ARTICLE pubs.acs.org/JPCA
Photoexcited Chemical Wave in the Ruthenium-Catalyzed BelousovZhabotinsky Reaction Satoshi Nakata,*,†,‡ Mariko Matsushita,‡,§ Taisuke Sato,† Nobuhiko J. Suematsu,†,|| Hiroyuki Kitahata,# Takashi Amemiya,^ and Yoshihito MoriO †
Graduate School of Science, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima 739-8526, Japan Department of Chemistry, Nara University of Education, Takabatake-cho, Nara 630-8528, Japan § Hikuma Junior High School, 4-2-15 Hikuma, Naka-ku, Hamamatsu 430-0901, Japan Meiji University, 1-1-1 Higashi-mita, Tama-ku, Kawasaki 214-8571, Japan # Department of Physics, Graduate School of Science, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan, and PRESTO, JST, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan ^ Graduate School of Environment and Information Sciences, Yokohama National University, 79-7 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan O Graduate School of Humanities and Sciences, Ochanomizu University, 2-1-1 Ohtsuka, Bunkyo-ku, Tokyo 112-8610, Japan
)
‡
bS Supporting Information ABSTRACT: The excitation of the photosensitive Belousov Zhabotinsky (BZ) reaction induced by light stimulation was systematically investigated. A stepwise increase in the light intensity induced the excitation, whereas a stepwise decrease did not induce the excitation. The threshold values for the excitation were found to be a function of the initial and final light intensities, time variation in light intensity, and the concentration of NaBrO3. The experimental results were qualitatively reproduced by a theoretical calculation based on a three-variable Oregonator model modified for the photosensitive BZ reaction. These results suggest that although the steady light irradiation is known to inhibit oscillation and chemical waves in the BZ system under almost all conditions, the stepwise increase in the light irradiation leads to the rapid production of an activator, resulting in the photoexcitation.
’ INTRODUCTION Studies of nonlinear chemical systems have experimentally and theoretically clarified the mechanism of spatiotemporal pattern formation, as seen in biological systems.14 In this strategy, many experimental systems in which the photosensitive oscillatory reaction occurs have been studied, for example, the BelousovZhabotinsky (BZ) reaction,58 BrayLiebhafsky reaction,9 BriggsRauscher reaction,10 pH oscillator,11 chlorine dioxideiodinemalonic acid system,12 and chlorate ion iodine system.13 In particular, the photosensitive BZ reaction has been widely studied, because in this reaction, it is easier to control the properties of the reaction kinetics and to initiate chemical waves without any physical contact stimulation.58 Gaspar et al. reported the photoinhibition and photoexcitation in the ferroin and Ru(bpy)32þ systems, but the mechanism was not perfectly clarified because both phenomena were observed at different periods of time in the same batch reactor.5,14 Toth et al. reported on light-induced chemical waves in the ferroin system.15 To clarify the mechanism of the photosensitive BZ reaction, researchers have focused on the role played by light irradiation in Ru(bpy)32þ-catalyzed BZ reaction. In general, light irradiation r 2011 American Chemical Society
produces bromide ions, which play a role of an inhibitor of the oscillatory reaction.58,16 However, a change from a reduced steady state to an oscillatory state with an increase in the light intensity was reported in the continuous-flow stirred tank reactor (CSTR) system that included Ru(bpy)32þ under the continuous irradiated condition.17 Systematic studies of the Ru(bpy)32þcatalyzed BZ reaction14,16,18 and Ru(bpy)32þ-catalyzed minimal bromate reaction1719 have led us to conclude that light functions either as an inhibitor or as an activator, depending on the solute compositions in the photosensitive BZ reaction. Thus, the Oregonator model has been modified to include the photochemical generation of the inhibitor (Br) and the activator (HBrO2),20 and the extended modified Oregonator-class models have exhibited a variety of photoinduced behavior in homogeneous systems2123 and reaction-diffusion systems.24 Petrov and co-workers have experimentally found the acceleration of a chemical wave under light irradiation.25 These studies noticed Received: February 6, 2011 Revised: May 11, 2011 Published: May 12, 2011 7406
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Figure 1. Schematic illustration of the experimental system based on the photosensitive BZ reaction (side view).
