Rotational Analysis of Spherical, Optically Anisotropic Janus Particles

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Rotational analysis of spherical, optically anisotropic Janus particles by dynamic microscopy Andrew Wittmeier, Andrew Leeth Holterhoff, Joel Johnson, and John G. Gibbs Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.5b02864 • Publication Date (Web): 09 Sep 2015 Downloaded from http://pubs.acs.org on September 12, 2015

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Andrew Wittmeier,1 Andrew Leeth Holterhoff,1 Joel Johnson,1 and John G. Gibbs1,2,* 1Department

of Physics and Astronomy for Bioengineering Innovation Northern Arizona University S San Francisco St, Flagstaff, AZ, USA 86011 2Center

*[email protected]

We analyze the rotational dynamics of spherical colloidal Janus particles made from silica (SiO2) with a hemispherical gold/palladium (Au/Pd) cap. Since the refractive index difference between the surrounding fluid and a two-faced, optically anisotropic Janus microsphere is a function of the particle’s orientation, it is possible to observe its rotational dynamics with bright-field optical microscopy. We investigate rotational diffusion and constant rotation of single Janus microspheres which are partially tethered to a solid surface so they are free to rotate but show little or no translational motion. Also, since the metal cap is a powerful catalyst in the breakdown of hydrogen peroxide, H2O2, the particles can be activated chemically. In this case, we analyze the motion of coupled Janus dimers which undergo a stable rotary motion about a mutual center. The analysis of both experimental and simulation data, which are microscopy and computergenerated videos, respectively, is based upon individual particle tracking and differential dynamic microscopy (DDM). DDM, which typically requires ensemble averages to extract meaningful information for colloidal dynamics, can be effective in certain situations for systems consisting of single entities. In particular, when translational motion is suppressed, both rotational diffusion and constant rotation can be probed.

KEYWORDS: Janus sphere, differential dynamic microscopy, active colloid, chemical propulsion

■ INTRODUCTION There is renewed interest in colloidal dynamics1-5 with the surge of recent research in actively driven colloidal particles. 6 This is true for a number of reasons: diffusion can be used for the selfassembly of nanoparticle systems,7,8 active non-equilibrium colloids undergoing enhanced diffusion exhibit novel physics,911 and it is possible to use diffusion to investigate microrheology,12-15 just to name a few examples. In order to accomplish these goals, one must exert some level of control over systems undergoing active mobility and diffusion, driving the necessity to understand colloidal dynamics both in and out of equilibrium. Therefore, it is important to develop techniques which allow high throughput analysis for systems of this type. A new class of particle, which has been highly investigated of late, consists of two faces; these are termed Janus particles.16,17 Because each face of a spherical Janus particle has different properties, it is possible to impart multiple

functionalities onto a single geometrically isotropic architecture. In this study, we take advantage of the fact Janus particles are optically anisotropic, allowing for the observation of rotational motion. We compare particle tracking with a microscopy technique called differential dynamic microscopy (DDM), which is a crossover of particle tracking and dynamic light scattering (DLS). Also, since the gold palladium (Au/Pd) metallic alloy cap catalyzes the decomposition of hydrogen peroxide (H2O2), the particles will be actively propelled when this fuel is present. We focus on a stable configuration in which two coupled dimer Janus particles rapidly spin around a mutual center. The active spinning dimers rotate at roughly a constant frequency, and we are able to extract this rotation rate with DDM, showing the technique is complimentary to tracking algorithms. Both rotational diffusion as well as constant rotation, including propelled spinning dimers, are compared with simulations. If a colloidal particle is shape anisotropic, 18 or if a spherical


