Mobility-induced phase separation in a binary mixture of active Brownian particles

TL;DR

This work investigates motility-induced phase separation in a two-dimensional binary mixture of active Brownian particles with non-additive, purely repulsive interactions inspired by glass-forming Lennard-Jones binaries. Using Brownian dynamics, the authors compare monocomponent and binary mixtures, analyzing structural measures such as radial distribution functions and hexatic order, along with dynamical measures like mean-square displacement. They find that the high-density coexisting phase in the binary case is spatially disordered, while the monocomponent dense phase remains solid-like; both coexisting states exhibit long-time diffusion, with diffusion in the monocomponent case aided by active topological defects. These results highlight how size-polydispersity and interaction choice influence phase behavior and dynamics in active matter, offering insight into defect-mediated transport in active crystals.

Abstract

In this paper, we report a Brownian dynamics simulation of the mobility-induced phase separation which occurs in a two-dimensional binary mixture of active soft Brownian particles, whose interactions are modeled by non-additive Weeks-Chandler-Andersen potentials inspired in Lennard-Jones potentials used for glass-forming passive mixtures. The analysis of structural properties, such as the radial distribution functions and the hexatic order parameter, shows that the high-density coexisting state in the binary case is spatially disordered, unlike the solid-like state observed for the monocomponent system. Characterization of the mean-square displacement of the active particles shows that both the low- and high-density coexisting states have diffusive behavior for long times. Thus, the high-density coexisting states are liquid-like in the binary cases. Moreover, diffusive behavior is also observed in the high-density solid-like state for the monocomponent system, which is driven by the presence of active topological defects.

Figures (8)

• Figure 1: Plot of the $1-$component density $\rho_1$ (continuous lines) and mole fraction $X_1$(dashed lines) as a function of the $x-$coordinate for values of the Péclet number $Pe=81, 100$ and $150$. For comparison, the value of the global mole fraction is represented by a straight horizontal line. Top figure corresponds to a global mole fraction of $X_1=0.5$ and the bottom figure to the case $X_1=0.75$.
• Figure 2: MIPS $\rho-Pe$ phase diagram for global mole fractions $X_1=1$ (blue triangles), $0.75$ (red squares) and $0.5$ (green circles). Open symbols are the densities of the coexisting stationary states obtained from the analysis of the density profiles, and the filled symbols correspond to the values obtained from the density PDFs.
• Figure 3: Snapshot of the $240\times 40$-cell simulation for $Pe=100$ for $X_1=0.5$ (a) and $X_1=1$ (b). Red disks correspond to $1-$type particles and blue disks to $2-$type particles. A region on the high-density regions is zoomed.
• Figure 4: Radial distribution functions $g_{11}, g_{12}$ and $g_{22}$ of the coexisting stationary states for $Pe=150$. The left column corresponds to the dilute state, and the right to the high-density state.
• Figure 5: Instantaneous hexatic order parameter over the last $10^6$ time steps for $X_A=1$ (blue line), $0.75$ (red line) and $0.5$ (green line). From top to bottom: $Pe = 81, 100$ and $150$.