Dynamics of Binary Active Clusters Driven by Ion-Exchange Particles

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Dynamics of Binary Active Clusters Driven by Ion-Exchange Particles Ran Niu, Andreas Fischer, Thomas Palberg, and Thomas Speck ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.8b04221 • Publication Date (Web): 15 Oct 2018 Downloaded from http://pubs.acs.org on October 20, 2018

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Dynamics of Binary Active Clusters Driven by Ion-Exchange Particles Ran Niu, Andreas Fischer, Thomas Palberg, and Thomas Speck∗ Institut f¨ ur Physik, Johannes Gutenberg Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany E-mail: [email protected] Abstract We present a framework to quantitatively predict the linear and rotational directed motion of synthetic modular microswimmers. To this end, we study binary dimers and characterize their approach motion as effective interactions within a minimal model. We apply this framework to the assembly of small aggregates composed of a cationic ion-exchange particle with up to five passive particles or anionic ion-exchange particles at dilute conditions. Particles sediment and move close to a substrate, above which the ion-exchange particles generate flow. This flow mediates long-range attractions leading to a slow collapse during which long-lived clusters of a few particles assemble. The effective interactions between unlike particles break Newton’s third law. Depending on their symmetry, assemblies thus can become linear or circle swimmers, or remain inert (no directed motion).

Keywords synthetic active matter, self-assembly, modular microswimmers, electro-osmotic flow, nonreciprocal forces 1

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The autonomous assembly and operation of nanomachines that perform useful tasks beyond the molecular scale have been a long-standing vision of nanotechnology. 1,2 A recent and potentially powerful strategy is active matter, which is constantly driven out of equilibrium and characterized by the directed motion of its constituents. The reason for its potential is twofold: First, active matter allows to exploit self-assembly pathways that are not available for systems governed by dynamics obeying detailed balance (which eventually reach thermodynamic equilibrium). Second, due to the directed motion, active matter is able to exert forces on its environment that can be harvested in the assembled device. Active suspensions have already been exploited to power microscale devices, 3–9 for templated self-assembly, 10 and to set up spontaneous flows on macroscopic lengths. 11 By now a wide range of mechanisms to achieve self-propulsion have been reported. 12 Most of these mechanisms are based on (spherical) Janus particles that break symmetry through a non-uniform surface (or bulk): catalysis of hydrogen peroxide 13,14 that can be controlled by light, 15 demixing of a near-critical binary solvent, 16 thermophoresis, 17,18 and dielectric colloidal particles in external electric fields. 19 In mixtures with passive particles, assembly into small clusters has been reported which are propelled by the Janus “motor”. 20–22 An alternative strategy is to build “colloidal molecules” 23 out of uniform particles, i.e., small clusters of particles with strong (or even permanent) bonds. Non-reciprocal (effective) forces in clusters composed of different particles then lead to a propulsion of the whole cluster. 24,25 For example, dimers composed of two dielectric colloidal particles with different diameters undergo directed motion in a perpendicular electric field, 26 and larger colloidal microswimmers can be built systematically. 27,28 Other realizations include the breaking of the symmetry of electroosmotic flow 29 and mixtures of absorbing and non-absorbing particles in a near-critical binary solution. 30 In this study, we demonstrate the autonomous assembly of active clusters of uniform, spherical particles from a dilute aqueous suspension in the absence of any external fields. This is achieved through mixing cationic ion-exchange particles (IEXs) with either anionic

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IEXs or passive particles of the same diameter. The IEX are uniform, spherical beads made of a porous ion-exchange resin (Methods). Close to a substrate, the IEXs generate an electroosmotic flow that leads to long-range effective interactions and is stable for several hours. 29 Similar solvent-mediated interactions have been realized through phoretic mechanisms, 31,32 and the possibility to obtain active clusters has been discussed theoretically 33 and demonstrated experimentally for IEXs. 29 The prediction of the dynamic behavior of these active clusters from first principles is challenging due the complex interplay of local gradients, solvent flow, surface properties, and boundaries conditions. Here we follow a different route and demonstrate that from facile measurements of approach speeds between components, our extended model is able to quantitatively predict swim speeds and circle swimming parameters of the self-assembled heterogeneous clusters. For our proof-of-principle, we employ well-characterized particles with diameter of 15 µm. We anticipate that our approach employing effective potentials is applicable to other phoretically propelling modular swimmers, and thus to be a significant advance in their description.