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particle has a refractive index anisotropy, rotational diffusion can be measured.19-21 Single-particle tracking of both translational and rotational motion of Janus spheres was presented by Anthony et al.,22 and a similar study to the one herein was reported using single magnetic colloidal Janus spheres; in the latter, the diffusion was constrained to one axis, i.e. one-dimensional (1D) diffusion, by an external magnetic field applied to a Janus particle with a permanent magnetic moment.23 Fluorescent Brownian modulated optical nanoprobes (MOONs) were also implemented to study Brownian rotational diffusion.24 The purpose of this report is to show it is not only possible to obtain rotational dynamics of spherical particles and dimers using a tracking algorithm, but a technique, which is analogous to DLS yet only requires a microscope and a camera, can be used to derive the same information, i.e. DDM.25-30 DDM has successfully been used for measuring ensemble averages for Brownian diffusion, along with several other systems, such as the dynamics of anisotropic colloids29 in which diffusion parallel and perpendicular to the axis of magnetized ellipsoidal colloids was investigated. Here we show it is possible to measure individual systems undergoing rotational motion with DDM and compare those results with particle tracking and simulations. DDM is therefore complementary to single-particle tracking for investigating rotational diffusion, and may in some cases be the preferable method. DDM for rotating objects could potentially be useful for probing a number of microscopic systems, and one example we focus upon is the retrieval of the rotational diffusion coefficient for single Janus particles which display little translational motion. However, the method is potentially useful for any system in which translational motion is suppressed due to its high-throughput nature, the simplicity of the technique, as well as the ability for most labs to implement DDM, which requires only standard laboratory equipment. Other systems could potentially take advantage of the technique for investigating the rotational Brownian motion of tethered nanowires, 31,32 probing the relaxation times of hinged magnetic/plasmonic nanorods after an external field is applied,33 or in the case of constant rotation, studying the dynamics of silicon nanowires driven by an A/C electric field.34 As another example, it was recently shown an optically isotropic microbead tethered to DNA could be used to probe local bending of the molecule. 35 If the bead were replaced by a Janus particle, then the response to a torque applied to the DNA, via the microbead, either by an external field or by thermal fluctuations (rotational diffusion), could be investigated. ■ MATERIALS & METHODS The fabrication process for the Janus particles can be seen in Figure 1. First, 2µm monodisperse SiO2 beads, obtained from Corpuscular Inc. 3590 Route 9, Suite 107, Cold Spring, NY 10516, were deposited onto clean Si(100) wafers by drop casting mixtures of beads and ethanol (1:5). Next, a thin layer of ~2nm of titanium (Ti) was deposited by thermal evaporation (Varian 3117) on top of the sub-monolayer. We then sputtered ~5nm of an Au/Pd alloy onto the Ti layer, shown schematically in the top of Figure 1, with a Denton Desk II Sputter Coater, which we obtained permission to use at the Imaging and

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Histology Core Facility of NAU. The Ti and the Au/Pd alloy coated only the top of the particles leading to half-coated microbeads with a metallic hemispherical cap. This method is one of the most popular routes for obtaining Janus particles although the yield tends to be quite low. Since the number of particles necessary to carry out these experiments is small, i.e. only individual particles were needed, we were not concerned with the overall yield of the manufacturing process. After deposition, we removed the Janus particles by submerging the substrate into a beaker filled with pure 18 MΩ H2O and placed the beaker into a sonication bath for 30 – 60s. We found this amount of time sufficient to remove an ample amount of particles from the surface without causing the metal caps to separate from the beads, which was observed when sonicating for longer periods. The optical microscopy image in the bottom-left of Figure 1, taken with a Keyence VHX-2000

Figure 1. The fabrication of Janus particles: a partial monolayer of SiO2 microbeads of 2μm diameter is dispersed onto an Si(100) wafer. An Au/Pd alloy is then sputtered onto the monolayer as seen in the top schematic. An optical micrograph showing this partial monolayer after the deposition is shown in the bottom-left; the bottom-right shows an SEM image of a single bead with scale bar = 500nm. The lighter color is the metal. An artificial Janus particle showing the location of the alloy (right) and the dielectric SiO2 (left) is shown to the left of the SEM image.

digital microscope at the NAU Imaging and Histology Core Facility, shows the beads on the wafer after the deposition, but before sonication. The sonication process releases the Janus particles into a colloidal suspension. The particles do not remain suspended as the metal cap causes them to settle under gravity very rapidly. An individual Janus particle with two hemispheres of SiO2 and Au/Pd is shown both schematically and by scanning electron microscopy (SEM) in the bottommiddle and bottom-right of Figure 1, respectively. The SEM image shows that the hemispherical metal caps are not always perfectly hemispherical but can have imperfections as visible in the image. The colloidal Janus spheres were observed by bright-field optical microscopy in pure H2O and in weak H2O2 environments, depending upon the experiment. The colloidal suspension was sealed with a clean glass coverslip, and the

