Active droploids

Abstract

Active matter comprises self-driven units, such as bacteria and synthetic microswimmers, that can spontaneously form complex patterns and assemble into functional microdevices. These processes are possible thanks to the out-of-equilibrium nature of active-matter systems, fueled by a one-way free-energy flow from the environment into the system. Here, we take the next step in the evolution of active matter by realizing a two-way coupling between active particles and their environment, where active particles act back on the environment giving rise to the formation of superstructures. In experiments and simulations we observe that, under light-illumination, colloidal particles and their near-critical environment create mutually-coupled co-evolving structures. These structures unify in the form of active superstructures featuring a droplet shape and a colloidal engine inducing self-propulsion. We call them active droploids-a portmanteau of droplet and colloids. Our results provide a pathway to create active superstructures through environmental feedback.

Fig. 1. Active droploid formation and growth.

a Schematic of the light-induced two-way coupling (feedback loop) between the colloids and their environment which results in active droploids. b–f Experiment and g–k simulation of the formation and growth of active droploids. b, g Single particles of two species, light-absorbing (black) and non-absorbing (white), are immersed in a near-critical mixture and, at low temperature, behave as passive particles in a standard liquid. c, h Upon illumination, absorbing particles heat up the surrounding liquid, providing phoretic forces that bring and hold particles together to form small colloidal molecules that move in the direction of the red arrows. d, i Eventually, local phase separation leads to water-rich droplets (blue shading) surrounding absorbing particles and colloidal molecules. e, j Over time, the active droploids move together with their active molecules (direction indicated by the red arrows), grow in size, and f, k eventually coalesce together to form even larger active droploids. The light irradiation is I = 150 μW μm⁻², composition ϕ₀ = 0.05 and initial temperature T₀ = 32.5 °C (and λ = 0.025 in simulations, see ‘Methods’ for other parameter values). Videos of experiment (Supplementary Movie 1) and simulation (Supplementary Movie 2) are provided in SI.

Fig. 2. Nonequilibrium phase diagram.

a Phase diagram as a function of the net energy input λ and the averaged relative concentration difference from the critical point ϕ₀. The evaluated state points from the experiment (red) fitted with λ = CIρ_a and C = 1 × 10⁻⁴ μm⁴ μW⁻¹, and the simulations (black) are indicated by crosses (purple region - disordered phase), triangles (yellow region - active molecules), filled circles (green region - active droploids), and empty circles (blue region - droplets with particles at the interface). Dashed lines indicate approximate boundaries between phases and serve as a guide to the eye. The quantitative criteria for the phases and the corresponding colors are given in the SI. The red-bordered numbers mark reference points that relate to different scenarios discussed in the main text. b Typical snapshots from experiments (top) and simulations (bottom) of the phases I–IV as indicated in the state diagram. Magnified concentration profiles of the composition in phases III (c) and IV (d) show that the gradient at the interface steepens as temperature locally increases from T₁ > T_c (active droploids, phase III) to T₂ > T₁ (immotile droploids, phase IV). Simulation parameters can be found in ‘Methods’.

Fig. 3. Droplet velocity and growth over time.

a Average size of active droploids (green) and immotile droplets (blue) over time calculated from experiments (dotted) and simulations (solid) for ϕ₀ = 0.05. The shaded area represents the standard deviation. The inset shows the delay in the formation of an immotile droplet at early times for an off-critical composition of ϕ₀ = 0.25. b Mean (and shaded standard deviation) of the total traveled distance of an active droploid over time measured from experiments (dotted) and simulations (solid). c Simulated active droploid velocity over time. d Velocity distribution of active droploids in experiments (left) and simulations (right). e Simulated mean velocity of active droploids after 30 s of light illumination (black curve) and fraction of non-absorbing particles located at the interface of the droplets $N_{\mathrm{na}}^{\mathrm{int}}/N_{\mathrm{na}}$ (gray curve simulations, gray dots experimental data fitted with λ = CIρ_a and C = 3 × 10⁻⁴ μm⁴ μW⁻¹) as a function of the energy input λ for ϕ₀ = 0.05. Note that the fitting factor C is different here than in Fig. 2 because the present measurements are based on a fixed concentration of ϕ₀ = 0.05, whereas those in Fig. 2 have been taken at various concentrations up to ϕ₀ = 0.2. The full list of simulation parameters is provided in the ‘Methods’ section.

Fig. 4. Examples of droplet behavior.

a–e Experimental snapshots (highlighting the segmentation of the droplets), and f–j simulated snapshots (background displays the relative concentration ϕ) of various behaviors: a, f Clusters of colloids deforming the boundary of the droplet at λ = 0.03. b, c and g, h Accumulation of absorbing particles in an off-critical supersaturated background phase (ϕ₀ = 0.2 in experiments, ϕ₀ = 0.25 in simulations) leading to an explosive formation of droplets within a very short time at λ = 0.095 (Supplementary Movies 3 and 4). d, e and i, j Formation of size-stabilized droplets around absorbing particles with periodic light illumination (on and off for 10 s each, Supplementary Movies 5 and 6) at λ = 0.025. Other simulation parameters can be found under ‘Methods’.