Active Janus particles in a complex plasma
aa r X i v : . [ phy s i c s . p l a s m - ph ] J u l Active Janus particles in a complex plasma
V. Nosenko, ∗ F. Luoni,
1, 2, 3, † A. Kaouk, M. Rubin-Zuzic, and H. Thomas Institut f¨ur Materialphysik im Weltraum, Deutsches Zentrum f¨ur Luft- und Raumfahrt (DLR), D-82234 Weßling, Germany GSI Helmholtzzentrum f¨ur Schwerionenforschung, D-64291 Darmstadt, Germany Technische Universit¨at Darmstadt, D-64277 Darmstadt, Germany Institut f¨ur Materialphysik im Weltraum, Deutsches Zentrum f¨ur Luft- und Raumfahrt (DLR), D-51170 Cologne, Germany (Dated: July 28, 2020)Active Janus particles suspended in a plasma were studied experimentally. The Janus particleswere micron-size plastic microspheres, one half of which was coated with a thin layer of platinum.They were suspended in the plasma sheath of a radio-frequency discharge in argon at low pressure.The Janus particles moved in characteristic looped trajectories suggesting a combination of spinningand circling motion; their interactions led to the emergence of rich dynamics characterized by non-Maxwellian velocity distribution. The particle propulsion mechanism is discussed, the force drivingthe particle motion is identified as photophoretic force.
PACS numbers: 52.27.Lw
I. INTRODUCTION
Active matter is a collection of active particles, eachof which can convert the energy coming from their en-vironment into directed motion, therefore driving thewhole system far from equilibrium [1, 2]. Active matterhas some intriguing physical properties and potentiallya number of applications. It has recently become a hottopic of multiple interdisciplinary studies.Complex plasmas, which are suspensions of micron-size solid particles in plasmas, are a particular instanceof soft condensed matter [3]. Complex plasmas are ex-cellent model systems which are used to study variousplasma-specific and generic phenomena at the level ofindividual particles. Their advantages include the possi-bility of directly observing virtually undamped dynamicsof the particles suspended in a rarefied gas, in real timeand with relative ease.A particle in a complex plasma can become activevia several mechanisms. First, the plasma wake effect,which makes the interparticle interaction nonreciprocal[4–6], can under certain conditions lead to the particleself-propulsion. Examples include channeling particles[7] and “torsions” [8]. Second, a particle can be drivenby a phoretic force, e.g., the photophoretic force fromthe illumination laser [9, 10]. Third, as a rather extremecase, a particle can be propelled by the “rocket force”due to the ablation and removal of the particle materialby a powerful laser irradiation [11, 12].A prominent example of particles that can be activein various environments is the so-called Janus particles(JP), which have two sides with different properties [13].Janus particles where two sides were made of (or coatedwith) different metals were found to be active in certainaqueous solutions [2]. In this paper, we experimentally ∗ [email protected] † [email protected] study Janus particles - polymer microspheres half-coatedwith a thin layer of platinum - suspended in a gas dis-charge plasma. We show that they become active in thisenvironment and discuss the mechanism involved. II. EXPERIMENTAL METHOD
Our experimental setup was a modified Gaseous Elec-tronics Conference (GEC) radio-frequency (rf) referencecell [12]. Plasma was produced by a rf capacitively cou-pled discharge at 13 .
