Self-Propulsion and Active Motion of Janus Ellipsoids - The Journal of

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Self-Propulsion and Active Motion of Janus Ellipsoids Onajite Shemi, and Michael J Solomon J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b08303 • Publication Date (Web): 23 Oct 2018 Downloaded from http://pubs.acs.org on October 27, 2018

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The Journal of Physical Chemistry

Self-Propulsion and Active Motion of Janus Ellipsoids

Onajite Shemi and Michael J. Solomon*

Department of Chemical Engineering, University of Michigan, Ann Arbor, MI, USA

ACS Paragon Plus Environment

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ABSTRACT

The propulsion of platinum-coated polystyrene prolate ellipsoids, as generated by catalytic decomposition of hydrogen peroxide, is characterized by direct visualization of the trajectories of the active particles. These Janus ellipsoids were fabricated by stretching micron-sized polystyrene spheres into different aspect ratios; half of the particle is then capped lengthwise along the ellipsoid’s major axis, with platinum deposition. These particles exhibit complex dynamical trajectories in aqueous solutions of hydrogen peroxide of concentration in the range of 2-8% (w/v). In this range, a transition from three-dimensional passive Brownian motion to two-dimensional active motion is observed as the hydrogen


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peroxide concentration is increased. This transition from passive to active motion is complete by 4% (w/v) hydrogen peroxide.

We quantify the effect of particle

aspect ratio on the mean-squared displacement and mean-squared angular displacement at the highest hydrogen peroxide concentration. The two-dimensional trajectories of the individual particles were grouped into three categories for dynamical analysis. In the first category, ballistic ellipsoids translate at least five times more than purely diffusive ellipsoids at the characteristic time scale of rotational diffusion.

In the second category, spinning ellipsoids move only short

distances with a dominant rotation about the minor axis; this rotation persists for many revolutions.

A third category captures trajectories that include both

significant translation and rotation.

We consider the physical origins of the

observed categories of motion and extract the forces and torques generated by the catalytically generated propulsion as a function of aspect ratio.

The particle

velocity – and therefore the active force – increases with the aspect ratio.


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1. INTRODUCTION Janus colloids are a type of anisotropic particle that incorporates dual interactions, material properties, and/or function1. In addition to their use for drug delivery2 and self-assembly3,4, Janus particles can exhibit self-propulsion and active motion.

To generate active motion, the colloidal particle is often capped

with a layer of platinum5–8. In the presence of a chemical fuel such as hydrogen peroxide5,7,9, the platinum catalyzes decomposition reactions that generate particle self-propulsion; the observed active motion shares common features with the swimming of flagellar bacteria. The observed phoretic motion is due to the presence of concentration gradients at the particle-solvent interface. These gradients are a consequence of the catalytically induced chemical reaction10. This process represents a transformation of locally available chemical energy at the molecular scale into directed motion of particles at the colloidal scale. Active motion has been observed in colloids of various shapes and Janus anisotropy including polystyrene-platinum spheres5,11,12, silica-platinum spheres9,


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silica-platinum rods13, and gold-platinum nanorods7. These studies have extended the

understanding

of

the

translation

and

rotation

that

results

from

the

diffusiophoretic motion of Janus particles. They have shown the effect of various physical properties on active motion. For example, in the case of spheres11, the particle radius determines the drag that balances the active force; the platinum layer thickness12 determines the catalytic activity that is balanced by drag; platinum surface coverage14 determines the abundance of active catalytic sites, a further determinant of the active force. This availability influences the localized concentration

gradients

around

the

particle

that

drive

self-diffusiophoresis.

Additional understanding of the effect of drag and propulsive forces on active motion may be obtained by systematically varying the shape of the Janus colloids. To date, suspensions of bimetallic rods7 and of silica-platinum rods13 have been studied. In this study, we observe the effect of shape on the motility and trajectories of active Janus particles in dilute suspensions; we find new active motion features, including trajectories that span from purely translational to purely rotational.


We

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study prolate Janus ellipsoids with a platinum coating along half the particle, running the length of the major axis.

This geometry allows for analysis of

rotational and translational motion generated by the localized decomposition of hydrogen peroxide. In addition, by systematically varying particle aspect ratio (and thereby surface area), the drag and propulsive forces generated by the catalytic activity are varied.

