Linking Catalyst-Coated Isotropic Colloids into âActiveâ Flexible

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Linking Catalyst-Coated Isotropic Colloids into "Active" Flexible Chains Enhances Their Diffusivity Bipul Biswas, Raj Kumar Manna, Abhrajit Laskar, Sunil Kumar P. B., Ronojoy Adhikari, and Guruswamy Kumaraswamy ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.7b04265 • Publication Date (Web): 12 Sep 2017 Downloaded from http://pubs.acs.org on September 16, 2017

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Linking Catalyst-Coated Isotropic Colloids into "Active" Flexible Chains Enhances Their Diffusivity Bipul Biswas,† Raj Kumar Manna,‡ Abhrajit Laskar,¶ Sunil Kumar P. B.,‡,§ Ronojoy Adhikari,∗,¶,k and Guruswamy Kumaraswamy∗,† Complex Fluids and Polymer Engineering, Polymer Science and Engineering, CSIR-National Chemical Laboratory, Dr. Homi Bhabha Road, Pune – 411008, India, Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India, The Institute of Mathematical Sciences-HBNI, CIT Campus, Chennai 600113, India, Department of Physics, Indian Institute of Technology Palakkad, Palakkad 678557, India, and DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK E-mail: [email protected]; [email protected] Phone: +91-20-25902182. Fax: +91-20-25902618 ABSTRACT: Active colloids are not constrained by equilibrium: ballistic propulsion, superdiffusive behaviour or enhanced diffusivities have been reported for active Janus particles. At high concentrations, interactions between active colloids give rise to complex ∗

To whom correspondence should be addressed Complex Fluids and Polymer Engineering, Polymer Science and Engineering, CSIR-National Chemical Laboratory, Dr. Homi Bhabha Road, Pune – 411008, India ‡ Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India ¶ The Institute of Mathematical Sciences-HBNI, CIT Campus, Chennai 600113, India § Department of Physics, Indian Institute of Technology Palakkad, Palakkad 678557, India k DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK †

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emergent behaviour. Their collective dynamics result in the formation of several hundred particle-strong flocks or swarms. Here, we demonstrate significant diffusivity enhancement for colloidal objects that neither have a Janus architecture, nor are at high concentrations. We employ uniformly catalyst-coated, viz. chemo-mechanically isotropic colloids and link them into a chain to enforce proximity. Activity arises from hydrodynamic interactions between enchained colloidal beads due to reaction-induced phoretic flows catalyzed by platinum nanoparticles on the colloid surface. This results in diffusivity enhancements of up to 60% for individual chains in dilute solution. Chains with increasing flexibility exhibit higher diffusivities. Simulations accounting for hydrodynamic interactions between enchained colloids due to active phoretic flows accurately capture the experimental diffusivity. These simulations reveal that the enhancement in diffusivity can be attributed to the interplay between chain conformational fluctuations and activity. Our results show that activity can be used to systematically modulate the mobility of soft slender bodies. KEYWORDS: active matter, colloidal assembly, diffusivity, Brownian motion, ice templating. Active systems are characterized by an energy flux through them - therefore, they are outof-equilibrium. 1 All living organisms are active in this sense − for example, motility within living cells relies on molecular motors that use chemical reactions to power mechanical motion and effect directed transport. 2–4 Synthetic systems that mimic active biological systems hold promise for applications ranging from micro-robots and micromixing to targeted drug delivery. 5–11 Several schemes to realize active colloidal systems have been demonstrated. 12–18 One class of active colloids relies on the imposition of external fields: electric, 19–21 magnetic 8,22,23 or light 12,24 to deliver energy to the colloidal system. In another class, chemical transformations are carried out on the colloidal surface to convert chemical energy to mechanical motion. 9,25–28 To effect self propulsion of individual colloids in dilute systems, it is necessary to break symmetry. This symmetry breaking can arise from interactions with external fields, for example, through electrohydrodynamic phenomena that result in colloidal rotation

