Non-Gaussian Rotational Diffusion and Swing Motion of Dumbbell Probes in Two Dimensional Colloids

TL;DR

The paper investigates non-Gaussian rotational diffusion of dicolloidal dumbbell probes in 2D colloids across the liquid–hexatic transition using discontinuous molecular dynamics. Probes reveal strong coupling between translation and rotation in HBOO-rich hexatic/solid phases through swing motion and intermittent $\pi/3$ rotational jumps, producing oscillatory but diffusive angular displacements and a stretched orientational correlation $U(t)$. The study shows a breakdown of Debye–Stokes–Einstein behavior at the ensemble level, while single-molecule dynamics remain swing-coupled; however, size polydispersity can erase HBOO and restore Brownian-like, Gaussian rotational motion. Overall, the work links HBOO with non-Gaussian probe dynamics and demonstrates how probe measurements can illuminate heterogeneous dynamics in 2D colloidal systems, including reentrant melting effects. $G(\varphi,t)$, $\alpha_{2,R}(t)$, and $U(t)$ serve as sensitive reporters of structural order and dynamic domains in the host medium.

Abstract

Two dimensional (2D) colloids exhibit intriguing phase behaviors distinct from those in three dimensions, as well as dynamic heterogeneity reminiscent of glass-forming liquids. Here, using discontinuous molecular dynamics simulations, we investigate the reporting dynamics of dicolloidal dumbbell probes in 2D colloids across the liquid-hexatic phase transition, where hexagonal bond-orientational order (HBOO) extends to quasi-long-ranged one. The rotational dynamics of dumbbell probes faithfully capture the structural and dynamical features of the host: Brownian in the isotropic liquid, and non-Gaussian in the hexatic and solid phases, reflecting both HBOO and dynamic heterogeneity of the medium. In the 2D hexatic and solid phases, probe rotation reflects heterogeneity as the dumbbells sample multiple dynamical domains of the host system: in mobile domains, they undergo rotational jumps of $π/3$ in accordance with HBOO, whereas in immobile domains they librate within cages formed by surrounding discs. Such non-Gaussianity disappears upon reentrant melting of the host medium driven by size polydispersity, highlighting a close connection between HBOO and probe dynamics. Furthermore, probe dynamics reveal both coupling (at a single particle level) and decoupling (at an ensemble-averaged level) between translation and rotation: swing motion emerges as their primary diffusion mode, while the Debye-Stokes-Einstein relation breaks down regardless of how the rotational diffusion coefficient is defined.

Figures (8)

• Figure 1: A representative simulation snapshot of 2D monodisperse colloids (gray) and ten dumbbell probes (red).
• Figure 2: Mean-squared displacements ($\langle (\Delta r(t))^2 \rangle$) of dumbbells (solid lines) and discs (dot lines) for different values of $\phi$.
• Figure 3: Rotational dynamics of dumbbell probes. (A) Mean-squared angular displacement, $\langle(\Delta \varphi(t))^2\rangle$, divided by ${(2\pi)}^2$, and (B) a rotational non-Gaussian parameter, $\alpha_{2,R}(t)$ (Eq. \ref{['eq:nonG']}).
• Figure 4: Gaussian and non-Gaussian rotational dynamics of dumbbell probes across the 2D freezing transition. (A,B) Probability distributions $G(\varphi,t)$ (Eq. \ref{['eq:gpt']}) of angular displacements of dumbbells at (A) $\phi = 0.65$ and (B) $\phi = 0.71$. Symbols denote simulation results; solid lines in (A) and dotted lines in (B) are Gaussian distributions (Eq. \ref{['GaussRot']}) with the rotational diffusion constant obtained from the MSAD in Fig. \ref{['fig:rotation']}(A). (C,D) Representative angular trajectories of dumbbells at (C) $\phi = 0.65$ and (D) $\phi = 0.71$. Here, $\phi(t)$ is the unbound rotational angle of each dumbbell.
• Figure 5: Dynamic heterogeneity in the rotational dynamics of dumbbell probes. (A) Time correlation function $U(t)$ of the normalized bond vectors of dumbbells. Symbols denote simulation results, dotted lines indicate the Gaussian approximation i.e., $U(t) = \exp[-\langle (\Delta \varphi(t))^2 \rangle / 2]$, and cyan solid lines are fits to the stretched-exponential function (Eq. \ref{['eq:kww']}) with $\beta = 0.85$, 0.88, and 0.90 for $\phi = 0.70$, 0.71, and 0.72, respectively. (B) Displacement map of 2D colloidal discs at $\phi = 0.71$ in the hexatic phase. Black vectors denote disc displacements during $\Delta t = 200\tau$, and filled colored circles represent dumbbell probes. The color of each dumbbell corresponds to $\varphi^{\mathrm{max}}/(\pi/3)$, its maximum rotational displacement normalized by $\pi/3$.