The anisotropic geometry produced in these ellipsoids

generates propulsive motion perpendicular to the major axis of the ellipsoid, a direction of motion that has only recently been studied for the case of spherocylinders coated along the length of the major axis; this work found that at low hydrogen peroxide concentration, the active Janus rods clustered as function of particle concentration and aspect ratio13; in addition, measurements at dilute concentration show that the active motion can be modeled as a random walk, with a translational diffusivity that is enhanced relative to the passive case. Others have found that the dynamic motion of Janus ellipsoids leads to interesting active trajectories, with varying contributions of translation and rotation15–17.

Of

particular interest here will be our finding of the existence of a range of hydrogen


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peroxide concentrations in which the ellipsoids spin in place, coexisting with other particles that show ballistic trajectories. Dynamic equilibrium between the two populations is observed. In pursuit of this aim, we characterize hydrogen peroxide-induced active motion of Janus ellipsoids for particles with aspect ratio between 2.4 and 6.7. The active motion is resolved and quantified by two-channel confocal microscopy and image analysis, respectively. Qualitatively, we find that the transition from threedimensional Brownian diffusion to two-dimensional active motion (in the plane of a bounding surface) is reached as hydrogen peroxide concentration is increased to 4%.

Both mean squared displacement (MSD) and mean squared angular

displacement (MSAD) are quantified at the particular case of 8% hydrogen peroxide concentration, a condition at which active motion is strongly apparent. The observed trajectories are classified into those that are predominantly translational as well as ones that are predominantly rotational.

The propulsive

forces and torques acting on the Janus ellipsoids are extracted from analysis of these types of trajectories.

The results show that subpopulations of Janus


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ellipsoids undergo dynamics that differ dramatically from that of a random walk, with potential implications in multiple areas, including active self-assembly.

2. EXPERIMENTAL METHODS 2.1. Janus Ellipsoid Synthesis.

Polystyrene ellipsoids were synthesized as in

the literature18,19. Briefly, 300 mL of a 2.0 vol% solution of carboxylate-modified polystyrene spheres (PS) (0.99um, F8821, Life Technologies) is added to 8 ml of 10% Polyvinyl alcohol (PVA) in water solution. The solution is well-mixed before pouring on an OmniTray (Thermo Scientific Nunc OmniTray, 242811) and allowed to dry for 16-24 hrs at room temperature.

Once dried, the film is cut

into 4 cm x 1 cm strips, assembled and clamped to a device that imposes a uniaxial deformation in a constant temperature oven.

To produce the ellipsoids,

the films are heated to 120°C, which is above the glass transition temperature of the polystyrene, kept at 120°C for 10 mins, and then uniaxially deformed. The ellipsoid aspect ratio is controlled by the strain of the uniaxial deformation.


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In this study, we produce ellipsoids of aspect ratio 2.4 ± 0.4 (major axis length = 1.9 ± 0.2, minor axis length = 0.8 ± 0.1), 4.8 ± 1.0 (major axis length = 2.8 ± 0.4, minor axis length = 0.6 ± 0.1), and 6.7 ± 0.8 (major axis length = 3.6 ± 0.3, minor axis length = 0.5 ± 0.04) by applying normal elongational strains (L/L0) of 0.38, 0.56, and 0.65, respectively. Once stretched, the oven is turned off, the films are allowed to cool, and then cut from the clamping apparatus. An approximately 1 cm long section at each end of the film is discarded to account for any inhomogeneous deformation in these regions due to clamping.

The

stretched films are suspended in DI water and sonicated in a bath sonicator (Branson Ultrasonics) for one hour.

The DI water is then exchanged 5 times

using centrifugation to remove the PVA from the particle suspension (5000G for 10min). The suspension of ellipsoids is then solvent-exchanged with 200 proof ethanol (E7023, Sigma-Aldrich) using centrifugation. These ellipsoids are spin-coated (WS400B-6NPP, Laurell) onto a glass microscope slide (glass coverslip, 35 mm × 50 nm × 0.13 mm, Fisher Scientific) at 300 rpm for 20 s, then 3000 rpm for 20 s.


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Next, a 20 nm layer of platinum is deposited along the ellipsoid’s long axis via physical vapor deposition (PVD) using an e-beam evaporator (Denton Vacuum). Scanning electron microscopy (SEM) images (Philips XL-30 FEG) of the Janus ellipsoids of different aspect ratios are shown in Figure 1(a-c).

Figure 1. Micrographs of polystyrene colloidal ellipsoids coated with a 20 nm platinum layer along one-half of the major axis. The aspect ratio (AR) of the fabricated Janus ellipsoids shown in the SEM images are (a) 2.4 ± 0.4, (b) 4.8 ± 1.0, and (c) 6.7 ± 0.8.