the effects of light under steady irradiation2022,25 or sinusoidal irradiation.24 Wang reported the numerical results26 for the excitation of the BZ reaction by pulsed irradiation, which was experimentally studied by Kaminaga et al.,27,28 using the Oregonator model that included the photo production of the inhibitor but not the activator.18 Considering that a pulsed irradiation process is composed of both a stepwise increase and a stepwise decrease in light intensity, it is not clear which process plays the essential role in the functioning of the irradiation process. Therefore, to obtain a fundamental understanding of the photosensitive BZ reaction, it is necessary to investigate the stepwise increase and decrease in the light intensity independently and to discuss them in relation to the photogeneration of the activator and the inhibitor. In the present study, we examined the effect of a stepwise increase or decrease on the light intensity in the photosensitive BZ reaction catalyzed with Ru(bpy)32þ. We found that wave propagation occurs when there is a stepwise increase in the light intensity, that is, photoexcitation, where no oscillation occurs under both the initial and final light intensities. We experimentally investigated the photoexcitation depending on parameters such as the initial and final light intensities, time variation in the light intensity, and the concentration of NaBrO3. The experimental results were qualitatively reproduced by numerical calculations based on a three-variable Oregonator model modified for the photosensitive BZ reaction.
’ EXPERIMENTS Ru(bpy)3Cl2, purchased from Sigma-Aldrich, was used as a catalyst for the photosensitive BZ reaction. The BZ solution consisted of [NaBrO3] = 0.45 to 0.55 M, [H2SO4] = 0.3 M, [CH2(COOH)2] = 0.16 M, [KBr] = 0.01 M, and [Ru(bpy)3Cl2] = 1.7 mM. A cellulose nitrate membrane filter (Advantec, A100A025A, diameter of the membrane = 25 mm, thickness = 150 μm) with a pore size of 1 μm was completely soaked in stirred BZ solution (5 mL) for about 1 min. The soaked membrane filter was gently wiped with another pure filter paper to remove excess solution and placed on a glass plate (77 52 1.3 mm3). The surface of the membrane filter was completely covered with 0.7 mL of silicone oil (Wako, WF-30) to prevent it
Figure 2. Schematic illustration of (a) a rectangular reaction field (top view) and (b) time variation in three features of light stimulations (experiments I, II, and III).
from drying. The experiments were carried out in an air-conditioned room at 298 ( 1 K. The medium was irradiated from below as shown schematically in Figure 1.29 The high-pressure mercury bulb of a liquid-crystal projector (Mitsubishi, LPV-XL8) was used as a light source, and a magnifying lens was used to adjust the focus. The spatial intensity distribution was controlled with a personal computer; the brightness was represented by the gray scale, where black and white corresponded to 0 and 100, respectively. A rectangular field (region L) was prepared for the experiments, on which the light intensity was φini, as indicated in Figure 2a. Inside region L, another smaller rectangular field (region S) was prepared as a light stimulation, the light intensity on which was changed from φini to φfin. As for the change in the light intensity, the gray scale in region S was temporally changed by running a program on a personal computer. The reaction medium showed no chemical wave or no oscillation in either the initial or the final stages, that is, the initial state on regions S and L was excitable before the light stimulation and the final state in region S was excitable or suppressed. The reaction field outside of region L was in a suppressed state both before and after the light stimulation. Three features of light irradiation were examined as experiments I, II, and III (see Figure 2b). With regard to experiment I, the initial light intensity (φini) was changed from 160 to 3700 lx (gray scale: 0 to 40), but the final intensity (φfin) was constant at 19300 lx (gray scale: 100). In experiment II, φini was constant at 160 lx (gray scale: 0), but φfin was changed from 180 to 19300 lx (gray scale: 10 to 100). In experiment III, φini and φfin were constant at 160 and 19300 lx, respectively, but the transition time on the increase in the light intensity was changed from 0 to 15 s. The transition of light intensity was carried out using a movie file that was composed of 30 fps and 256 gray scales. The light intensity at the irradiated section was measured with a light intensity meter (As-one, LX-100). Actually, we linearly increased the gray scale, but the relationship between light intensity and gray scale was not completely linear (see Figure S3b). At least 20 examinations were performed for the same experimental condition. 7407
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Figure 5. Experimental results of the probability on the photoexcitation depending on the transition time of the light intensity from dark to bright in experiment III. The concentration of NaBrO3 was 0.52 M.
Figure 3. Experimental results are shown as follows: (a) Space-time diagram and (b) typical snapshots of photoexcitation and wave propagation in experiment I (top view). The initial light intensity was 160 lx (gray scale: 0) and the final light intensity in region S was 19300 lx. Space-time diagram in (a) was obtained by the analysis on the horizontal line at the middle of the field of view in (b).