56 MHz in argon. The gas pressurewas varied in the range of p Ar = 0 . . P rf = 1–20 W.A manual particle dispenser mounted in the upperflange was used to inject dust particles into the plasma.The particles were suspended in the plasma sheath abovethe rf electrode. They were illuminated by a horizon-tal laser sheet with the wavelength λ = 660 nm andmaximum output power of 100 mW. The particles wereimaged from above using the Photron FASTCAM miniWX100 camera paired with the long-distance microscopeQuestar QM100 (or the Nikon Micro-Nikkor 105-mm lensfitted with a matched bandpass interference filter in theexperiment with a 2D layer of particles). The particlecoordinates and velocities were calculated in each framewith subpixel resolution using a moment method [14].Note that the present optical setup does not allow us toresolve the particle spin.Janus particles were prepared using the followingmethod. Melamine-formaldehyde (MF) microspheres[15] with a diameter of 9 . µ m and mass m = 6 . × − kg (respectively, 9 . µ m and 6 . × − kg inthe experiment with a 2D layer of particles) were dis-persed in isopropanol. A drop of the mixture was placedon a Si wafer. After isopropanol evaporated, the parti-cles formed a monolayer on the wafer surface. They weresputter-coated on one side with a ≈
10 nm layer of plat-inum. The resulting Janus particles were then collectedby scratching them off the wafer by a sharp blade, placed
FIG. 1. Trajectories of Janus particles suspended as a 2Dlayer in rf plasma sheath. 545 frames of the top-view video(during 2 .
18 s) were superposed, the brightness and contrastwere adjusted for better viewing. Note a characteristic curlyappearance of many trajectories. The argon pressure was p Ar = 0 .
66 Pa, the rf discharge power was P rf = 20 W. in a standard container and dispensed into the plasma ina regular way. III. RESULTS
Two-dimensional (2D) suspensions of regular MF mi-crospheres in plasmas are well studied both experimen-tally and theoretically [3]. Therefore, as a first test withJanus particles we studied their 2D suspension. The ex-perimental procedure was similar to that of Ref. [16].A 2D layer of 9 . µ m Janus particles was suspendedin argon plasma at the low pressure of p Ar = 0 .
66 Paand discharge power of P rf = 20 W. Top-view video ofthe particle suspension was recorded at the rate of 250frames per second.We observed that the particles energetically movedaround in unusual curly trajectories, see Fig. 1. Suchtrajectories are not normally seen for regular MF parti-cles in similar experiments. This is a clear hint that JPssuspended in plasma behave as circle swimmers - a kindof active particles which tend to perform circular motion[17]. This hypothesis needs further study.The distributions of the particle velocity v x,y are shownin Fig. 2. Up to v ≈ . T x = 7 . T y = 7 . v > . . c oun t v (mm /s ) v x v y FIG. 2. Distributions of the particle velocity v x,y in the exper-iment of Fig. 1. The lines are Gaussian fits for v < . y direction. electron yields of aluminium and its oxide), an experi-ment with all-stainless-steel rf electrode system may behelpful. This is reserved for future work.To get insight into the mechanisms responsible for theobserved particle behaviour, we studied the most basicsystem, a single JP suspended in plasma [19]. This al-lowed us to exclude interparticle collisions and collectiveeffects, e.g. instabilities mediated by the plasma wakes[16]. Experimental parameters (argon pressure, illumi-nation laser power) were varied in wide ranges and theireffect on the Janus particles’ behaviour was studied. Sin-gle JPs were trapped in a potential well created by aconfining ring placed in the center of the rf electrode [20]and imaged by the top-view video camera operating atthe rate of 60 frames per second (see Ref. [21] for detailsof the experimental procedure).We observed that every single JP, when suspended inplasma, moved along a trajectory of one of the follow-ing three types: (1) circular, (2) complex trajectorieswhich are best described as epitrochoids , and (3) appar-ently random, see Fig. 3. Out of the 21 particles usedin our experiments, 9 had circular trajectories, 8 epitro-choidal, and 4 random trajectories. The particle tra-jectory size, circling frequency, and other characteristicsdepended on the experimental conditions. The circlingdirection appeared randomly distributed between clock-wise and counterclockwise.For comparison, we performed similar experimentswith single regular MF particles suspended in plasma.They had mostly random [as in Fig. 3(f)] and