Single-orientation Crystalline Domains of Active Brownian Particles Lead to Collective Motions

Abstract

Active Brownian particles, even without attractive and anisotropic inter-particle interactions, can form a high-density phase featuring structure-ordered domains as well as collective motion regions under thermal noise. However, the mechanism, particularly the relationship between the motion and structure, remains unclear. In this study, we show that the motion-correlation regions are spatially coincident with the single-orientation crystalline domains. Each domain translates or rotates as a whole due to the net active force or torque acting upon it, allowing relative motions between these crystalline domains. The particles at domain boundaries usually have the active forces pointing inward, which helps to stabilize these structure-ordered domains and their corresponding collective motion regions.

Figures (7)

• Figure 1: Probability distribution functions (PDFs) show the local density at different packing fractions for Pe = 80 (left) and Pe = 100 (right). The isosbestic point of these PDFs is indicated by the dashed line. Inset: An enlarged view near the isosbestic point.
• Figure 2: Structure of the high-density phase at different packing fractions for Pe = 100. In the top row, particles are colored according to the magnitude of the bond-orientational order parameter, $|\psi_i|$. Green particles have a locally hexagonal environment, while the others are defects. In the middle row, particles are colored according to the arguments of $\psi_i$. The bottom row shows the single-orientation crystalline domains, obtained by the DBSCAN clustering algorithm. Red points represent noise particles that do not belong to any domains.
• Figure 3: Structure and collective motion in the high-density phase. The top row shows the (scaled) velocities superimposed on crystalline domains at different packing fractions for Pe = 100. Zoomed views of the areas marked by red squares are shown in the middle row. The bottom row displays the same conformation, with black arrows indicating the direction of the active forces.
• Figure 4: Size of structure-ordered domains and spatial correlation of motion. (a) Single-orientation crystalline domains in one part of the high-density phase at $\phi=0.5$ and Pe = 100 (noise points omitted). Each black circle is positioned at the centroid of a domain, with its radius equal to the gyration radius of the domain. (b) Spatial velocity correlations in the high-density phase at different packing fractions for Pe = 100. The solid line is a theoretical fitting (see main text) to the data. To make the correlations easier to distinguish, each correlation is divided by a constant $c_0$ (which does not affect the correlation length). (c) Comparison between the velocity-correlation length and the weighted-average gyration radius for Pe = 80 and Pe = 100.
• Figure 5: Direction of active force at boundary of domains. (a) Schematic defining the angle $\alpha_i$. The particle at the domain edge ($i$, black circle) and its neighbors (green circles) are shown. The red point marks the centroid of these neighbors. (b) Probability density functions of $\alpha_i$ at various packing fractions for Pe = 100. (c) A particle trapped at the edge of a domain requires a larger escape angle for larger domains.