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about an axis normal to the imposed electric field. 20 Symmetry breaking can also arise from hydrodynamic interactions of colloids with boundaries. 29 In colloidal systems that convert chemical to mechanical energy, symmetry breaking typically arises from the preparation of chemically anisotropic colloids, such as Janus colloids. 7,19,27,28,30 One can also induce symmetry breaking by interactions between colloids in concentrated systems. For example, recent work has demonstrated the formation of self-assembled swarms, bundles and strings through interactions between active colloidal moieties. 19–24,31–34 In these reports, asymmetry at the level of the individual colloidal particle renders them active. The strength and directionality of interactions between these active colloids governs emergent assembly in concentrated colloidal dispersions. Another way to induce symmetry breaking is to bond together colloidal particles, each of which is isotropic, to form chains. Recent simulations have demonstrated that semiflexible chains comprising active beads can exhibit autonomous motion, 35–39 reminiscent of flagellar beating. Two aspects were important for observing active effects in these simulations: (i) the semiflexible nature of the chain allows noise to continually break symmetry and (ii) covalent bonding of individual active beads along the chain allows for spatial proximity so that there is strong hydrodynamic coupling between them. Thus, while each of the beads is isotropic, symmetry breaking happens due to Brownian fluctuations in chain conformations. In such systems, out-of-equilibrium dynamics results from bead-bead interactions due to active flows. However, an experimental realization of this system has not been reported. One advantage of such a system is the ease of preparation of isotropic colloids relative to Janus entities. These synthetic systems also hold promise as models for studying the mechanisms that govern biological flagellar dynamics. 40–44 Combining these mechanistic insights with the ease of fabrication of such active systems might provide a way to address the challenge of enhancing transport phenomena at small length scales.

Here, we report the facile preparation of active colloidal chains that exhibit over 60%

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enhancement in diffusivity over their passive counterparts. The colloids that are enchained to form necklaces are uniformly coated with platinum nanoparticles that catalyze the decomposition of hydrogen peroxide − unlike self-motile Janus colloids. We combine experiments and simulations to show that the "active" enhancement in diffusivity arises from interactions between enchained colloids due to phoretic hydrodynamic flows.

RESULTS AND DISCUSSION Experimental Results. We modify a previously reported 45 protocol (Fig. 1, details in method) to prepare active colloidal chains. Briefly, we freeze a dilute aqueous dispersion of colloidal particles, polyethyleneimine (PEI) and diepoxy crosslinker so that the colloids assemble into chain-like and sheet-like aggregates. 45 We note in passing that above a threshold concentration, ice templating results in the formation of percolated colloidal aggregates. 46 Here, we work at concentrations that are over two orders of magnitude below this threshold. Crosslinking PEI in the frozen state results in the formation of a polymer mesh that traps colloidal particles in the aggregated state. The aggregates formed in this manner are polydisperse in size, and the aggregate size distribution obtained from ice-templating has been investigated in detail previously. 45 We harvest the aggregates by thawing the mixture and work with dilute dispersions so that our investigations are restricted to isolated linear chain-like colloidal assemblies. We vary the stiffness (SI: SI-V1 and SI-V2) of the chains by varying the crosslinking duration and the variation of normalized end to end distances of rigid and semiflexible chains is shown in SI (Fig. S7). We characterize the variation in center-to-center distance for bonded colloids and in the angle between three consecutive colloids (SI: Fig. S5). From these, we estimate the spring constant that characterizes colloidal bonding and the barrier for bond bending. Both these increase systematically with increase in crosslinking duration.

