Thermal- and Magnetic-Sensitive Particle Flocking Motion at the Air

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Thermal- and Magnetic-Sensitive Particle Flocking Motion at the Air-Water Interface Jennifer E. Satterwhite-Warden, Dilip Kendepudi, James A. Dixon, and James F. Rusling J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.9b00414 • Publication Date (Web): 08 Apr 2019 Downloaded from http://pubs.acs.org on April 8, 2019

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The Journal of Physical Chemistry

Thermal- and Magnetic-Sensitive Particle Flocking Motion at the Air-Water Interface Jennifer E. Satterwhite-Warden,a Dilip K. Kondepudi,b James A. Dixon,cd and James F. Rusling*aefg aDepartment

of Chemistry (U-3060), University of Connecticut, 55 North Eagleville Road,

Storrs, Connecticut 06269, United States, Email: [email protected] bDepartment

of Chemistry, Wake Forest University, Salem Hall, Box 7486, Winston-Salem,

North Carolina 27109, United States cDepartment

of Psychology (U-1020), University of Connecticut, 406 Babbidge Road, Storrs,

Connecticut 06269, United States dInstitute

of Materials Science, University of Connecticut, 97 North Eagleville Road, Storrs,

Connecticut 06269, United States eDepartment

of Surgery and Neag Cancer Center, University of Connecticut Health Center,

Farmington, Connecticut 06032, United States fSchool

of Chemistry, National University of Ireland, Galway, University Road, Galway, Ireland

ABSTRACT. Collective self-motion of particulate systems provides novel opportunities for developing flocking and sensing functions from seemingly inanimate objects. In this paper, we report videos documenting spontaneous collective flocking of multiple irregularly-shaped macroscopic benzoquinone (BQ) particles at the air-water interface. Self-propulsion occurs due to Gibbs-Marangoni effect surface tension gradients generated by the BQ particles. The air-water interface develops inhomogeneous interfacial tension fields created by differential dissolution at

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points and edges of BQ particles, causing interfacial tension variations along the solid-liquid-air interfaces. Responses of irregularly shaped BQ particles to these driving forces does not result in random motion but leads to cooperative hydrodynamic flocking. Curiously, the flocking behavior was very evident for irregularly shaped particles, but not observed for symmetric circular BQ disks. The flock responds to changes in its local environment as it forages for interfacial free energy. It exhibits warm and cool thermotaxis, and thus can sense local temperature changes. Also, though a single magnetic bead is not confined to a part of the petri dish by an applied magnetic field, when this magnetic bead is a member of a flock in which all the other beads are not magnetic, the flock as a whole moves and hovers around the region where the field is maximum. In other words, the magnetic bead becomes a kind of "sensor" for the flock to respond to a magnetic field, the response being a drift in the direction of the field.

INTRODUCTION Non-equilibrium self-organizing systems provide physical insight into the nature and origin of organisms.1--4 Such systems that exhibit self-motion are broadly classified as active matter, in which self-motion is a consequence of fluctuating non-equilibrium thermodynamic forces driving them towards equilibrium.6-9 These systems generate entropy that for some irreversible processes can drive a system that is far from equilibrium to self-organize. The resulting dissipative structures are maintained through continuous dissipation of free energy and entropy generation.2,9 Dissipative particulate systems have similarities to biological systems that are also dissipative when structure and behavior arises from entropy generating processes. 10,11,12-13 Non-living dissipative structures can exhibit behavior such as foraging, energy seeking, and self-healing needed to sustain structure, similar to behavior of biological systems.14 2 ACS Paragon Plus Environment

