Phase behaviour and dynamical features of a two-dimensional binary mixture of active/passive spherical particles

TL;DR

This study investigates phase behavior and dynamics in a two-dimensional binary mixture of active and passive Brownian particles using Brownian Dynamics with a purely repulsive WCA interaction. It maps $\rho$-$\mathrm{Pe}$ state diagrams across varying passive fractions $N_p/N$, finding that passive components hinder MIPS but do not abolish it, with MIPS persisting up to about $0.7$ in $N_p/N$ and the state diagrams collapsing onto a master curve when expressed as $\rho/\rho_0$ vs $\mathrm{Pe}/\mathrm{Pe}_0$. The authors show that dense phases in MIPS are formed by active fronts encapsulating passive bulks, leading to crystal-like short-range order and a lever-rule-like redistribution of phases, while diffusion measurements reveal an inflection in active diffusivity at the MIPS density and a maximum in passive diffusivity. The observed non-Gaussian displacement distributions for active particles within MIPS indicate dynamic heterogeneity, and the work provides insights into active matter in heterogeneous media with potential applications in microrheology and driven self-assembly.

Abstract

In this work we have characterized the phase behaviour and the dynamics of bidimensional mixtures of active and passive Brownian particles. We have evaluated state diagrams at several concentrations of the passive components finding that, while passive agents tend to hinder phase separation, active agents force crystal-like structures on passive colloids. In order to study how passive particles affect the dynamics of the mixture, we have computed the long-time diffusion coefficient of each species, concluding that active particles induce activity and super-diffusive behaviour on passive ones. Interestingly, at the density at which the system enters a MIPS state the active particles' diffusivity shows an inflection point and the passive particles' one goes through a maximum, due to the change in the dynamics of the active components, as shown in the displacement's probability distribution function.

Figures (8)

• Figure 1: Snapshots of ABP at $\rho=0.5$ and $N_p=0$ showing a) no phase separation (Pe=40), b) its $P(\rho)$ distribution $P(\rho)$ is centered at $0.2$ and c) MIPS (Pe=120) and d) its $P(\rho)$ distribution.
• Figure 2: $\rho$-Pe state diagrams of monodisperse mixtures of active/passive particles. Coloured areas correspond to MIPS, different colours representing different fractions $N_p/N$ of passive components. Black dashed line is for purely active WCA particles from Ref. Stenhammar.
• Figure 3: State diagrams (coloured lines) as in Fig. \ref{['fig:phase']} where $\rho$ and Pe have been normalized by the estimated values of $\rho_0$ and Pe$_0$ for each $N_p/N$. Black line (purely active case). Gray curves: dispersion estimated fitting the state diagrams to a binodal curve. Inset: linear behaviour of $\rho_0$ versus Pe$_0$.
• Figure 4: Top: snapshots of monodisperse phase-separated mixtures of passive (blue)/active (red) colloids: a) $N_p/N = 0.6$, $\rho = 1.018$, $\text{Pe}=190$, b) $N_p/N = 0.3$, $\rho = 0.891$, $\text{Pe}=170$. Bottom: radial distribution functions corresponding to the top panels.
• Figure 5: a-g) Snapshots at $\rho = 1.018$, Pe $=120$ and several $N_p/N$ fractions (passive particles in blue and active ones in red): a) $N_p/N=0.1$ b) $N_p/N=0.2$ c) $N_p/N=0.3$ d)$N_p/N=0.4$ e) $N_p/N=0.5$ f) $N_p/N=0.6$ g) $N_p/N=0.7$. a), b), c), d), e) and f) show MIPS, while in g), the high $N_p/N$ forbids MIPS. Movies of panel b), d) and e) can be found in the Supplementary Information.