Figure 4. Experimental results of the probability on the photoexcitation depending on (a) the initial light intensity (φini) in experiment I and on (b) the final light intensity (φfin) in experiment II. The concentration of NaBrO3 was 0.52 M.
The experiments were monitored from above with a digital video camera (Sony, DCR-VX700). A blue optical filter (Asahi Techno Glass, V-43) with a maximum transparency at 410 nm was used to enhance the images of the green-colored solution, which corresponds to the oxidized state, Ru(bpy)33þ. The wave propagation was analyzed by an image-processing system (National Institutes of Health, ImageJ).
’ RESULTS Figure 3 shows the typical experimental results from the snapshots of a chemical wave generated by the light stimulation
Figure 6. Experimental results of the probability on the photoexcitation depending on (a) the concentration of NaBrO3 at the same initial light intensity (φini = 160 lx, gray scale: 0) and (b) the initial light intensity (φini) for different concentrations of NaBrO3 (filled diamond: 0.47 M, filled circle: 0.48 M, filled square: 0.50 M, filled triangle: 0.52 M) in experiment I.
in experiment I. The excitation occurred inside region S and a chemical wave propagated outward from the edge of region S. In the present reaction field, two directional chemical waves, that is, the opposite directional waves propagating along the long axis of region L, were observed, and they then propagated at a constant velocity. Figure 4 shows the experimental results of the probability on the generation of a chemical wave depending on (a) the initial light intensity (φini) and (b) the final light intensity (φfin), which correspond to experiments I and II, respectively. Here, the probability was derived from at least 20 examinations for the individual conditions. As indicated in Figure 4a, no photoexcitation was observed when the initial light intensity was higher than 2100 lx. In contrast, the photoexcitation was observed with a higher probability (>80%) when φini was lower than 1000 lx. In Figure 4b, no photoexcitation was observed when φfin was lower than 2100 lx. In contrast, the photoexcitation was observed with a higher probability (>80%) when φfin was higher than 17000 lx. Figure 5 shows the experimental results of the probability on the generation of a chemical wave depending on the transition time on the scan of the irradiated light intensity in experiment III. When the transition time was shorter than 3 s, the probability of the photoexcitation was close to 100%. In contrast, the probability was 0% when the transition time was longer than 10 s. Figure 6 shows the experimental results of the probability on the generation of a chemical wave depending on (a) the concentration of NaBrO3 at φini = 160 lx and on (b) φini for different concentrations of NaBrO3 in the experiment I. As indicated in Figure 6a, the photoexcitation was observed when the concentration of NaBrO3 was over 0.46 M. In contrast, the 7408
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oscillation was observed over 0.52 M even without light stimulation. As indicated in Figure 6b, no photoexcitation was observed for every concentration region of NaBrO3 when φini was higher than 2100 lx. In addition, the probability of the photoexcitation increased with the increase in the concentration of NaBrO3.
’ DISCUSSION Based on the experimental results, we discuss the nature of photoexcitation in the BZ reaction. It is known that light irradiation produces Br from bromomalonic acid due to the photochemical reactions of the catalyst.58,16 Since Br works as an inhibitor in the BZ reaction, light irradiation can inhibit the BZ reaction (photoinhibition process). There is another photochemical process in the BZ reaction, in which HBrO2, the activator of the BZ reaction, is produced from BrO3 (photoactivation process). The first process is dominant under continuous light irradiation, and this is the reason why the excitation or chemical waves did not occur at the initial stage. However, a chemical wave was generated by the stepwise increase in the light intensity on region L. The latter process should occupy an important role in this phenomenon. Here, we introduced a photoactivation scheme into the mathematical model based on the Ru(bpy)32þ-catalyzed minimal bromate oscillator,8 that is, the inorganic part of the Ru(bpy)32þcatalyzed BZ reaction, as follows.
Figure 7. Numerical results. (a) Typical properties of the photoexcitation and chemical wave propagation induced by the instantaneous increase in the light intensity at τ = 0. The space-time diagram of w is shown. White and black regions correspond to the higher and lower w, respectively. The parameters are T = 0, A = 0.52, φini = 0.01, and φfin = 0.02. (b) Phase space for φini vs φfin, which shows the success or failure in the photoexcitation. The gray and black regions denote success and failure, respectively. The parameters are T = 0 and A = 0.52.