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slides used as the bottom of the cell were cleaned with O2 plasma before each experiment as well. The colloids were imaged with a 100× oil immersion objective with numerical aperture NA = 1.25 or a 40× dry objective. The AmScope Trinocular Advance Darkfield Compound LED Microscope was coupled to a digital MU1400, 14MP CMOS camera, and videos were taken at ~11 frames per second (fps). For the actively driven system, 5% H2O2 was added to the catalytically active microspheres, and videos were recorded at 30 fps. The videos were processed using the tracking plugin called MTrack2 with the public image processing software, ImageJ. The software for DDM, as well as the simulation software, were custom designed in the laboratory. ■ RESULTS One-dimensional rotational diffusion of individual Janus spheres which are partially tethered to the surface was first observed. We then compare tracking to DDM & both methods give a consistent value for the rotational diffusion coefficient. Then rotational diffusion & constant rotation of individual Janus particles are simulated and compared with experiment. Finally, since we do not have a constant rotation experiment for individual particles, we observe actively propelled dimers which consist of two single Janus spheres rotating about a mutual center at roughly constant frequency. Rotational diffusion & particle tracking. A particle of this size undergoes reorientation in H2O as the result of the thermal motion of the surrounding H2O molecules and their collisions with the particle, or Brownian motion. We observed individual particles partially tethered to the surface so their orientation could be observed, rotation was not completely restricted, and little to no translational motion was present. Particles of this type, i.e. those which show little translational motion yet are free to rotate, made up only a fraction of the total observed ~5%. These particles were seen to be oriented with the plane separating the two hemispheres remaining perpendicular to the surface of the bottom of the cell, as shown schematically Figure 2(a). The objective is positioned directly above the particle, i.e. perpendicular to the observation slide, so that the two hemispheres are resolvable. The partially tethered Janus particles were observed to be situated this way exclusively and is also the reason diffusion was restricted to 1D. Since the underlying details for this effect are beyond the scope of the paper, we will not attempt to explain it here. However, a possible explanation is simply the van der Waals force. The other particles observed were either completely immobilized or were free to diffuse in the plane, i.e. they were confined to 2D by gravity. Although the heavy metal side tends to orient the particles metal-down, the latter were able to rotate with both degrees of freedom. We first present data for rotational diffusion of a single particle then give the average for several particles. In the brightfield microscopy video frames shown in Figure 2(c), the dark contrast displays the location of the metal coating. It is known the darker region is the metal hemisphere since bare beads were also observed, in which the light contrast was seen symmetrically around the entirety of the particle. The contrast arising from the difference between the refractive index of the

Figure 2. (a) a schematic which shows the orientation with respect to the bottom of the observation cell and the microscope objective. The top-right (b) shows the reorientation at an oblique angle. (c) shows video frames for the progression of Δt = 5s. The orientation of the Janus particle can be observed by focusing on the lighter region, over which the vectors are positioned. Over Δt, the orientation changes by Δθ, as shown to the right of the images. The row below (d) shows the same images converted to binary, used for tracking, with scale bar = 2μm. The curve on the right of the binary images (e) shows the to-scale rotational tracking trajectory for Δt = 25s. A larger version of the same trajectory, plotted in 2D with the axes in μm, is shown to the right. Each of the five colors in the plot show increments of 5s. The sequence of colors is the following: black, red, blue, green to cyan. The middle-right plot (f) shows the magnified translational motion of the bead.

metal and the surrounding fluid vs. the refractive index of the SiO2 and the surrounding fluid allows us to observe the particle’s orientation and therefore rotational motion. This contrast allowed us to investigate rotational diffusion using the particle tracking algorithm described in the previous section. This tracking procedure is graphically explained, in part, in Figure 2. In the bottom-left row of Figure 2(d), we show the same two images as the middle row, except they have been converted to binary for tracking. The dashed blue line through the center of these two images is intended to guide the eye showing the center of the particle has not moved significantly (in the vertical direction), i.e. there is no, or very little, translational diffusion. The trajectory shown on the right of the two binary images is the tracked movement of the dark spot, which is to scale with the images. This path sweeps out roughly a circle, as expected, and the colors in the plot display five separate 5s intervals, for a total of 25s: The sequence of colors is the following: black, red, blue, green to cyan. A larger version of this trajectory is presented in Figure 2(e). In order to be confident the tracking algorithm has returned reasonable results, we verified visually the initial and final angles are

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qualitatively consistent with the software’s output.