Results and Discussions The IEXs are confined by gravity to two-dimensional motion on the bottom substrate of the sample cell, for experimental details see Methods. Figure 1(a) shows a typical snapshot of the experimental system with a number of clusters of varying size and composition. These clusters form due to the combination of long-range attraction and short-range repulsion between the IEXs mediated through the solvent. The mechanism leading to these interactions has been discussed in previous publications 29,34 and can be summarized as follows: Cationic IEXs exchange stored protons for residual cations, the different diffusion coefficients of which lead to local diffusio-electric fields while maintaining overal charge neutrality. In the double layer of the negatively charged substrate, these local fields generate a converging electroosmotic flow pumping solvent towards each cationic IEX. For two cationic IEXs, the resulting

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(b)

(a)

(c)

(d)

100 µm

100 µm

Figure 1: Binary active clusters. (a) Snapshot of the experimental system showing several clusters with different sizes, compositions, and structures (cationic IEXs appear red and anionic IEXs appear blue). (b,c) Time-traces of (b) a trimer and (c) a tetramer with two cationic IEX. Both exhibit straight swimming motion due to their reflection symmetry. (d) In contrast, for the pentamer this symmetry is broken and, in addition, the cluster rotates. The total motion is that of a circle swimmer. asymmetry in the superposed flow leads to an effective attraction at large separation. Coming closer, geometric effects of the backflow out of the plane of the substrate (and possibly electrophoretic flow) lead to an effective repulsion. In combination with the attractive interactions, two cationic IEXs reach an equilibrium position (plus fluctuations) and thus are able to form stable aggregates (“molecules”) that grow over time due to the addition of further monomers and the fusion of aggregates. It has been shown that the dynamics of this process is well described assuming a potential flow in two dimensions (with effective sources and sinks), leading to an effective conservative potential governing the motion of the IEXs, although the system (solvent plus particles) is strongly driven away from thermal equilibrium. 29

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Placing an inert, passive particle in the vicinity of an IEX, the passive particle is advected by the flow. We study assemblies of polystyrene spheres with approximately the same diameter as the IEXs. To study the flow, we first consider an isolated pair (all other particles are at least 10 times their diameter away) of one cationic IEX and one passive particle. For large separations, we observe that the passive particle approaches the cationic IEX, which remains stationary. This is in agreement with previous measurements using smaller passive tracer particles. 29 However, in contrast to a pair of identical cationic IEX, as two particles get close their center-of-mass starts to translate (see Supplementary Video 2). The two particles thus assemble into a dimer that performs a linear, directed “swimming” motion along its symmetry axis (pointing towards the cationic IEX). Qualitatively, we can understand this behavior by postulating an additional reciprocal component of the solvent flow that couples both particles hydrodynamically. As the passive particle comes closer, this flow “pushes” the IEX forward and the passive particle backward. It thus opposes the advection of the passive particle until the speed of both particles is the same. To be more quantitative, we measure the relative drift speed vCP (r) and the center-ofmass speed VCP (r) as a function of the separation r. To this end, we track the particle positions of the selected isolated pair and calculate the displacements between two frames. The resulting speeds [Fig. 2(a)] are binned according to the separation and averaged over approx. 160 independent trajectories. Denoting the positions of the particles rP and rC with separation r = |rC − rP |, for their motion we assume

r˙ P = −∇P [uC (r) + UP (r)],

r˙ C = −∇C UP (r),

(1)

where ∇i denotes the gradient with respect to the position of particle i. Absorbing the mobilities of the particles, here we have introduced the effective potentials uC (r) for the symmetric electroosmotic flow generated by the cationic IEX and UP (r) accounting for the additional solvent flow that results from the presence of the passive particle.

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Figure 2: Binary pair of cationic IEX and passive particle. (a) Measured relative drift speed vCP (r) (orange symbols, divided by two) and center-of-mass speed VCP (r) (blue symbols) as a function of the particle separation r. Green symbols show the magnitude of the differential speed, which equals the reciprocal contribution. The black diamond indicates the measured speed of the dimer, whereas the dashed line is the model prediction for the dimer separation rCP . The blue and green lines are fits to the experimental values using the potentials Eq. (2). The orange line is obtained by adding the two fits. (b,c) Experimental histograms of (b) the speed and (c) the center-to-center separation of the assembled dimer, where the black dashed lines indicate the mean values. (d) Center-of-mass speeds of larger clusters CPN (shown in the snapshots below, the red particle is the cationic IEX). Blue symbols and bars represent the experimental speed distributions, shown are median (symbol) and first-to-third quartile (bars) of the distributions. Note that the statistical uncertainty of the median is comparable to the symbol size. Dashed lines indicate the speed predicted by the model [Eq. (3)] depending only on the number N1 of direct neighbors. Even without explicit knowledge of the potentials, our ansatz Eq. (1) reproduces the observed behavior. From Eq. (1), we obtain the drift speed vCP (r) = u0C (r) + 2UP0 (r) and the center-of-mass speed VCP (r) = 21 u0C (r), which only depends on the non-reciprocal electroosmotic flow. The prime denotes the derivative with respect to the argument r. For large separation r, we expect UP (r) to vanish and thus VCP (r) = 21 vCP (r) in agreement with the measured speeds [Fig. 2(a)]. As the particles approach, the additional flow starts to counteract the converging electroosmotic flow until at separation rCP the drift speed vanishes.