sometimes“smeared” circular [as in Fig. 3(e)] trajectories [22, 23],but never clear epitrochoidal trajectories. The circlingdirection was either clockwise or counterclockwise. Fur-thermore, after properly centering the confining ring onthe rf electrode, their trajectories were always random[24, 25]. In contrast, JPs had circular or epitrochoidaltrajectories with the same occurrence regardless of theexact centering of the confining ring.The force driving a Janus particle can be either plasma-related (e.g., asymmetric ion drag) or caused by the illu-mination laser light (radiation pressure or photophoreticforce). To discriminate between these forces, the exper-iment with a single JP was repeated using various com-binations of the experimental parameters. The particletrajectories were recorded and from these, the averagetrajectory radius r tr and circling frequency ω were cal-culated. They were typically in the ranges of r tr = 0 . . ω = 1 . − . Note that for a uniformlycircling particle, the tangential component of the drivingforce is given by F t = mγ E ωr tr (assuming balance of thedriving force and gas friction). The Epstein neutral gasdamping rate γ E was calculated as in Ref. [23]. We used F t as a convenient measure of the driving force acting ona particle in the following experiments.For the particles with circular trajectories, F t appliesdirectly as a measure of the driving force. We performeda series of experiments with single JPs that had circulartrajectories. The argon pressure was varied while keepingconstant the rf discharge power. The tangential compo-nent of the driving force F t is shown in Fig. 4 as a functionof the argon pressure, for two settings of the illuminationlaser power. (When the laser power was set to 0, the par-ticles were illuminated by a flashlight with a low-powerincandescent lamp supplied with the microscope.) Thereis a clear trend for F t to increase for higher gas pressuresand higher illumination laser power in the ranges studied(except for one data point at p Ar = 10 Pa).For the particles with epitrochoidal trajectories, F t provides only an estimate of the driving force. For threedifferent JPs with epitrochoidal trajectories, we mea-sured F t as a function of the illumination laser powerat constant argon pressure and the rf discharge power,see Fig. 5. While the data points scatter is large, thereis a trend for the driving force to increase with the laserpower for two out of three particles. y (a) y x(d) (b) x(e) (c) x(f) 100 m m FIG. 3. Typical trajectories of single Janus particles sus-pended in rf plasma sheath: (a) circular, (b-e) epitrochoidal ,(f) apparently random. Regular MF particles have either ran-dom or sometimes “smeared” circular trajectories, as in pan-els (f) and (e), respectively. F t ( - N ) gas pressure (Pa) FIG. 4. Tangential component F t of the driving force actingon single Janus particles with circular trajectories as a func-tion of the argon pressure p Ar . The particles were illuminatedeither by a laser with output power of 99 mW (circles) or bya flashlight with a low-power incandescent lamp (diamonds).The lines are linear fits F t ∝ p Ar . The rf discharge power was P rf = 5 W. F t ( - N ) illumination laser power (mW) FIG. 5. Tangential component F t of the driving force actingon single Janus particles with epitrochoidal trajectories asa function of the illumination laser power. Data for threedifferent particles are shown by different symbols. The argonpressure was p Ar = 1 . P rf =5 W. We observed that epitrochoidal trajectories becomelarger and cleaner as the illumination laser power is in-creased. When the laser is switched off, the trajectoriesalways become circular.These observations indicate that the illumination laserradiation plays an important role in the particle drive,at least for the particles with circular and epitrochoidaltrajectories. The particles with random trajectories, onthe contrary, did not show any remarkable trend withrespect to the illumination laser power.In a separate test, the driving force on a single Janusparticle with epitrochoidal trajectory diminished whenthe discharge power was increased in the range of P rf =1–20 W while keeping constant the argon pressure of p Ar = 1 . x (b) x (c)x (a) y
