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

Abstract

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 [Interface Focus 7, 20160161 (2017)], 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.

Self-assembly and entropic effects in pear-shaped colloid systems: II. Depletion attraction of pear-shaped particles in a hard sphere solvent

“…Pear-shaped colloids, or rather their contact function, have been modelled using the self-non-addivitive pear hard Gaussian overlap (PHGO) model which is a computationally much faster approximation than the proper hard pears of revolution (HPR) model. We showed in part 1 [13] and other earlier studies that pear-shaped particles, which contact is approximated by the PHGO potential [14], spontaneously form cubic, bicontinuous phases, like the double gyroid [15,16] or, when diluted with a small amount of hard-sphere solvent, the double diamond [17]. We define pear-shaped particles by the Bézier-curve which, when extended to a solid of revolution, yields the pear-shaped particle shape with a smooth bounding surface [14] (see also FIG.…”

“…that during the rearrangement of inversion asymmetric particles from a configuration where the colloids are separated to one where they are in contact due to depletion interactions, the colloids are likely to first approach each other with their bigger ends before eventually equilibrating into the most compact formation. Note that an indication of this blunt-endattraction can be seen in the gyroid-phase self-assembly [13] where the blunt ends form the network-like domains of the bicontinuous cubic phase [15][16][17]. This indicates that also the hard HPR pears has a tendency to cluster with their blunt ends.…”

“…cially for the HPR model) by dealing with only two particles with complicated contact functions. Secondly and more importantly, in all liquid crystal phases, obtained for the PHGO system so far [15][16][17], the arrangement of each pear is highly affected by a multitude of next nearest neighbours. This elaborate interplay of particles coupled with the aspherical pear-shape, which features a significant degree of complexity, makes a more detailed analysis of the direct influence between adjacent particles in one-component systems impracticable.…”

Self-assembly and entropic effects in pear-shaped colloid systems. II. Depletion attraction of pear-shaped particles in a hard-sphere solvent

“…The study of depletion effects between two pear-shaped particles in a solvent of hard spheres can also help understand the collective self-assembly mechanisms behind the one-component pear particle system. In all liquid crystal phases, obtained for the PHGO system so far [19][20][21], the arrangement of each pear is highly affected by a multitude of next nearest neighbours. This elaborate interplay of particles coupled with the aspherical pear-shape, which features a significant degree of complexity, makes a more detailed analysis of the direct influence between adjacent particles in one-component systems impracticable.…”

“…pear-shaped particles spontaneously form cubic, bicontinuous phases, like the double gyroid [19,20] or, when diluted with a small amount of hard-sphere solvent, the double diamond [21]. Even though PHGO particles are best illustrated by This is the author's peer reviewed, accepted manuscript.…”