The brighter half of the particle is the side with the

platinum coating. (d) Two-channel overlay CLSM image of Janus ellipsoid with platinum (green) and polystyrene (red). Scale bars are 1 µm (a-c) and 3 µm (d).


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2.2. Janus Particle Self-Propulsion. Experiments are conducted in Lab-Tek™ II 8-well chambered cover glass (155409, Fisher Scientific). The wells are precleaned in a photosensitized oxidative chamber (Jelight UVO Cleaner) for 20 min. 150 µl of the polystyrene/platinum particles in DI water are transferred to the well; the particles are allowed to sediment for one hour. An equal volume of hydrogen peroxide solution is then added and allowed to mix. The final concentration of the hydrogen peroxide solution is between 2-8% (w/v). 2.3. Confocal Laser Scanning Microscopy.

Janus particle dynamics are

observed by confocal laser scanning microscopy (CLSM, Nikon A1R).

Time

series of CLSM images were acquired with a 100×, 1.4 NA, oil immersion objective.

The platinum cap of the Janus ellipsoid is imaged in reflection mode

with a 488 nm laser, and the fluorescent polystyrene is imaged with a 561 nm excitation and emission band of 570 to 620 nm. The combined two-color image of a Janus ellipsoid is shown in Figure 1d.

The platinum side of the Janus

ellipsoid is colored green; the fluorescence of the polystyrene is colored red. 256 x 256 square pixel images were recorded for 30 seconds at a rate for 30 frames


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per second. A set of reference images of spheres and ellipsoids immobilized on the surface were used to determine the static error20 of the imaging system. 2.4. Image Analysis and Particle Tracking.

The centroids and orientation of

particles recorded in each frame are determined in ImageJ and analyzed in Matlab. The 2D time series of CLSM images are processed in ImageJ by first performing a threshold sweep of the pixel intensity, then applying appropriate size (squared pixel area) and circularity parameters ranging within 0 – 1, to discriminate the particles from image noise and the occasional debris. These steps resulted in identification of particle centroids and angular orientation (for the ellipsoids) with respect to the lab view plane in each frame, as shown in Figure 2. Figure 2(a,c) are CLSM images and Figure 2(b,d) overlay images after image analysis with detection parameters based on pixel size and particle eccentricity. As shown in Figure 2b, we detect spheres (blue) while excluding the occasional dimer and other non-circular shapes (black). We furthermore correctly detect the 2D motion and orientation of ellipsoids while excluding the occasional debris and other circular shapes, also distinguished by the color (Figure 2d).


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Figure 2. Images of Janus spheres and ellipsoids in suspension. CLSM images identify the (a) Janus spheres and (c) Janus ellipsoids. Image processing software can identify particles based on pixel size and eccentricity for (b) spheres and (d) ellipsoids. All scale bars are 10 µm.

The particles are linked from frame to frame to identify individual trajectories using an open source image-processing code Simple Tracker21. The centroid and orientation data determined in ImageJ is transferred and processed in Matlab. The code is set to link particles with a centroidal distance of 3 μm or less from frame-to-frame, a distance appropriate for the dilute concentrations of this study. Particles are permitted to move out of frame for up to five consecutive frames and still be assigned as a continuous particle trajectory. We apply the same linking routine to the


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reference image series of immobilized spheres and ellipsoids to characterize the static error in the imaging system.

3. RESULTS To establish the performance of the fabricated particles and the imaging system, we first characterize the dynamics of spheres (both passive and active).

Figure

3 compares the mean-squared displacement (MSD) of dilute suspensions of polystyrene spheres in water, Janus spheres in water, and Janus spheres in 8% (w/v) hydrogen peroxide solution.

All displacements measured are well above

the static error of the imaging system.

The plots show the MSD, 〈Δ𝑟2(Δ𝑡)〉 =

〈[𝑟(𝑡 + Δ𝑡) ― 𝑟(𝑡)]2〉, of all identified particles. The isotropic spheres in water are diffusive with a diffusion coefficient D = 0.40 µm2/s. The Janus spheres in water (with no added fuel) show a MSD with D = 0.42 µm2/s. The expected value for these particles, from the Stokes-Einstein equation, is D = 0.46 µm2/s. These


