p2B). The radii of the p 1 and p 2 particles are denoted by R 1 and R 2 , respectively, and are given in units of R 0 , the root-meansquare end-to-end distance of the chain. These nanoparticles are comparable in size to the copolymers, and this correspondence of scales contributes to the unique structural organization within these nanocomposites.To determine the structure of the mixture, we now modify our previous SCF/DFT approach [8][9][10], which combines a self-consistent field theory (SCF) for diblocks with a density funct...

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