J. Phys. Chem. 1996, 100, 14941-14948
14941
Photoinduced Bifurcation and Multistability in the Oscillatory Briggs-Rauscher Reaction Noriaki Okazaki, Yoshihito Mori,† and Ichiro Hanazaki* Institute for Molecular Science, Myodaiji, Okazaki 444, Japan ReceiVed: April 8, 1996; In Final Form: June 18, 1996X
The effect of continuous light irradiation on the Briggs-Rauscher system has been investigated by the light intensity scanning method. A state diagram has been established in the control parameter plane spanned by the initial concentration of I- ([I-]0) and the light power (P). An increase of [I-]0 leads to a transition from the large-amplitude oscillatory state (OS) to the reduced steady state (SSI), whereas an increase of P gives rise to a transition from OS to the oxidized steady state (SSII). Both transitions are accompanied by hysteresis, resulting in tristability among OS, SSI, and SSII in the overlapped part of the two hysteresis regions. In addition to the photoinhibition reported previously, the photoinduction of oscillations has been found in a certain range of [I-]0. In the low-[I-]0 region, bistability between OS and another oscillatory state with small amplitude (OS′) has also been discovered. The origin of the transitions is discussed on the basis of photoinduced autocatalytic processes.
Introduction The effects of light irradiation on the nonlinear chemical systems have been attracting much interest in recent years. Photoinduced bifurcations such as the photoinduction and -inhibition of chemical oscillations in well-stirred homogeneous solutions have been discovered for several systems.1-10 The image formation and its modulation by light irradiation in unstirred solutions have also been reported.11-14 The use of light is advantageous in the investigation of nonlinear chemical systems not only for its feasibility in changing irradiation power and wavelength, but also for its possibility in elucidating the reaction mechanism with a wider perspective. In order to establish the mechanism of photoirradiation effects, a unified treatment based on the concept of relative cross section has been developed15 and applied to several chemical oscillator systems5,16,17 for the identification of the primary light absorber. In most cases of the photoresponse of nonlinear chemical systems, the photoexcited species undergoes photochemical reactions to produce or consume the key species, which is essential in the positive- or negative-feedback loop. This may eventually lead to the photoinduction or -inhibition of oscillations. For example, the photoinduced bifurcations in the [Ru(bpy)3]2+-catalyzed Belousov-Zhabotinsky (BZ) system2-4 as well as those in the [Ru(bpy)3]2+-catalyzed minimal bromate oscillator7 have been interpreted as a result of the production or consumption of the key species HBrO2 and Br- by the photoexcited catalyst *[Ru(bpy)3]2+. Another type of photoinduced bifurcations may occur due to the nonlinear competition among light absorption by more than one species (screening effect). The photoinduced multistability18 and the broadening of oscillatory region19 have been reported to arise from the screening effect. Photoirradiation may also provide a new positive feedback loop (photoautocatalysis), where the photoexcitation process is involved in the autocatalytic loop as one of the component steps. This would lead to a novel oscillatory state or a multiple stability. However, no clear experimental evidence has so far been reported except for the photodecomposition of iodomalonic acid, which is claimed to be acompanied by the autocatalytic † Present address: Nagoya Institute of Technology, Showa-ku, Nagoya 466, Japan. X Abstract published in AdVance ACS Abstracts, August 15, 1996.
S0022-3654(96)01050-7 CCC: $12.00
formation of I- and I2 under certain conditions.20 We started the present study with the expectation that the Briggs-Rauscher (BR) system21 would provide a clear evidence for the photoautocatalysis that leads to a novel photoinduced bifurcation. The photoresponse of the BR system was first reported by Dulos and De Kepper.5 They found the photoinhibition of oscillations under continuous illumination and the synchronization of oscillations with periodic light.5 A model calculation has been made for these phenomena by Kumpinsky et al.22 Photoinduced image formation14 and photoinduced phase transitions under a batch configuration have been reported.23,24 We have confirmed from the action spectrum study that the primary photochemical process responsible for the photoinhibition of oscillations is the photodissociation of I2 both in the starchfree and starch-added systems.17 However, the study of the photoresponse of the BR system is still far from completeness. In order to establish its photoresponse, it is necessary to determine the photoinduced bifurcation structure and state diagram as functions of external control parameters including the irradiation light power. In addition, although the photoinhibition of oscillations has been found,5 there is no report on the photoinduction of oscillations in this system. In this paper, we extended the study on the photoresponse of the BR system by determining the bifurcation structure as a function of irradiation light power (P) under the continuous-flow stirred tank reactor (CSTR) configuration. The measurement is repeated for various initial concentrations of I- ([I-]0), to establish the state diagram taking P and [I-]0 as external control parameters. All the experiments have been carried out by means of the continuous light intensity scanning method recently developed by us,9,17,25 where the light intensity is slowly increased or decreased while the change in system behavior is continuously monitored. The scanning method is especially advantageous in characterizing the system behavior close to the bifurcation point, where a discrete change in the control parameter would lead to a large perturbation to the system and obstruct the accurate determination of the critical point. Experimental Section25 Reagent grade KIO3, MnSO4‚nH2O (n ) 4-5), HClO4, KI (Katayama Chemical), and stabilizer-free H2O2 (Mitsubishi Gas © 1996 American Chemical Society
14942 J. Phys. Chem., Vol. 100, No. 36, 1996
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Figure 1. Schematic drawing of the CSTR system designed for the continuous light intensity scanning experiment.
