(525c) Effect of Particle Anisotropy and Rotational Symmetry on the Kinetics of Disorder-to-Order Phase Transitions

It is well-known that the phase behavior of polyhedral colloidal nanoparticles is influenced by their anisotropy and rotational symmetry.^1,2 In this study Metropolis Monte Carlo simulations are conducted to understand the effect of anisotropy and rotational symmetry on the kinetics of disorder to order transitions in athermal systems. Previous simulation studies have explored the effect on transition kinetics in particles with high rotational symmetry and minimal anisotropy.^3–5 This study thus primarily focuses on the effect of particle anisotropy and is exemplified through simulations of a system with limited rotational symmetry, namely, a family of gyrobifastigia (GBF) whose aspect ratio (AR) is varied keeping rotational symmetry unaffected.

A regular GBF (AR=√3) has a disordered phase and a crystal phase and no mesophases in-between. The disorder-to-order transition for GBF undergoes nucleation and growth with very large free energy barriers for low-to-moderate degrees of supersaturation, requiring biased simulations to overcome such barriers. This transition is precluded by glassy jamming at high degrees of supersaturation. In addition, the nuclei are aspherical and faceted. To elucidate this unique nucleus shape, direct measurement of the interfacial free energy was conducted for different crystal planes using the cleaving walls method. These measurements were used to perform a Wulff construction which predicts a nucleus shape consistent with our previously reported observations made through nucleus-size pinning.⁶

The unique kinetics for GBF is then studied for selected aspect ratios by varying the height of its triangles along the long axis while maintaining a square base. While reducing the GBF aspect ratio (up to AR=1) maintains a kinetic behavior akin to that of the base case (AR=√3), an elongation of the GBF (up to AR=2√3-1) lowers the nucleation barrier enough such that the ordering transition can be spontaneously observed in unbiased simulations. This trend is related to the change in interfacial free energy and nucleus geometry. A further increase in aspect ratio (i.e. to AR=3) stabilizes an orientationally ordered but translationally disordered mesophase which is also spontaneously formed in unbiased simulations (see Image). This nematic-like mesophase transitions to the crystalline phase upon compression. Translational and orientational order parameters allow us to follow these transitions and elucidate their mechanisms. These findings reveal that both phase behavior and the kinetics of phase transition of polyhedral nanoparticles can be engineered by controlling their aspect ratio, making otherwise inaccessible phases accessible. While the effect of AR on phase and kinetic behavior has been studied before through simulations of axisymmetric particle shapes (like spherocylinders^7,8) hence having high rotation symmetry around the main particle axis, GBF shapes, lacking such symmetry, and having pronounced facet-facet interactions and complex ABCD crystal packing, introduce additional constraints on the entropic degrees of freedom leading to more complex phase ordering mechanisms.

Complementary studies were also performed on particle shapes with high rotational symmetry and minimal anisotropy. Such systems tend to form plastic ‘rotator’ mesophases that have particles arranged on a lattice but are not orientationally aligned, wherein the rotator lattice need not fully match that of the ensuing crystalline phase. To illustrate the effect of this incongruence, simulations were conducted for two particle shapes from the truncated cubes family with truncation parameter s=0.527 (TC52) and s=0.572 (TC57). TC52 has a dissimilar lattice geometry between its rotator and crystal while TC57 has an identical lattice. Our results illustrate how such differences set the stage for qualitatively distinct mechanisms of the diffusionless mesophase-to-crystal transition, the extend of cooperativity, and the appearance of novel intermediates.

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