Letter pubs.acs.org/JPCL
Oscillation of Speed of a Self-Propelled Belousov−Zhabotinsky Droplet Nobuhiko J. Suematsu,*,†,‡ Yoshihito Mori,§ Takashi Amemiya,∥ and Satoshi Nakata⊥ †
Graduate School of Advanced Mathematical Sciences, Meiji University, 4-21-1 Nakano, Tokyo 164-8525, Japan Meiji Institute of Advanced Study of Mathematical Sciences, Meiji University, 4-21-1 Nakano, Tokyo 164-8525, Japan § Graduate School of Humanities and Sciences, Ochanomizu University, 2-1-1 Ohtsuka, Bunkyo-ku, Tokyo 112-8610, Japan ∥ Graduate School of Environment and Information Sciences, Yokohama National University, 79-7 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan ⊥ Graduate School of Science, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima 739-8526, Japan ‡
S Supporting Information *
ABSTRACT: Self-propelled objects can become potential biomimetic micromachines, but a versatile strategy is required to add the desired functions. Introducing a characteristic chemical reaction is a simple answer; however, the problem is how the chemical reaction is coupled to the self-propelled motion. We propose a strategy to select the chemical reaction so that its product or intermediate affects the driving force of a selfpropelled object. To demonstrate this strategy, we put an aqueous droplet of nonlinear chemical reaction, the Belousov−Zhabotinsky (BZ) reaction, into an oil phase including a surfactant, where an aqueous droplet was driven by an interfacial reaction of the surfactant and bromine. The results exhibited oscillation of speed, and it was synchronized with the redox oscillation of the BZ reaction in the droplet. Bromine is one of the intermediates of the BZ reaction, and thus the droplet motion well-reflected the characteristics of the BZ reaction.
S
example, a BZ droplet or gel shows a reciprocating motion driven by a chemical wave propagating inside them.28−30 This type of motion requires chemical-wave generation, and it restricts the reflection of features of the nonlinear chemical reaction in a self-propelled motion. In the present paper, we propose a strategy to realize a selfpropelled object that reflects the features of nonlinear chemical reactions. We prepared a self-propelled droplet, which could move without a chemical wave, and introduced the BZ reaction to the aqueous droplet. Our strategy is that if the concentration of the products or intermediates of the BZ reaction affects the driving force, the self-propelled motion might show high nonlinearity. Recently, Herminghaus et al. have briefly reported the oscillatory motion of a BZ droplet in a similar system.14,34 However, systematic experiments and understanding the coupling mechanism are still under investigation. To demonstrate our strategy, we prepared a BZ droplet (∼0.2 μL in volume and ∼1 mm in diameter) into a monoolein (MO) squalane solution (10 mM) using a micropipet. Owing to its higher weight density, the aqueous droplet settled down and moved in 2D at the bottom of a glass Petri dish. The droplet motion was observed at every second using a microscope (SMZ1000, Nikon, Japan), and the movies were
everal types of self-propelled objects have been developed using nonliving materials,1−4 for example, colloidal particles swimming in H2O2 solution,5−9 a solid particle or an oil droplet driven by the difference in the interfacial tension around them,10,11 and an oil or aqueous droplet propelled by Marangoni flow.12−14 In the latter case, the driving force is induced by the interfacial chemical reaction of a surfactant.15,16 Following the recent progress in these systems, various functionalities have been added to a self-propelled object, such as thermotaxitc7 and chemotactic behaviors,17,18 photosensitivities,19,20 and several types of collective motion.8,9,21−23 However, these advancements fall very short from living organisms that acquire a variety of environmental responsive strategies.24 One of the successful nonliving systems that mimic biological properties is a nonlinear chemical system such as the Belousov−Zhabotinsky (BZ) reaction. The BZ reaction is a redox reaction catalyzed by a metal ion or a metal complex ion and successfully reproduces several characteristics observed in living systems, for example, periodic oscillation, pattern formation, hysteresis, and bifurcation.25 Therefore, selfpropelled objects well coupled in a nonlinear chemical reaction is a promising system that can exhibit biomimetic functionalities. Steinbock and Müller first suggested the possibility of BZ droplet motion in 1998,26 and Kitahata et al. demonstrated it in 2002.27 Since then, several types of self-propelled objects coupled to the BZ reaction have been investigated.14,27−33 For © XXXX American Chemical Society
Received: July 13, 2016 Accepted: August 17, 2016