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Examples of cooperative dynamic behavior include flocking birds, swimming bacteria, cell suspensions, collections of cytoskeletal filaments, and molecular motors.15 Non-equilibrium long-range order in model nonliving dissipative systems can improve understanding of processes in living systems. There are a wide range of chemical and physical causes and proposed theories for self-motion.16,18 Self-motion of a benzoquinone (BQ) disk at the air-water interface is an example of a dissipative system that generates heterogeneous interfacial tension gradients from slow dissolution of the weakly surfaceactive BQ.19-20,21 The resulting motion is an example of the Marangoni effect resulting from interfacial tension variations along solid particle-liquid-air interfaces. Single particle studies demonstrated continuous, intermittent and velocity-decay motion, modulated by chemical reactions and UV light. Dynamic self-assemblies of meticulously engineered camphor- and ethanol loaded gel particles have demonstrated diverse assembly structure and motions from open lattice formation to collective swarming.22-29 Motion of different structures depended on size and shape of the engineered particles. We recently described associative motion due to so called Marangoni “surfing”18 caused by slow dissolution of non-engineered BQ disks on an air-water interface leading to continuous, transient cooperative motion.30 Events such as paired travel emerged from particle interactions controlled by interfacial tension gradients. We also observed that irregularly shaped BQ particles showed unique and definitive collective behavior. Our goal in the present work was to develop the irregularly shaped BQ multiparticles on the air-water interface as a spontaneous particle flocking system that responds collectively to external stimuli. We use a non-equilibrium thermodynamics framework to 3 ACS Paragon Plus Environment


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relate the behavior of this system to flocking or swarming phenomena in the natural world. In this paper, we present results on dynamic co-operative features of collective dissipative structures formed by irregularly shaped BQ particles on an air-aq. 0.1 NaCl interface driven by local interfacial tension fields due to slow BQ dissolution. The particle shape is critical for cooperative motion, and self-organization of the irregular particles into flocks emerges spontaneously. Circular BQ disks do not flock or respond to external stimuli. The self-propelled flock responds to local temperature changes, and to a magnetic field when a single magnetic BQ-iron oxide particle is included to the flock. EXPERIMENTAL Materials. 1,4-Benzoquinone (BQ), iron (II, III) oxide nanopowder (Fe3O4, 50-100 nm particle size, 97%), lycopodium, and sodium chloride (NaCl) were from Sigma Aldrich. Nanopure water (18 M·cm) was from house-distilled water purified by a Hydro Service and Supplies system. Methods. BQ powder was finely ground in a mortar and then molded into a pellet (either 3 mm diameter, 1 mm thick or 13 mm diameter, 1 mm thick) using a die set and either a hand (Pike Technology, Model No. 161-1100) or hydraulic press (Carver Inc., Model No. 4350L). Two distinctive particle classifications were implemented: circular 3 mm BQ disks or irregular shaped and sized BQ fragments. Irregular BQ particles were prepared by breaking 13 mm BQ disks into pieces. Irregular fragments have exposed sharp edges. Particles were lightly dusted with lycopodium powder, a hydrophobic material that helps “float” the particles and extend the observation time of self-motion. Aqueous 0.1 M NaCl was poured into a rigorously cleaned surfactant-free glass petri dish (90 mm diameter. Aqueous volume included within the petri dish, was chose such that BQ particles did not touch the bottom on the petri dish. BQ particles were then added gently to the air-water 4 ACS Paragon Plus Environment

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interface. Motion of particles was monitored with a digital camera (JVC-HD GZ-E200BU, frame rate: 30 frames per second (fps)). Observations were made until particles dissolved or sank. Analysis was done using image analysis software (ImageJ 1.41, NIH). Individual [x,y] coordinates for each particle was manually acquired in ImageJ using the MTrackJ plugin to track the moving objects. The corresponding [x,y] coordinates were statistically analyzed in R programming language using statistical computing software. A copper wire was attached to a soldering iron and once flocking locomotion was used to generate high temperature. The free end of the copper wire was positioned above the air-water interface opposite the flock structure. For low temperatures, a metal probe was submerged in ice for 10 min and then placed at the air-water interface. Particle movement was monitored with a digital and thermal infrared (IR) imaging cameras (FLIR Instruments, Model No. A655sc). The thermal IR FLIR camera and ResearchIR 4.0 software was used for thermal pattern analysis. Magnetic sensing by irregular BQ fragments included one BQ-iron oxide nanopowder particle as a sensor element. These were made by finely grinding BQ (~0.150 g) and iron oxide nanopowder (~0.030 g) together in a mortar and then molding into pellets and fragmenting as above. For the sensing experiment, a sensor element was added to the interface, and a magnetic bar was held above and height was optimized until there was no effect on the sensor fragment. Threshold height was optimized for each experiment. Subsequently, the magnet was removed and non-sensor elements added to the air-water interface were allowed to interact with the sensor element. Once a flock formed, the magnet was repositioned above and motion was monitored. UV-Visible spectroscopy (HP/Agilent 8453) was used to measure the rate of BQ dissolution. Solution was obtained from identical locations within the glass petri dish and absorbance monitored every 10 s throughout BQ particle locomotion over a 7 min period. Concentrations of 5 ACS Paragon Plus Environment