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experiments therefore agree with the theory; the relative deviation is 𝜂 = 0.14 for isotropic spheres and 𝜂 = 0.095 for Janus spheres. As described in Howse et al5, active Janus spheres exhibit complex dynamics in which the MSD transitions from primarily ballistic behavior at short times to effective diffusion at long times. The characteristic time scale for the transition from ballistic motion to effective diffusion is the inverse of the rotational diffusion coefficient, 𝜏𝑅―1 = 𝑘𝐵𝑇 𝜉𝑅, where the friction coefficient 𝜉𝑅 varies with particle shape and dimension22. To further quantify the dynamics of these spheres, we fit the results to the following equation for active motion, valid a short times: 〈Δ𝑟2(Δ𝑡)〉 = 𝑣2∆𝑡2 +4𝐷∆𝑡 and at long time scales: 〈Δ𝑟2(Δ𝑡)〉 = (4𝐷 + 𝑣2𝜏)∆𝑡. Here 𝑣 is the average velocity of the particles. By applying these expressions, Janus spheres in 8% hydrogen peroxide (H2O2) yield a fit of D = 0.60 µm2/s, an average velocity, v = 1.9 µm2/s, and characteristic time scale  = 1.8 s. These values are consistent with literature values. For example, for a 1.0 micron Janus sphere with a 5 nm thick platinum layer in 10% H2O2, Howse et al. report D = 0.31 µm2/s, v = 3.1 µm2/s, and  = 3.9 s. Given that our system has lower hydrogen peroxide concentration with a thicker platinum coating, a higher effective diffusivity but decreased velocity and characteristic time scale are consistent with the literature11,12.


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Figure 3. Mean squared displacement of spheres in water and in 8% (w/v) aqueous

hydrogen

peroxide

solution.

The

MSD

〈Δ𝑟2(Δ𝑡)〉

of

Brownian

homogeneous PS spheres, Brownian PS-Pt spheres and active PS-Pt spheres in the aqueous solution of hydrogen peroxide are plotted. The error bars are not easily visible because they are small with respect to the average value and datum point size.

The active motion of Janus ellipsoids in an aqueous suspension of 8% H2O2 solution is reported in Figure 4. It is representative of the Janus ellipsoid dynamics in that it displays trajectories that


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vary considerably in the degree of translation and rotation both from particle to particle and for any given particle over time. Figure 4 shows frame-to-frame micrographs, a temporal projection, and a centroidal trajectory of a representative ballistic ellipsoid (a-c) and a representative spinning ellipsoid (d-f). Figure 4a is a time-lapse montage of a ballistic ellipsoid moving right to left in a span of approximately 2 sec. Figure 4b shows the overlapping micrographs depicting translational and (some) rotational motion of the ballistic spheroid. Figure 4c shows the overall centroidal trajectory; over this period the trajectory is ballistic, with minimal reorientation observed. Figure 4d is a time lapse montage of a spinning ellipsoid rotating clockwise for a span of approximately 1 sec. Figure 4e is a temporal projection of the frames in Figure 4d; the projection indicates that the spinning ellipsoid completes ~1.6 rotations in approximately 1 sec. Figure 4f shows the overall centroidal trajectory with minimal translation observed. The projections of the ballistic and spinning ellipsoid confirm that the particles propel in a direction perpendicular to the major axis of the particle.


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Figure 4. CLSM images and centroidal trajectories of Janus ellipsoids in motion in 8% hydrogen peroxide. (a) Time series images of a Janus ellipsoid exhibiting primarily translational motion (ballistic) in ~2 min with (b) a superimposed time lapse image of the particle and (c) the complete trajectory for the ballistic particle. (d) Time series images of a Janus ellipsoid exhibiting a primarily rotational motion (spinning) in ~ 1 min with (e) a superimposed time lapse image of the particle and (f) the complete trajectory for the spinning particle. All scale bars are 5 µm.

In this study, numerous particles show ballistic (i.e. linear translational) trajectories, with motion perpendicular to the major axis of the particle. Another set of trajectories show very little translation, but significant rotation. Such particles, which we refer to as spinners, are primarily situated at a particular location while rotating. Other particles show trajectories intermediate between these two regimes with a transition from one limit to the other occurring over time. Inspection of these active particles in 8% hydrogen peroxide intermediate trajectories shows the intermittent nature of the transition from ballistic to spinning particles, and vice versa. The abundance of these transitional particles would be expected to vary with particle concentration as they appear to be consequence of stochastic effects and particles otherwise interrupted in their ballistic or spinning modes by interactions with approaching particles. To characterize the effect of particle shape on active motion, we compare average measures of centroidal displacement and angular rotation. As shown in Figure 5, 𝑟(∆𝑡) gives the displacement


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of the ellipsoid over a time interval, Δ𝑡 = 𝑡1 ― 𝑡0, from the laboratory frame centroid positions of the ellipsoids given by (𝑥0, 𝑦0) and (𝑥1, 𝑦1). The orientation of the ellipsoid, 𝜃, is defined as the angle between the vector 𝑢 normal to the particle’s major axis and a vector defining the laboratory 2

reference frame. The angular displacement is the given by the MSAD relation, 〈Δ𝜃 (Δ𝑡)〉 =

〈[𝜃(𝑡 + Δ𝑡) ― 𝜃(𝑡)]2〉.