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surface tension, a chemical wave generates high inhomogeneity in the interfacial tension and thus induces Marangoni flow from the reduced to the oxidized region. This mechanism is similar to the previous system reported by Kitahata et al.27−29 The advantages of our system are that the BZ droplet moved under both the presence and absence of a chemical wave and maintained the motion direction even after the wave passed through the droplet (see also Movie 1 and Movie 2 in the SI). These differences are attributed to the presence of the driving force induced by the interfacial chemical reaction of MO in addition to that by a chemical wave. With the decrease in the droplet size, oxidation occurred near the center of the droplet and isotropically propagated outside. Such a size-dependent bifurcation has been investigated for the BZ reaction occurred into a small bead, where uniform oscillation was observed instead of a chemical-wave generation.37 The threshold diameter for the bifurcation was reported to be 600−800 μm and was determined by the comparison between traveling length of a chemical wave and diffusion length of the activator.37 Similar to the BZ bead, a submillimeter-sized BZ droplet exhibited uniform oxidation, as shown in Figure 2b. After passing through the oxidized state, the droplet then gradually and homogeneously returned to the initial reduced state (Figure 2b) (see Movie 3 in the SI). With the oscillation of the redox state of the BZ droplet, the motion speed also oscillated (Figure 2b), where the speed increased during the oxidation process. The speed of the self-propelled motion was synchronized in phase with the redox state of the aqueous phase (see also Figure S1 in SI). By adjusting the chemical condition, a BZ droplet with reduced/oxidized steady state was prepared, and the droplet continuously moved with a small fluctuation (Figure 2a,c). These results indicated that the oscillatory motion was not a fluctuation but was induced by coupling with the chemical oscillation inside the droplet. This oscillation in the speed (Figure 2b) supports our strategy. In the case of a smaller droplet, the inhomogeneity induced by the chemical wave was not very effective because the chemical wave was generated near the center of the droplet and isotropically propagated (Figure 2b). Therefore, the oscillatory motion cannot be explained by inhomogeneity due to the chemical wave. Here, we have to consider the role of the Br2 concentration. Thutupalli et al. suggested that the surfactant MO reacts with Br2 in the aqueous phase, and this interfacial chemical reaction triggers a self-propelled motion of the aqueous droplet.14 In the BZ reaction, Br2 is one of the intermediates, and thus the Br2 concentration oscillates, as is discussed later.38,39 Therefore, the droplet motion was influenced by the BZ reaction through the Br2 concentration and exhibited a characteristic oscillatory motion, as shown in Figure 2b. Although this result is similar to that in the previous reports by Herminghaus et al.,14,34 we newly found two types of oscillation of speed with and without a chemical wave (Figures 1 and 2b), the oscillation with a large amplitude at least 10 times greater than that of the previous one,34 and the bifurcation of the droplet motion depending on the BZ condition (Figure 2). In addition, we analyzed the synchronization between speed and redox state (see Figure S1 in the SI) that clearly indicated the droplet motion was controlled by the BZ reaction. These systematic experiments and analysis strongly support our strategy. Furthermore, we theoretically addressed the issue of oscillatory motion in the following part. A theoretical approach for the drift bifurcation of the droplet motion has been reported in which the surfactants lose their
analyzed using image analysis software (ImageJ, National Institutes of Health (NIH), USA) on a PC. In the BZ droplet with a larger size, the propagation of a chemical wave was periodically observed inside the droplet. An oxidized region (blue-color region) was locally generated at the edge of the droplet and propagated to the other side (Figure 1a). When a chemical wave was generated, the droplet rapidly
Figure 1. (a) Time series of the droplet motion images with and without a chemical wave. Before the “jumping” behavior, the homogeneous red droplet slowly moved (1200−1300 s). Then, an oxidized region (blue region) was locally generated at the edge of the droplet (1341 s) and propagated to the top (1341−1346 s). Concurrent with the chemical-wave propagation, the droplet rapidly accelerated toward the top. After the wave passed through the droplet, the droplet gradually decelerated and slowly moved again (1350−1450 s). (b) Time series of the speed and brightness of the blue color. When no chemical wave appeared, the speed was almost 10 μm s−1. This slow movement suddenly accelerated by almost 10 times when a chemical wave appeared. The diameter of the droplet was 1440 μm.