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Rotational diffusion is characterized by the decorrelation of the orientation vector, r(t). An example progression a single particle’s reorientation, shown over a time Δt = 5s, as indicated by the vectors r(t) and r(t+Δt), is shown in Figure 2. The topright schematic of Figure 2(b) shows this reorientation from an oblique point-of-view. In the left image of Figure 2(c), which is a single frame from a video, we consider the particle to be oriented in the direction r(t) at t = 0s. The frame to the right shows the particle at a later time, Δt = 5s, now with orientation r(Δt+t). The relative angle between the two vectors is indicated as Δθ shown to the right of the video frames. From this point on, we consider t = 0s and restrict our attention to Δt only. The angle of orientation was determined by calculating the scalar product of the two vectors, r(t)·r(Δt) = r(t)r(Δt)cos(Δθ), in which we fix the vector r(t=0s) as the initial orientation. For each subsequent frame, separated by 1/11s, a new vector r(Δt) is assigned. Since this method only determines the direction of each vector with respect to the original orientation, then the range of angles runs from 0 to π. Larger angles are unnecessary since the rotational diffusion coefficient was calculated for short time intervals only. A video of this particular particle and another video of several particles undergoing partially tethered rotational motion can be seen in the supporting information (SI) videos V1 &V2, respectively. Proper analysis of diffusive motion involves investigating the mean-squared displacement (MSD) and the mean-squared rotation (MSR), which are appropriate for translational and rotational diffusion, respectively. For the latter, the following equation,  2  2Dr t

(1)

valid for short times, allows for the calculation of Dr, the rotational diffusion coefficient. The plot in Figure 3(a) shows the MSR for the same single particle presented in Figure 2. The expected value for a spherical particle is Dr = kBT / 8πηr3, where kBT, η, and r are the thermal energy, fluid viscosity, and particle radius, respectively. Since the deposited metallic film is thin (< 10nm), we assume our Janus particles are very nearly spherical in shape, and so the equation is expected to hold approximately. This is important since morphology plays a major role at low Reynold’s number; i.e. the viscous drag dominates and inertia is ignored, so variations in shape will have significant effects. From the above equation and by using the following numbers kB = 1.38 × 10-23 m2kg/s2K, η = 8.90 × 10−4 Pa·s, T = 298 K, we expect the value of the rotational diffusion coefficient to be Dr = 0.18 rad2/s. Since the linearity of eq. (1) only holds for short times, as is seen in Figure 3(a), we only estimate the slope of the curve for 0 < Δt < 10s. In doing so, we find Dr = 0.19 ± 0.01 rad2/s, a close match to the expected value. Surprisingly, for this particular single particle, we are able to retrieve the correct value without taking into consideration steric or hydrodynamic effects. Hydrodynamic interactions with the surface of the cell should reduce the rotational diffusion coefficient.36 The measured value being close to the expected value for this single point is likely due to the limited data taken for this specific particle, i.e. the total length of the video. The slightly higher than expected value for Dr is possibly due to the large changes in orientation over short times during this video (SI video V1).

Figure 3. (a) Mean-squared rotation (MSR) for a single particle; (b) MSR for the average of ten individual particles.

The close match between the two values actually shows the limitation of measuring diffusion for a single particle. To retrieve a more accurate number, one should take sufficiently long videos of an individual diffusing Janus sphere or average the MSR of several separate particles; we performed the latter. The MSR of 10 particles, similar to the one shown in Figure 2, were averaged. The results are revealed in Figure 3(a). The data becomes noisier as Δt increases due to the smaller number of data points in the average. By fitting the curve from Δt = 0.1s to Δt = 10s we find Dr ~ 0.1 rad2/s for the average. The smaller value of Dr than what is expected far from the wall aligns better with expectations than what was measured for the single particle shown in Figure 3(b). Furthermore, when the data is fit to MSR ~ DrΔtα we find better qualitative agreement with α ~ 0.7. This may be indicative of rotational sub-diffusion37,38 which could be caused by the particles partially “sticking” to the solid surface39 consistent with partial tethering. There is slight translational motion which can also be tracked using the same algorithm. This motion arises not only from thermal agitation, i.e. translational Brownian motion, as well as incomplete adherence to the surface, but also from vibrations in the microscope-camera system. The plot of Figure 2(e) shows the tracked path of the translational movement on the same scale as the rotation, and there is also a zoomed-in version in the plot immediately above (Figure 2(f)). When the translational path is seen on the same scale as the rotational trajectory, which is itself significantly smaller than the particle diameter, it can be seen very little translational movement is occurring. This fact will be important when we utilize DDM as translational motion will also contribute to the signal, complicating processing. The ring shape seen in the zoomed-in translational trajectory in the plot of Figure 2(f) is a result of the way in which the tracking program locates the position of the entire particle minus the dark spot: The translational trajectory is the average position of the white pixels in the binary images. Therefore, the dark spot causes a slight offset from the true center of the particle, and thus the ring shape is an artifact of the tracking procedure. We next compare these results to a dynamic microscopy technique. Differential dynamic microscopy. A new microscopy technique called differential dynamic microscopy (DDM) is an analogue dynamic light scattering (DLS) method which uses only a light microscope, a camera for video capture, and appropriate software for video analysis and processing. The method is a sub-category of digital Fourier microscopy (DFM), which has been growing in popularity of late.30 DDM only