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BQ were assessed from measured absorbance using a standard calibration curve. Surface tension measurements employed a EZ-Piplus surface tensiometer (Kibron). RESULTS Videos are the primary data documenting collective motion described in this paper. Supplementary videos clips in the supporting information that illustrate results described herein are important to view for a full understanding of the results. Multiple irregularly shaped BQ fragments, N = 4, 6, 8, 10, 12, or 15, in a single petri dish, each being broadly different in both size and shape per experiment, were carefully added onto the surfactantfree aqueous phase. Instantly, self-motion of the particles emerged at the air-water interface. Motion was observed with a camera until particles sank or were completely dissolved. To begin an experiment, BQ particles were spread across the air-water interface in a petri dish, and they immediately began moving around the interface. Over several minutes, multiple interactions of the irregularly shaped BQ particles emerged and transient flocks were observed. (Video S1, ESI file). Water depth was controlled so that particles at the air-water interface did not touch the bottom of the petri dish. Most studies used a water depth of 3.9 cm. No obvious difference in particle motion or flocking was found in a subset of experiments done at 4.7 mm water depth. As seen in the video, particles drift toward a dynamic flock, become a part of the flock and a few drift out of the flock. Curiously, transient flocking was observed for irregularly shaped particles but not for regularly shaped =3 mm diam. circular BQ disks. In particular, the circular disks were spread across the interface and immediate locomotion occurred. As observed in = control = Video S2 (please

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examine Video S1 and S2 side-by-side), a multiple disk flock did not form, and disk collisions predominated. Figure 1 shows still photos of these experiments (Figure 1A). As time passed, irregularshaped BQ particles form multiple small group collectives (Figure 1B, C. At 120 s, these small fluently voyaging cooperative groups organized into a larger flock (Figure 1D). As seen in Video S1 (ESI) and Figure 1E, F and G, these self-organized flocks remained in dynamic motion. Due to particles constantly associating and disassociating the area occupied by an identified flock changes continuously. To show that water vaporization is not significant in the flocking motion of irregularly shaped BQ particles spread across the air-water interface in a petri dish with a cover carefully placed atop to minimize water vaporization. Even with the petri dish covered, multiple interactions of the irregularly shaped BQ particles emerged and transient flocking was observed (Video S3, view ESI file). Also, if vaporization was a flock issue, we would not expect the big differences found between motion of spherical and irregular BQ particles. Response to Temperature. When either a cold or hot probe was positioned at the aqueous interface a temperature gradient zone was produced within the dish and measured with an infrared camera. Figure 2 and Video S4 (ESI) show that the flock migrated toward the warmer temperature zone. Of the total 15 BQ particles, a flock of N = 10 moved collectively (Figure 2A) at ambient conditions of 22°C (Figure 2B). When the hot probe was placed at the interface a distance away from the flock (Figure 2C), the flock and other BQ fragments migrated toward the hot zone. The temperature probe, Figure 2D, created a 40°C hot spot



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(d = 2 mm) and the 9 mm surrounding zone ranged from 26 to 30°C. Eventually, 13 out of 15 BQ fragments flocked near the warmer zone from ~ 27 to 32°C (Figure 2E and F). Figure 3 and Video S5 (ESI), revealed that in response to a cold temperature probe, the flock drifts away from cooler temperatures toward warmer regions. Small groups (two N = 7 out 15) moved cooperatively (Figure 3A) at ambient conditions of 22°C (Figure 3B). When a cold-finger probe was placed at the interface very near the flock (Figure 3C), BQ fragments immediately migrated away from the probe. The probe (Figure 3C) created a cool spot (d = 3 mm) at ~ 13°C with surrounding zone (d = 5 mm) from 18 to 20°C. After 25 s, the 11 of 15 particles were distant from the cool region (Figure 3E,F). Figure

1.