100 m m FIG. 6. Trajectories of a single Janus particle in the experi-ment with varying discharge power: (a) P rf = 1 W, (b) 5 W,(f) 20 W. The argon pressure was p Ar = 1 . This happened due to the decrease of both the trajectorysize and circling frequency. The respective particle tra-jectories are shown in Fig. 6. Since increasing P rf resultsin a larger plasma density and therefore larger plasma-related forces such as the asymmetric ion drag force,these forces must be directed opposite to the main self-propulsion force, thus reducing the net force for larger P rf . In the experimental runs shown in Figs. 4 and 5, weused a middle setting of the discharge power of 5 W. IV. PARTICLE PROPULSION MECHANISM
The loops observed in the epitrochoidal particle trajec-tories, see Figs. 1 and 3(b),(c),(d), are a strong indicationthat these particles spin on top of their circling motion.It is natural to assume that the spinning frequency ν isequal to the circling frequency ω for circular trajectories,or is a multiple of the circling frequency ( ν = nω ) for epitrochoidal trajectories, e.g., n = 2 in Fig. 3(b) and n = 3 in Figs. 3(c),(d). This kind of the coupled spin-ning and circling motion of a single driven particle (notof Janus type) was discussed in Refs. [17, 26]. To drivethis kind of particle motion, the spinning and circling fre-quencies must be locked and the spinning direction fixedand normal to the confining plane. In the simulations ofRef. [17], these conditions were set manually. For a Janusparticle with one half of its surface coated, the sphericalsymmetry is broken and the axis connecting the centers ofits two hemispheres is the axis of the self-propulsion force.This force is fixed in the particle frame of reference (theso-called body-fixed force). A Janus particle confined inthe plasma potential trap will perform a circular motion,if the axis of the self-propulsion force is in the horizontalplane and directed tangentially to the particle’s trajec-tory. For the particle to move in an epitrochoidal trajec-tory, this axis must additionally precess causing the par-ticle spinning with a certain frequency with respect to thefrequency of the circular motion. Since a direct observa-tion of the particle spin would require a more advancedoptical setup than used in the present paper, we leavethe experimental verification and clarifying the physicalorigin of these important conditions for future work.While the self-propulsion force can possibly arise fromthe asymmetry of many properties of a Janus parti- cle halves (different surface charge densities, secondaryelectron emission coefficients, and temperatures, underelectron and ion bombardments or laser illumination),our experimental observations point at the photophoreticforce as the main driving mechanism for JPs. Indeed, theobserved dependence of the driving force on the illumi-nation laser power and gas pressure and the body-fixednature of the force are consistent with the photophoreticforce but not with the radiation pressure force (which isindependent of the gas pressure). Photophoretic force isknown to drive particles in various circling trajectories,e.g. “circular” and “complex” photophoresis in Ref. [27].On the other hand, plasma-related forces such as theasymmetric ion drag force are apparently directed op-posite to the photophoretic force thus reducing the netself-propulsion force. In addition, a possible mechanismof rotation excited by a combination of the vertical com-ponent of Earth’s magnetic field and radial electric fieldsat the edge of the rf electrode [28] is ruled out by theapparently random circling direction of Janus particlesobserved in our experiments.The photophoretic force acts on a nonuniform objectsurrounded by neutral gas when their temperatures arenot equal [9, 12, 26, 27, 29–32]. There are two distinctvarieties of the photophoretic force: ∆ T and ∆ α forces.∆ T force arises when a particle is heated nonuniformly.The Pt-coated side of our Janus particles is expected tohave a higher temperature than the opposite side. In-deed, in the experiments of Ref. [12], MF particles withthin Pd coating absorbed much more laser radiation thanregular MF particles. Enhanced radiation absorbtion bythe Pt or Pd coating may be due to the excitation of asurface plasmon in it [33]. ∆ α force arises when the ther-mal accommodation coefficient of the particle surface isnot uniform. ∆ α photophoretic force, also called the “ac-commodation force” [30], is a body-fixed force, which canprovide propulsion and torque on the particles of irregu-lar shape [26]. For Janus particles such as those used inour experiment, the ∆ T photophoretic force can also bebody-fixed.The total photophoretic force (including the ∆ T and∆ α components) acting on a JP can be estimated usingthe following simple formula: F ph = πr p k B n (cid:16) α T + (1 − α ) T − α T − (1 − α ) T (cid:17) = πr p k B n