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requires basic equipment making it attractive since it can therefore be implemented in most laboratories. Furthermore, since the technique does not require one to resolve the sample, particles of sub-diffraction limit dimensions can be probed. We will not give a detailed background of the method here, as excellent references from the pioneers of the technique are available.25,26,28,30 However, we give a brief description. Video are captured by a microscope & camera system, just as is done for particle tracking. Indeed, the same videos are used for both methods in this study. A single video frame taken at time t is subtracted from a second frame separated from the first by time difference, Δt. This step eliminates the static signal, i.e.

simultaneously, which is advantageous for certain systems, e.g. swimming bacteria.26 The FFT of the difference images is then averaged for each Δt giving the differential intensity correlation function (DICF) FD q, t 

2

 Aq 1  f q, t   Bq 

(4)

in which A(q) depends upon the imaging system, and B(q) represents the camera noise. The function f(q,Δt), called the intermediate scattering function, must match the particular system of interest. For example,

f q, t   e  Dq t 2

(5)

describes translational diffusion of a monodisperse sample of spheres undergoing Brownian motion with a characteristic relaxation time of τ = 1/Dq2. Since the relaxation time is a function of q, the translational diffusion coefficient can be extracted, which was verified in the original description of DDM.25 DDM is generally used this way, i.e. to study ensembles of particles, but it can be also utilized for single rotating systems, as we show here. It is well known the reorientation correlation for rotational diffusion can be characterized by a single exponential decay

r(t )  r(t )  e l (l 1) Dr t

(6)

in which the brackets represent the ensemble average of the scalar product between the two orientations separated by Δt. Therefore, for an ensemble of particles undergoing rotational diffusion, we have Figure 4. (a) power spectra for a range of q values for a single rotating Janus particle; (b) characteristic decay time for the same particle showing roughly an average value of ~2.8s; (c) control experiment showing a randomly selected q value for a Janus particle (black curve) vs. a bare particle (red curve); (d) the averaged power spectrum for 10 (experimental) particles. The red curve gives the fit of Eq. (4) giving a value of Dr = 0.1 rad2/s

single camera pixels which register the same value (between 0 & 255) in both frames. However, for a video capturing diffusive motion, the difference signal given by

DI r(t )  I r(t )  I r(t ) (2) where I is the light intensity at r = r(x,y) on the sensor plane, increases with Δt. This signal will increase until saturation is reached,25 and the characteristic time at which this saturation is reached depends upon the dynamics of the sample in question. A radially averaged Fourier transform FD q, t    DI r, t e iqr dr

(3)

is taken of the difference signal where q is the scattering wave vector on the image plane, defined by the location of the sensor, or camera pixel. Since the method actually calculates the discrete Fourier transform, the algorithm is a fast Fourier transform (FFT). The difference in the initial and scattered wave vectors, ki and ks, respectively, is given by Q = ki – ks. Therefore, Q = (q, qz), where qz is the out-of-plane component. Since the camera is a 2D array of sensors, the method allows for the capture of many low-angle scattering directions

f (q, t )  e l (l 1) Dr t

(7)

where the characteristic decay time is

1 (8) Dr l (l  1) in which l = 1 for our case. Therefore we expect τ = 2.8s using the derived value of Dr = 0.18 rad2/s. We first focus on the signal from an individual particle, the same one presented in Figure 3. Figure 4 shows the power spectra for various scattering values, q. Videos were taken at a resolution of 75 pixels2 (L2) and for this system 14 pixels = 1μm. The lowest q value then is given by 2πu/L = 1.17μm-1 where u is the spatial frequency. It is expected the rotational diffusion is q-independent, and this is roughly what we observe. A few representative power spectra are shown in Figure 4(a). The plot of Figure 4(b) shows the characteristic decay time found from fitting to a single exponential decay for the first twenty q-values. The dashed red line shows the expected value of τ = 2.8s. As the q values increase in the top-left plot, the fitting becomes less reliable leading to widely varying values for τ. Furthermore, the power spectra for each q value has an oscillatory nature at long Δt which further complicates fitting with a single decay. Nevertheless, since the decay is q-independent, an average value for the decay time can be obtained which allows for the extraction of Dr. When removing the outlier of τ ~ 10s, the average gives τ = 2.8 ± 0.7s.

