Hexatic Order Coupled with Thermal Noise Produces Bubbles in Two-Dimensional Active Matter

Abstract

The phase separation of purely-repulsive particles induced by self-propulsion is among the most well-studied non-equilibrium phase transitions. However, some notable features of this transition remain open questions, including the origin of bubbles within the dense phase in two dimensions. Various explanations have been proposed, ranging from a reversal of the Ostwald ripening process to topological defects at the borders of hexatic domains. We present particle-based simulations that disentangle the effect of hexatic domains on the bubble size and number distribution through the introduction of polydispersity. While hexatic order is found to be necessary for bubble formation, we also identify thermal translational noise is required for bubble generation. Intriguingly, the magnitude of the thermal noise needed for bubble formation can be remarkably small in comparison with the particle activity but cannot be identically zero. The cooperative motion evidenced within the dense phase of the thermal hexatic domains may may be necessary for bubble production.

Figures (5)

• Figure 1: Representative snapshots of simulations at various values of thermalization for both monodisperse and polydisperse cases, rendered using Ovito Stukowski2010VisualizationTool. Bubbles within the liquid phase were uncommon in all polydisperse and all athermal simulations.
• Figure 2: The dependence of $n(A)$ on thermal noise for both polydisperse and monodisperse systems.
• Figure 3: Top: Snapshots of $\mathcal{T}=0$ (left) and $\mathcal{T}=1/100$ (right) monodisperse simulations colored by hexatic domain orientation, rendered using Ovito Stukowski2010VisualizationTool. (a) Hexatic order parameter spatial correlation functions. (b) Probability distribution of hexatic domain areas, $A_{\rm hex}$, for thermalized monodisperse simulations. Polydisperse simulations not shown due to the lack of domains. Monodisperse $\mathcal{T} = 0$ not shown due to the sluggish kinetics and the presence of only a few large domains leading to poor statistics.
• Figure 4: (a) Spatial correlations of velocity orientation obtained by averaging Eq. \ref{['eq:caprinicorr']} over all particles, employing a time separation $\Delta t$ that maximizes nearest-neighbor correlations. (b) Mean squared displacement of dense phase particles at each simulation condition, normalized by time. Diffusive dynamics should converge to a constant. Vertical dashed line corresponds to $\tau_R$, the timescale beyond which we might expect diffusive dynamics.
• Figure 5: Probability distribution of observing a bubble of size $A$ at various simulation conditions. Although the thermalized polydisperse systems are noisy due to the scarcity of bubbles, the scaling appears similar to the thermalized monodisperse systems.