accelerated in the same direction as the chemical-wave propagation and gradually decelerated after the wave reached the other edge of the droplet (Figure 1). At this instant, the motion direction was maintained after the wave passed through half of the droplet, and a back-and-forth motion was not observed; that is, a large shift in the center of mass was observed (see Movie 1 in the Supporting Information (SI)). Furthermore, the droplet slowly moved when no chemical wave appeared (Figure 1a). In other words, the BZ droplet periodically repeated the slow motion and rapid acceleration (Figure 1b). The rapid acceleration was caused by the inhomogeneity of interfacial tension on the droplet surface, which was induced by the chemical-wave generation. The oxidized state of the BZ solution has higher surface tension rather than the reduced state,27,35 and thus a chemical wave induces Marangoni flow as was first reported by Miike et al.36 Assuming that interfacial tension at the oil/water interface exhibits the same tendency of 3425
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Figure 2. Time series of the speed of the self-propelled motion (black line) and brightness of the blue color (blue line), which indicates the redox state of the droplet. The inset images show the color change during droplet motion. (a) Reduced steady state ([BrO3−] = 0.20 M, [H2SO4] = 0.60 M, [CH2(COOH)2] = 0.10 M, [Br−] = 0.030 M, and [Fe(phen)32+] = 4.0 mM). (b) Oscillatory state ([BrO3−] = 0.40 M, [H2SO4] = 0.60 M, [CH2(COOH)2] = 0.20 M, [Br−] = 0.030 M, and [Fe(phen)32+] = 2.0 mM). (c) Oxidized steady state ([BrO3−] = 0.40 M, [H2SO4] = 0.60 M, [CH2(COOH)2] = 0.050 M, [Br−] = 0.030 M, and [Fe(phen)32+] = 2.0 mM). The diameter of droplet was (a) 570, (b) 690, and (c) 730 μm.
surface activity after characteristic time κs−1.16 In our case, the surfactant MO reacts with Br2, and the interfacial tension then increases.14 Thus, κs is considered to be proportional to the Br2 concentration, assuming that the interfacial chemical reaction is linear. To clarify the effect of the Br2 concentration, we consider the relationship between the speed of the droplet motion u and characteristic time κs−1. The speed of the droplet u can be expressed as follows (see also the SI)16 u ≅ u0 1 −
u1* u1
U → atmosphere
where P is HOBr, Y is Br−, and U is Br2. The O8 process represents the physical removal process of Br2. In our case, an aqueous BZ droplet is covered by an oil phase, and thus such a physical process can be ignored. However, we have to consider the interfacial chemical reaction of Br2 instead of the physical removal process. By assuming that the average surface concentration of MO is constant in time, the rate of interfacial reaction is proportional to the Br2 concentration. Therefore, the O8 process can be considered to represent this interfacial chemical reaction in our system, and thus we can use the modified Oregonator model by only tuning the rate constant of the O8 reaction. The numerical approach using the modified Oregonator model indicates that the Br2 concentration rapidly increases with the oxidation of the catalyst and then gradually decreases with the reduced process (see Figure S3 in the SI).40 The theoretical approach and the numerical calculation reveal that the oscillation in the speed of the BZ droplet (Figure 2b) originates from the oscillation of the Br2 concentration inside the droplet, as shown in Figure S3. In other words, the BZ reaction controls the self-propelled motion through the Br2 concentration and reflects its own features to the mechanical behavior of the droplet. These conditions tell us that we succeeded in realizing a novel type of self-propelled system coupled to a chemical oscillatory reaction. As explained in the introduction, we suggested that if nonlinear chemical reactions affect the driving force of the droplet motion, the self-propelled droplet can reflect the features of nonlinear chemistry (Figure 3). Our experimental observations indicate that we succeeded in demonstrating such strategy. In conclusion, we have attempted to realize a novel type of self-propelled system that shows characteristic behavior originating from a nonlinear chemical reaction. To construct such system, we introduced the BZ reaction into a selfpropelled droplet driven by interfacial chemical reaction of a MO surfactant and Br2. Here the chemical oscillatory reaction and self-propelled motion were coupled through the concentration of one chemical (Br2 in this study) that was both an intermediate of the oscillatory reaction and a fuel for the selfpropelled motion (Figure 3). Consequently, we successfully observed periodical “jumping” behavior (Figure 1) and oscillatory motion of the BZ droplet (Figure 2b). In this study, we only succeeded in realizing an oscillatory motion.