l 

It should also be noted problems can arise when the particle is not tethered to the surface very well, and the signal from translational motion becomes significant, increasing the

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Figure 5. (a) MSR for the average of 10 Brownian rotational diffusion simulations. The fit for 0 < Δt < 10s gives Dr = 0.23 ± 0.2 rad2/s. (b) Average power spectrum for 10 simulations. The red curve is a fit giving a rotational diffusion coefficient = 0.2 rad2/s.

difficulty in the fit. In order to determine whether the signal, such as seen in the top-left graphs of Figure 4(a), is a result of rotational motion only or from rotation and translation, we performed a control experiment in which several optically isotropic spherical microbeads, i.e. bare microbeads, were analyzed with DDM. Little signal is recovered from a tethered non-Janus particle, as expected, yet the signal does grow slightly with respect to Δt showing incomplete surface immobilization. However, it can be seen in the plot in Figure 4 (c) the signal from a bare particle is negligible in comparison to the rotational signal from the Janus sphere for a randomly selected scattering value. In this way, we expect the majority of the signal arises from rotation. Figure 4(d) illustrates the averaged power spectrum for ten diffusing particles, which are the same as those presented in Figure 3. The red line is the fit (eq. (4)) which gives Dr = 0.1 rad2/s. As discussed before, the lower value of the diffusion coefficient is again most likely a result hydrodynamic interactions.36 However, encouragingly, the value obtained is close for both tracking and DDM. To compare with the experimental data, we performed simulations of rotational diffusion by generating videos of artificial rotating Janus spheres, projected in 2D. In order to do so, we produced videos by writing an algorithm which rotated an image of an artificial Janus particle and stacking the images. The magnitude of each successive angular displacement away from the previous orientation was based upon a Gaussian probability distribution given by

P( ) 

1 2

2

  2 exp   2  2

   

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Figure 6. (a) The first “scattering” value power spectra for three rotation frequencies: 0.1, 0.5, and 1 Hz. (b) Power spectrum of the first “scattering value” for a Janus particle spinning at constant rotation (1Hz) which is not centered in the video; the inset shows a single frame from this video.

the fits to 0 < Δt < 10s. For the MSR, the linear fit gives Dr ~ 0.23 rad2/s. The red curve in the plot of Figure 5(b) is the fit for eq. (4), using the form of eq. (7), giving a value of Dr = 0.2 rad2/s. These simulations reinforce that either direct particle tracking or DDM are effective methods in obtaining reasonable values for Dr. Constant rotation. We also implemented simulations to investigate constant rotation of a single Janus particle as well as for the coupled dimer system discussed in greater detail in the following section. For a single particle rotating at a constant rate, we expect the power spectrum to become periodic with respect to the delay time, Δt. By altering the rotational frequency, we were able to obtain signals according to specific rotational rates. This rate can be extracted, as can be seen plot of Figure 6(a), by determining the difference in Δt between the minima, and taking the inverse. These minima correspond to one single rotation. The values of 0.1, 0.5, and 1Hz were recovered using DDM. Furthermore, the algorithm is capable of returning the correct rotational frequency even if the Janus particle is not centered in the video. The power spectrum of the lowest q value is shown in Figure 6(b), and there is an inset which shows a single video frame for this simulation. In this video, the Janus particle has a frequency of 1Hz, and this frequency is determined by the period of the power spectrum. Chemical propulsion. Since the Au/Pd alloy catalyzes the break-down of hydrogen peroxide H2O2, these Janus particles

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in which σ2 = 2Drδt, where δt is the change in time (distinguished from Δt which is reserved for time differences between frames in this study). The following values were used to simulate a 2μm diameter Janus particle undergoing rotational diffusion: room temperature (298K) and the viscosity of H2O, η = 8.90 × 10−4 Pa·s. We also chose δt = 1/fps = 1/11s to coincide with the experiments. Figure 5 shows the data for ten simulated Janus diffusers with the average MSR is shown in the Figure 5(a). The averaged DDM power spectrum for a single “scattering” angle is shown in the graph in Figure 5(b). As Δt increases, the error in both plots becomes greater, so we restrict

Figure 7. (a) tracks of Brownian movement of Au/Pd Janus particles (shown in red) and active particles in H2O2 (shown in black); (b) mean-squared displacement for the same particles shown in the top plot with fits shown as solid lines. The Brownian motion shows characteristic linear dependence, while the active motion has an exponent >1.

