Long-Range Ordering of Symmetric Block Copolymer Domains by Chaining of Superparamagnetic Nanoparticles in External Magnetic Fields

A new method to achieve long-range orientational order in symmetric diblock copolymer nanodomains through the alignment and chaining of superparamagnetic nanoparticles in a magnetic field is investigated computationally and theoretically. The effects of nanoparticle size, volume fraction, and magnetization strength are explored using the hybrid particle field (HPF) technique for particles that selectively segregate into one domain of a symmetric diblock copolymer assembly. A critical selectivity of the particles for one nanodomain is observed, above which strong alignment results and below which comparatively disordered structures are formed. The 2D simulations reveal that, for a given nanoparticle volume fraction, only a nanoparticle size commensurate with the block copolymer domain spacing yields well-aligned nanostructures. Nanoparticles significantly larger than the domain spacing break the symmetry of the lamellar phase and result in poor alignment, while high defect densities are observed for smaller particles owing to colloidal jamming within the preferred domains. Small field strengths produce a high degree of alignment in simulations, but as corroborated by scaling calculations, high magnetization strengths are required to lower the equilibrium defect density for such nematic-isotropic phase transitions in lamellar thin films. Simulations also elucidate a window of optimal nanoparticle volume fractions over which alignment is achieved. For low nanoparticle volume fractions, only local alignment is observed, while high volume fractions lead to an order order phase transition from lamellae to a hexagonal phase.