Time

sequence of flocking irregularly

shaped

BQ particles at airwater interface. (AG)

Flock

particles

at

of 30

15 s

intervals and (H) BQ particle shapes and sizes. See Video S1 (ESI). Figure 2. Photos with corresponding timetemperature gradient for 15 irregularly shaped BQ particles and a hot probe: (A) Initial flocks, (B) IR photo, (C) after 7 s, hot probe placed at interface and flock migrates toward (D) warmer conditions, shown by the small purple and blue diameter circle. At 30 s (E) flock migrated to warm zone, (F) as seen


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by bright purple semicircle in IR photo. Please view Video S4 (ESI). Magnetic Sensing. A single paramagnetism BQ particle including iron oxide nanopowder was placed on the air-water interface, and magnetic above was adjusted so as not to confine this magnetic particle to a part of the petri dish. In the presence of the magnetic field, the magnetic particle moved freely to all parts of the dish with no clear confinement.

The

magnetic sensor element was free enough to move and become a part of a flock, bit not restricted by the magnetic field (Video S6, ESI). That is, the sensor particle self-motion had enough kinetic energy to overcome the magnetic potential energy well. Threshold height was checked and corrected for each experiment due to variation in magnetic particle shape and size. When non-magnetic irregular BQ particles were added to the interface, flocking included both sensor and non-sensor particles (Figure 4A, flock size N = 12 out of 15), then the magnet was positioned away from the flock (Figure 4B). Over time (Figures 4C, D) the entire flock encompassing the sensor element “sensed” the magnetic field. A majority of elements (N > 11) maintained flocking behavior beneath the magnet (Figure 4E,F, Video S7). Because one of the particles was magnetic, the entire flock sensed and moved toward the magnetic field. The flock with the sensor moves and stays close to the magnet but the sensor particle by itself does not. As a member of the flock, the magnetic particle or sensor does not acquire enough translational kinetic energy to move away from the magnetic field, but kinetic energy seems to be moderated by the flock. Control experiments confirmed that sensing of the magnetic field relies on transient flock formation with both sensor and non-sensor components. First, 15 BQ non-sensor particles on the air-water interface and self-organized collective motion was achieved, then the magnet was positioned as before away from the center of flock (Figure 5B). These non9 ACS Paragon Plus Environment


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magnetic BQ particles were incapable of sensing the magnetic field (Figure 5C-F, Video S8). Thus, sensing the magnetic field by the flock is an emergent collective property requiring the magnetic “sensor” particle. Figure 3. Photos of times-temperature gradients for 15 irregularly shaped BQ particles with cold probe: (A) Initial, (B) IR photo, then C) after 15 s of self-motion a cold probe was positioned near the interface and flock migrated in the opposite direction. Cooler conditions in (D) as small red zone. At 25 s, (E) particles continued moving away from cold probe, with (F) cooler zone seen by dark green and surrounding red region. Please view the Video S5 (ESI).

Figure 4. Time sequence showing a flocking collective that senses a magnetic field, constructed using a single magnetic BQ sensor particle (circled in red) and 14 irregularshaped BQ non-sensor particles. The time sequence of photos shows positioning the magnet away from the flock (B), with the gradual motion of the flock to positions under the magnet (C to F). See Video S7 (ESI). 10 ACS Paragon Plus Environment

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Next, we used circular BQ disks (Figure 6, Video S9, ESI), to demonstrate sensing dependency on strong flock formation and the magnetic sensor particle. A single BQ-iron oxide 3 mm sensor disk and 14 non-sensor BQ 3 mm disk elements were subjected to the magnetic sensing experiment, Figure 6A. Although some interactions were evident, strong collective, dynamic flocking was not achieved (Figure 6B, Video S9, ESI), and the BQ disks were incapable of sensing the magnetic field (Figure 6C-F, Video S9, ESI). While a sensor element was present, the absence of transient flocking by these disk-shaped particles prohibited the collective from sensing the magnetic field. To quantify the magnetic field effect on location of particles, we defined a circular region beneath the magnet of sufficient size to contain all 15 BQ particles (~2 cm in diameter). Figure

5.

Time

sequence of a BQ flock, constructed from 15 nonsensor

elements.