RuðbpyÞ3 2þ þ RuðbpyÞ3 2þ þ BrO3 þ 3Hþ The experimental results suggest the conditions to obtain the higher probability of photoexcitation: (i) the larger difference in the initial and final light intensities, φfin φini (Figure 4), (ii) the faster increase in the light intensity (Figure 5), and (iii) the higher concentration of NaBrO3 (Figure 6). As discussed above, the photoexcitation highly depends on the manner of time variation in light intensity. To systematically examine the features of photoexcitation, we performed numerical calculations based on a modified three-variable Oregonator model for describing the photosensitive BZ reaction.24 Du 1 ¼ ½qv uv þ uð1 uÞ þ p2 φ þ Du r2 u Dτ ε
ð1Þ
Dv 1 ¼ 0 ½qv uv þ fw þ p1 φ þ Dv r2 v Dτ ε
ð2Þ
Dw p1 ¼ uwþ þ p2 φ þ Dw r2 w Dτ 2
ð3Þ
where u, v, and w are dimensionless variables that correspond to the concentrations of the activator (HBrO2), inhibitor (Br), and oxidized catalyst (Ru(bpy)33þ), respectively, f, ε, ε0 , and q are positive parameters that determine the nature of the BZ reaction, φ corresponds to the light intensity, p1 and p2 are positive parameters that correspond to the Br production process and HBrO2 production process by light irradiation, respectively, and f is a stoichiometric parameter that was set to be 1.2 in the present study.30 These parameters, except for f, are determined by the initial concentrations as follows: k05 M 0:119M ¼ k03 A HA
ð5Þ
2k01 k04 ¼ 0:0000952 k02 k03
ð6Þ
p1 ¼
V 0:089 þ V þ 15H 2 A
ð7Þ
p2 ¼
15H 2 A 0:089 þ V þ 15H 2 A
ð8Þ
q¼
f 2RuðbpyÞ3 3þ þ HBrO2 þ H2 O
ε¼
2k04 k05 M 0:000238M ¼ k02 k03 A HA
ε0 ¼
ð4Þ
where k01, k02, k03, k04, and k05 are the rate constants for each chemical process reported in the previous paper.23 The time τ is rescaled with a time unit of 1/(k05M) (s). H, M, A, and V are the concentrations of the hydrogen ion, malonic acid, bromate ion, and bromomalonic acid measured in M. Du, Dv, and Dw are the diffusion constants for u, v, and w, respectively. For the diffusion constants, we set Du = Dv = Dw = 1. Considering that the diffusion coefficients are around 1.0 109 m2/s, the spatial scale in the calculation corresponds to 0.035 mm. The calculation is performed in a one-dimensional space with the size of 256 by the Euler method with a time step Δτ = 104; the spatial mesh size, Δx, is 1.0. In our numerical calculation, the parameters are set so that the system is in an excitable state. From the experimental condition, we fixed the values for H, M, and V as H = 0.6 (double the concentration of sulfuric acid), M = 0.16, and V = 0.015. Here, the concentration of bromomalonic acid is calculated by assuming that the following chemical reaction proceeds completely: 2Br þ BrO3 þ 3CH2 ðCOOHÞ2 þ 3Hþ f 3CHBrðCOOHÞ2 þ 3H2 O though V might be less in the experiment. In the initial condition, the value for φ is constant all through the field, that is, φ = φini. After allowing for enough time for the system to reach the steady state, the light intensity φ is changed to 7409
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Figure 8. Numerical results represented by the phase space (a) for T and φfin and (b) for A and φfin. φini is fixed as φini = 0.01. The gray and black regions represent the success and failure of photoexcitation, respectively. For (a), A is fixed as A = 0.52, and for (b), T is fixed as T = 0.
