Active Atoms and Interstitials in Two-Dimensional Colloidal Crystals

Kilian Dietrich, Giovanni Volpe, Muhammad Nasruddin Sulaiman, Damian Renggli, Ivo Buttinoni, and Lucio Isa

Phys. Rev. Lett. 120, 268004 – Published 29 June 2018

Abstract

We study experimentally and numerically the motion of a self-phoretic active particle in two-dimensional loosely packed colloidal crystals at fluid interfaces. Two scenarios emerge depending on the interactions between the active particle and the lattice: the active particle either navigates throughout the crystal as an interstitial or is part of the lattice and behaves as an active atom. Active interstitials undergo a run-and-tumble-like motion, with the passive colloids of the crystal acting as tumbling sites. Instead, active atoms exhibit an intermittent motion, stemming from the interplay between the periodic potential landscape of the passive crystal and the particle’s self-propulsion. Our results constitute the first step towards the realization of non-close-packed crystalline phases with internal activity.

Received 11 October 2017
Revised 29 May 2018

DOI:https://doi.org/10.1103/PhysRevLett.120.268004

Physics Subject Headings (PhySH)

Crystal defects Crystal phenomena Polycrystals

Charged colloids Colloidal crystal Colloids Janus particles Liquid-liquid interfaces Living matter & active matter

Brownian dynamics Crystallization Optical microscopy

Polymers & Soft Matter

Authors & Affiliations

Kilian Dietrich¹, Giovanni Volpe², Muhammad Nasruddin Sulaiman³, Damian Renggli¹, Ivo Buttinoni^1,3,*, and Lucio Isa^1,†

¹Laboratory for Interfaces, Soft Matter and Assembly, Department of Materials, ETH Zurich, Zurich 8093, Switzerland
²Department of Physics, University of Gothenburg, Göteborg 41296, Sweden
³Physical and Theoretical Chemistry Laboratory, Department of Chemistry, Oxford OX1 3QZ, United Kingdom

^*ivo.buttinoni@chem.ox.ac.uk
^†lucio.isa@mat.ethz.ch

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Vol. 120, Iss. 26 — 29 June 2018

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Images

Figure 1
Active particles in a loosely packed colloidal crystal with lattice constant $L$ . (a),(b) Interactions between active and passive particles at the water-oil interface: (a) active interstitial and (b) active atom. The orange arrows sketch the magnitude of the dipolar coupling. (c),(d) Experimental trajectories and (e),(f) corresponding numerical simulations. Blue, active interstitial. Red, active atom. Black, passive colloids. The color gradients represent time from $t = 0 s$ (green-yellow-gray) to $t = 30 s$ (blue-red-black). $L = 10 R$ , $V_{0} = 38 μ m / s$ (active interstitials, coupling $c = 0.001$ ) and $V_{0} = 6 μ m / s$ (active atoms, coupling $c = 1$ ). (g) Velocity and (h) normalized nearest-neighbor distance (center-to-center) probability distributions for the trajectories shown in (c), (d), (e), and (f). Solid histograms, experiments. Transparent histograms, simulations. The dashed line in (h) marks the experimental lattice constant. Experiments are made at $[H_{2} O_{2}] = 3 %$ and images are recorded at $10 fps$ .
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Figure 2
Active interstitials. (a)–(c) Experimental trajectories of active interstitials in colloidal lattices with (a) $L = 22 R$ , (b) $L = 16 R$ , and (c) $L = 10 R$ ( $[H_{2} O_{2}] = 3 %$ , $V_{0} = 38 μ m / s$ ). The insets show the experimental absolute angular velocity $| ϕ^{'} |$ measured in sequential frames. When $| ϕ^{'} |$ reaches a value greater than $200 τ^{- 1}$ (horizontal black line, $τ$ is the free rotational diffusion time), a tumbling event is registered (see also [23]). The color code highlights the relative particle speed. (d)–(f) Corresponding numerical simulations obtained using $c = 0.001$ and $V_{0} = 38 μ m / s$ . (g) Frame sequence of an active interstitial interacting with a passive colloid. The direction of the swimming velocity (blue arrow) with respect to the particle orientation (green arrow) changes when the swimmer is captured. Details of the detection of the particle orientation are in [23]. (h) Experimental (blue) and numerical (cyan) tumbling frequency plotted as a function of the lattice constant. The inset shows that the maximum speed corresponds to the free swimming velocity $V_{0} = 38 μ m / s$ (dashed horizontal line).
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Figure 3
Active atoms. (a) Time evolution of the velocity of an active atom in a crystalline monolayer with $L = 10 R$ ( $[H_{2} O_{2}] = 3 %$ , $V_{0} = 6 μ m / s$ ). The black vertical lines mark the times at which two (or more) nearest neighbors of the active particle change, suggesting a cell swap. (b)–(d) Corresponding Voronoi diagram (b) before, (c) during, and (d) after the cell swap indicated by the black arrow in (a). (e)–(g) Potential landscape and trajectory of the active atom (e),(f) before and (g) during the cell swap indicated by the blue arrow in (a). The potential is normalized by the value at the particle surface. In (b)–(g) the length of the arrows is proportional to the particle velocity.
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Figure 4
(a),(b) Numerical color maps of (a) the coordination number $N_{coord}$ and (b) residual motility $V / V_{0}$ , i.e., the mean velocity $V$ normalized by the mean free swimming speed $V_{0}$ , as a function of $V_{0}$ , $L$ , and $c$ . The dots correspond to the simulated values. (c) Experimental (black symbols) and numerical (blue line) mean velocity normalized by the maximum speed in the lattice $V_{\max}$ ( $\approx V_{0}$ ), plotted as a function of the coupling $c$ . The blue band marks the standard deviation of the numerical results. (d) Numerical data for fixed free swimming velocity ( $V_{0} = 1 μ m / s$ ) and variable $L$ and $c$ , revealing mobile (empty symbols) and caged (filled symbols) states. A particle is labeled as caged if the maximum value of its root mean square displacement is smaller than $L$ . The gray band highlights the transition.
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