The

flock was incapable of sensing

the

magnetic

field due to the absence of

sensor

particle.

(Video S7 (ESI). Figure 6. Time sequence a 3 mm sensor BQ-iron oxide disk (in red) and 14 3 mm BQ circular nonsensor disks at the airwater

interface.

This

system was incapable of flock

formation

or

sensing the magnetic field (Video S8, ESI). 11 ACS Paragon Plus Environment


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Figure 7. Probability of two or more particles being in a region beneath the magnet.

Using video data, we calculated the probability that 2 or more particles would be in this region for the period during which the magnetic field was applied (Figure 7) for the experimental condition or 15 irregularly shaped BQ particles with one ferrous particle, and the two controls (i.e., 15 irregularly shaped BQ particles with no ferrous particle and 15 circular BQ particles). As can be seen, the region directly below the magnet is occupied by the BQ particles under the sensing conditions compared to the controls. Dynamic and Thermodynamics. Quantitative modeling of the motion of a collection of particles a in our BQ systems is a formidable task that involves complex nonlinear interaction between the surface-tension field and the particles. Surface-tension gradients around the particles and the particles themselves change the local surface-tension gradients and, BQ is also dissolving. To this end, one might define new parameters that quantify flocking, or turn to a non-equilibrium thermodynamic description. While separation of an active particles into dense and dilute phases takes place in systems with large number of particles,42,43 our study in a system with smaller number of particles the tendency to aggregate can manifests as formation of dynamic flocks. Dynamic formation and dispersal of clusters has been observed in light-activated colloidal particles.48 While active matter at air-water interfaces has generated significant interest, there is little 12 ACS Paragon Plus Environment

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in the way of descriptive theory for a system like ours in which both Reynolds and Peclet numbers are well above 10, suggesting local turbulent flow dynamics.18,42 We can postulate, however, that steric trapping in clusters is likely to generate flocks. We can rationalize thus why in our BQ particle system, irregular particles form clearly observable flocks while more symmetrical circular particles do not. Irregularity of shape causes the particle's direction of motion to change more frequently than a symmetrically shaped circular particle, as clearly observed by comparing videos. Small anisotropies in local surface tension and convection current fields seem to have greater effect in changing the direction of irregular-shaped particle motion than on a particle with circular symmetry. Consequently, the rotational diffusion constant of irregular particles will be larger than that of the circular particle, which is turn leads to higher steric trapping of a particle in a flock. Once an irregular particle is in a flock, it tends to remain in the flock for a longer period, thus making a flock of irregular particles more stable than a flock of circular particles. Formation of non-equilibrium dissipative structures, such as BQ flocks, depend on entropy generating processes, which in this case is the irreversible conversion of BQ into the solution and vapor phases.2,11,30 The significance of this parameter is of interest because of the hypothesis of "maximum entropy production" (MEP), which, to be more precise, is the hypothesis of maximum rate of entropy production. This hypothesis states that systems that are far from thermodynamic equilibrium reach states that maximize the rate of entropy production.2,9.31 -33 The universal validity of this hypothesis, however, is still under active discussion, with proponents and skeptics. Only when we collect experimental evidence for this hypothesis, can we decide on its validity. For this reason, we included the measurement of rates of entropy production in our study. The system can make a transition to states of 13 ACS Paragon Plus Environment


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organization that have higher rates of entropy production. If MEP applies to our system, it implies that flocking is associated with higher rates of entropy production. To estimate of the rate of entropy production, the rate of increasing concentration of BQ in the solution due to BQ dissolution was measured by UV absorption of samples of the solution phase for different numbers on circular irregularly shaped particles on the interface. If C0 is the BQ concentration at saturation and C(t) is concentration at any time, t, the rate of increase in C(t) is then proportional to (C0 – C(t)). Thus:

(1) where rate constant k depends on surface area of the solid BQ particles, shape, and factors such as fluid convection around the solid phase, etc. The solution to equation (1) is: (2)