φfin only in the left half of the one-dimensional field (x < 0 in Figure 7a). The manner of the change in φ on the region x < 0 is characterized by T; that is, φ is described as the function of time t, where the time origin is set as when the change in the light intensity begins: 8 > ðτ < 0Þ φini > > < ðφfin φini Þτ ð9Þ φðτÞ ¼ φini þ ð0 < τ < TÞ > T > > : φfin ðτ > TÞ:
The results of numerical calculations based on the above differential equations are shown in Figures 7 and 8. At first, we fixed T = 0 (actually, φ was changed from φini to φfin at one time step Δτ; in this manuscript, we describe this situation as T = 0), and A = 0.52 from the experiments shown in Figures 4 and 5. We changed φ from φini to φfin and examined whether a photoexcitation was induced or not. The typical property of the photoexcitation and a chemical wave is exhibited by the space-time diagram of w in Figure 7a. After the change in the light intensity, the photoexcitation of the BZ reaction occurs, and a chemical wave begins to propagate. Figure 7b shows the phase space for φini vs φfin, which represents the success or failure in the photoexcitation. From Figure 7b, we can see that the photoexcitation occurs only when the light intensity is increased and that the difference in the light intensity is important, that is, the photoexcitation occurs with the large difference in the light intensity. Figure 8 shows the dependency on T and A under the condition of the fixed φini = 0.01. In each figure, φfin was also changed. Figure 8a shows that the rapid increase in the light intensity effectively induces the photoexcitation. The results in Figure 8a also correspond to the experimental results in Figure 5, where T in the numerical calculation corresponds to the transition time in the experiment. It is noted that the φin versus T diagram was similar to
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that in Figure 8a, even when the light intensity was changed in a sigmoidal manner (data not shown). From Figure 8b, we can see that the photoexcitation is induced by the higher concentration of NaBrO3, which corresponds to the experimental results, as shown in Figure 6a. It is noted that the threshold value of φ, below which spontaneous oscillation is induced, is 0.0034 under the present conditions. In the above experiments and numerical calculation, the edge of the region where the light intensity was changed was as sharp as possible. However, it is possible that the sharpness of the edge affects the photoexcitation. Thus, we made both the experiments and numerical calculations to investigate the photoexcitation depending on the spatial gradient of light stimulation. We could not obtain any results that suggest the effects of the spatial gradient either in experiments or numerical calculations (see Supporting Information). Thus, we suppose that the photoexcitation is induced only by the time change in the light intensity. Our experimental and numerical results indicated that the photoexcitation occurred not with the stepwise decrease, but with the stepwise increase in the light intensity. These processes can be understood by a scenario based on the change in the nullcline. Toth et al. discussed the photoexcitation in a ferroincatalyzed BZ system by the photoinduced removal of the inhibitor, Br, by using the description of the nullcline approach.15 In contrast, our scenario is different from that mentioned above; light irradiation may produce both HBrO2 and Br in the present system, and thus, light works as either an activator or an inhibitor depending on the solute compositions. Assuming that ε0 is of infinitesimal value, the change in the variable v is so fast that it can reach the equilibrium soon. Because the equilibrium value was determined by u and w, v can be regarded as a function of u and w; then, the chemical condition of the system is represented by a phase point in the two-dimensional space of u and w. The nullclines of u and w, which are the curves that satisfy du/dτ = 0 and dw/dτ = 0, respectively, can be described as follows: " # 1 uþq p1 φ ð10Þ w ¼ ðuð1 uÞ þ p2 φÞ f uq p1 þ p2 φ w ¼ uþ 2
ð11Þ
In the initial condition, the system is in the steady state, which corresponds to the phase point that is at the cross point of the two nullclines (Figure 9b(i)). With an increase in the light intensity φ (as shown in Figure 9a), the nullclines of both u and w shift in the positive direction of w, and as a result, the cross point moves upward (Figure 9b(ii)). Here, the moving cross point is also the steady state. If the rate of the shift is slow enough, the phase point can follow the cross point. Therefore, the system is always in the pseudosteady state and no excitation occurs. However, with a rapid shift of the nullclines, the phase point fails to follow the cross point and transfers to the right side branch due to the rapid production of the activator followed by undergoing a roundabout orbit before reaching the new steady state (Figure 9b(iii)). That is, the photoexcitation is observed. This mechanism agrees with our experimental observations (see Figure 5) and numerical calculations (see Figure 8a). 7410
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Figure 9. Schematic illustration used to discuss the mechanism of photoexcitation. (a) Time variation in the light intensity and (b) dependence of nullclines on the light intensity. In the initial condition, the system is in the steady state (b(i)). In response to an increase in the light intensity, the nullcline shifts from the dashed line to the solid line at t = tl. If the shift rapidly occurs in comparison with the rate of chemical reactions, the phase point (appearing circle mark) cannot follow the change in the cross point (b(ii)). Therefore, the phase point moves along the trajectory indicated by arrows; that is, the photoexcitation occurs (b(iii)).
This successful explanation requires the photoproduction term of the activator (photoactivation). Under the model in common use, 31 the nullclines of u and w are described as follows: " # 1 uð1 uÞðu þ qÞ φ ð12Þ w¼ f uq w¼u
ð13Þ
In this model, the light irradiation affects only the nullcline of u. An increase in the light intensity leads the shift of the nullcline of u in the negative direction of w, and the cross point also moves in the negative direction of w. 32,33 Then, photoexcitation does not occur in conjunction with an increase in the light intensity. Therefore, the photoproduction of HBrO 2 is necessary to explain the photoexcitation resulting from the increase in the light intensity.