Chemical) were used without further purification. Reagent grade CH2(COOH)2 (Wako Pure Chemical) was recrystallized once from acetone prior to use.26 Distilled and deionized water was used throughout. Concentrations of HClO4 and H2O2 were determined iodometrically. The concentration of MnSO4 was determined by the conventional ethylenediaminetetraacetic acid (EDTA) titration. Four stock solutions were prepared every day immediately before each experiment. The first stock solution contained KIO3 and CH2(COOH)2, the second MnSO4 and HClO4, the third H2O2, and the fourth KI. MnSO4 was dissolved in the acidic solution in order to avoid possible air oxidation. Negligible amount of surfactant (Extran MA 02, Merck) was added to the fourth stock solution in order to minimize oxygen bubbles, which causes undesirable light scattering. Addition of a small amount of surfactant (20 ppm in the reactor) was proved not to affect the system behavior in both the presence and absence of illumination. The initial concentrations employed throughout this work were [KIO3]0 ) 17 mM, [MnSO4]0 ) 2.3 mM, [HClO4]0 ) 25 mM, [H2O2]0 ) 200 mM, and [CH2(COOH)2]0 ) 2.0 mM, where [X]0 denotes the concentration of X in the reactor to be attained if no chemical reaction took place. The initial concentration of KI was varied from 0 to 0.072 mM. Figure 1 shows a schematic drawing of the CSTR system designed for the continuous light intensity scanning experiment. A cylindrical Pyrex glass reactor with a volume of 8.24 cm3 was embedded in a water jacket made of acrylic resin equipped with quartz windows for illumination. The four stock solutions were separately fed to the reactor by a peristaltic pump (Eyela, MP-3) through Teflon and Pharmed (Eyela) tubes. The reaction mixture was stirred vigorously by a Teflon-coated magnetic stirrer bar and overflowed from the top of the reactor. The inverse residence time was fixed at k0 ) 4.69 × 10-3 s-1. The reaction temperature was maintained at 25.0 ( 0.1 °C by heat exchange with pure water circulated between the water jacket and a pure-water pool immersed in a thermostated water bath (Eyela, NTT-1300). Monochromatic light was supplied by the combination of a 500-W ultra-high-pressure Hg lamp (Ushio, USH-500D) and a monochromator (Ritsu, MC-20L). Spectral band width, optical path length, and beam cross section were 10.8 nm, 1.78 cm, and 0.21 cm2, respectively. The light intensity was controlled by a continuously variable neutral-density filter (Sigma Koki,
Σ-782(U)), which was equipped with a stepping motor (Oriental Motor, UPD534M-A) driven by a control board (Contec, PMC1(98)H). A part of the incident beam was taken with a quartz beam splitter (Sigma Koki, BS4-50C05-10-550) immediately before the reactor cell and was continuously monitored by a photodiode (Hamamatsu, S1723-05). The incident beam intensity was calibrated to the sampled beam intensity prior to each experiment. The optical setup allowed us continuous light intensity scanning with a desired time profile, by applying proportional-integral-differential (PID) control of the stepping motor with reference to the sampled beam intensity. The typical scan rate of the incident beam intensity was 0.5-1.0 µW/min for the 460-nm light. The measurement was carried out by a calibrated iodideselective electrode (Horiba, 8004-06T) for [I-] and by a combined Pt-Ag|AgCl electrode (Horiba, 6861-10C) for the redox potential. The change in [I2] was followed by absorption spectroscopy at 460 nm with a photodiode (Hamamatsu, S172305) which monitors the transmitted light power. The Ag|AgCl electrode of the combined electrode was commonly used as a reference for both the iodide-selective and platinum electrodes. Electrode potentials were recorded on a personal computer (NEC, PC-9801RX) through a 12-bit A/D converter (Contec, AD12-16F(98)). Photocurrent signals from the photodiodes were also recorded through photosensor amplifiers (Hamamatsu, C2719). Results 1. Photoinduced Bifurcation Structures. A typical result of the light intensity scanning experiment is given in Figure 2 for [I-]0 ) 0 mM, where the 460-nm monochromatic light intensity (P) is increased (a) and decreased (b). The photoinduced bifurcation structure can directly be visualized by this method. The oscillatory wave forms are shown in Figure 3 at P ≈ 95 µW. Figure 3 shows that the Pt potential (EPt) gives almost the same wave form as log ([I2]/[I-]2), confirming the argument that EPt is predominantly determined by the equilibrium27