𝑙𝑛 (𝐶𝑜 ― 𝐶(𝑡)) = ― 𝑘𝑡

By plotting ln (C0 – C(t)) vs t (Figure S1, S2, ESI), the value of k is found as the slope. (Figure S1C), as the number of particles in a petri dish increases, k increases as expected. Values of k for irregular particles is slightly higher than those of circular particles. The slopes of these curves (Figure S1C) is 12% higher for irregular particles, showing that as the number of particles increase the rate entropy production (dS/dt proportional to k)9 is larger for irregular particles, presumably due to cooperative flocking. Quantifying Flocking Behavior. Flocking reflects a characteristic collective motion observed only with the irregularly shaped BQ particles. To demonstrate emergence of collective \motion, [x, y] trajectories were acquired from the videos for each individual BQ particle. These time-resolved 2D trajectory paths (Figure 8, Figure S3, ESI) are consistent with collective co-operative motion between particles reflected in the 14 ACS Paragon Plus Environment

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correspondence of the traces with one another. The closeness of the individual particle trajectories throughout the time courses provide a graphic picture of the flocking observed visually in the videos. To further quantify the flocking, we calculated the Euclidean distance matrix for all particles from the data sets described for Figure 9 (and Figure S4, ESI). We defined a flock as the set of particles within a radius r of any other particle in the flock. Thus, particles within the radius r are linked to one another, and ultimately that set of linked particles is defined as a flock. This guarantees that all particles in a flock are within r of some other particle in the flock, but allows the shape of the flock and degree of spread within the flock to vary. The number of particles in a flock varied from 2 to the maximum particle number for that experiment. For each time frame, we varied r from 25 to 250 pixels in increments of 25 pixels. We anticipated that for the irregularly shaped particles the probability of a

Figure 8. Trajectory traces illustrating flocking behavior, plotted as pixel units, of individual irregularly shaped BQ particles at the air-water interface for numbers of particles: A) four, B) ten, and C) fifteen. particle being in a flock would increase sharply with increases in r. For circular BQ particles, we anticipated the increase in the probability of being in a flock would be a shallower, nearly linear function of r. Figure S5 shows the probability of a particle being in a flock as a function of chosen radius, r, with separate curves for the number of particles. The right panel shows results for irregular 15 ACS Paragon Plus Environment


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particles; the left panel shows results for circular particles. As can be seen, when the number of particles in the dish is greater than 4, the probability of being in a flock increases quadratically, for the irregular particles. For the circular particles, the increase is almost linear. DISCUSSION Results above illustrate a non-engineered macroscopic multi- particle system at the air-water interface that show flocking (Figure 1 and Videos S1, ESI), and remarkable collective responses to external stimuli (Figures 2-4 and Videos S3-SA6). Each particle is an individual with a different size and shape. As such, this system is a rudimentary model for natural flocking, as with birds, where each bird is an individual with different size and shape. The motion of the BQ particles is fundamentally driven by the Gibbs energy of conversion of solid BQ phase to solution and interfacial phases, most likely driven by continual changes in the 3-phase interfacial tension located at particle interfaces related to changes in interfacial tension gradients due to slow dissolution of the BQ particles. The flocking particles move in the direction of higher surface free energy, and thus the flocks forage for free energy. Slow dissolution of BQ at the water-BQ interface first generates interfacial tension (free energy) variations at 3-phase air-water-particle interfaces surrounding each particle. This in turn, generates Marangoni convection that results in the flocking motion featuring co-operative motion of BQ particles. Interfacial tension driving force was confirmed in our earlier work by the total cessation of motion of circular BQ disks when adding a small amount of a strong surface-active agent to the airwater interface.30 In the present work, flocks demonstrated thermotaxis (Video S4 and S5, ESI), and sensed a magnetic field when a single magnetic particle was included in the flock (Video S7, ESI). However, particles with circular shapes did not display flocking behavior (Video S2, ESI). In most experimental cases, multiple initial flocks combine into a single transient, self-organized flock. The