’ CONCLUSION The major finding of this study is that the photosensitive BZ system can be excited by a rapid increase in the light intensity. The condition under which photoexcitation occurs was examined with regard to the time change in the light intensity and the concentration of NaBrO3, and the experimental results could be qualitatively reproduced by the numerical calculations based on a three-variable Oregonator model modified for the photosensitive BZ reaction. As the threshold value between excitation and no excitation is broad, the development of the experimental system should be necessary to determine the threshold value more precisely in the future study. The mechanism of photoexcitation was discussed in relation to the relaxation process of the cross point of two nullclines on the theoretical model. The experimental and numerical results obtained using our system not only provide the justification for the modification of the Oregonator model, but also clarify the distinction between the reaction kinetics of the photoactivation and photoinhibition processes in the BZ reaction. ’ ASSOCIATED CONTENT
bS
Supporting Information. Additional information on the spatial effect on the photoexcitation of a chemical wave and experimental observations. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*Tel./Fax: þ81-82-424-7409. E-mail:
[email protected].
’ ACKNOWLEDGMENT This work was supported in part by a Grant-in-Aid for Scientific Research (No. 23111715) and by the Meiji University Global COE Program “Formation and Development of Mathematical Sciences Based on Modeling and Analysis”. ’ REFERENCES (1) Zaikin, A. N.; Zhabotinsky, A. M. Nature 1970, 225, 535–537. (2) Field, R. J., Burger, M., Eds.; Oscillations and Traveling Waves in Chemical Systems; Wiley: New York, 1985. (3) Kapral, R., Showalter, K., Eds.; Chemical Waves and Patterns; Kluwer Academic: Dordrecht, 1995. (4) Magnani, A.; Marchettini, N.; Ristori, S.; Rossi, C.; Rossi, F.; Rustici, M.; Spalla, O.; Tiezzi, E. J. Am. Chem. Soc. 2004, 126, 11406–11407. (5) Gaspar, V.; Bazsa, G.; Beck, M. T. Z. Phys. Chem. (Leipzig) 1983, 264, 43–48. (6) Kuhnert, L. Nature 1986, 319, 393–394. (7) Kuhnert, L.; Agladze, K. I.; Krinsky, V. I. Nature 1989, 337, 244–247. (8) Jinguji, M.; Ishihara, M.; Nakazawa, T. J. Phys. Chem. 1992, 96, 4279–4281. (9) Sharma, K. R.; Noyes, R. M. J. Am. Chem. Soc. 1975, 97, 202–204. (10) Dulos, E.; De Kepper, P. Biophys. Chem. 1983, 18, 211–223. (11) Rabai, G.; Kustin, K.; Epstein, I. R. J. Am. Chem. Soc. 1989, 111, 8271–8273. (12) Mu~ nuzuri, A. P.; Dolnik, M.; Zhabotinsky, A. N.; R. Epstein, I. R. J. Am. Chem. Soc. 1999, 121, 8065–8069. (13) Galajda, M.; Lente, G.; Fabian, I. J. Am. Chem. Soc. 2007, 129, 7738–7739. (14) T oth, R.; Taylor, A. F. Prog. React. Kinet. Mech. 2006, 31, 59–115. (15) T oth, R.; Gaspar, V.; Belmonte, A.; O’Connell, M. C.; Taylor, A.; Scott, S. K. Phys. Chem. Chem. Phys. 2000, 2, 413–416. (16) Yamaguchi, T.; Shimamoto, Y.; Amemiya, T.; Yoshimoto, M.; Ohmori, T.; Nakaiwa, M.; Akiya, T.; Sato, M.; Matsumura-Inoue, T. Chem. Phys. Lett. 1996, 259, 219–224. (17) Mori, Y.; Nakamichi, Y.; Sekiguchi, T.; Okazaki, N.; Matsumura, T.; Hanazaki, I. Chem. Phys. Lett. 1993, 211, 421–424. (18) Kaminaga, A.; Mori, Y.; Hanasaki, I. Chem. Phys. Lett. 1997, 279, 339–343. (19) Sekiguchi, T.; Mori, Y.; Okazaki, N.; Hanazaki, I. Chem. Phys. Lett. 1994, 219, 81–85. 7411
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