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Figure 9. (a) experimental power spectral density for a single spinning dimer assembly; (b) power spectrum of a simulated single spinning dimer rotating at 1Hz.

occurring in the same video & corresponding to the data in Figure 7, can be found in SI video V3 as well.

Figure 8. Five video frames of a counter clockwise rotating active dimer with frames separated by 1/15 s are shown with schematic representations immediately above each frame. Scale bar = 5 μm. The schematic in the lower left shows the forces applied to the dimer based upon the location of the catalyst leading to rotary motion. The bottom-right shows the corresponding power spectra for the same rotating dimer. The dotted lines show the peak-to-peak separation.

can be actively propelled via chemical means. The standard enthalpy of the reaction 2H2O2  2H2O + O2 is ΔrH⊖ = −98.2 kJ/mol showing it is exothermic. This energy can be converted to movement in the following way: near the metallic surface, the reaction products of H2O2 decomposition are at a higher concentration, leading to a concentration gradient. Although the exact mechanism is still under investigation, the propulsion is likely due to this concentration gradient as described by the selfdiffusiophoresis10 or self-electrophoresis40-42 mechanisms. Several reviews are available describing the state of the art of chemical propulsion.43-45 In Figure 7(a), the trajectories of both active Janus particles and non-active (no metal coating) moving in H2O2 are shown as black and red paths, respectively. The active particles traverse greater total path lengths compared with the Brownian diffusers. The paths are obtained from the tracking procedure described in the experimental section. The analysis of the active motion vs. Brownian motion is accomplished by determining the mean squared displacement (MSD) of the particles.10 As can be seen in Figure 7(b), the MSD for Brownian motion is linear with respect to Δt, as is expected. The active particles undergo directed propulsion at short time scales with respect to the rotational diffusion characteristic time, and therefore the MSD for these active particles for short time is non-linear. In general, the MSD ∝ tα. For Brownian motion, we have α = 1, and for superdiffusion we have α > 1. In particular, for our case, α = 1.702 ± 0.003 for active motion shown by the solid black line fit in Figure 7(b). The linear fit for Brownian motion (red) gives a slope of m = 4.06 ± 0.03 μm2/s. In short, Figure 7 shows the catalyst-coated particles are active when in the presence of the H2O2 fuel. A video of active vs. passive particles, with both

Active particles are expected to adhere to one another due to a number of effects such as phoretic attraction.46 A configuration of two aggregated Janus particles, which have formed a stable dimer, spin at roughly constant rates while translating only slightly. For reasons not understood, the particles lock together with their metallic hemispheres oriented in opposite directions to one another, and the two are joined at their equators, as shown in Figure 8. Once locked in this configuration, the dimers undergo surprisingly regular rotation with only slight translational deviations. Since the rotational frequency is roughly constant, DDM of a single spinning dimer arrangement can recover this frequency as in the previous section. Figure 8 shows five video frames of a rotating dimer configuration, with frames separated by 1/15s. An example video can be found in SI video V6. Time is increasing from left to right, as indicated by the arrow between the frames and the schematic representations above each frame, showing rotation to be occurring in a counter clockwise fashion. The top row images are similar to those implemented in the simulations to compare with experiment. The rotation direction is consistent with the observation of propulsion away from the catalyst site, which has been shown to be the case for motors with an electrically insulating underlying structure.10,47,48 The bottomright of Figure 8 shows the power spectral densities for the first three, smallest scattering vectors; each spectrum is capable of indicating the correct rotational frequency. The dashed lines show the location of the most easily distinguishable peaks, and the peak-to-peak separation is expected to yield the time for one half-rotation. With the tracking algorithm, the average rotation frequency for this particular dimer is f ~ 1.66 Hz while the DDM spectra gives fDDM ~ 1.58 Hz, a close match. Figure 9(a) shows the power spectrum of another example rotary dimer. The right plot shows a simulation of a rotating dimer with a frequency of 1Hz. The power spectral density can be fit ∝ sin2(2πfDDMΔt) in which the frequency, fDDM, can be retrieved. Although not a perfect fit due to slight translational motion contributing to the signal, i.e. additional features are attributed to small spatial variations (translational motion), by fitting the experimental data on the left, we find a frequency of 1.67Hz which is close to the value recorded with the tracking algorithm. The experimental data in Figure 9(a) shows local and

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global minima whereas the simulation data in Figure 9(b) shows only global minima since no translational motion is present. Other stable spinning morphologies such as a trimer were tested and their frequencies were recoverable using this method as well.

up for simultaneously investigating rotational and translational diffusion requiring only two modifications. Furthermore, the use of a coherent light source may not be necessary and the white light on the microscope may be sufficient as originally shown for DDM of translational diffusion.