(2)
where u0 is the characteristic speed, u1 is the strength of the chemomechanical coupling, and u1* is the critical point of the drift bifurcation. To focus our attention on the value of κs, u0 and u1 are considered constant, and only u1* is considered as the parameter, which can be expressed as a + κs u1* = b(1 − β /κs) (3) where a, b, and β are constant. This function has a minimum value of u1* at a critical value of κs*. (See also Figure S2 in the SI.) Thus, with assuming that the condition κs < κs*, u increases with κs in accordance with the Br2 concentration. Therefore, if the BZ reaction induces the oscillation of the Br2 concentration, then the speed will also oscillate. The mechanism of the chemical reactions in the BZ suggests that HBrO 2 (activator) is exponentially produced by autocatalytic reaction during the oxidation process.38,39 HBrO2 is known to react with Br− (inhibitor) and produces Br2, as expressed by the following chemical reactions40 HBrO2 + H+ + Br − → 2HOBr HOBr + Br − + H+ → Br2 + H 2O
Therefore, the Br2 concentration would be high during the oxidation process. In addition, a mathematical model to consider the effect of Br2 has been suggested by Field in 1986.41 They added the following three steps to the Oregonator model, which constructed five chemical equations (O1−O5), as expressed in the SI
P→Y
(O6)
Y+P↔U
(O7)
(O8)
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in part by Research Project Grant (B) of the Institute of Science and Technology Meiji University (N.J.S.) and in part by JGC-S Grant for Young Researcher (N.J.S.).
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(1) Paxton, F. W.; Sundararajan, S.; Mallouk, E. T.; Sen, A. Chemical Locomotion. Angew. Chem., Int. Ed. 2006, 45, 5420−5429. (2) Solovev, A. A.; Sanchez, S.; Schmidt, G. O. Collective Behaviour of Self-Propelled Catalytic Micromotors. Nanoscale 2013, 5, 1284− 1293. (3) Wang, J. Nanomachines; Wiley-VCH: Weinheim, Germany, 2013. (4) Nakata, S.; Nagayama, M.; Kitahata, H.; Suematsu, N. J.; Hasegawa, T. Physicochemical Design and Analysis of Self-Propelled Objects that are Characteristically Sensitive to Environments. Phys. Chem. Chem. Phys. 2015, 17 (17), 10326. (5) Paxton, W. F.; Kistler, K. C.; Olmeda, C. C.; Sen, A.; St. Angelo, S. K.; Cao, Y.; Mallouk, T. E.; Lammert, P. E.; Crespi, V. H. Catalytic Nanomotors: Autonomous Movement of Striped Nanorods. J. Am. Chem. Soc. 2004, 126, 13424−13431. (6) Yao, K.; Manjare, M.; Barrett, A. C.; Yang, B.; Salguero, T. T.; Zhao, Y. Nanostructured Scrolls from Graphene Oxide for Microjet Engines. J. Phys. Chem. Lett. 2012, 3, 2204−2208. (7) Sanchez, S.; Ananth, N. A.; Fomin, M. V.; Viehrig, M.; Schmidt, G. O. Superfast Motion of Catalytic Microjet Engines at Physiological Temperature. J. Am. Chem. Soc. 2011, 133, 14860−14863. (8) Gao, W.; Pei, A.; Feng, X.; Hennessy, C.; Wang, J. Organized Self-Assembly of Janus Micromotors with Hydrophobic Hemispheres. J. Am. Chem. Soc. 2013, 135, 998−1001. (9) Ke, H.; Ye, S.; Carroll, R. L.; Showalter, K. Motion Analysis of