Artificial living crystals in confined environment

Wen Yang, Vyacheslav R. Misko, Jacques Tempere, Minghui Kong, and Francois M. Peeters

Phys. Rev. E 95, 062602 – Published 5 June 2017

Abstract

Similar to the spontaneous formation of colonies of bacteria, flocks of birds, or schools of fish, “living crystals” can be formed by artificial self-propelled particles such as Janus colloids. Unlike usual solids, these “crystals” are far from thermodynamic equilibrium. They fluctuate in time forming a crystalline structure, breaking apart and re-forming again. We propose a method to stabilize living crystals by applying a weak confinement potential that does not suppress the ability of the particles to perform self-propelled motion, but it stabilizes the structure and shape of the dynamical clusters. This gives rise to such configurations of living crystals as “living shells” formed by Janus colloids. Moreover, the shape of the stable living clusters can be controlled by tuning the potential strength. Our proposal can be verified experimentally with either artificial microswimmers such as Janus colloids, or with living active matter.

Received 11 July 2016
Revised 1 April 2017

DOI:https://doi.org/10.1103/PhysRevE.95.062602

Physics Subject Headings (PhySH)

Chemical Physics & Physical Chemistry

Interdisciplinary Physics

Authors & Affiliations

Wen Yang^1,2, Vyacheslav R. Misko^2,3, Jacques Tempere^3,4, Minghui Kong⁵, and Francois M. Peeters^2,6

¹College of Materials Science and Engineering, Taiyuan University of Science and Technology, Taiyuan 030024, People's Republic of China
²Departement Fysica, Universiteit Antwerpen, Groenenborgerlaan 171, B-2020 Antwerpen, Belgium
³TQC, Universiteit Antwerpen, Universiteitsplein 1, B-2610 Antwerpen, Belgium
⁴Lyman Laboratory of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
⁵Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031, People's Republic of China
⁶Departamento de Física, Universidade Federal do Ceará, Caixa Postal 6030, Campus do Pici, 60455-760 Fortaleza, Ceará, Brazil

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Vol. 95, Iss. 6 — June 2017

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Images

Figure 1
The number of microswimmers in the trap $N_{i}$ versus simulation time $t$ of systems with the total particle number varied from $N = 100$ to 12 500, for the rotational diffusion coefficient $D_{r} = 0.005$ , the self-propulsion velocity $v_{0} = 1.0$ , and the maximum potential strength $A = 0.1$ . The step value of total number $N$ has been chosen as follows: $Δ N = 100$ for $N < 2000$ ; $Δ N = 200$ for $N = 2000 - 5000$ ; and $Δ N = 500$ for $N > 5000$ . The total number $N$ (when $N \leq 1000$ ) is shown in the plot for the corresponding curves.
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Figure 2
The number of microswimmers in the trap $N_{i}$ versus the total particle number $N$ varying from $N = 100$ to 12 500, for $D_{r} = 0.005, v_{0} = 1.0, A = 0.1$ . The step value of $N$ is the same as in Fig. 1. Regions labeled with I, II, and III correspond to “lattice,” “elastically deformed lattice,” and “saturated” state. Inset (a): Snapshot of the microswimmers for $N = 2000$ , where the parabolic trap is shown by the red circle. Inset (b): The mean square displacement (MSD) of the microswimmers versus the total particle number $N$ , in the $x y$ plane (squares); the $x$ and $y$ components of the MSD (circles and triangles, respectively).
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Figure 3
(a)–(d) Structures formed by $N = 500$ microswimmers for varying parameters: (a) $D_{r} = 0.005, v_{0} = 1.0, A = 0.05$ ; (b) $D_{r} = 0.005, v_{0} = 1.0, A = 0.1$ ; (c) $D_{r} = 0.005, v_{0} = 1.0, A = 0.5$ ; (d) $D_{r} = 0.005, v_{0} = 5.0, A = 0.5$ . Insets in (a)–(d) are the corresponding radial distribution functions $[g (r)]$ .
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Figure 4
(a),(b) Structures formed by $N = 500$ microswimmers for varying parameters: (a) $D_{r} = 0.005, v_{0} = 1.5, A = 0.2$ ; and (b) $D_{r} = 5.0, v_{0} = 1.5, A = 0.2$ . The corresponding radial distribution functions $g (r)$ are presented in (c) and (d). For the highly ordered structure (a), the function $g (r)$ shows clear peaks indicating strong hexagonal correlations (c). For the case of much higher rotational noise (b), the hexagonal correlations are suppressed (d).
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Figure 5
Phase diagram of the systems in the plane “self-velocity $v_{0}$ versus trap strength $A$ ,” for the total number of particles $N = 100$ (a) and $N = 500$ (b), for $D_{r} = 0.005$ and varying $A$ and $v_{0}$ . The phases, i.e., free, shell, and close-packed, are indicated in the plot. The theoretical phase boundary between the free and shell phases, calculated using a single-particle model, $v_{0} / A = D / 2 = 15$ , is shown by a solid magenta line.
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Figure 6
(a)–(d) Formation of clusters outside the trap in “saturated” systems (when the trap is filled by microswimmers), for $D_{r} = 0.005, v_{0} = 1.0, A = 0.1$ and varying particle numbers: $N = 6000$ (a), $N = 6500$ (b), $N = 8000$ (c), and $N = 10 000$ (d).
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