I2 + 2e- h 2ILight intensity scanning experiments similar to that given in Figure 2 was carried out for various [I-]0 values. The results
Oscillatory Briggs-Rauscher Reaction
J. Phys. Chem., Vol. 100, No. 36, 1996 14943
Figure 2. Effect of 460-nm monochromatic light irradiation in the BR system monitored by [I-], Pt potential (EPt), and [I2]. The light power (P) was slowly (a) increased or (b) decreased as shown in the bottom panels. Experimental conditions: [KIO3]0 ) 17 mM, [MnSO4]0 ) 2.3 mM, [HClO4]0 ) 25 mM, [H2O2]0 ) 200 mM, [CH2(COOH)2]0 ) 2.0 mM, [KI]0 ) 0 mM; temperature 25.0 °C; residence time 3.6 min.
Figure 3. Oscillatory wave forms in (a) log([I-]), (b) [I2], (c) log([I2]/[I-]2) calculated from (a) and (b), and (d) Pt potential (EPt) at P ≈ 95 µW. Other conditions are the same as those given in Figure 2.
are summarized in Figures 4 and 5 for [I-] and [I2], respectively. On the basis of Figures 4 and 5, the system behavior is classified into five regions according to the values of [I-]0. (i) [I-]0 ) 0 and 0.009 mM (Figure 4a,b and Figure 5a,b). In this range, the system exhibits a regular large-amplitude oscillations (OS) under dark conditions. With increasing P, the oscillation amplitude and the period decrease monotonously. Both minimum and maximum values of [I2] tend to increase with P, indicating that I2 is generated by photoirradiation. At a certain critical light power, PO+ C , the oscillatory amplitude shrinks abruptly and the system undergoes a transition from OS to a yellow-colored steady state, SSII (photoinhibition of oscillations). A slight tailing of the small-amplitude oscillations is discernible in the vicinity of this transition point. SSII is characterized by relatively low [I-] and high [I2], in agreement with the previous reports.28,29 In SSII, both [I-] and [I2] tend to increase with increase in P. When P is reduced back from SSII, SSII remains stable until P reaches the critical light power PIIC, where small-amplitude oscillations (OS′) emerge. This oscillatory state is persistent
Figure 4. Photoinduced bifurcation structure in [I-] measured for various [I-]0: [I-]0 ) (a) 0, (b) 0.009, (c) 0.018, (d) 0.027, (e) 0.036, (f) 0.045, (g) 0.054, (h) 0.063, and (i) 0.072 mM. Other conditions are the same as those given in Figure 2. The minimum and maximum values of oscillations are plotted for the oscillatory states. The critical light powers PCO+, PCO-, PCO′, PCI, and PCII are also shown.
until P reaches PO′ C , where an abrupt increase in oscillation amplitude is followed by the transition back into OS. We confirmed the stability of OS′ by fixing the light power at a II point between PO′ C and PC. Consequently, we observed bistability between two different oscillatory states, OS and OS′, in O+ II the range PO′ C < P < min(PC ,PC). The transition between OS′ and SSII in the high light power region may be accompanied by a slight hysteresis. However, we could not obtain any detailed information because of insufficient experimental precision compared with the extreme instability of the system around this transition point. (ii) [I-]0 ) 0.018 mM (Figure 4c and Figure 5c). In this chemical composition, the system does not show oscillations in darkness when we start the reactant inflow after filling the reactor with pure water. The system finally reaches a colorless steady state, SSI,28,29 characterized by high [I-] and low [I2].
14944 J. Phys. Chem., Vol. 100, No. 36, 1996
Figure 5. Photoinduced bifurcation structure in [I2] measured for various [I-]0: [I-]0 ) (a) 0, (b) 0.009, (c) 0.018, (d) 0.027, (e) 0.036, (f) 0.045, (g) 0.054, (h) 0.063, and (i) 0.072 mM. Other conditions are the same as those given in Figure 2. The minimum and maximum values of oscillations are plotted for the oscillatory states.