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Colloidal chains are electrostatically complexed with negatively charged 1.5nm platinum nanoparticles (PtNP), resulting in an average coverage of 5.9×103 PtNP per PS colloid (viz. average inter-PtNP spacing ≈ 25 nm). Chains are rendered active by addition of hydrogen peroxide. PtNP on the surface of the PS colloids catalyze peroxide decomposition into water and oxygen, and set up diffusophoretic flows. 27,28 The activity is proportional to reaction rate which is, in turn, proportional to the available peroxide concentration. We use a high peroxide concentration and work with dilute chain dispersions so that there is no measurable change in peroxide concentration (SI: Fig. S2; Section I.C) over a time scale of ∼ 30 minutes, significantly longer than the period over which chain motions are studied. Thus, all our experiments are conducted at constant peroxide concentration or, equivalently, at constant value of activity. The microscope slide is carefully sealed to eliminate possible artefacts due to convective effects 47 (SI: Fig. S3). Finally, we note that our experiments are at sufficiently dilute chain concentrations so that there is no observable evolution of oxygen bubbles. We use fluorescence microscopy to resolve the center, ri , i = 1, . . . , N , of each bead in the colloidal chain. We ensure that colloidal chains are at least several tens of microns from the top and bottom slide surfaces during the time scale of observation (on the order of several minutes). Over this time scale, sedimentation effects due to gravity are unimportant. Thus, wall effects on chain dynamics can be neglected. The positions, {ri (t)}, of the N beads are used to estimate the configurational distributions and chain diffusivity. Due to configurational fluctuations, the magnitude of the end-to-end distance RN (t) = rN (t)−r1 (t) differs from the contour length L = (N − 1)b, where b ≈ 1.1µm, is the mean bond length. We define the chain flexibility ξ as h(RN (t) − hRN i)2 i = ξ 2 L2 . We investigate chains with N = 3, . . . , 12, with ξ varying ten-fold, from ξ = 4 × 10−4 for stiff chains to ξ = 5 × 10−3 for semi-flexible chains. We use ξ as a measure of flexibility since the persistence length is difficult to estimate reliably in short chains. We measure chain diffusivity in the usual P manner by calculating the MSD of the center of mass r(t) = N1 i ri (t) and extracting the 5


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chain and the elastic Hamiltonian in the simulations. This results in discrepancies between the Kirkwood average 54 and experimental results. However, the trends from our simulation results agree well with those observed in the experiments: the diffusivity increases with flexibility. The most rigid chains (ξ ∼ 1.0 x 10−3 ) exhibit diffusivities similar to the passive chains. Finally, the enhancement in diffusivity for active chains with higher flexibility (ξ ∼ 5 x 10−3 ) relative to their rigid counterparts is the greatest for the longest chains. To understand the mechanism behind this enhancement, we turn to Eq. 1. It is clear that the active term breaks detailed balance (Eq. 1) and, therefore, the non-equilibrium stationary state has to be determined from a balance of conservative, dissipative and thermal forces. 35,36,38 To estimate the influence of departure of the chain conformations from equilibrium, we first compute the RHS of Eq. 2 over the non-equilibrium trajectories. The hydrodynamic radius estimated from this non-equilibrium extension of Kirkwood’s formula does not differ appreciably from that of passive chains nor does it show a strong dependence on chain flexibility. This is consistent with the estimates of the hydrodynamic radius from experiment (SI: Fig. S8). The trends observed for the chain diffusivity, then, are clearly not observed in the hydrodynamic radius (see Fig. 5 and more detailed comparisions with the Kirkwood formula in SI: Fig. S12a), which leads us to conclude that active reduction of chain size is not the mechanism underlying the enhanced diffusivity. Rather, the enhanced diffusivity arises primarily due to active hydrodynamic interactions from phoretic flows. For chain lengths much smaller than the persistence length the enhancement of the center of mass diffusion results from an interplay of thermal fluctuations and activity (SI: Fig. S13). The former generate fluctuations in the chain curvature while the latter drive the chain locally in the direction opposite to this induced curvature. Since the thermal curvature fluctuations are unbiased, the active displacements resulting from such fluctuations are random and, when integrated over several chain relaxation time scales, produce an additional diffusive contribution to the chain motion.

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CONCLUSION In summary, our work demonstrates that large diffusivity enhancements, comparable to those demonstrated for Janus colloids, can be achieved for colloidal systems that are uniformly coated with catalytic nanoparticles. In our work, individual colloids along the chain are chemo-mechanically isotropic. Phoretic flows from catalytic reactions on the surfaces of colloidal monomers result in active hydrodynamic interactions between enchained colloids. Brownian fluctuations in the conformations of the semiflexible chains break the symmetry of the active fluid flow. The combination of active hydrodynamic flows and Brownian fluctuations results in an enhancement in chain center-of-mass diffusivity. Thermal forces more readily induce conformational transitions in flexible chains. Therefore, the enhancement in chain diffusivity is larger for more flexible chains. Experimental trends are captured accurately by Brownian microhydrodynamic simulations that incorporate phoretic flows due to activity.

