Density-Independent transient caging in the high-density phase of motility-induced phase separation

Abstract

We investigate the nonequilibrium dynamics of active matter using a two-dimensional active Brownian particles model. In these systems, self-propelled particles undergo motility-induced phase separation (MIPS), spontaneously segregating into dense and dilute phases. We find that in the high-density phase, local particle mobility exhibits transient caging, with diffusivity remaining unchanged despite variations in the global system density. As global density increases further, the system undergoes a transition to a solid-like state through an intermediate regime with pronounced dynamical arrest. Our findings identify a distinct high-density regime characterized by transient caging and dynamical slowing down in a monodisperse active system, shedding new light on the connection between MIPS and nonequilibrium arrest.

Figures (6)

• Figure 1: (a) Density dependence of the cluster fraction $\beta_{\text{cluster}}$ and bond-orientational order parameter $Q_6$. Squares and circles show the results of numerical simulations for $\beta_{\text{cluster}}$ and $Q_6$, respectively. Error bars represent the standard deviation. The background color indicates the system state: purple (liquid), green (unstable MIPS), yellow (MIPS), light red (dynamical arrest), and gray (solid-like). (b)-(e) Representative snapshots at different global densities:$\rho = 0.5$, $1.0$, $1.5$, and $1.7$.
• Figure 2: Probability distribution of the local density, $p(\rho_{\mathrm{local}})$, measured in the steady state for three global densities $\rho=0.7,\,1.0$, and 1.3. The distributions are bimodal, with a low-density peak (gas phase) and a high-density peak (dense phase), demonstrating phase coexistence in the MIPS regime.
• Figure 3: (a) Mean squared interparticle distance (MSID) in the high-density phase of MIPS for different global density ($\rho=0.7, 1.0,$ and $1.3$). Squares, circles, and triangles correspond to the numerical simulation results for $\rho=0.7, 1.0,$ and $1.3$, respectively. The solid line represents Eq. \ref{['MSD in the harmonic potential']} with $\rho_{\text{HD}}=1.38$, the density of the high-density phase obtained from the numerical simulations. (b) MSID at higher global densities ($\rho=1.5$, $1.6$, and $1.7$). Squares, circles, and triangles correspond to the numerical simulation results for $\rho=1.5$, $1.6$, and $1.7$, respectively. Crosses show the numerical simulation result for the high-density phase at $\rho=1.3$ as a reference. The solid lines represent Eq. \ref{['MSD in the harmonic potential']}.
• Figure 4: Hexagonal close-packed structure. $r_{\text{avg}}$ is the optimal particle distance in the hexagonal close-packing structure.
• Figure 5: Two independent harmonic potentials. The distance between the two potential minima is $r_{\text{avg}}$. By approximating the motion of ABPs in the high-density phase to the motion of particles in this potential, the plateau value of the MSID can be calculated.