In SSI, [I2] remains almost constant with increase in P while [I-] shows a slight decrease toward a critical light power PIC, where the system undergoes a discontinuous transition into OS. This is the first observation of the photoinduction of oscillations in the BR system. With further increases in light intensity, the oscillation amplitude and period decrease monotonously as in the case i. At PO+ C , a transition takes place from OS to SSII, where both of [I-] and [I2] increase with P similarly to case i. When P is decreased back from SSII, SSII remains stable until P reaches PIIC, where the system undergoes a discontinuous transition to OS. In this case, the small-amplitude oscillations are not observed. The transition between SSII and OS is accompanied by a large hysteresis since PIIC is significantly lower than PO+ C . The system remains in OS down to P ) 0. Thus, at [I-]0 ) 0.018 mM, the system is bistable between SSI and OS for 0 e P < PIC, monostable (OS) for PIC < P
PO+ C . (iii) [I-]0 ) 0.027 and 0.036 mM (Figure 4d,e and Figure 5d,e). In this region, SSI is stable up to the maximum available light power and is almost photoinsensitive: [I-] and [I2] do not change significantly with P. It is impossible, therefore, to observe any other state starting from SSI. However, this does not necessarily mean that the other states are nonexistent. It is indeed possible to stabilize SSII and OS in this region by perturbing the system in SSI by interrupting the reactant inflow for 2 or 3 min under the appropriate light power conditions. After realizing SSII at higher P, a decrease in P causes a transition into OS at PIIC. On the other hand, when P is increased from OS, the transition from OS to SSII takes place at PO+ C . The characteristics of these transitions are essentially the same as (ii) with the hysteresis region being much wider. It should be noted that this hysteresis region is overlapped with the stable region of SSI, exhibiting a tristability among SSI, SSII, and OS for PIIC < P < PO+ C . With decreasing P in OS, the oscillation amplitude and period increase monotonously until the trnasition from OS to SSI takes place discontinuously at POC . (iV) [I-]0 ) 0.045, 0.054 and 0.063 mM (Figure 4f-h and Figure 5f-h). A further increase of [I-]0 from region iii brings Oabout a monotonous increase in PO+ C and PC and a monotoII II nous decrease in PC. As a result, PC becomes lower than as shown in Figures 4f and 5f. In this case, a direct POC transition from SSII to SSI takes place at PIIC. Some transient oscillations have been observed by destabilizing SSII near the transition point. However, the oscillations die out soon even if P is held constant at PIIC. The stable region of OS becomes narrower and shifts toward higher P with increasing [I-]0. (V) [I-]0 ) 0.072 mM (Figure 4i and Figure 5i). No sustained oscillations were observed although the flow-interrupt perturbations were repeatedly applied under various light Ointensities. Since PO+ C and PC come close to each other with increasing [I-]0, the stable region of OS would disappear for [I-]0 > 0.072 mM. The transition from SSII to SSI takes place in a manner similar to (iv) but at a lower light intensity. 2. State Diagram. These results can be compiled in the form of a two-dimensional state diagram spanned by [I-]0 and P as shown in Figure 6. It is essentially composed of four states; namely, the large-amplitude oscillatory state OS, the smallamplitude oscillatory state OS′, the reduced steady state SSI, and the oxidized steady state SSII. The stable regions for these states are bounded by five bifurcation curves, γO+, γO-, γO′, OO′ γI, and γII, each corresponding to the locus of PO+ C , PC , PC , I II PC, and PC, respectively, obtained by varying [I-]0. The complicated state diagram may be understood basically as a variant of the cross-shaped phase diagram (XPD),30 in which bifurcation curves γI and γII, intersecting each other at point P, divide the diagram into four regions: SSI, SSII, OS, and bistable (SSI + SSII). The complex nature of the diagram arises mainly from the existence of hysteresis regions. The bifurcation curve γI, coupled with γO-, gives rise to the bistability between OS and SSI, while γII, coupled with γO+, gives rise to the bistability between OS and SSII. As a result, the tristable region consisting of OS, SSI, and SSII appears (PQRS in Figure 6). To our knowledge, the tristability including an oscillatory state was found for the first time in the present work, although tristability
Oscillatory Briggs-Rauscher Reaction
J. Phys. Chem., Vol. 100, No. 36, 1996 14945 which the absorption spectrum has been quantitatively analyzed by Roux and Vidal.35 These characteristics are essentially the same as those reported earlier for the photoinhibition of oscillations.17 Discussion 1. Dark Behavior. A qualitative interpretation has been made for the dark BR reaction,28,29,36 using the reaction scheme summarized in Table 1. Among them, the combination (D4) + 2(D6) gives rise to the autocatalytic step:
HIO2 + IO3- + 2Mn2+ + H+ + H2O f 2HIO2 + 2MnOH2+ (AC) If one starts at a high [I-] value, the rate of formation of HIO2 can be written as
d[HIO2]/dt ) kD4[H+][IO3-][HIO2] - kD2[H+][I-][HIO2] - k0[HIO2] ) kD2[HIO2][H+] ([I-]th - [I-]) Figure 6. Two-dimensional state diagram spanned by the initial concentration of I- ([I-]0), and the 460-nm monochromatic light intensity (P). The symbols OS, OS′, SSI, and SSII represent the largeamplitude oscillatory state, the small-amplitude oscillatory state, the reduced steady state, and the oxidized steady state, respectively. The bifurcation curves γO+, γO-, γO′, γI, and γII represent the loci of PCO+, PCO-, PCO′, PCI, and PCII, respectively.