Our results indicate how chain flexibility and activity can be used to tune diffusivity of colloidal objects. Faster than equilibrium dynamics of active chains have implications for their use in drug delivery and mixing. We have previously demonstrated the preparation of completely biocompatible ice-templated colloidal aggregates. 46 Biocompatible active colloidal chains powered by enzymatic catalysts 7,28 represent fascinating constructs with potential for directed therapeutic delivery. Hydrodynamically driven active chains grafted on the walls of microfluidic devices could have implications for technologically important problems such as mixing at low Reynolds number. The active colloidal chains presented here are well represented by a mathematical model and therefore, represent an attractive model system for fundamental investigations of active flexible fibers that are ubiquitous motifs in biology, such as bacterial flagellae.

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METHODS Materials: Polyethyleneimine (PEI) (50 % w/v solution; Mw = 750kg/mol, specified by the supplier) and polyethyleneglycol diepoxide (PEG-diepoxide, molecular weight = 500gm/mol, specified by the supplier), chloroplatinic acid hexahydrate and horseradish peroxidase (HRP) were obtained from Sigma-Aldrich and were used as received. A 2.5% w/v dispersion of fluorescent (Rhodamine-B labelled) polystyrene (PS) beads with a size of 1.08 µm and 4% polydispersity were used as received from Microparticle GmbH, Germany. Sulphonate groups present on the surface rendered the PS particles negatively charged. Hydrogen peroxide (30% aqueous solution), 4-aminoantipyrine (4-AAP) 98% and phenol, 98% were used as received from Avra Synthesis Pvt. Ltd. Synthesis of Active Colloidal Chains: 1 µL of polystyrene (PS) latex comprising ∼ 108 particles was added to 200 µL DI water. After sonication for two minutes to disperse the particles, this was added to 5 µL of PEI stock solution (comprising 100 mg PEI in 1mL DI water) and the mixture was vortexed for 5 minutes. This dispersion was centrifuged and the supernatant was removed to separate unabsorbed PEI. This was diluted with DI water and sonicated for two minutes to redisperse the PEI coated PS colloids. The zeta potential of the PS particle changes from -30mV to +57mV after treatment with PEI, confirming coating of the PS surface.To this was added 1 µL PEG-diepoxide diluted in 1mL DI water and the mixture was then vortexed and subsequently sonicated for 1 minute. This mixture was then stored in a refrigerator maintained at -18o C. The water is transformed into ice on freezing, and the colloids, polymer and crosslinker are concentrated at the boundaries between ice crystals. PEI is crosslinked by PEG-diepoxide in the frozen state. We observe that allowing the crosslinking to proceed for 12 hours results in the formation of a rigid chain (SI: SI-V1). Decreasing the crosslinking time to 8 hours yields semiflexible chains (SI: SI-V2) and highly flexible chains are obtained when we crosslink for 4 hours. After crosslinking, we thaw the frozen sample at room temperature. We synthesized PtNPs according to a previously reported protocol. 55 An aqueous disper13


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sion of colloidal chains, comprising PS colloids in a crosslinked PEI mesh, is treated with an excess of platinum nanoparticles (PtNP). PtNPs are negatively charged and adsorb on the surface of the colloidal chains. Elemental mapping (SI: Fig. S1b) confirms the presence of platinum on the surface of extensively washed PEI-coated PS colloids, confirming adsorption of PtNPs on the colloid surface. We verify that the colloids are isotropically coated with PtNP catalyst as follows. In control experiments, we measure the diffusion of single PS colloids coated with PEI and with PtNP adsorbed on their surface. The diffusivity of such colloids in the presence of hydrogen peroxide is experimentally indistinguishable from that in water (after accounting for differences in solvent viscosity, SI: Fig. S6). This suggests that there is no significant asymmetry in the coverage of PtNP over the PS colloid surface. We estimate a PtNP coverage of 5.9 ×103 PtNP adsorbed per PS colloid (SI: Experimental Details). A dispersion of PtNP coated colloidal chains is added to an equal volume of 30% (w/v) hydrogen peroxide. The PtNP on the particle surface catalyse decomposition of the hydrogen peroxide, rendering the chains active. There is no chance in concentration of hydrogen peroxide during the experimental duration when the chains are visualized (SI: Experimental Details) Video Recording and Data Analysis: Laser Scanning Fluorescence Microscopy (Carl Zeiss Axio Observer) was used with a 63X objective (NA=1.4 and working distance = 0.19 mm). Samples were taken in a cavity slide. Great care was taken to seal the slides to eliminate convective effects (SI: Experimental Details). Fluorescent PS beads were excited with laser light (wavelength = 543 nm). We recorded images at 20fps for more than 40 seconds. Image analysis was performed using ImageJ software and Matlab. To find the centre of mass of the colloidal chain, we used Image J. We substract a constant background and then thresholded the images. We used the inbuilt Particle Analysis function in ImageJ to obtain the centre of mass of the chain. A sequence of images was then used to obtain the MSD for the chain center of mass. We calculate the mean square displacement in 2-

