Shape-Determined Kinetic Pathways in 2D Solid-Solid Phase Transitions

Solid-solid phase transitions are ubiquitous in nature, but the kinetic pathway of anisotropic particle systems remains elusive, where the coupling between translational and rotational motions plays a critical role in various kinetic processes. Here we investigate this problem by molecular dynamics simulation for two-dimensional ball-stick polygon systems, where pentagon, hexagon, and octagon systems all undergo an isostructural solid-solid phase transition. During heating, the translational motion exhibits merely a homogeneous expansion, whereas the time evolution of body-orientation is shape-determined. The local defects of body-orientation self-organize into a vague stripe for pentagon, a random pattern for hexagon, while a distinct stripe for octagon. The underlying kinetic pathway of octagon adheres to the quasi-equilibrium assumption, whereas the pathways of hexagon and pentagon are governed by translational and rotational motion, respectively. This diversity is originated from different kinetic coupling modes determined by the anisotropy of molecules, and can affect the phase transition rates. The reverse process in terms of cooling follows the same mechanism, with more diverse kinetic pathways attributed to the possible kinetic traps. Our findings promote the theoretical understanding of microscopic kinetics of solid-solid phase transitions as well as provide direct guidance for the rational design of materials utilizing desired kinetic features.

💡 Research Summary

In this work the authors investigate the microscopic kinetics of solid‑solid (s‑s) phase transitions in two‑dimensional anisotropic particle systems by means of molecular‑dynamics (MD) simulations of “ball‑stick” polygons. Each monomer consists of Lennard‑Jones (LJ) beads at the vertices of a regular polygon linked by rigid bonds, allowing both translational (center‑of‑mass) and rotational (body‑orientation) degrees of freedom. Three shapes—pentagon, hexagon and octagon—are studied under comparable pressure and temperature conditions. All three undergo an isostructural transition from a close‑packed crystal to a rotator crystal: the lattice expands uniformly while the symmetry of the translational lattice (six‑fold) is preserved, but the orientational order of the monomers is lost.

The translational motion is shown to be a simple homogeneous expansion. Voronoi cell areas shift uniformly to larger values, and the density drop coincides with the rise in potential energy, confirming a discontinuous transition. The rotational dynamics, however, display striking shape‑dependent behavior. By defining a local “defect” as a site where the body‑orientation changes abruptly, the authors map the spatial distribution of defects during heating. Pentagons generate a vague stripe of defects aligned with a crystal axis; hexagons produce a completely random defect pattern; octagons develop a well‑defined stripe that spreads across the simulation box.

To uncover the underlying kinetic coupling between translation and rotation, the authors perform “fixed‑COM” simulations: the particle centers are frozen at a given volume while the monomers are allowed to rotate freely in an NVT ensemble. Comparing the equilibrium orientational order parameter Φ obtained from these constrained runs with that from the original (unfixed) MD trajectories reveals three qualitatively different kinetic pathways. In the pentagon system Φ from the fixed runs is equal to or slightly larger than that from the unfixed runs, indicating that rotation proceeds faster than lattice expansion – a rotation‑dominated pathway. In the hexagon system Φ from the fixed runs is consistently lower, showing that translational expansion outpaces rotation – a translation‑dominated pathway. For the octagon, Φ values coincide in both simulations, meaning that translation and rotation evolve synchronously and the transition follows the quasi‑equilibrium (free‑energy) pathway.

These findings explain the observed defect morphologies. When translation dominates (hexagon), the larger inter‑particle spacing after expansion permits independent rotations, leading to a random distribution of defects. When rotation is hindered by close packing (pentagon, octagon), a change in orientation of one particle tends to induce reorientation of its nearest neighbors, propagating defects along a crystal axis and forming stripe‑like domains. The pentagon’s weaker rotational constraint yields occasional isolated defects besides the main stripe, whereas the octagon’s stronger coupling produces a clean stripe.

The authors further show that the kinetic pathway influences the transition rate: rotation‑dominated pathways are slower due to rotational barriers, translation‑dominated pathways are faster, and quasi‑equilibrium pathways are the most rapid because both motions cooperate. Upon cooling, the same mechanisms operate but kinetic traps become more prevalent, resulting in a richer variety of reverse pathways and possible hysteresis.

Overall, the study demonstrates that particle shape dictates the kinetic coupling mode between translational and rotational motions in 2D solid‑solid transitions. This shape‑determined kinetic diversity affects defect formation, transition speed, and reversibility, providing a new design principle for anisotropic colloidal or molecular crystals where specific kinetic features—such as rapid switching or controlled defect patterns—are desired.