among three steady states is known for several chemical oscillators including the BR system.30,31 Another interesting feature is the appearance of a bistability between two oscillatory states, OS and OS′, in the low-[I-]0 region. The bistability between two stable limit cycles is known in several systems such as the Duffing equation32 and the Ro¨ssler equation.33 The present result is presumably the first experimental observation of such a bistability in the chemical systems. 3. Primary Photochemical Process. Wavelength depenOI II dence of the critical light powers PO+ C , PC , PC, and PC has O+ Obeen determined experimentally, from which σR , σR , σIR, and σIIR, the relative cross sections for the corresponding primary photochemical processes, are calculated as functions of wavelength. The relative cross section is defined by
σR ) (hνD/PC)[1 - exp(-2.303D)]-1
(1)
where PC is the critical light power, D is the optical density of the reaction mixture at the bifurcation point, and hν is the photon energy.15 The σR plotted against wavelength is the “action spectrum” for the photoinduced bifurcation (Figure 7). II I The action spectra for σO+ R , σR, and σR have been deterOII mined at [I-]0 ) 0.018 mM, and those for σO+ R , σR , and σR have been determined at [I ]0 ) 0.054 mM. Since D keeps Ooscillating in OS until P reaches PO+ C or PC , at which OS O+ Odestabilizes discontinuously, σR and σR have been calculated by replacing D in eq 1 with the optical density averaged over a single period of oscillations at a point close to bifurcation. As is obvious from Figure 7, all action spectra possess a single broad peak around 450 nm, sharing a common feature with the absorption spectrum of an aqueous solution of I2. This indicates strongly that the primary light absorber responsible for destabilizing OS, SSI, and SSII is commonly I2 and that all these bifurcations are triggered by the photodecomposition of I2. The prominent increase in σR’s at the ultraviolet region is to be ascribed to the photodecomposition of iodomalonic acid34 for
(2)
where
[I-]th ≡ (kD4/kD2)[IO3-]0 - (k0/kD2)/[H+]0
(3)
In (3), [IO3-]0 and [H+]0 have been replaced with their initial concentrations, since they are large and do not change appreciably during the reaction. [I-] decreases by (D1), (D2), and (D3), the rate of which exceeds the formation rate by (D9) and the rate of external supply. The autocatalysis (AC) fires when [I-] becomes smaller than [I-]th to accumulate HIO2. When (AC) stops because of the contribution of (D5), I- begins increasing mainly by (D10) and (D9) and by the external supply. HIO2 decreases by (D2) and (D5). When [I-] becomes higher than [I-]th, (AC) can never fire, while MnOH2+ returns back to Mn2+ by (D7) and (D8). The system then returns to the initial stage and repeats oscillations. If the consumption of I- is compensated by the external supply of I-, [I-] can never decrease below [I-]th. The system then undergoes a transition into SSI. On the other hand, if [I-] < [I-]th holds throughout, the system bifurcates into SSII, where (AC) is always operating. Thus, I- serves as a controlling species which switches on or off the autocatalysis with respect to HIO2 through (D2). 2. Bifurcation Curves γI and γO-. The state diagram (Figure 6) indicates that, under dark conditions, the system stays in OS at a lower [I-]0. The OS is destabilized across γO- on increasing [I-]0. On the other hand, SSI is destabilized at γI on decreasing [I-]0. A hysteresis region appears between γI and γO-. These bifurcations can be understood with the model discussed above. As can be seen from Figure 6, the bifurcations taking place across γI and γO- are extentions of the dark bifurcations modified by the light irradiation. The positive slopes for both curves in the ([I-]0, P)-plane indicate that the critical values of [I-]0 for these bifurcations tend to increase with P. Whether I- is produced or consumed by the light irradiation is predictable from the slope of a bifurcation curve, provided that [I-]th is held constant along the bifurcation curve.7,9 The steep positive slope of γI would suggest slow consumption of I- in SSI by light irradiation, which is compensated by the increase of external supply of I- to keep [I-] > [I-]th. Similarly, the less steep γO- suggests rapid consumption of I- due to light irradiation in OS.