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flock is dynamic, and BQ particles are associating and disassociating, and coexistent with a few particles in random motion that are not in the main fraction flocking. The rather tightly coordinated time-dependent particle trajectories represented in Figure 8 support the view of a strongly flocking system. Compared to the non-flocking circular disks, irregularly shaped BQ particles appear to have stronger interparticle hydrodynamic interactions that permit them to cooperatively self-propel as a flock to forage for interfacial free energy. For both shapes, surface tension gradients generate GibbsMarangoni convection flows due to variation in surface tension at 3-phase contact lines. However, we suspect, that irregular BQ fragments elicit larger interfacial free energy differences near particle points and edges, since dissolution at such points is faster than at smooth regions of a particle.34,35 This creates a greater local driving force for particles to cooperate. As is obvious in the videos, statistical analysis (Figure S5) supports the emergence of a strong cooperative flock for irregular shaped BQ particles. A characteristic feature of living systems is their ability to sense and respond to external stimuli.36 These taxis responses involves two steps: perception of the stimulus and transduction into an internal signal that triggers an action response.37 Hence, non-living self-propelled systems designed to mimic living systems should show a perception-action “sensor’ response to external stimuli. The energy (and/or matter) needed for motion is obtained by the system from its environment. Therefore, such a system forages for energy sources and can be termed as a “proto-sensor”. Self-propelled objects like camphor and camphoric acid boats show chemotaxis by accelerating and decelerating with the addition of chemical stimuli.17,38 Engineered gel-infused camphor assemblies displayed taxis to both solution depth and temperature gradients.28 Our BQ flock displays thermotaxis, as introduction of hot (Figure 2) or cold (Figure 3) probes revealed dynamic flock response to local temperature variations. BQ movement produces a heterogenous concentration gradient on the


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surrounding water surface, which generates free energy gradients around the particle that drive its motion. This decreases local surface tension gradients significantly more than the change in temperature, as surface tension changes39 less than ±20% for the local temperature changes of -9 and +18 oC caused by the probes. BQ sublimates just slightly above room temperature. Thus, we postulate that when the hot probe is placed at the air-water interface, the 40 oC local temperature sublimates BQ locally, causing a region of higher surface tension, and so the flock moves towards the hot probe. The converse occurs for the cold probe. The second proto-sensor system incorporated a magnetic BQ particle sensor within a flock of irregular BQ particles. The energy flow that maintains flock structure couples the magnetic and nonmagnetic particles so that the entire flock travels toward the magnetic field (Figure 4, Video S7, ESI). Thus, the behavior of one sensor particle controls the behavior of the entire dissipative structure. In these experiments, a single magnetic particle acts as a sensor for a flock of non-magnetic particles. The BQ system is not at thermodynamic equilibrium. An important feature of self-organizing non-equilibrium dissipative structures is the rate of entropy production. When a system is not in thermodynamic equilibrium, irreversible processes that drive the system towards equilibrium, generate entropy. As noted above, the rate of this entropy production is of interest because of the hypothesis of "maximum entropy production" (MEP) which posits that systems far from thermodynamic equilibrium evolve to states that maximize entropy production.2,9,31-32,33 When a system is close to thermodynamic equilibrium, minimum entropy production applies.40-41,42 There is a class of systems for which the MEP hypothesis is valid, but it is not universal. As it might be useful in this system, we explored the rate of entropy production. In earlier work on an electrically driven non-equilibrium system, we found consistent evolution to states with higher entropy production.13


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For the active BQ particles, the rate of entropy production is proportional to the rate of Gibbs surface free energy dissipation. Particle motion increases this rate of free energy dissipation because the fragments to regions of higher surface free energy (lower concentration) and thus increase the rate of their own dissolution. It appears that the formation and motion of the flock is yet another way the system increases the rate of entropy production. In other words, the question is whether the rate of dissolution of the BQ system featuring a flock is higher when compared to a system that does not exhibit flocking behavior. The BQ particles translate from the initial solid phase, BQ (s), to the solution phase, BQ (aq). Including conversion to the vapor phase BQ (g) we have these reactions: BQ (s)  BQ (aq)

(3)

BQ (s)  BQ (g)

(4)

The fraction of BQ transforming into the vapor phase is small, and can be neglected for quantitative calculations, but we include it here for theoretical completeness. Initially the solid phase dissolves and spreads on the liquid surface to decrease the surface tension. For a solution of BQ, the surface tension decreases with increasing concentration, from about 72.8 nN m-1 at zero concentration to nearly 68.6 mN m-1 at 100 mM (Figure S5). Since the decrease in surface tension is not uniform and isotropic, surface tension gradients are generated close to the dissolving particles. Thus, a complex process involving dynamics of particle dissolution, surface tension variations at the 3-phase intersection on particles, and particle motion are initiated which moves particles to regions of lower surface concentration and thus speeds up dissolution. If we denote the corresponding chemical potential of the three phases by s, aq, and g respectively, and the affinity, A, the driving thermodynamic forces for this reaction are: A = s - aq