Self-Propelled Pt-Silica Particles in Hydrogen Peroxide Solutions. J. Phys. Chem. A 2010, 114, 5462−5467. (10) Bánsági, T., Jr.; Wrobel, M. M.; Scott, K. S.; Taylor, F. A. Motion and Interaction of Aspirin Crystals at Aqueous−Air Interfaces. J. Phys. Chem. B 2013, 117, 13572−13577. (11) Sumino, Y.; Magome, N.; Hamada, T.; Yoshikawa, K. SelfRunning Droplet: Emergence of Regular Motion from Nonequilibrium Noise. Phys. Rev. Lett. 2005, 94, 068301. (12) Toyota, T.; Maru, N.; Hanczyc, M. M.; Ikegami, T.; Sugawara, T. Self-Propelled Oil Droplets Consuming “Fuel” Surfactant. J. Am. Chem. Soc. 2009, 131, 5012−5013. (13) Hanczyc, M. M.; Toyota, T.; Ikegami, T.; Packard, N.; Sugawara, T. Fatty Acid Chemistry at the Oil-Water Interface: SelfPropelled Oil Droplets. J. Am. Chem. Soc. 2007, 129, 9386−9391. (14) Thutupalli, S.; Seemann, R. S.; Herminghaus, S. Swarming Behavior of Simple Model Squirmers. New J. Phys. 2011, 13, 073021. (15) Levan, M. D.; Holbrook, A. J. Motion of a Droplet Containing Surfactant. J. Colloid Interface Sci. 1989, 131, 242−251. (16) Yoshinaga, N.; Nagai, K. H.; Sumino, Y.; Kitahata, H. Drift Instability in the Motion of a Fluid Droplet with a Chemically Reactive Surface Driven. Phys. Rev. E 2012, 86, 016108. (17) Ban, T.; Tani, K.; Nakata, H.; Okano, Y. Self-Propelled Droplets for Extracting Rare-Earth Metal Ions. Soft Matter 2014, 10, 6316− 6320. (18) Miura, S.; Banno, T.; Tonooka, T.; Osaki, T.; Takeuchi, S.; Toyota, T. pH-Induced Motion Control of Self-Propelled Oil Droplets Using a Hydrolyzable Gemini Cationic Surfactant. Langmuir 2014, 30, 7977−7985. (19) Diguet, A.; Guillermic, R.-M.; Magome, N.; Saint-Jalmes, A.; Chen, Y.; Yoshikawa, K.; Baigl, D. Photomanipulation of a Droplet by the Chromocapillary Effect. Angew. Chem., Int. Ed. 2009, 48, 9281− 9284. (20) Palacci, J.; Sacanna, S.; Steinberg, A. P.; Pine, J. D.; Chaikin, M. P. Living Crystals of Light-Activated Colloidal Surfers. Science 2013, 339, 936−940. (21) Suematsu, J. N.; Tateno, K.; Nakata, S.; Nishimori, H. Synchronized Intermittent Motion Induced by the Interaction between Camphor Disks. J. Phys. Soc. Jpn. 2015, 84, 034802.
Figure 3. Schematic illustration of the relationship between the BZ reaction and self-propelled motion. The BZ reaction induces oscillation of the Br2 concentration, by which the speed of the selfpropelled motion is determined through the interfacial chemical reaction of MO. As a result, the speed of the droplet motion oscillates and synchronizes with the redox state. A red particle and a pink particle with stick represent Br2 and MO, respectively.
However, this type of self-propelled droplet is a promising system that can reflect various features of nonlinear chemical reactions such as oscillation, bifurcation, hysteresis, and so on. In addition, our system has a potential to show characteristic collective behavior, such as swarm oscillator.42 We believe that the self-propelled BZ droplet will play a role in a useful prototype system of self-propelled object that is coupled to the characteristic chemical reactions.
