Structure and Dynamics of a Phase-Separating Active Colloidal Fluid

Gabriel S. Redner, Michael F. Hagan, and Aparna Baskaran

Phys. Rev. Lett. 110, 055701 – Published 31 January 2013

Abstract

We examine a minimal model for an active colloidal fluid in the form of self-propelled Brownian spheres that interact purely through excluded volume with no aligning interaction. Using simulations and analytic modeling, we quantify the phase diagram and separation kinetics. We show that this nonequilibrium active system undergoes an analog of an equilibrium continuous phase transition, with a binodal curve beneath which the system separates into dense and dilute phases whose concentrations depend only on activity. The dense phase is a unique material that we call an active solid, which exhibits the structural signatures of a crystalline solid near the crystal-hexatic transition point, and anomalous dynamics including superdiffusive motion on intermediate time scales.

Received 6 July 2012

DOI:https://doi.org/10.1103/PhysRevLett.110.055701

Authors & Affiliations

Gabriel S. Redner, Michael F. Hagan^*, and Aparna Baskaran^†

Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts, USA

^*hagan@brandeis.edu
^†aparna@brandeis.edu

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Vol. 110, Iss. 5 — 1 February 2013

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Images

Figure 1
A visual summary of our results. Top left: beyond critical density and activity levels the active colloidal fluid separates into dense and dilute phases. The clusters coarsen over time (see S1 in the Supplemental Material in [34]). Top right: the static structure factor $S (k) = \frac{1}{N} ⟨ \sum_{i j} e^{i k \cdot r_{i j}} ⟩$ , restricted to the interiors of large clusters. These signatures resemble those of a high temperature colloidal crystal near the crystal-hexatic phase transition. Bottom left: a heat map of the pressure in the active solid material. It is heterogeneous and highly dynamic, indicating that external stresses would produce a complex response. Bottom right: log-log plot of the mean square displacement of a tagged particle in the active solid. At intermediate time scales, it exhibits anomalous superdiffusive transport.Reuse & Permissions
Figure 2
(a) Phase densities as a function of Péclet number (Pe) for a range of overall $ϕ$ . At low Pe the system is single-phase, while at increased Pe it phase-separates. The coexistence boundary is analogous to the binodal curve of an equilibrium fluid, with Pe acting as an attraction strength. (b) Observed density distributions for various Péclet numbers. In the single-phase region below $Pe \approx 50$ , $P (ϕ)$ is peaked about the overall system density (here $ϕ = 0.65$ ). It broadens and flattens as the critical point is approached, and becomes bimodal as the system phase separates.Reuse & Permissions
Figure 3
Left: contour map of cluster fraction $f_{c} (Pe, ϕ)$ measured from simulations. The dashed curve marks the approximate location of the binodal. Right: cluster fraction as predicted by our analytic theory [Eq. (3)]. These plots have been restricted to packing fractions that are low enough for the assumptions of our kinetic model to be valid, and for cluster identification to be unambiguous.Reuse & Permissions
Figure 4
(a) Defect structures in a large cluster. Regions of high crystalline order (white) coexist with isolated and linear defects (dark). The color of each particle indicates its $| q_{6} |$ . Inset shows pairs of $5 / 7$ defects. (b) Log-log plot of the correlation function $⟨ q_{6}^{*} (r) q_{6} (r^{'}) ⟩$ for clusters at various Péclet numbers in systems with $N = 128 000$ , showing a transition from liquidlike exponential to hexaticlike power-law decay as activity is increased. For systems with $N = 512 000$ (black dashed line), a crystal-like plateau is also observed.Reuse & Permissions
Figure 5
Examples of phase separation kinetics. Left: a system with $Pe = 100$ , $ϕ = 0.45$ in which a delayed nucleation event leads quickly to steady state. For shallowly quenched systems, the nucleation time can be long enough that artificial seeding is needed to make nucleation computationally accessible. Right: a system with $Pe = 80$ , $ϕ = 0.6$ where spinodal decomposition leads to a coarsening regime which slowly evolves toward steady state. Inset shows mean cluster size scaling approximately as $t^{(1 / 2)}$ (see S1 and S8 in the Supplemental Material [34]).Reuse & Permissions

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