14946 J. Phys. Chem., Vol. 100, No. 36, 1996
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Figure 7. Wavelength dependences of the relative cross sections (action spectra) for [I-]0 ) (a) 0.018 and (b) 0.054 mM. The relative cross sections σRO+, σRO-, σRI, and σRII are determined for the critical light powers PCO+, PCO-, PCI, and PCII, respectively.
TABLE 1: Component Reaction Steps Relevant to the Briggs-Rauscher Systema,b IO3- + 2H+ + I- f HOI + HIO2 H+ + HIO2 + I- f 2HOI HOI + I- + H+ h I2 + H2O HIO2 + IO3- + H+ f 2IO2• + H2O 2HIO2 f HOI + IO3- + H+ IO2• + Mn2+ + H2O f HIO2 + MnOH2+ H2O2 + MnOH2+ f HO2• + Mn2+ + H2O 2HO2• f H2O2 + O2 I2 + MA f IMA + I- + H+ HOI + H2O2 f I- + O2 + H+ + H2O
(D1) (D2) (D3) (D4) (D5) (D6) (D7) (D8) (D9) (D10)
a From refs 28 and 29. b MA and IMA stand for malonic acid and iodomalonic acid, respectively.
Photoconsumption of I- is accomplished by (D3), where HOI is supplied by the reaction of photoproduced I•:
I• + H2O2 f HOI + HO•
(4)
When the system is in SSI, the concentration of I2 is kept extremely low. Hence, strong illumination is required to produce sufficient amount of I• to consume I-, resulting in the steep slope of γI. A decrease of P in OS close to γO- causes the increase of [I-] for the same reason. However, the effect is much more pronounced since the average [I2] is much higher in OS. This difference in [I2] between SSI and OS is just the reason for the appearance of hysteresis. 3. Bifuracation Curves γII and γO+. If P is decreased in SSII with [I-]0 being fixed, it loses stability at γII, while OS loses its stability at γO+ if P is increased in OS. If we simply apply the dark switching scheme to these bifurcations, in which the (AC) controlled by I- governs the behavior, the bifurcation should be determined by [I-] relative to [I-]th. In SSII, where (AC) is always operating, the reduction of P should increase [I-] to exceed [I-]th. The system goes to OS′, OS, or SSI, depending on [I-]0. However, this simple view seems to fail in accounting for the observed behavior of [I-] in Figure 4, where [I-] decreases with decreasing P down to PIIC. There is no simple explanation for decreasing [I-] leading to instability of the SSII. To see the corresponding behavior in OS, [I-], the average [I-] in a single cycle of oscillation, is calculated as shown in Figure 8. Although the physical meaning of [I-] and its relation to [I-]th is not clear, it shows a decreasing tendency with increasing P for each [I-]0 as expected from the simple argument given above, and the critical [I-] value for OS f SSI (γO-) is not dependent sharply on [I-]0, in agreement with the assumption of constant [I-]th. However, the critical [I-]
Figure 8. Dependence of [I-] in OS upon P, where [I-] represents [I-] averaged over a single period. Symbols: [I-]0 ) 0 (O), 0.009 (b), 0.018 (0), 0.027 (9), 0.036 (4), 0.045 (2), 0.054, (3) and 0.063 mM (1). The solid and dotted lines indicate the transition points for OS f SSI and OS f SSII, respectively.
