(244b) Kinetics of Diffusionless Transitions of Colloidal Truncated Cubes

Polyhedral particles with significant rotational symmetry can form rotator mesophases with high translational order but significant orientational disorder.¹ The transitions from these mesophases to crystals are inherently diffusionless as particles displacements are small compared to the lattice constant.² Truncated cubes are a family of shapes obtained upon systematic truncation of cubes. At a range of truncations (defined by truncation parameter ) the particles exhibit rotator mesophase behavior.³ In these rotator phases the particles prefer to orient in three different orientations spread randomly throughout the lattice instead of just one orientation of the crystal. Previously, it was reported⁴ that if a large lattice distortion is required for the rotator-crystal transition (as is true for certain truncations) then the compression of rotator phase can instead result in an orientational salt where two particle orientations occupy well-defined sites of the unit cell.

In this study, we focus on the mechanism through which such rotator-crystal and rotator-salt transitions take place. First, we construct order parameters to track both these transitions. Then we use these order parameters to obtain correlation functions to establish the nature of these transitions. We find that the transitions take place through increase in robust connectivity of the largest contiguous grain. We measure the robustness of the connectivity using k-stub decomposition.⁵ We also employ rare-event sampling techniques to calculate the free energy barriers of the feasible transitions. Through these analyses we determine that both these transitions take place through spinodal decomposition when the free energy barrier between the two states entirely vanishes. This study will be useful in understanding diffusionless transitions and spinodal decomposition in colloidal systems and in other contexts.

(1) Agarwal, U.; Escobedo, F. A. Mesophase Behaviour of Polyhedral Particles. Nature Materials 2011, 10, 230–235.

(2) Delaey, L. Diffusionless Transformations. In Phase Transformations in Materials; Wiley-VCH Verlag GmbH & Co. KGaA: Weinheim, FRG, 2005; pp 583–654.

(3) Gantapara, A. P.; de Graaf, J.; van Roij, R.; Dijkstra, M. Phase Behavior of a Family of Truncated Hard Cubes. Journal of Chemical Physics 2015, 142, 054904.

(4) Sharma, A.; Escobedo, F. Diffusionless rotator-crystal transitions in colloidal truncated cubes: lattice distortion and kinetic pathways https://meetings.aps.org/Meeting/MAR22/Session/M25.3 (accessed Apr 7, 2022).

(5) Mohseni-Kabir, A.; Pant, M.; Towsley, D.; Guha, S.; Swami, A. Percolation Thresholds for Robust Network Connectivity. Journal of Statistical Mechanics: Theory and Experiment 2021, 2021, 013212.