2

The MSD 〈Δ𝑟2(Δ𝑡)〉 and MSAD 〈Δ𝜃 (Δ𝑡)〉 are calculated for two-

dimensional translation motion and rotational motion, respectively.

Figure 5. Schematic of the hypothetical orientation of a single ellipsoidal particle and the dynamics over a time interval. The parameters shown are used to characterize centroidal particle displacement of the two-dimensional translational motion. In addition, the two-dimensional angular displacement is determined by change in orientation angle with respect to laboratory reference frame. Variables are as defined in the text.


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Figure 6. Mobility of Janus ellipsoids (AR = 6.7 ± 0.8) in 8% hydrogen peroxide solution. The linear MSD 〈Δ𝑟2(Δ𝑡)〉 of (a) selected particles for three identified types of mobility (details of trajectory selection are described in the text). A loglog plot of (b) 〈Δ𝑟2(Δ𝑡)〉 compares the translational motion and (c)

〈Δ𝜃2(Δ𝑡)〉

compares the rotational motion, of ballistic and spinning ellipsoids referencing a slope = 1. The error bars reflect an average of 5 particle trajectories; in some cases they are not easily visible due their size with respect to the averaged values and datum points.

In the characterization of centroidal displacement and angular motion, the ellipsoidal particles exhibited varied active motion with the same experimental sample. Figure 6 shows the measured MSD of particles with similar behavior to the complete trajectories presented in earlier (Fig. 4), in addition to a group of transitional ellipsoids that fall within the limits of ballistic and spinning particles. Particles were analyzed within the confines of a set spatial scale of CLSM images and/or a minimum of 5 secs of continuous data of the approximately 30000


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frames (recordings of 30 secs at a rate for 30 fps) collected in each experiment. We analyze five particles within each of the three grouping (ballistic, spinning, and transitional); Figure 6a illustrates the differentiated MSD of observed trajectories. At short times, the translational motion of ballistic ellipsoids yields a rapidly increasing MSD, but at long times, this class of active ellipsoids has moved out of the imaged region.

The sublinear MSD of the spinners is

functionally different than the ballistic particles and their trajectories differ substantially from the expanded random walk reported for spheres.

These

spinners have a squared displacement at five seconds that is equivalent to what ballistic ellipsoids attain in less than 0.30 seconds.

The MSD of transitional

ellipsoids exhibits a combination of these ballistic and spinning features. Transitional ellipsoids can spontaneously evolve from a dominantly translational motion to a rotational trajectory or as a result of an impetus, e.g. a collision with another particle. For these particles, at short time scales (t < 1 s) the particle MSD is parabolic – characteristic of ballistic motion – but at longer times, as spinning

motion

intermittently

occurs,

the

displacement


becomes

variable.

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Because these trajectories are a mix of the two limiting cases of ballistic and spinning, we continue further analysis only for the two limiting classes.

The

relative abundances of the three trajectory types, and the nature of the transitions among them, should be the subject of future work. The power law slope of the MSD behavior for ballistic ellipsoids is nearly two, consistent with pure rectilinear motion; the MSD scaling with time for the spinning ellipsoids approaches unity – a value consistent with Brownian translation (Figure 6b). In addition, the MSAD behavior of the same set of ballistic and spinning ellipsoids shows the mobility of the spinning ellipsoids is better represented as active with a power law slope of 1.9 while the plot shows on average ballistic ellipsoids exhibit minimal rotational motion with a power law slope of 1.3 (Figure 6c). The deviation of the slope of the ballistic MSAD from unity is consistent with the presence of rotational motion, even though it is not dominant.

This rotation

leads to directional changes in ballistic trajectories. Conversely, the spinner’s MSAD

slope

of

approximately

two

indicates

that

these

particles

rotate

continuously. Note that these spinning particles are not permanently fixed to the


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substrate; this was confirmed both by the fact that their MSD is measurable and that they sometimes transition from spinner to ballistic trajectories.


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Figure 7. Active motion of Janus ellipsoids with various aspect ratios in 8% hydrogen peroxide solution. (a) The MSD for ballistic particles and (b) the MSAD for spinning particles as function of particle aspect ratio. The error bars reflect an average of 5 particle trajectories; in some cases the error bars are not easily visible due to their size with respect to the averaged values and datum points.