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Table 1: Values of the fitted parameters for the three different fits performed. The expressions for uC and UP are given in Eq. (2), whereas uA (r) was fitted with an exponential, uA (r) = αA exp(−r/ξA ), cf. Fig. 3. UP uA uC 3 γ ' 7328 µm /s α ' 8106 µm3 /s αP ' 4008 µm3 /s αA ' 43.4 µm2 /s ξ ' 24.9 µm ξP ' 9.4 µm ξA ' 19.7 µm Both particles of the resulting dimer then move with speed VCP1 = 12 u0C (rCP ) = −UP0 (rCP ). Both the speed and the bond length fluctuate as shown in Fig. 2(b,c). Hence, in principle we should include noise terms in Eq. (1) arising from fluctuations of the flow. However, in the following we will focus on the average speeds (and cluster geometries) and drop the noise. To model the effective potentials in Eq. (1), we assume the following forms γ α uC (r) = − + e−r/ξ , r r

UP (r) =

αP −r/ξP e . r

(2)

The ansatz for the generated flow uC (r) has been suggested in Ref. 29, where the long-range 1/r contribution is suggested by the decay of the proton concentration c(r) ∼ 1/r with solvent velocity vs ∝ ∇c. Closer to the particle, the concentration profile as well as the generated flow are more complicated, which we take into account through a Yukawa-like repulsive contribution with decay length ξ. As shown in Fig. 2(a), this form of uC (r) excellently fits the experimental results (blue curve). Also plotted in Fig. 2(a) is the reciprocal contribution UP0 (r) =

1 v (r) 2 CP

− VCP (r), which is well described by a purely repulsive Yukawa ansatz

(green curve). Adding both fits indeed follows the measured relative drift speeds (orange curve). The parameters of all fits are summarized in Table 1. This analysis of the approach behavior in terms of effective potentials allows a prediction of the steady state center-of-mass speed VCP1 ' 1.11 µm/s, which is very close to the experimentally measured value 1.16 µm/s. However, the predicted steady-state separation rCP ' 27 µm is notably larger than the average separation observed experimentally, rCP ' 19 µm [cf. prediction in Fig. 2(a) vs. measured separation in Fig. 2(c)]. This discrep7


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ancy can be explained as an effect of the moving dimer distorting its pH gradient, 35 which becomes asymmetric and allows the passive particle to be closer while the dimer speed is approximately unchanged. In the following, we account for this effect through employing the experimental bond length rCP ' 19 µm. We now consider clusters with more particles. Although in principle metastable, at the dilute conditions we are working at, single clusters can be observed for at least 5 minutes, which allows to gather sufficient statistics. After the first passive particle breaks the symmetry and the dimer starts moving, the following particles assemble on the same side of the cationic IEX. Clusters with a reflection symmetry move linearly, whereas clusters lacking that symmetry perform circular motion. In principle, clusters with an inversion symmetry should be inert without directed motion. However, such clusters were not observed experimentally since monomers are added sequentially and always assemble behind the leading cationic IEX. Circularly moving structures were observed for a short time but are unstable and transform into linearly moving structures possessing a reflection symmetry. The measured speeds for a number of these clusters composed of one cationic IEX and n passive particles is shown in Fig. 2(d). The speeds are very similar, V ' 1.5 µm/s, almost independent of size and structure. The largest dependence is on the number of direct neighbors (either two or three). To predict the linear center-of-mass (“swimming”) speed of clusters, we exploit that all particles have to move with the same average speed to maintain the cluster shape. Hence, it is sufficient to consider the cationic IEX. We assume that only the N1 passive particles that are its direct neighbors will contribute to the reciprocal flow propelling the cationic IEX so that N

