J. Phys. Chem. 1996, 100, 3221-3226
3221
Effect of Electric Current in the Minimal Bromate Reaction W. Hohmann, D. Lebender, R. Blittersdorf, and F. W. Schneider* Institut fu¨ r Physikalische Chemie der UniVersita¨ t Wu¨ rzburg, Marcusstrasse 9-11, 97070 Wu¨ rzburg, Germany ReceiVed: August 25, 1995; In Final Form: NoVember 7, 1995X
Experiments and calculations of two electrically coupled flow reactors are presented in which the minimal bromate (MB) reaction is carried out in its bistable region consisting of the thermodynamically controlled state which is characterized by a high Ce4+ concentration and the kinetically controlled state which shows low Ce4+ concentrations. Application of an electric current causes redox processes on the working electrodes. Inside the region of bistability a transition from the thermodynamic branch to the kinetic branch occurs in both the anodic and the cathodic reactors when the potential of the applied current exceeds certain threshold values. However, in the MB reaction a transition from the kinetic to the thermodynamic branch is not possible by the application of an electrical current. On the thermodynamic branch outside the bistability region, chemical oscillations are generated in both reactors when the electric current exceeds a threshold value. When the electric current is further increased, the oscillations give way to a steady state of a low Ce4+ concentration. After turning off the electric current the system returns to its original thermodynamic branch. On the kinetic branch at high flow rates the effect of the electric current on the redox potential is minimal. The experimental results are in good agreement with simulations using the NFT model provided that the effect of the electric current is specifically applied to the rate term for the bromine dioxide radical.
Introduction Electrical coupling represents an easy and efficient method to achieve interactions between chemical oscillators through Pt working electrodes. Crowley and Field2 used amplified electrical potentials between two Belousov-Zhabotinsky (BZ) oscillators in order to study phenomena such as entrainment, quasiperiodicity, and chaos as a function of electrical coupling strength. Nonamplified (passive) electrical coupling of oscillating BZ reactions served to build an electrochemical concentration cell representing a battery.3,4 This battery is able to produce alternating as well as quasiperiodic and chaotic currents. In previous work we also demonstrated that an electrical current induces transitions between steady states in the bistability region of the BZ reaction in a continuous flow stirred tank reactor (CSTR).5 On the basis of this new effect, we implemented the Boolean functions AND, OR, NAND, and NOR by the electrical coupling of three chemical reactors according to a simple feedforward network.6 In the present study we extend the method of electrical coupling to the minimal bromate (MB) system which represents the inorganic part of the BZ reaction. We will show that the MB system behaves differently from the BZ reaction regarding the switching between the chemical steady states through electrode processes which allows to draw interesting new conclusions about its mechanism. In accompanying model calculations we use a mechanism proposed by Noyes, Field, and Thompson1 (NFT) which is known to describe the kinetics of the minimal bromate reaction very well. We choose the so-called stage “e” of a reduced NFT mechanism according to Bar-Eli.7 Numerical simulations of the redox processes suggest that the major processes are the anodic oxidation of the intermediate radical bromine dioxide to bromate and the cathodic reduction of bromine dioxide to bromous acid. This assumption leads to good agreement between experiments and model calculations. Redox processes on the electrodes involving Ce3+ and Ce4+ do occur, but they * To whom correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, January 15, 1996.
0022-3654/96/20100-3221$12.00/0
Figure 1. Setup of two electrically coupled CSTRs: (1) Pt working electrodes, (2) potentiostat, (3) Pt/Ag/AlCl reference electrodes in each reactor, (4) Teflon membranes (1-2 µm pore size), and (5) salt bridge with sulfuric acid (1.0 M) which flows through the salt bridge. Three inlets for the reactants are placed at the bottom of each CSTR. The solutions are thermostated at 25 ( 0.2 °C and stirred with magnetic stirrers (6) at 600 rpm. The arrows indicate the outflow of the solution under aspirator vacuum.