The effect of aspect ratio on the translational and rotational motion in 8% hydrogen peroxide solution is plotted in Figure 7. The MSDs of ballistic trajectories of the aspect ratio 2.4 and 4.8 Janus ellipsoids (Figure 7a) are comparable to each other and significantly less than for the largest aspect ratio of 6.7. The MSAD (Figure 7b) of the spinning Janus ellipsoids behaves similarly with power law slopes of the angular displacement of the three aspect ratios – 2.4, 4.8, 6.7 – being 1.8, 1.9, and 1.9, respectively.

These power law slopes showing higher

than unity, are consistent with sustained, rather than random, rotation of the ellipsoids. The spinning state of the ellipsoids persists for many seconds, longer than the characteristic time for rotational diffusion.


Janus ellipsoids of AR = 6.7

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exhibits approximately twice the squared rotation on the same time scale compared with AR = 2.4 particles. At short time scales, particles of AR = 4.8 exhibit similar MSAD to AR = 6.7, but at longer time scales, the particles behave as AR = 2.4 particles. We estimate the velocity for the ballistic ellipsoids using the same short-time equation for spheres. To apply the equation to ballistic ellipsoids, the (Brownian) diffusion coefficient is first computed from theory23 before a single parameter fit is applied to determine the translational velocity shown in Table 1. The spinner rotation is modeled using the MSAD relationship of 〈Δ𝜃 (Δ𝑡)〉 = 𝜔2∆𝑡2 +2𝐷𝑅∆𝑡 as 2

done by Ebbens et al24. For each particle aspect ratio, 𝐷𝑅 and 𝜔2 are determined from a parameter fit of the MSAD equation to experimental measurements (Table 1). From the translational and angular velocities, we can calculate the force acting on ballistic ellipsoids and the torque acting on spinning ellipsoids, respectively. Recall that the ellipsoids are observed to displace in a direction normal to the major axis of the ellipsoid; the active force normal to the major axis is given by25:


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(1)

𝐹 = 6𝜋𝜇𝑎𝑣𝐶1

where the viscosity 𝜇, and a geometric factor 𝐶1, related to the ellipsoid eccentricity 𝑒 = 1 ― 𝑏2 𝑎2, are used. The torque on the spinning ellipsoids is a function of 𝜇, 𝜔, and is scaled by the major axis 𝑎, the minor axis 𝑏, and a geometric factor also related to 𝑒25: (2)

𝛵 = 8𝜋𝜇𝑎𝑏2𝜔𝐶2 The coefficients C1 and C2 are:

[

16 1+𝑒 𝐶1 = 𝑒3 2𝑒 + (3𝑒2 ― 1)ln 3 1―𝑒

]

―1

( )[

4 2 ― 𝑒2 1+𝑒 𝐶2 = 𝑒3 ―2𝑒 + (1 + 𝑒2)𝑙𝑛 2 3 1―𝑒 1―𝑒

(3)

]

―1

(4)

The tabulated data for ellipsoids of the various aspect ratios and trajectory types are reported in Table 1.

Table 1. Characteristics of active motion in ballistic and spinning ellipsoids as a function of aspect ratio in 8% hydrogen peroxide solution

AR = 2.4 ±

AR = 4.8 ±

AR = 6.7 ±

0.4

1.0

0.8

𝟐 Pt surface area (𝝁𝒎 )

2.0

2.1

2.2

𝒆

0.91

0.98

0.99

𝑪𝟏

0.64

0.49

0.42

𝑪𝟐

1.8

4.2

8.0

𝑫𝑻 (𝝁𝒎𝟐/𝒔) ― 𝒄𝒂𝒍𝒄.

0.38

Ballistic Ellipsoids 0.34

0.31

𝒗 (𝝁𝒎/𝒔) ― 𝒇𝒊𝒕 𝒖𝒎 𝑭 𝒌𝒈 ∙ 𝟐 ― 𝒆𝒒𝒏 (𝟏) 𝒔

)

1.80

2.16

10.0

3.85 x10-8

5.17 x 10-8

2.67 x 10-7

𝑫𝑹 (𝒓𝒂𝒅𝟐/𝒔) ― 𝒇𝒊𝒕

1.27

𝝎 (𝒓𝒂𝒅/𝒔) ― 𝒇𝒊𝒕

2.43

(

Spinning Ellipsoids 0.49

3.35

2.32

4.93


27


(

𝜯 𝒌𝒈 ∙ 𝝁𝒎𝟐 ∙

)

𝒓𝒂𝒅 𝒔𝟐

― 𝒆𝒒𝒏 (𝟐)

1.24 x 10-7

2.32 x 10-7

Page 28 of 45

8.33 x 10-7

For Janus spheres in 8% hydrogen peroxide solution, the estimated platinum coverage is 1.6 µm2, calculated diffusion coefficient, D = 0.46 µm2·s-1, estimated velocity, v = 2.2 µm·s-1, and estimated force, 1.9 x10-8 kg·um·s-2.

