Solid-phase nucleation free-energy barriers in truncated cubes: interplay of localized orientational order and facet alignment

Diffusionless rotator-crystal transitions in colloidal truncated cubes

Upon osmotic compression, rotationally symmetric faceted colloidal particles can form translationally ordered, orientationally disordered rotator mesophases. This study explores the mechanism of rotator-to-crystal phase transitions where orientational order is gained in a translationally ordered phase, using rotator-phase forming truncated cubes as a testbed. Monte Carlo simulations were conducted for two selected truncations (s), one for s = 0.527 where the rotator and crystal lattices are dissimilar and one for s = 0.572 where the two phases have identical lattices. These differences set the stage for a qualitative difference in their rotator-crystal transitions, highlighting the effect of lattice distortion on phase transition kinetics. Our simulations reveal that significant lattice deviatoric effects could hinder the rotator-to-crystal transition and favor arrangements of lower packing fraction instead. Indeed, upon compression, it is found that for s = 0.527, the rotator phase does not spontaneously transition into the stable, densely packed crystal due to the high lattice strains involved but instead transitions into a metastable solid phase to be colloquially referred to as "orientational salt" for short, which has a similar lattice as the rotator phase and exhibits two distinct particle orientations having substitutional order, alternating regularly throughout the system. This study paves the way for further analysis of diffusionless transformations in nanoparticle systems and how lattice-distortion could influence crystallization kinetics.

Effect of particle anisotropy on the thermodynamics and kinetics of ordering transitions in hard faceted particles

Monte Carlo simulations were used to study the influence of particle aspect ratio on the kinetics and phase behavior of hard gyrobifastigia (GBF). First, the formation of a highly anisotropic nucleus shape in the isotropic-to-crystal transition in regular GBF is explained by the differences in interfacial free energies of various crystal planes and the nucleus geometry predicted by the Wulff construction. GBF-related shapes with various aspect ratios were then studied, mapping their equations of state, determining phase coexistence conditions via interfacial pinning, and computing nucleation free-energy barriers via umbrella sampling using suitable order parameters. Our simulations reveal a reduction of the kinetic barrier for isotropic-crystal transition upon an increase in aspect ratio, and that for highly oblate and prolate aspect ratios, an intermediate nematic phase is stabilized. Our results and observations also support two conjectures for the formation of the crystalline state from the isotropic phase: that low phase free energies at the ordering phase transition correlate with low transition barriers and that the emergence of a mesophase provides a steppingstone that expedites crystallization.

Coarse-grained modelling to predict the packing of porous organic cages

How molecules pack has vital ramifications for their applications as functional molecular materials. Small changes in a molecule's functionality can lead to large, non-intuitive, changes in their global solid-state packing, resulting in difficulty in targeted design. Predicting the crystal structure of organic molecules from only their molecular structure is a well-known problem plaguing crystal engineering. Although relevant to the properties of many organic molecules, the packing behaviour of modular porous materials, such as porous organic cages (POCs), greatly impacts the properties of the material. We present a novel way of predicting the solid-state phase behaviour of POCs by using a simplistic model containing the dominant degrees of freedom driving crystalline phase formation. We employ coarse-grained simulations to systematically study how chemical functionality of pseudo-octahedral cages can be used to manipulate the solid-state phase formation of POCs. Our results support those of experimentally reported structures, showing that for cages which pack via their windows forming a porous network, only one phase is formed, whereas when cages pack via their windows and arenes, the phase behaviour is more complex. While presenting a lower computational cost route for predicting molecular crystal packing, coarse-grained models also allow for the development of design rules which we start to formulate through our results.

Low Interfacial Free Energy Describes the Bulk Ordering Transition in Colloidal Cubes

Many hard faceted nanoparticles are known to undergo disorder-to-order phase transitions following a classical nucleation and growth mechanism. In a previous study [J. Phys. Chem. B 2018, 122, 9264-9273], it was shown that hard cubes undergo a nonclassical phase transition with a bulk character instead of originating from consolidated nuclei. Significantly, an unusually high fraction of ordered particles was observed in the metastable basin of the disordered phase, even for very low degrees of supersaturation. This work aims to substantiate the conjecture that these unique properties originate from a comparatively low interfacial free energy between the disordered and ordered phases for hard cubes relative to other hard particle systems. Using the cleaving wall method to directly measure the interfacial free energy for cubes, it is found that its values are indeed small; e.g., at phase coexistence conditions, it is only one-fifth that for hard spheres. A theoretical nucleation model is used to explore the broader implications of low interfacial tension values and how this could result in a bulk ordering mechanism.

Phase behavior and design rules for plastic colloidal crystals of hard polyhedra via consideration of directional entropic forces

Plastic crystals - like liquid crystals - are mesophases that can exist between liquids and crystals and possess some of the characteristic traits of each of these states of matter. Plastic crystals exhibit translational order but orientational disorder. Here, we characterize the phase behavior in systems of hard polyhedra that self-assemble plastic face-centered cubic (pFCC) colloidal crystals. We report a first-order transition from a pFCC to a body-centered tetragonal (BCT) crystal, a smooth crossover from pFCC to an orientationally-ordered FCC crystal, and an apparent orientational glass transition wherein long-range order fails to develop from a plastic crystal upon an increase in density. Using global order parameters and local environment descriptors, we describe how particle shape influences the development of orientational order with increasing density, and we provide design rules based on the arrangement of facets for engineering plastic crystal behavior in colloidal systems.