Heuristic Rule for Binary Superlattice Coassembly: Mixed Plastic Mesophases of Hard Polyhedral Nanoparticles

Abstract

Sought-after ordered structures of mixtures of hard anisotropic nanoparticles can often be thermodynamically unfavorable due to the components' geometric incompatibility to densely pack into regular lattices. A simple compatibilization rule is identified wherein the particle sizes are chosen such that the order-disorder transition pressures of the pure components match (and the entropies of the ordered phases are similar). Using this rule with representative polyhedra from the truncatedcube family that form pure-component plastic-crystals, Monte Carlo simulations show the formation of plastic-solid solutions for all compositions and for a wide range of volume fractions.Polyhedral colloidal nanoparticles are versatile building blocks towards designing novel materials with targeted emergent properties. Recent developments in experimental techniques [1][2][3][4][5][6][7] to controllably synthesize and manipulate polyhedral nanoparticles have fueled many theoretical [8,9] and simulation studies [10][11][12][13][14][15][16][17][18][19][20] to understand their packing and phase behavior. These building blocks have been shown to exhibit a rich phase behavior at finite osmotic pressures unveiling the presence of novel mesophases. A mesophase is a partially ordered phase whose properties are intermediate between those of disordered liquids and ordered crystals, such as liquidcrystals, rotator plastic-crystals, and quasicrystals.Binary mixtures of polyhedra[21] exhibit a competition between mixing and packing entropy that often leads to phase separation at high pressures; indeed, assembly into binary superlattices using just entropic forces is difficult to achieve [22]. An earlier study [21] on the miscibility trends of binary polyhedra mixtures revealed the importance of the relative size ratio of the components and of similarity in their mesophase behavior [10]. One of our aims is to identify shapes and sizes that favor the formation of entropic rotator mixtures.A family of truncated cubes, which is readily synthesizable [3,4], has been recently shown to exhibit a diverse set of phases [12]. Further, the kinetics of the disorderto-order transition for some members of this family has been shown to be substantially faster than that of hard spheres[23], making them appealing choices for applications requiring fast self-assembly. In addition to cuboctahedra (COs) and truncated octahedra (TOs), we choose here a truncated cube with truncation parameter 0.4 (TC4) [12], since, like COs and TOs, TC4 also exhibits a rotator mesophase [12]. These choices are motivated by the hypothesis that mesophasic partial disorder can provide enough structural leeway to facilitate ordered solutions to form despite the entropy costs associated with differences in packing. The main mixtures studied are the three possible pairings of these three shapes, and are denoted henceforth as COTO, TC4TO and TC4CO.For any target solid mixture, the relative component size-ratio is an important determinant to control the crystal lattice spacing. A recent stu...

Multi-component superstructures self-assembled from nanocrystal building blocks

“…It is also noteworthy to mention that advanced techniques, including 3D tomography electron microscopy with atomic resolution, 90,126 external pressure treatments and the simultaneous collection of wideand small-angle X-ray scattering, 98,127,128 synchrotron-based X-ray supercrystallography, [129][130][131][132] along with improved theoretical modeling and simulations, have together provided a more in-depth understanding of these complicated systems from different aspects. 62,133,134 Moreover, post-processing (e.g., pressure sintering), which has been recently employed for single-component superstructures, [135][136][137] can be easily transferred to well-defined MCSs to generate novel materials with undiscovered properties.…”

Self-assembly of a space-tessellating structure in the binary system of hard tetrahedra and octahedra

“…Previous studies of this system did not observe the self-assembly of the space-filling structure unless attractive interactions were added 12 . Other studies on binary mixtures of different shapes produced disordered mixed lattices, but not the formation of ordered structures 13,14 .…”

“…Superlattices of other combinations of two shapes have been studied recently, e.g., spheres and octahedra, as well as spheres and cubes 27 . The coexistence of multiple solid phases, on the other hand, had previously been discovered in systems of spheres with two different radii 28 , but has not directly been observed in a number of studies on binary systems with polyhedra [12][13][14] .…”

Superlattices assembled through shape-induced directional binding

“…At a general level, different particle shapes will exhibit significantly different anisotropic interactions in a system, thereby imposing conflicting local constraints that may override intended bonding directionality. Such conflicts can be resolved via complementary-shaped particles due to the favourable packing 37 38 39 , certain shapes can be accommodated at the right size regimes 40 or by optimizing a delicate balance of interactions and space-filling requirements 11 41 . In our approach, the use of DNA permits tuning the interaction ‘softness' due to DNA's polymeric nature.…”