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dimensions as, MSD(t)=< (x(t) − x(0))2 > + < (y(t) − y(0))2 >, where x(t) and y(t) are the center of mass coordinates at time t, obtained from ImageJ. The MSD is linear in time with a slope = 4D, where D is diffusion coefficient (since we track the colloidal chains in 2 dimensions). As a check on the ImageJ analysis, we used the particle tracking function in Matlab to obtain the centre of mass for each colloidal monomer and calculated the chain center of mass based on these coordinates. Analysis using ImageJ was consistent with that using Matlab. We used the Matlab center of mass positions of the colloidal beads in a chain to estimate chain flexibility. Simulation details: The active colloidal chain is modelled as a series of N beads of radius a, that can generate spontaneous flows in the surrounding fluid. 35,37,38 We model the generation of spontaneous flow by the beads through extensile stresslets (to leading order), that are oriented along the local tangent to the chain. We derive a set of update equations by considering an instantaneous force balance between dissipative, thermal and conservative forces. Together, these equations represent a set of coupled stochastic equations of motion for N beads of the model chain.

√ dri = (µij · Fj + πij · Sj )dt + ( 2D)ij · dWj . Here, ri is the position of the i-th bead. The mobility matrix µij and the propulsion matrix πij are defined as

8πηµij (r, r′ ) = Fi0 Fj0 G(r, r′ ), 8πηπij (r, r′ ) = Fi0 Fj1 ∇j G(r, r′ ). Gij (r, r′ ) =

δij ρ

+

ρi ρ j ρ3

2

a is the Oseen tensor with ρ = r−r′ and Fil = (1+ 4l+6 ∇2i ). The diffusion

matrix D is defined as Dij = kB T µij . 15


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The body force, Fi is obtained from the gradient of the potential, U = U C + U E + U S which, in sequence, are potentials enforcing connectivity, stiffness and self-avoidance. The connectivity potential is a two body harmonic spring potential U C (ri , ri+1 ) = 21 k(r − b0 )2 , where b0 refers to the equilibrium bond length and r = |ri − ri+1 |. The stiffness potential, U E = κ ¯ (1 − cos φ), penalizes any departure of the angle φ between consecutive bond vectors from its equilibrium value of zero. The rigidity parameter κ ¯ is related to the bending rigidity κ, as κ ¯ = κ/b0 . Steric effects are incorporated through the Weeks-ChandlerAndersen potential which vanishes if the distance between any two beads rij = |ri − rj | exceeds rmin = 2a. The stresslet tensor of j-th bead, Sj , which is aligned along the local tangent tj of the chain with its strength S0 is defined as,

Sj = S0 (tj tj − δ/3).

ASSOCIATED CONTENT The authors declare no competing financial interest. Supporting Information: Videos of rigid and semi-flexible chain motions from experiments (SI-V1 and SI-V2); trajectories of chain motion from simulations of active and passive chains (SI-V3). Experimental details: PtNP synthesis and characterization, video data collection and analysis and control experiments. Simulation details: model for passive and active chains, effect of activity on enhancement of diffusion.

AUTHOR INFORMATION Corresponding Author Emails: [email protected] and [email protected]. Author Contributions Experiments were conducted by BB. RKM and AL performed simulations. The research was 16


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supervised by PBSK, RA and GK.

ACKNOWLEDGMENTS BB acknowledges an Inspire fellowship from the Department of Science and Technology, India. GK thanks the Chemical Engineering PAC of the SERB, DST for funding this project through grant number SB/S3/CE/072/2014.We thank Dr. Omkar Deshmukh for helping with analysis of the microscopy data and Dr. Jhumur Seth and Dr. B. L. V. Prasad for providing us with PtNPs. Numerical simulations were performed on the HPCE clusters at IIT Madras.

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