The parameters characterizing active motion can be compared to geometric descriptors of the ellipsoidal particles (Table 1). The table shows that the amount of platinum surface coverage increases as aspect ratio is increased. The surface area of ellipsoids is greater than spheres by 22%, 27% and 31% for AR = 2.4, 4.8 and 6.7, respectively. This increased platinum coverage likely increases the overall rate of catalytic decomposition of hydrogen peroxide. In terms of particle shape, there is a 7.4% difference in eccentricity from ellipsoids with AR = 2.4 to 4.8, but only a 1.0% difference from AR = 4.8 to 6.7. The ballistic and spinning dynamics are both comparable for AR = 2.4 and 4.8 ellipsoids. However, for AR = 6.7 these dynamics are significantly enhanced relative to the lower aspect ratio particles. The translational velocities are comparable for spheres and ellipsoids with AR = 2.4 and 4.8, but significantly higher for AR = 6.7.

Likewise, the computed active forces increase with aspect


28

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ratio.

With the spinning ellipsoids, there is no significant difference in angular

velocities between AR = 2.4 to 4.8; however, the angular velocity doubles for AR = 6.7 with 4.93 𝑟𝑎𝑑 𝑠. The torque derived from these measurements displays an equivalent trend.

4. DISCUSSION This study has shown that active Janus ellipsoids undergo motion that spans between two limits. trajectories.

These limits are referred to as ballistic and spinning

Measuring the translational and rotational velocities for these two

cases enables the characterization of the active force and torque generated by the propulsion.

Here we discuss potential mechanisms for the ballistic and

spinning motion. Transition between these two limits could be generated by the stochastic effects of Brownian motion or by interactions with other Janus ellipsoids. Such transitions could act to generate the distribution of trajectories that are observed between the two limiting cases.


29


Page 30 of 45

In our findings (Supplementary Movie 1), the propulsive motion is perpendicular to the major axis of the ellipsoid, however the orientation of the platinum Janus face of the particle relative to the direction of motion is inconclusively known. This inconclusive determination of the orientation of the propulsion is a consequence of the platinum coverage along the hemispheroidal surface that runs along the major axis and wall effects. As the perpendicular motion persists, particles show some spontaneous tilting that cause fluctuations in the intensity of polystyrene and platinum hemispheres in the two-color confocal images. However, the direction of the ellipsoids is suggestive that the mechanism for the active motion is similar to that spheres. For Janus spheres, catalytic decomposition of hydrogen peroxide at the platinum surface is thought to generate concentration gradients in species density.

These gradients drive solute advection that

generates self-diffusiophoretic motion of the colloid. Observing the ellipsoids move perpendicularly to the particle asymmetry suggests that advection is the cause of the active motion.


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While the translational displacement and active force of the ballistic trajectories appears analogous to the case of Janus sphere propulsion, our characterization of propulsive torque for the class of spinning trajectories appears different. First, there is no significant translational component to this mode active motion. Indeed, the trajectories appear qualitatively different than the expanded random walks that have been characteristic of active particle motion observations to date. Instead, the spinning trajectory type seems more related to the rotational motion of Janus dimer and trimer particles has been previously observed6,24.

The rotational

motions in such clusters are thought to be the consequence of the Janus sphere configuration and orientation in the cluster. If the spheres are configured in antisymmetric orientations, translational displacement is frustrated because the active force of each particle is cancelled out by the others. In some cases (e.g. trimer clusters) although active forces cancel, but active torques do not. These particles then rotate but do not translate. Although full understanding of the purely rotational trajectories (i.e. spinners) must await theoretical analysis that is beyond the scope of the present


31


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communication, here we evaluate a number of hypotheses vis a vis the measurements. First, the rotation could result from asymmetric deposition of platinum or asymmetric shape of the particle itself. The explanation seems unlikely because of this work’s observation that any given particle will from time to time transition between the ballistic and spinning trajectory states. Asymmetry of the particle produced at the time of synthesis would more likely yield particles that were either always in the ballistic state or always in the spinning state.