(5)


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A' = s -g

(6)

Furthermore, if dξaq and dξg are molar amounts of BQ converted from solid to aqueous and gas phases in time dt, respectively. Total rate of entropy production is:

(7) In practice, dξg/dt is very small and the amount of solid converted to the gas phase is virtually zero on the time scale of the experiment. Hence, we ignore it and measure the total entropy production in terms of the conversion to the aqueous phase. It is interesting that the motion generated by the surface tension gradients increases dξaq/dt and hence the rate of entropy production. These entropy-generating processes not only generate self-motion, but also produce self-organized motion manifested in the flocking behavior of irregularly shaped fragments. Since the flocking is not observed for circular BQ pellets, it raises the question if the flocking increases the rate of entropy production as self-organization generally does in non-equilibrium systems. In terms of the concentration C(t) of the BQ solution, this would mean that C(t) would increase faster for systems that demonstrates flocking. Neglecting the gas phase, the rate of entropy production is:

(8) Combing equation (8) with equation (1), we obtain

(9) For flocking, dissolution rate constant k was larger than for non-flocking systems. The k obtained values from rate of dissolution studies (Figure S1 and S2 ESI) plotted against the number of particles have slopes (Figure S1C) that show a 12% difference, suggesting from equation (9) that the rate of entropy production is slightly larger for the irregular-shaped flocking BQ particles. Thus, it is likely that


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attractive interactions between irregular BQ particles leading to increased entropy production contribute to flocking and foraging for interfacial free energy. Finally, the flock is dynamic structure whose members are in a state of flux and exhibits properties that the individual particles do not, such as in the magnetic field response. None of the members of the flock can detect a weak magnetic field, not even a lone magnetic particle. Its motion has too much kinetic energy to be confined to a region of the petri dish by the magnet. But the flock does, as a unit, move towards the magnet and hover around it, and thus "sense the field". The most probable reason for this is the dispersal of kinetic energy of the single magnetic particle into the flock due to particle interaction. By itself, the magnetic particle gains enough kinetic energy form the surface-tension gradients to overcome the magnetic field but, if it is in a flock, some of the gain in kinetic energy is transferred to other particles and the magnetic particle does not have quite enough kinetic energy to escape the magnet's force of attraction and slowly drifts toward it. As the magnetic particle drifts towards the magnet, the flock moves with it towards the magnet. In this sense, the flock as a whole is able to detect a magnetic field due to the presence of a "sensor particle". CONCLUSIONS Results described above illustrate a novel multi-particle self-motion system that forages for free energy. Spontaneous flock formation between multiple irregularly shaped BQ particles is driven by free energy gradients at particles on the air-water interface that develop from differential BQ dissolution at irregular surface points to drive co-operative motion. This dissipative flock structure demonstrated perception-action behavior by detecting and responding to temperature and magnetic fields, the latter when including only a single magnetic particle in the flock. Results may foreshadow more sophisticated systems based on these principles that could serve as the basis for simple but reliable sensors.


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ASSOCIATED CONTENT Supporting Information. Electronic supplementary document has 5 additional figures. In addition, eight video clips demonstrating self-motion events described here are available. AUTHOR INFORMATION Corresponding Author *Department of Chemistry (U-3060), University of Connecticut, 55 North Eagleville Road, Storrs, Connecticut 06269, United States, Email: [email protected] Author Contributions The manuscript was written through contributions of all authors. Funding Sources This work was financially supported by National Science Foundation’s INSPIRE Track 1 Program, Grant No. BCS-1344725. ACKNOWLEDGMENT The authors thank Professors Bruce Kay, Michael Turvey, Claudia Carello, and Jeffrey KinsellaShaw (University of Connecticut) for helpful discussions. We thank Gayatri Phadke and Kiki Chen for experimental assistance. REFERENCES

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Thermal- and Magnetic-Sensitive Particle Flocking Motion at the Air

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