VCPN

1 ri 2 X VCP1 , = N1 + 1 i=1 rCP

(3)

where ri = rC −rPi is the vector pointing from the (average) position of the ith passive particle to the cationic IEX with distance |ri | ≈ rCP . As shown in Fig. 2(d), the agreement with the experimental speeds is very good. We see that the passive particles that are not direct neighbors of the IEX slightly lower the swimming speed (presumably indirectly through 8


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influencing the cluster geometry). In a second step, we replace the passive particles by anionic IEX with again approximately the same diameter. In principle, the flow mechanism of the anionic IEXs is the same as for the cationic IEXs, but now hydroxide ions are exchanged for chloride ions. The resulting flow is diverging (pointing away from the IEXs) due to the opposite charge of the exchanged ions. Therefore, anionic IEXs repel each other. Moreover, the difference in diffusion coefficients between these anions is much smaller and, consequently, we expect the generated flow to be weaker and shorter in range. We observe that anionic IEXs in the flow range of a cationic IEX (∼ 120 µm) are advected towards the cationic IEX. As they get close, we observe the same qualitative behavior as for passive particles: their motion couples and they start selfpropelling in the direction of the cationic IEX. We extend our previous model Eq. (1) through accounting for the flow generated by the anionic IEX with effective potential uA (r),

r˙ A = −∇A [µA uC (r) + UA (r)],

r˙ C = −∇C [uA (r) + UA (r)],

(4)

where r = |rC − rA | is again the separation between both particles. For the center-of-mass speed, we find VCA (r) = µA VCP (r) for separations r > 45 µm with multiplicative factor µA ' 0.76. We thus conclude that the electroosmotic flow of the cationic IEX is the same as before but the mobility of the anionic IEX is reduced (due to diverse factors including a different surface charge and a different ζ-potential), which we take into account through the reduced mobility µA (relative to the passive mobility) of anionic IEXs in the flow generated by the cationic IEX. In Fig. 3, we plot the average relative drift vCA (r) and center-ofmass speed VCA (r) for an isolated cationic-anionic IEX pair. Employing the potential uC (r) obtained from studying the dimer with a passive particle, we can extract the contribution u0A (r) = 2[µA VCP (r) − VCA (r)] due to the electroosmotic flow of the anionic particle as well as the reciprocal contribution UA0 (r) = 21 vCA (r) + VCA (r) − 2µA VCP (r), which are also plotted

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1.2

VCA 1v 2 CA

0.8 speed [ m/s]

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0.4 0.0 0.4 0.8 40 80 distance r [ m]

UA0 (r) uA0 (r) 120

Figure 3: Cationic-anionic IEX pair. Measured relative drift speed vCA (r) (orange symbols, divided by two) and center-of-mass speed VCA (r) (blue symbols) as a function of the particle separation r. The black diamond indicates the measured speed of the dimer and the dashed black line shows the model prediction for the dimer separation rCA . The blue line is the model prediction for the center-of-mass speed. Gray symbols show the generated flow of the anionic particle u0A (r) while green symbols represent the reciprocal flow UA0 (r). Gray and green lines are guides to the eye. in Fig. 3. As expected, the flow generated by the anionic IEX is weaker and, in particular, short-ranged (it can be fitted by an exponential). Moreover, this flow is diverging, i.e., flowing away from the anionic IEX. The reciprocal flow UA0 (r) is now pulling the particles together and vanishes as they reach their equilibrium separation. In contrast to clusters with passive particles, the measured average dimer separation now agrees with the model prediction (rCA ' 18 µm). In Fig. 4, the most common self-propelling clusters (inert clusters were now observed but are not included) with one cationic IEX are depicted. One notices the decrease of bond length between cationic IEX and anionic IEX for larger clusters, which is not observed for cationic-passive clusters. This presumably results from the stronger neutralization of the acidic pH gradient by many anionic IEXs. The trimer and the two tetramers are linear swimmers, whereas the pentamer occurs in one linear swimming and two circularly moving

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Figure 4: (a) Center-of-mass speeds VCAN of cationic-anionic clusters obtained from experimental measurements (circles) and model predictions from Eq. (5) and Eq. (6) (black crosses). The dashed line indicates the average dimer speed VCA1 . Symbols and bars again show median and first-to-third quartile of experimental speed distributions. For circle swimmers, we also show the angular speeds ωCAN and radii RCAN of the circle motion. In the snapshots of the corresponding clusters, the cationic IEX appears red and the anionic IEX particles appear dark (blue). Red arrows indicate linear and circular self-propelling directions. (b) Global comparison of model predictions and measurements for all linear speeds. isomeric structures. All three hexameric isomers are circle swimmers. Larger clusters than shown here are likely to have more than one cationic IEX. Following similar arguments as before, the speed of the cationic IEX within a stable cluster is now determined primarily by the diverging flow of the anionic IEX. We thus find N