Although

asymmetry across the minor axis seems an unlikely explanation for the spinning trajectory, we note that symmetric differences in platinum thickness from the center to the tip of the ellipsoid could result from the method of production. Such a gradient in platinum deposition thickness would depend on aspect ratio, and represent a difference between ellipsoidal and spherical Janus particles. Second, the proximity of the ellipsoids to the substrate could affect the solute concentration gradients that drive the self-diffusiophoretic motion. Specifically, as the hydrogen peroxide is consumed to produce water and oxygen, there are two


32

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competing gradient profiles across the anisotropic particle. The concentration gradient of chemical products is depicted in Figure 8.

The catalytic conversion

of hydrogen peroxide at the active platinum surface leads to a higher concentration of products and a lower concentration of reactants at the platinum cap than the polystyrene surface; this gradient is the origin of the phoretic motion. For the case of spheres in an unbounded fluid, the direction and magnitude of motion is set by the surface fraction of the sphere that is catalytically active, the strength of the interaction between solute and colloid, the solute diffusivity, and the reactant concentration26. Proximity to a substrate can lead to skimming and stationary states, depending on the surface fraction of the Janus colloid that is capped.

The present work introduces the possibility that particle shape affects

solute concentrations gradients analogously to how platinum surface area affects Janus sphere motion.

A key difference for the Janus ellipsoids is the stable

rotational state; with Janus spheres the state lacks both translation and rotation. In addition, the work suggests that sufficient anisotropy of the platinum layer can lead to a range of trajectories.


33


Page 34 of 45

Third, effects on hydrodynamic drag due to the proximity of colloid and substrate could play a role in the observed dynamics. Unusual dynamics of ellipsoids and other anisometric particles in the vicinity of substrates has been well documented. For example, in a simple shear flow system, the wall effects of elongated particles decrease as the particle shape deviates from a sphere and the reverse is true for torque. Therefore, ellipsoids have a propensity for oscillating towards and away from the wall in a way that is aspect ratio dependent27.

In addition,

swimming rods have exhibited hydrodynamic interactions so as to generate circular trajectories28. A decreased wall effect due to aspect ratio could explain why particles with the highest aspect ratio in this study had the highest ballistic velocity and how, in the case of spinning ellipsoids, oscillation could induce asymmetric lubrication flow. A central feature of the rotating trajectories is that they are limited to high aspect ratio.

There is no indication of rotation in Janus spheres or the low

aspect ratio ellipsoids that were studied. Thus, it appears likely that the spinning state is a consequence of the combined effects of the Janus ellipsoidal shape,


34

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the particle’s close proximity to the substrate, and the effect of these two on solute gradients generated by the H2O2 decomposition.

The confinement can

affect the gradients in product and reactant concentrations relative to the unbounded cases; it furthermore affects the hydrodynamic drag.

Further

investigation is warranted to understand if these effects can lead to the unbalanced forces and torques that would be necessary for the observed ballistic and spinning states in the Janus ellipsoids.


35


Page 36 of 45

Figure 8. Schematic of the hypothetical mechanism for active Janus ellipsoid rotation near the coverslip, showing the potential for unbalanced gradients in species concentration and in hydrodynamic drag.

In conclusion, the active motion of Janus particles has previously been found to depend on particle size, shape, and platinum coating thickness. The present work adds particle shape as an additional determinant of propulsion and trajectory. Specifically, there are strong effects of particle geometry on translational and rotational active motion; these effects yield a complex set of trajectories that are distributed

between

translationally

and

rotationally

dominant

limits.

The

measurements reported here demonstrate that ballistic and spinning ellipsoids each experience both translational and rotational motion. However, the relative magnitude of these two contributions varies considerably. In addition, we observed transitions between these two states within the same trajectory; the transitions were either spontaneous or induced by interactions with surrounding particles. Future work could address the fundamental origin of the stable spinning, the


36

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conditions under which transitions between the ballistic and spinning states are induced, the conditions for stability of the two different trajectory states, and the potential utilization of the spinning trajectories for applications in actuation, transduction, and assembly.

ASSOCIATED CONTENT

Supporting Information. Supplemental Movie 1. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION

Corresponding Author

*Email: [email protected]

Notes

The authors declare no competing financial interest.


37


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ACKNOWLEDGEMENTS

This work is supported in part by the University of Michigan Rackham Merit Fellowship, the U.S. Army Research Office under Grant Award W911NF-10-10518, and the NSF under Grant Award CBET-1702418.

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Self-Propulsion and Active Motion of Janus Ellipsoids - The Journal of

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