T (cid:16) α (cid:18) T T − (cid:19) − α (cid:18) T T − (cid:19)(cid:17) , (1)where r p is the Janus particle radius, k B is Boltz-mann’s constant, n and T are respectively the neutralgas number density and temperature, α , and T , arerespectively the thermal accommodation coefficients andtemperatures of the particle’s two different halves. Thisformula assumes that α , and T , are uniform over theparticle halves and, in a major simplification, it does notanswer the important question of how T , depend on theillumination intensity and the particle properties [34], butit includes the essential physics of the photophoretic force[35] and can be used for estimates.If a particle is heated uniformly, T = T = T , then F ph = πr p k B n ( T − T )( α − α ). This formula givesthe pure ∆ α component of the photophoretic force. Itvanishes, if the particle has the same temperature asthe surrounding gas. If the accommodation coefficientis uniform over the particle surface, α = α = α , then F ph = πr p k B n ( T − T ) α . This is the pure ∆ T compo-nent. In real situations, both components will act simul-taneously.Reliable data on thermal accommodation coefficientseven of common materials are hard to find in the lit-erature. In a recent paper [31], it was experimentallyshown that for the range of materials and gases studied,the accommodation coefficient depends more on the gastype than on the surface material, implying that the roleof the ∆ α force should be small. In Ref. [30], the ∆ α force (called “accommodation force” there) was experi-mentally estimated as 2–3% of the total photophoreticforce acting on a steel particle in helium.Assuming that the ∆ T force is dominant in our exper-iments, we analyse the results shown in Fig. 4. The lineshere are fits F t ∝ p Ar , they fit the data points reasonablywell. This kind of pressure dependence is consistent withthe ∆ T force. Using α = 0 .
95 for the accommodationcoefficient of argon atoms on both Pt [31] and MF sur-faces and assuming that argon behaves as an ideal gasat T = 300 K, from the slope of the fit for the illumi-nation laser power of 99 mW we obtain ∆ T ≃ − K.This shows how sensitive the Janus particles are to a verysmall difference of temperature on their surface. For thecase when the particle was illuminated by a low-powerincandescent lamp, we calculate the temperature differ-ence of ∆ T ≃ − K. This was probably due to thecombined effect of illumination and plasma heating.The photophoretic force and in particular the torquethat it exerts on a particle strongly depend on small devi-ations from the surface homogeneity and spherical shapeof the particle. This may explain the fairly large scatterof measurements in our experiments and also the exis- tence of different types of trajectories for Janus particlesfrom the same sample (the particles with random trajec-tories probably did not receive any coating at all duringpreparation due to their position on the wafer). Thisalso makes the photophoretic force, especially of the ∆ α type, a strong candidate for the driving mechanism ofthe so-called “abnormal” particles, which are sometimesobserved in complex plasma experiments [9]. They movearound with high speed and have involved trajectories.These particles may have inhomogeneities of their sur-face properties or deviations from the spherical shape [9],which give rise to the photophoretic force. Since Janusparticles can be considered an extreme case of such inho-mogeneous particles, they can be used as a study modelfor the “abnormal” particles, possibly helping to developa method of controlling them in experiments with com-plex plasmas.To summarize, we experimentally observed that Janusparticles, which were plastic microspheres half-coatedwith a thin layer of platinum become active when sus-pended in argon discharge plasma. Single Janus particlesperform periodic motion along circular or epitrochoidaltrajectories. Photophoretic force from the illuminationlaser is proposed as the driving force providing a combi-nation of propulsion and torque on the particles. In a 2Densemble of Janus particles, their interactions lead to theemergence of rich dynamics characterized by non-trivialvelocity distribution. Such ensembles of active Janus par-ticles suspended in a plasma are promising model systemsto study active Brownian motion [36], where the particledamping and propulsion can be tuned. An interestingtopic of future research is building an analytical descrip-tion of Janus particle collective dynamics [37]. V. ACKNOWLEDGMENTS
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