VCAN =

ri 2 X VCA (ri ) N + 1 i=1 ri

(5)

but now including all N anionic IEX. For the angular speed of circularly moving clusters,

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we find (see Methods for derivation) PN ω CAN =

0 0 i=1 [µA uC (ri )xAi − uA (ri )xC ] P 2 x2C + N i=1 xAi

× (ri /ri )

(6)

with xα = rα − R the relative position of particle α to the cluster’s center of mass R. The numerator is the total effective torque with respect to R and the denominator expresses that a larger cluster has a higher resistance to rotation. The relative positions of the particles within a clusters were extracted from the experimental data and their average values were used as an input for Eq. (5) and Eq. (6). In Fig. 4(a), the measured linear and angular speeds are plotted. While these values seem to scatter randomly, their subtle dependence on the cluster geometry is confirmed by our model predictions, which agree very well with the experimental values. Also plotted are the values for the radius RCAN of circle swimmers, cf. Fig. 1(d) showing a single trajectory. This confirms that the properties of the motion of the clusters is determined by their structure, and that the superposition of the effective two-body interactions yields accurate predictions for the dynamics of larger clusters [cf. Fig. 4(b) for a global comparison of the linear speeds]. The physical mechanism we exploit here also holds for smaller particles.

We have

performed preliminary experiments using cationic IEXs with diameter 5 µm and passive polystyrene particles with diameter 2.4 µm. Supplementary Video 1 shows the directed motion of a modular swimmer composed of N = 8 passive particles after assembly. As expected, fluctuations are now much stronger and influence the swimmer geometry so that a description in terms of the average structure is not sufficient anymore. The measured linear speed is plotted in Fig. 5(a) as a function of time. Also shown in Fig. 5(b) is the speed of another, slightly smaller active cluster. Clearly, directed motion is stable over several minutes. Ultimately, downsizing depends on the availability of small and heavy particles. So far, IEX particles smaller than 5 µm are not available, but modular swimmers based on materials such as hematite 15 or AgCl 36,37 should be feasible. Downsizing particles to even smaller scales

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Figure 5: Active clusters driven by small IEX particles. Linear speed as a function of time for two modular swimmers with (a) N = 8 (same as shown in Supplementary Video 1) and (b) N = 6 passive particles with diameter 2.4 µm. The dashed line is the median and the bars indicate the first-to-third quartile of the speed distributions. Note that in (b) another passive particle is stuck to the IEX. The diameter of the cationic IEX is 5 µm. The snapshots at two different times indicate strong structural fluctuations, however, swimming is stable over minutes. (∼ 100 nm) presents a challenge for all phoretic swimmers that rely on a surface. One possible route is to increase the confinement in order to bind the particles to the substrate. This will alter the flow leading to different functional forms of the effective potentials, although the general formalism developed here should still be applicable.

Conclusions We have analyzed the dynamics of ion-exchange particles in dilute, binary suspensions. These particles move and assemble autonomously into small clusters that are stable over minutes to hours. Depending on symmetry, clusters perform linear or circular directed motion, i.e., they become modular microswimmers. Compared to catalytic swimmers, ion-exchange based swimmers utilize micromolar impurity cations rather than potentially hazardous fuel for propulsion. Both the assembly process and the self-propulsion are based on the same mechanism: breaking the symmetry of the self-electroosmotic flow generated by the ion-

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exchange particles. This flow is long-ranged, mediating interactions over sub-millimeter distances. Our approach is designed to be rather generic. We have not attempted to model the microscopic mechanisms of the electroosmotic flow, which are complex and highly dependent on surface chemistry, dielectric properties, surface charge, and geometry of the colloidal particles. Rather, here we use a single experimental input in combination with simple symmetry arguments in order to gain insight into the effective interactions of two particles. Our model does not rely on resolving the commonly employed but complex hydrodynamic interactions to produce collective motion, but instead is based on pairwise interactions. Although here demonstrated only for cationic-passive and the novel cationic-anionic modular swimmers, we stress that our approach through measuring the dimer approach behavior is applicable to other phoretic mechanisms (as long as they can be related to the electrokinetic effects addressed here). A straightforward extension is to model passive particles with different diameters. Finally, for a better control of the assembled structures it will be imperative to incorporate external factors such as patterned substrates, magnetic fields, and gravity into the model.

