Diffusion-Coefficient Power Laws and Defect-Driven Glassy Dynamics in Swap Acceleration

Particle swaps can drastically accelerate dynamics in glass. The mechanism is expected to be vital for a fundamental understanding of glassy dynamics. To extract defining features, we propose a partial swap model with a fraction ${\varphi }_s$ of swap-initiating particles, which can only swap locally with each other or with regular particles. We focus on the swap-dominating regime. At all temperatures studied, particle diffusion coefficients scale with ${\varphi }_s$ in unexpected power laws with temperature-dependent exponents, consistent with the kinetic picture of glassy dynamics. At small ${\varphi }_s$, swap initiators, becoming defect particles, induce remarkably typical glassy dynamics of regular particles. This supports defect models of glass.

Figure 1

A system with a fraction ${\varphi }_s=0.026$ of swap-initiating particles (red circles), only which can exchange positions with regular particles or with each other. The regular particles are color coded according to their displacements over a duration 0.015 at $T=0.16$. Stringlike motions can be observed.

Figure 2

Diffusion coefficients (a) $D_r$ of regular particles and (b) $D_s$ of swap initiators against the fraction ${\varphi }_s$ of swap initiators.

Figure 3

Scaling exponent $\alpha$ measured from regular particles (blue) and swap initiators (red) against temperature $T$. Inset: exponent $\alpha$ against $T$ from distinguishable particle lattice model simulations.

Figure 4

A 1600 particle system with ${\varphi }_s=0.003$ at $T=0.08$ showing facilitation. Regular particles (colored according to their displacements during a time interval of 0.32) are more mobile when they are close to a pair of swap initiators (red).

Figure 5

Plots of $x$ coordinates of all five swap initiators (randomly colored) in a system with 1600 particles for ${\varphi }_s=0.003$ against time $t$ at (a) $T=0.5$ and (b) $T=0.08$. The coordinates are unwrapped with respect to the periodic boundary conditions for clarity. In (a), motions are consistent with simple random walks. In (b), some swap initiators are strongly trapped, but two initiators close to each other are more mobile.