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ASSOCIATED CONTENT
S Supporting Information *
These materials are available free of charge via the Internet at The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.6b01539. Analysis of the synchronization of the speed and redox state and detailed explanations of the theoretical approach for speed u and the modified Oregonator model. (PDF) Movie 1. Movie for “jumping” behavior. (AVI) Movie 2. Movie for oscillatory motion with a chemical wave. (MPG) Movie 3. Movie for oscillatory motion without a chemical wave. (MPG)
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REFERENCES
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We thank Prof. T. Yamaguchi and Prof. V. Gáspár for their helpful discussions about the BZ reaction and Ms. K. Ito for her support in carrying out experiments. This work was supported 3427
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The Journal of Physical Chemistry Letters (22) Soh, S.; Branicki, M.; Grzybowski, A. B. Swarming in Shallow Waters. J. Phys. Chem. Lett. 2011, 2, 770−774. (23) Vicsek, T.; Zafeiris, A. Collective Motion. Phys. Rep. 2012, 517, 71−140. (24) Alvarez, L.; Friedrich, M. B.; Gompper, G.; Kaupp, U. B. The Computational Sperm Cell. Trends Cell Biol. 2014, 24, 198−207. (25) Kapral, R.; Showalter, K. Chemical Waves and Patterns; Springer, 1995. (26) Steinbock, O.; Müller, S. Radius-Dependent Inhibition and Activation of Chemical Oscillations in Small Droplets. J. Phys. Chem. A 1998, 102, 6485−6490. (27) Kitahata, H.; Aihara, R.; Magome, N.; Yoshikawa, K. Convective and Periodic Motion Driven by a Chemical Wave. J. Chem. Phys. 2002, 116, 5666−5672. (28) Kitahata, H.; Yoshinaga, N.; Nagai, H. K.; Sumino, Y. Spontaneous Motion of a Droplet Coupled with a Chemical Wave. Phys. Rev. E 2011, 84, 015101. (29) Kitawaki, S.; Shioiri, K.; Sakurai, T.; Kitahata, H. Control of the Self-Motion of a Ruthenium-Catalyzed Belousov−Zhabotinsky Droplet. J. Phys. Chem. C 2012, 116, 26805−26809. (30) Nakata, S.; Yoshii, M.; Suzuki, S.; Yoshida, R. Periodic Reciprocating Motion of a Polymer Gel on an Aqueous Phase Synchronized with the Belousov−Zhabotinsky Reaction. Langmuir 2014, 30, 517−521. (31) Hara, Y.; Saiki, M.; Suzuki, T.; Kikuchi, K. A Meniscus-climbing Gel Robot. Chem. Lett. 2014, 43, 938−940. (32) Szymanski, J.; Gorecki, J.; Hauser, J. B. M. Chemo-Mechanical Coupling in Reactive Droplets. J. Phys. Chem. C 2013, 117, 13080− 13086. (33) Izri, Z.; van der Linden, N. M.; Michelin, S.; Dauchot, O. SelfPropulsion of Pure Water Droplets by Spontaneous Marangoni-StressDriven Motion. Phys. Rev. Lett. 2014, 113, 248302. (34) Herminghaus, S.; Maass, C. C.; Krüger, C.; Thutupalli, S.; Goehring, L.; Bahr, C. Interfacial Mechanisms in Active Emulsions. Soft Matter 2014, 10, 7008−7022. (35) Yoshikawa, K.; Kusumi, T.; Ukitsu, M.; Nakata, S. Generation of Periodic Force with Oscillating Chemical Reaction. Chem. Phys. Lett. 1993, 211, 211−213. (36) Miike, H.; Müller, C. S.; Hess, B. Oscillatory Deformation of Chemical Waves Induced by Surface Flow. Phys. Rev. Lett. 1988, 61, 2109−2112. (37) Aihara, R.; Yoshikawa, K. Size-Dependent Switching of the Spatiotemporal Structure between a Traveling Wave and Global Rhythm. J. Phys. Chem. A 2001, 105, 8445−8448. (38) Field, J. R.; Boyd, M. P. Bromine-Hydrolysis Control in the Cerium Ion-Bromate Ion-Oxalic Acid-Acetone Belousov-Zhabotlnskli Oscillator. J. Phys. Chem. 1985, 89, 3707−3714. (39) Field, J. R.; Kórós, E.; Noyes, M. R. Oscillations in Chemical Systems. II. Thorough Analysis of Temporal Oscillations in the Bromate-Cerium-Malonic Acid System. J. Am. Chem. Soc. 1972, 94, 8649−8664. (40) Heeb, B. M.; Criquet, J.; Zimmermann-Steffens, G. S.; von Gunten, U. Oxidative Treatment of Bromide-Containing Waters: Formation of Bromine and Its Reactions with Inorganic and Organic Compounds A Critical Review. Water Res. 2014, 48, 15−42. (41) Field, J. R.; Forsterling, H.-D. On the Oxybromine Chemistry Rate Constants with Cerium Ions in the Field-Koros-Noyes Mechanism of the Belousov-Zhabotinskii Reaction: The Equilibrium HBrO2 + BrO3− + H+ ↔ 2BrO2• + H2O. J. Phys. Chem. 1986, 90, 5400−5407. (42) Tanaka, D. General Chemotactic Model of Oscillators. Phys. Rev. Lett. 2007, 99, 134103.
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