Methods Materials. The particles used for the experiments are commercial cationic ion exchange resin particles (CK10S, Mitsubishi Chemical Corporation, Japan) with diameter 2a = 14.9± 1.4 µm and counter ions Na+ , anionic ion exchange resin particles (CA08S, Mitsubishi Chemical Corporation, Japan) with diameter 2a = 15.0 ± 1.6 µm and counter ions Cl− , and negatively charged polystyrene spheres (PS/Q-F-L1488, MicroParticles GmbH, Germany) with diameter 2a = 15.17±0.14 µm and stabilized by sulfate surface groups. Prior to experiments, the cationic and anionic particles were washed with 20 wt% hydrochloride acid (HCl) and 20 wt% sodium hydroxide (NaOH) solutions to exchange the counter ions into H+ and OH− ,

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respectively. They were rinsed with doubly deionized water several times until solution pH of ∼ 7 and dried at 80◦ C for 2 h. The PS suspension was diluted and deionized using mixed bed ion exchange resin (Amberlite K306, Roth GmbH, Germany). The sample cell was built from a circular Perspex ring (inner diameter of 20 mm, height of 1 mm) fixed to microscopy slides (soda lime glass of hydrolytic class 3 by VWR international) by hydrolytically inert epoxy glue and dried for 24 h before use. The glass slides were washed with alkaline solution (Hellmanex III, Hellma Analytics) for 30 min under sonication, and subsequently rinsed with tap water and deionized water for several times. The ζ-potential of the washed glass slide in deionized water is −(105 ± 5) mV. 34,38 Sample preparation. For the experiments with cationic-anionic clusters, weighted amounts of particles were dispersed into deionized water saturated with atmospheric CO2 . Subsequently, 400 µl of particle suspension was added into the sample cell. To distinguish the two kinds of IEX particles, tiny amounts of pH indicator solution (Universal indicator 4-10, Sigma Aldrich) was added into the sample cell to mark them reddish and bluish, respectively. For the experiments of cationic-passive clusters, a few cationic IEX particles were placed in the sample cell followed by injection of 400 µL of dilute deionized PS suspension saturated with atmospheric CO2 and tiny amounts of pH indicator solution. Particles settled to the bottom of the cell within minutes. Movies were then taken at a frame rate of 0.5 Hz using an inverted scientific microscope (DMIRBE by Leica, Germany) equipped with a standard video camera. Derivation of angular speed. In order to derive an expression for the angular speed of the clusters, we start from the “torque” balance equation (absorbing the mobilities) for one cationic and N passive/anionic IEX X

(rα − R) × r˙ α =

α

X

(rα − R) × Fα

(7)

α

with Fα the effective forces (˙rα = Fα ). Introducing xα = rα − R and changing to polar

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coordinates (xα , ϕ, z), the left hand side can be rewritten into X

xα (exα × ϕ˙ α eϕα ) +

α

X

˙ = ϕe xα × R ˙ z

α

X

x2α

α

where ϕ˙ α = ϕ˙ was used, which follows from assuming that the cluster is a rigid body. The angular velocity ω = ϕe ˙ z is then given by P α xα × Fα ω= P , 2 α |xα |

(8)

which can be recast into Eq. (6).

Acknowledgement We are grateful to B. Liebchen and H. Löwen for stimulating discussions. We acknowledge the DFG for funding within the priority program SPP 1726 (grant numbers PA 459/18-2 and SP 1382/3-2). AF acknowledges funding by the DFG through the Graduate School of Excellence “Materials Science in Mainz” (GSC 266).

Supporting Information Available Two supplemental videos showing directed motion and approach dynamics. This material is available free of charge via the Internet at http://pubs.acs.org.

