Clusters, asters, and collective oscillations in chemotactic colloids

Suropriya Saha, Ramin Golestanian, and Sriram Ramaswamy

Phys. Rev. E 89, 062316 – Published 26 June 2014

Abstract

The creation of synthetic systems that emulate the defining properties of living matter, such as motility, gradient-sensing, signaling, and replication, is a grand challenge of biomimetics. Such imitations of life crucially contain active components that transform chemical energy into directed motion. These artificial realizations of motility point in the direction of a new paradigm in engineering, through the design of emergent behavior by manipulating properties at the scale of the individual components. Catalytic colloidal swimmers are a particularly promising example of such systems. Here we present a comprehensive theoretical description of gradient-sensing of an individual swimmer, leading controllably to chemotactic or anti-chemotactic behavior, and use it to construct a framework for studying their collective behavior. We find that both the positional and the orientational degrees of freedom of the active colloids can exhibit condensation, signaling formation of clusters and asters. The kinetics of catalysis introduces a natural control parameter for the range of the interaction mediated by the diffusing chemical species. For various regimes in parameter space in the long-ranged limit our system displays precise analogs to gravitational collapse, plasma oscillations, and electrostatic screening. We present prescriptions for how to tune the surface properties of the colloids during fabrication to achieve each type of behavior.

Received 30 March 2014

DOI:https://doi.org/10.1103/PhysRevE.89.062316

Authors & Affiliations

Suropriya Saha^1,2,*, Ramin Golestanian^3,†, and Sriram Ramaswamy^2,1,‡

¹Department of Physics, Indian Institute of Science, Bangalore 560 012, India
²TIFR Centre for Interdisciplinary Sciences, 21 Brundavan Colony, Osman Sagar Road, Narsingi, Hyderabad 500 075, India
³Rudolf Peierls Center for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, United Kingdom

^*suropriya@physics.iisc.ernet.in
^†ramin.golestanian@physics.ox.ac.uk
^‡sriram@tifrh.res.in

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Issue

Vol. 89, Iss. 6 — June 2014

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Images

Figure 1
A schematic summary of the four different ways a single swimmer responds to gradients corresponding to the different terms in Eq. (1). In each panel, three consecutive snapshots (with equal time intervals) are sketched together with typical connecting trajectories. In (i) and (ii) the polarity of the colloid controls the direction of motion. In (iii) the motion will be along the main symmetry axis of the colloid but driven by the gradient (hence the colloid can move forward or backward instantaneously). In (iv) the motion is independent of the polarity and symmetry axis of the colloid. Processes (i) and (iv) represent steady angular and linear drift while in (ii) and (iii) the gradient-seeking behavior is assisted by noise. Each mechanism is controlled by the relevant spherical harmonics coefficient of the material-dependent particle mobility and activity, which can be modified by construction.
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Figure 2
The phase diagram in the reaction-limited regime (with abundant fuel) shows a variety of possible states in the parameter space spanned by suitably non-dimensionalized effective chemotactic ( $A$ ) and phoretic ( $B$ ) response coefficients, defined in Eq. (9). The dashed line and the $A$ -axes correspond to independent changes of the fundamental and first harmonic ( $μ_{p 0}$ and $μ_{p 1}$ ) of the mobility corresponding to the reaction product, respectively. They represent possible experimental paths that can be explored in sequences of experiments on particles designed with suitable mobility coats.
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Figure 3
The diffusion-limited regime (with limited fuel supply) exhibits different types of instability in the parameter space spanned by suitably non-dimensionalized effective chemotactic ( $A$ ) and phoretic ( $B$ ) response coefficients, defined in Eq. (9). The effective diffusivity $D^{'}$ [defined in Eq. (11)] is negative in the green region and positive in the white or yellow regions, signaling the presence of an instability upon going from the yellow or white to green. The dominant fluctuations on approaching the instability signal a tendency to form modulations (across the red line) or clumps (across the blue line) state, depending on the sign of the parameter $γ$ [defined in Eq. (12)]. The character of the fluctuations on the stability boundary changes at the location shown by the black dot. The axes corresponding to possible experimental changes of the fundamental and first harmonic ( $μ_{p 0}$ and $μ_{p 1}$ ) of the mobility corresponding to the reaction product, respectively, are shown by two dashed lines.
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Figure 4
Angular velocity coefficient for spherical colloids as a function of $θ_{1}$ (that parametrizes the size of the catalytic coating) for different values of $θ_{2}$ (that parametrizes the mobility pattern) quoted in the legend.
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