value for the OS f SSII transition (γO+) depends strongly on [I-]0, which seems to be in contradiction with the assumption of constant [I-]th. Thus, the simple scheme of switching of (AC) based on the constant [I-]th seems to fail in accounting for the bifurcations at γII and γO+. It should also be noted that [I2] increases monotonously with P in both OS and SSII (see Figure 5), in spite of the increasing rate of photodecomposition of I2 with increasing P. This means that any alternative scheme to account for the observation should include a positive feedback of I2 under the light irradiation. In the following, two possible schemes will be examined on the basis of the present observations. 4. Kumpinsky-Epstein-De Kepper (KED) Model. In order to explain the BR system behavior under continuous and periodic light irradiation,5 Kumpinsky et al. proposed a model,22 in which the BR skeleton model28,29 is augmented by the elementary steps listed in Table 2. Under visible light irradiation, I2 undergoes photodecomposition (K1), as experimentally verified in section 3 of Results to form I• radicals. A part of I• may react with either HO2• or H2O2 to produce I- or HOI, respectively ((K2) and (K3)). The products I- and HOI are
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J. Phys. Chem., Vol. 100, No. 36, 1996 14947 gives a novel photoinduced autocatalytic process
TABLE 2: Supplemental Reaction Steps for the Briggs-Rauscher System under Photoirradiation22 I2 + hν h 2I• I• + HO2• f I- + O2 + H+ I• + H2O2 f HOI + HO• HO• + H2O2 f HO2• + H2O
hν
(1/2)I2 + IO3- + HIO2 + 2Mn2+ + (1/2)H2O2 + H2O 98
(K1) (K2) (K3) (K4)
2HIO2 + I- + 2MnOH2+ + (1/2)O2 (AC′)
the possible source of regenerating I2 taking into account the dark reaction (D3). On the basis of the KED model,22 one may consider the positive feedback channels hν
I2 + 2I- + H2O2 + 2H+ 98 2I2 + 2HO• + 2H2O
(5)
hν
(7)
where X is the photoproduced I• or any species produced by the reaction of I•. However, competition of (7) with (D2) and (D4) adds a negative term in the dark reaction (2) and henceforth adds a negative term to (3), which reduces [I-]th with increasing P. This does not account for the observation given above. To obtain the increasing tendency of [I-]th with P, the photoassisted multiplication of HIO2 is essential to compete with (D2) and (D4). We propose the following process as a candidate for such multiplication process
I• + IO3- + HIO2 + (1/2)H2O2 f 2IO2• + I- + (1/2)O2 + H2O (8) which, combined with (D6) and the photodissociation process hν
I2 98 2I•
(10)
HO• + (1/2)H2O2 f H2O + (1/2)O2
(11)
d[HIO2]/dt ) k10[I•][HIO2][IO3-]
(6)
which is composed of (K1) + 2(K2) + 2(D3). Although the KED mechanism has been shown to account for the photoinhibition of oscillations qualitatively,22 the present results reveal some serious discrepancies between the model C , the critical rate and observation. First, the typical value of kK1 of (K1) corresponding to the photoinhibition, estimated from 37 is of the order of ∼10-4 PO+ C obtained in the present study, -1 s , which is 8 orders of magnitude smaller than the value of ∼104 s-1 according to the KED model. Second, the KED model predicts a decrease of [I2] with kK1 around the photoinhibition point,37 resulting in relatively low [I2] in SSII. This is in contradiction with the present observation. Third, the KED model fails in reproducing the photoinduced multistability, which has been prominently observed in this study. Finally, it is difficult to find any suitable switching mechanism to control the autocatalysis with respect to I2. The photoautocatalysis for I2 ((5) or (6)) can never give rise to the new bifurcations (γII and γO+) without a switching mechanism such as (D2) in the case of the autocatalysis of HIO2 in the dark reaction. 5. Photoregulation of [I-]th. We have so far assumed a constant threshold to control the photoinduced bifurcation. An alternative scheme may involve the variation of [I-]th with P. If [I-]th decreases with decreasing P in SSII more steeply than [I-], [I-] could become greater than [I-]th to suppress (AC) at a certain level of P, even if [I-] is on the decrease. This accounts for the observed decrease of [I-] in SSII when P is decreased to the critical value for the transition to OS or SSI. To incorporate the variation of [I-]th with P, one may consider the photoassisted consumption of HIO2 such as
HIO2 + X f products
I• + HIO2 + IO3- f 2IO2• + HO• + I-
If step 10 is rate-determining, the rate of production of HIO2 by (8) + (D6) is
which is composed of (K1) + 2(K3) + 2(D3), and
I2 + 2HOI + 2HO2• 98 2I2 + 2O2 + 2H2O
Reaction 8 may be decomposed into the following elementary processes.