References 1. Wang, J. Nanomachines: Fundamentals and Applications; John Wiley & Sons, 2013. 2. Coskun, A.; Banaszak, M.; Astumian, R. D.; Stoddart, J. F.; Grzybowski, B. A. Great

16


Page 17 of 21 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Nano

Expectations: Can Artificial Molecular Machines Deliver on their Promise? Chem. Soc. Rev. 2012, 41, 19–30. 3. Sokolov, A.; Apodaca, M. M.; Grzybowski, B. A.; Aranson, I. S. Swimming Bacteria Power Microscopic Gears. Proc. Natl. Acad. Sci. U.S.A. 2009, 107, 969–974. 4. Di Leonardo, R.; Angelani, L.; DellArciprete, D.; Ruocco, G.; Iebba, V.; Schippa, S.; Conte, M. P.; Mecarini, F.; De Angelis, F.; Di Fabrizio, E. Bacterial Ratchet Motors. Proc. Natl. Acad. Sci. U.S.A. 2010, 107, 9541–9545. 5. Kaiser, A.; Peshkov, A.; Sokolov, A.; ten Hagen, B.; Löwen, H.; Aranson, I. S. Transport Powered by Bacterial Turbulence. Phys. Rev. Lett. 2014, 112, 158101. 6. Maggi, C.; Simmchen, J.; Saglimbeni, F.; Katuri, J.; Dipalo, M.; Angelis, F. D.; Sanchez, S.; Leonardo, R. D. Self-Assembly of Micromachining Systems Powered by Janus Micromotors. Small 2015, 12, 446–451. 7. Krishnamurthy, S.; Ghosh, S.; Chatterji, D.; Ganapathy, R.; Sood, A. K. A MicrometreSized Heat Engine Operating between Bacterial Reservoirs. Nat. Phys. 2016, 12, 1134– 1138. 8. Vizsnyiczai, G.; Frangipane, G.; Maggi, C.; Saglimbeni, F.; Bianchi, S.; Leonardo, R. D. Light Controlled 3D Micromotors Powered by Bacteria. Nat. Commun. 2017, 8, 15974. 9. Guo, J.; Gallegos, J. J.; Tom, A. R.; Fan, D. Electric-Field-Guided Precision Manipulation of Catalytic Nanomotors for Cargo Delivery and Powering Nanoelectromechanical Devices. ACS Nano 2018, 12, 1179–1187. 10. Stenhammar, J.; Wittkowski, R.; Marenduzzo, D.; Cates, M. E. Light-Induced SelfAssembly of Active Rectification Devices. Science Adv. 2016, 2, e1501850–e1501850. 11. Wu, K.-T.; Hishamunda, J. B.; Chen, D. T. N.; DeCamp, S. J.; Chang, Y.-W.;

17


ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Fernández-Nieves, A.; Fraden, S.; Dogic, Z. Transition from Turbulent to Coherent Flows in Confined Three-Dimensional Active Fluids. Science 2017, 355, eaal1979. 12. Dey, K. K.; Sen, A. Chemically Propelled Molecules and Machines. J. Am. Chem. Soc. 2017, 139, 7666–7676. 13. Paxton, W. F.; Kistler, K. C.; Olmeda, C. C.; Sen, A.; St. Angelo, S. K.; Cao, Y.; Mallouk, T. E.; Lammert, P. E.; Crespi, V. H. Catalytic Nanomotors: Autonomous Movement of Striped Nanorods. J. Am. Chem. Soc. 2004, 126, 13424–13431. 14. Theurkauff, I.; Cottin-Bizonne, C.; Palacci, J.; Ybert, C.; Bocquet, L. Dynamic Clustering in Active Colloidal Suspensions with Chemical Signaling. Phys. Rev. Lett. 2012, 108, 268303. 15. Palacci, J.; Sacanna, S.; Steinberg, A. P.; Pine, D. J.; Chaikin, P. M. Living Crystals of Light-Activated Colloidal Surfers. Science 2013, 339, 936–940. 16. Buttinoni, I.; Bialké, J.; K¨ ummel, F.; Löwen, H.; Bechinger, C.; Speck, T. Dynamical Clustering and Phase Separation in Suspensions of Self-Propelled Colloidal Particles. Phys. Rev. Lett. 2013, 110, 238301. 17. Jiang, H.-R.; Yoshinaga, N.; Sano, M. Active Motion of a Janus Particle by SelfThermophoresis in a Defocused Laser Beam. Phys. Rev. Lett. 2010, 105, 268302. 18. Bregulla, A. P.; Yang, H.; Cichos, F. Stochastic Localization of Microswimmers by Photon Nudging. ACS Nano 2014, 8, 6542–6550. 19. Yan, J.; Han, M.; Zhang, J.; Xu, C.; Luijten, E.; Granick, S. Reconfiguring Active Particles by Electrostatic Imbalance. Nat. Mater. 2016, 15, 1095–1099. 20. Gao, W.; Pei, A.; Feng, X.; Hennessy, C.; Wang, J. Organized Self-Assembly of Janus Micromotors with Hydrophobic Hemispheres. J. Am. Chem. Soc. 2013, 135, 998–1001.

