Double diamond phase in pear-shaped nanoparticle systems with hard sphere solvent

The mechanisms behind the formation of bicontinuous nanogeometries, in particular in vivo, remain intriguing. Of particular interest are the many systems where more than one type or symmetry occurs, such as the Schwarz’ diamond surface and Schoen’s gyroid surface; a current example are the butterfly nanostructures often based on the gyroid, and the beetle nanostructures often based on the diamond surface. Here, we present a computational study of self-assembly of the bicontinuous Pn3m diamond phase in an equilibrium ensemble of pear-shaped particles when a small amount of a hard-sphere ‘solvent’ is added. Our results are based on previous work that showed the emergence of the gyroid Ia3d phase in a pure system of pear-shaped particles (Schönhöfer et al 2017 Interface Focus 7 20160161), in which the pear-shaped particles form an interdigitating bilayer reminiscent of a warped smectic structure. We here show that the addition of a small amount of hard spherical particles tends to drive the system towards the bicontinuous Pn3m double diamond phase, based on Schwarz diamond minimal surface. This result is consistent with the higher degree of spatial heterogeneity of the diamond minimal surface as compared to the gyroid minimal surface, with the hard-sphere ‘solvent’ acting as an agent to relieve packing frustration. However, the mechanism by which this relief is achieved is contrary to the corresponding mechanism in copolymeric systems; the spherical solvent tends to aggregate within the matrix phase, near the minimal surface, rather than within the labyrinthine channels. While it may relate to the specific form of the potential used to approximate the particle shape, this mechanism hints at an alternative way for particle systems to both release packing frustration and satisfy geometrical restrictions in double diamond configurations. Interestingly, the lattice parameters of the gyroid and the diamond phase appear to be commensurate with those of the isometric Bonnet transform.