(9)
(12)
We may apply the steady state approximation with respect to the reactive species I•:
d[I•]/dt ) 2k9P[I2] - k10[I•][HIO2][IO3-] kK3[H2O2][I•] - k0[I•] ≈ 0 (13) from which we get the stationary concentration of I•:
[I•] ≈ RP[I2]
(14)
R ≡ 2k9/{k10[HIO2][IO3-] + kK3[H2O2] + k0}
(15)
where
If we assume that (AC′) as well as (AC) competes with (D2) for the production of HIO2, (2) becomes
d[HIO2]/dt ) [HIO2]{k10[I•][IO3-] + kD4[IO3-][H+] - kD2[I-][H+] - k0} (16) We may then redefine [I-]th as
[I-]th ≡ (kD4/kD2)[IO3-]0 {1 - (k0/kD4)/([IO3-]0[H+]0) + (Rk10/kD4)P[I2]/[H+]0} (17) instead of (3) for the dark reaction. The observed behavior of the system in SSII can qualitatively be accounted for by this model; for example, (AC′) predicts the production of I- by photoirradiation, which would account for the increase of [I-] with P in SSII (Figure 4). It is also suggested that one molecule of I2 produces two I• atoms by (9), which produces two I- by (AC′). They, in turn, produce two I2 molecules through (D3). Therefore, the photoassisted multiplication of I2 is predicted, which may account for the observation that [I2] increases with P in SSII (Figure 5) even if I2 is being decomposed by light. As discussed above, the transition SSII f SSI cannot be understood on the basis of a constant [I-]th. This difficulty can be overcome by employing the new definition of [I-]th in (17), where [I-]th increases with P. When P is decreased in SSII, [I-] decreases, as observed experimentally and predicted by (AC′). The transition to SSI or OS can occur if [I-]th decreases more steeply with decreasing P so that [I-] > [I-]th is realized at a certain level of P. The negative slope of the bifurcation curve γII in Figure 6 may also be understood on this basis. In SSII, the stationary value of [I-] does not change significantly with [I-]0, as can be seen in Figure 4. This would suggest that
14948 J. Phys. Chem., Vol. 100, No. 36, 1996 the excess I- introduced by an increase of [I-]0 is readily consumed in reaction D2, leading to the reduction of [HIO2]. Thus, R in (17) is considered to increase with increasing [I-]0. For higher [I-]0, the same value of [I-]th could be attained at a lower level of P, resulting in the negative slope of γII in the state diagram. We have assumed two independent autocatalytic processes, (AC) and (AC′), both of which are controlled by a single switching mechanism with a single quantity [I-]th defined by (17). If (Rk10/kD4)[I2][H+]0, the coefficient of P in (17), were constant, ∆P and ∆[IO3-]0 would affect [I-]th in the same way, resulting in a similar P-[I-]0 state diagram to the [IO3-]0[I-]0 diagram in the dark except for the sign of change of the parameter. The complexity observed in the state diagram in Figure 6 arises from the variation of the coefficient of P in (17) depending on the state of the system. The variation of R discussed above is an example of such variations. An even more typical example may be seen if we increase P, starting from the dark SSI at a high [I-]0. As can be seen in Figures 4-6, the system stays in SSI even at the highest P available in the present experiment. This is because the third term in (17) contributes little to [I-]th since [I2] is kept extremely low as far as the system stays in SSI. Such a variation of the effect of P on [I-]th causes the unusually large hysteresis in the photoinduced bifurcation and brings about the complicated multistability in the BR system. Conclusions The effect of continuous light irradiation on the BR system has been investigated thoroughly by the continuous light intensity scanning method. We have established a complete state diagram in the control parameter plane spanned by [I-]0 and P. This led us to new discoveries of the photoinduction of oscillations in this system, of the tristability among OS, SS, and SSII, and of the bistability between two oscillatory states, OS and OS′. The state diagram looks like a so-called crossshaped diagram. However, detailed analysis have revealed that, although the pair of bifurcations γI and γO- is the photomodulation of the dark bifurcation, the other pair, γII and γO+ cannot be accounted for by a simple modulation of the dark mechanism. We have proposed a novel photoautocatalytic scheme to explain the latter. Although there is no direct evidence for this scheme at present, it has been shown to account for the photoresponse of the BR system qualitatively very well. The characteristic feature of the proposed scheme is that it provides new photoassisted autocatalytic loop for HIO2 in addition to the dark autocatalysis, resulting in the light modulation of the threshold [I-]th for the bifurcation. This type of photoresponse seems to be rather unusual at present but should reveal its importance when the nature of photoresponse is clarified more extensively for many other chemical oscillators and, possibly, for biological systems. Future study should include a search for such novel photosensitive systems as well as the direct experimental verification of the present scheme using the simpler subsystems of the BR reaction, such as the Bray-Liebhafsky reaction.38,39 Acknowledgment. N.O. is obliged to the JSPS Research Fellowship for Young Scientists for financial support. This
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