18


Page 18 of 21

Page 19 of 21 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Nano

21. Palacci, J.; Sacanna, S.; Vatchinsky, A.; Chaikin, P. M.; Pine, D. J. Photoactivated Colloidal Dockers for Cargo Transportation. J. Am. Chem. Soc. 2013, 135, 15978–15981. 22. Singh, D. P.; Choudhury, U.; Fischer, P.; Mark, A. G. Non-Equilibrium Assembly of Light-Activated Colloidal Mixtures. Adv. Mater. 2017, 29, 1701328. 23. Manoharan, V. N.; Elsesser, M. T.; Pine, D. J. Dense Packing and Symmetry in Small Clusters of Microspheres. Science 2003, 301, 483–487. 24. Löwen, H. Active Colloidal Molecules. EPL (Europhysics Letters) 2018, 121, 58001. 25. Niu, R.; Palberg, T. Modular Approach to Microswimming. Soft Matter 2018, 14, 7554– 7568. 26. Ma, F.; Yang, X.; Zhao, H.; Wu, N. Inducing Propulsion of Colloidal Dimers by Breaking the Symmetry in Electrohydrodynamic Flow. Phys. Rev. Lett. 2015, 115, 208302. 27. Ma, F.; Wang, S.; Wu, D. T.; Wu, N. Electric-Field–Induced Assembly and Propulsion of Chiral Colloidal Clusters. Proc. Natl. Acad. Sci. U.S.A. 2015, 112, 6307–6312. 28. Ni, S.; Marini, E.; Buttinoni, I.; Wolf, H.; Isa, L. Hybrid Colloidal Microswimmers through Sequential Capillary Assembly. Soft Matter 2017, 13, 4252–4259. 29. Niu, R.; Palberg, T.; Speck, T. Self-Assembly of Colloidal Molecules due to SelfGenerated Flow. Phys. Rev. Lett. 2017, 119, 028001. 30. Schmidt, F.; Liebchen, B.; Löwen, H.; Volpe, G. Light-Controlled Assembly of Active Colloidal Molecules. arXiv:1801.06868 31. Weinert, F. M.; Braun, D. Observation of Slip Flow in Thermophoresis. Phys. Rev. Lett. 2008, 101, 168301. 32. Leonardo, R. D.; Ianni, F.; Ruocco, G. Colloidal Attraction Induced by a Temperature Gradient. Langmuir 2009, 25, 4247–4250. 19


ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

33. Soto, R.; Golestanian, R. Self-Assembly of Catalytically Active Colloidal Molecules: Tailoring Activity Through Surface Chemistry. Phys. Rev. Lett. 2014, 112, 068301. 34. Niu, R.; Kreissl, P.; Brown, A. T.; Rempfer, G.; Botin, D.; Holm, C.; Palberg, T.; de Graaf, J. Microfluidic Pumping by Micromolar Salt Concentrations. Soft Matter 2017, 13, 1505–1518. 35. Niu, R.; Khodorov, S.; Weber, J.; Reinm¨ uller, A.; Palberg, T. Large Scale MicroPhotometry for High Resolution pH-Characterization during Electro-Osmotic Pumping and Modular Micro-Swimming. New J. Phys. 2017, 19, 115014. 36. Ibele, M.; Mallouk, T. E.; Sen, A. Schooling Behavior of Light-Powered Autonomous Micromotors in Water. Angew. Chem. 2009, 121, 3358–3362. 37. Simmchen, J.; Baeza, A.; Miguel-Lopez, A.; Stanton, M. M.; Vallet-Regi, M.; RuizMolina, D.; Sánchez, S. Dynamics of Novel Photoactive AgCl Microstars and Their Environmental Applications. ChemNanoMat 2016, 3, 65–71. 38. Botin, D.; Wenzl, J.; Niu, R.; Palberg, T. Colloidal Electro-Phoresis in the Presence of Symmetric and Asymmetric Electro-Osmotic Flow. Soft Matter 2018, DOI:10.1039/c8sm00934a.

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Graphical TOC Entry 1 v 2

(a) 2.0

V

0.8

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1 v 2

0.4 0.0 0

40

80

120

frequency

distance r [ m] (b)

1.5

1.0

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0.5

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VCP [ m/s]

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V [ m/s]

speed [ m/s]

1.2

15 20 25

rCP [ m]

(d)

Dynamics of Binary Active Clusters Driven by Ion-Exchange Particles

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