■ DISCUSSION

■ CONCLUSIONS

Although a number of methods could potentially probe rotational diffusion or constant rotation of single dynamic particles, such as the tracking method we have shown here, DDM is a method allowing for rapid, high-throughput processing complimenting tracking algorithms. Therefore, expanding the technique to be capable of investigating single particles could reduce the analysis time for a number of systems. Additionally, it could be the only viable method for certain situations: for example, if one wished to measure the rotational diffusion of a particle inside a highly scattering medium, DDM may be the best method. In this case, tracking may not be a realistic option yet DDM could potentially still extract the dynamic information in highly scattering media. 27 For example, a Janus particle could be immobilized (translationally) inside of a polymer but still able to rotate either via diffusion or by some other means such as an external field. Resolving the Janus sphere within the gel in order to track the motion may be difficult or impossible, but DDM does not require the particle to be resolved and could therefore be a practical method to probe the polymer’s rheological properties.

It is possible to analyze the rotational dynamics of spherical microparticles by differential dynamic microscopy (DDM), and we have shown DDM can recover the rotational diffusion coefficient of single optically anisotropic Janus particles. DDM has never been shown to be effective on systems with single entities, nor has it been used to study constant rotational motion. Since the particles we used were coated with Au/Pd, a catalyst in the breakdown of H2O2, we showed the particles can be actively propelled. In this case, we have studied Janus particle dimers undergoing roughly constant rotation, and their frequency can be recovered with DDM as well. The results are supported by custom simulations of single particles and dimer pairs rotating either in a constant fashion or undergoing artificial diffusion. Future work will focus upon the decoupling of translation and rotation, making ensemble measurements of anisotropic particles, and using the method herein to measure rheological properties of complex fluids in order to further broaden the applicability of DDM.

Using DDM for studying individual rotating systems may expedite the analysis of video data, but one must be careful unwanted factors are not contributing to the signal. Slight translational motion can contribute to the signal and can cause difficulties in data analysis. As we have shown here, however, translational motion does not have to be completely suppressed in order for the method to work. It is expected a video containing several particles undergoing both translational and rotational diffusion simultaneously can be extracted with DDM by decoupling the two signals, and this will be investigated in the future.

Supporting Information. Videos showing the rotational diffusion dynamics as well as videos of the simulations are available. Video V1: rotational diffusion of a single particle; Video V2: a video showing several particles both tethered and untethered. Video V3: active and Brownian motion together, corresponding to the data presented in Figure 7; Video V4: simulation of a single Janus particle rotating in one direction at a constant rotational frequency of 1 Hz; Video V5: simulation showing rotational Brownian motion of a single Janus particle with 1/11s between frames; Video V6: a single experimental coupled active dimer assembly rotating around a mutual center.

An experimental set-up similar to one presented by Mantegazza et al.49 could potentially be used to extend DDM to measure the rotational diffusion of anisotropic colloids with or without suppressed translational diffusion, although the experimental complexity would need to be increased, moving away from one of the main advantages of the method. The significant differences between their set-up49 and the one presented here are the samples (anisotropic colloidal dispersions) were illuminated by a coherent light source (HeNe laser) and a rotatable polarizer was placed between the microscope objective and the CCD. The analyzing polarizer allowed for the measurement of both polarized and depolarized light components, VV and VH, respectively, and since the depolarized signal contains information about the rotational diffusion of anisotropic particles, the rotational diffusion coefficient could be extracted. In contrast to the DDM algorithm, this study utilized a CCD to capture static images at different exposure times and so the decay rates were limited by only the exposure time of the camera, not its frame rate. 50 The DDM algorithm could be used with the same experimental set-

■ ASSOCIATED CONTENT

■ AUTHOR INFORMATION

Corresponding Author *E-mail: [email protected]

Notes The authors declare no competing financial interest. ■ ACKNOWLEDGMENTS We acknowledge the Imaging and Histology Core Facility at Northern Arizona University (NAU) for their assistance with sputtering, plasma etching, and use of the SEM and digital microscope. In particular we would like to give special thanks to Aubrey Funke for her invaluable assistance with these instruments. We would also like to thank the College of Engineering, Forestry, & Natural Sciences (CEFNS) at NAU for the project’s financial support.

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Rotational Analysis of Spherical, Optically Anisotropic Janus Particles

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