TABLE 1 [H+]0 [BrO3-]0 [Br-]0 [Ce3+]0
numerical
experimental
1.5 M 4.5 × 10-2 M 2.0 × 10-4 M 1.5 × 10-4 M
2.0 M 4.5 × 10-2 M 1.8 × 10-3 M 3.0 × 10-4 M
do not seem to be important for the dynamic behavior of the MB reaction. Experimental Results The setup of the two electrically coupled CSTRs (3.2 mL volume each) is shown in Figure 1. Pt working electrodes (1) (3.0 cm2 surface) are immersed in each reactor and are connected to a potentiostat (2) supplying a constant potential at a given © 1996 American Chemical Society
3222 J. Phys. Chem., Vol. 100, No. 8, 1996
Figure 2. Experimental (a) and modeled (b) hysteresis diagram for the MB system. Label A marks the thermodynamic branch, B the region of bistability, and C the kinetic branch.
Hohmann et al. current. The measured potentials are monitored with a Pt/Ag/ AgCl reference electrode (3) inserted in each reactor. The signals are registered with a two-channel chart recorder, and the data are computer-collected at 1 Hz. A salt bridge (5) flushed by a constant flow of a solution of 1.0 M H2SO4 avoids mass exchange between the two reactors, and it allows contact through Teflon membranes (4) (1-2 µm pore size). Step-motor syringe pumps deliver three reactant feedstreams which enter through the bottom of each CSTR.8 The outflow of solutions is effected by an aspirator. The reactor concentrations of the inflow species are given in Table 1. All reactants are of analytical grade and used without further purification. The experiments are carried out at a temperature of 25.0 ( 0.2 °C and a stirring rate of 800 rpm using magnetic stirrers (6). The experimental bifurcation diagram (Figure 2a) represents the bistability region of the MB system with the flow rate kf as the bifurcation parameter. The transition from the thermodynamic branch to the kinetic branch occurs at a flow rate of kf ) 0.0062 ( 0.0003 s-1, whereas the system returns to the thermodynamic branch at a lower kf ) 0.0038 ( 0.0003 s-1 displaying the phenomenon of hysteresis. Between these flow rates the MB system shows bistability. Inside the bistability region the difference between the thermodynamic and kinetic branches is about 100 mV. Notice that the bifurcation diagram of the MB reaction is different from that of the BZ reaction. In the BZ reaction the thermodynamic branch displays low Ce4+ concentrations whereas the kinetic branch displays high Ce4+ concentrations.
Figure 3. Measured redox potential in the anodic and cathodic reactor at a flow rate of 0.0032 s-1 (region A). The arrows a and b indicate the switching on and off of the applied current. (a) Applied potential of 0.4 V (55 µA). The observed potentials in both reactors are shifted to lower values during application of the electric current. (b) Applied potential of 0.45 (65 µA). The potential in the anodic reactor oscillates whereas the potential in the cathodic reactor is shifted to a lower value. (c) Applied potential of 0.65 V (170 µA). The potential in the cathodic reactor oscillates whereas the potential in the anodic reactor is switched to a lower value where some perturbations can be observed due to variations in the current. (d) Applied potential of 0.7 V (190 µA). The cathodic reactor is switched to a steady state of low potential and returns to its original state with an overshoot after switching off the electric current. The anodic reactor behaves similarly as in (c).
Minimal Bromate Reaction
Figure 4. Measured redox potentials in the anodic and cathodic reactor at a flow rate of 0.005 s-1 (region B). The arrows a and b indicate the switching on and off of the applied current. (a) Applied potential of 0.40 V (55 µA). The system in the anodic reactor is switched from the thermodynamic to the kinetic branch. After turning off the electric current the system in the anodic reactor remains on the kinetic branch. (b) Applied potential of 0.65 V (160 µA). The system in the anodic and cathodic reactor is switched from the thermodynamic to the kinetic branch. After turning off the electric current the system remains on the kinetic branch. (c) Applied potential of 1.0 V (750 µA). Starting on the kinetic branch the potential in the anodic reactor is shifted to slightly higher values whereas in the cathodic reactor the potential remains almost constant.
Effect of Electric Current on Mutually Coupled MB Systems The measured redox potentials depend mainly on the Ce4+ concentration,9 and they are proportional to the logarithm of the Ce4+/Ce3+ ratio in the homogeneous reaction medium.
J. Phys. Chem., Vol. 100, No. 8, 1996 3223 Deviations of the potential from that given by the simple Nernst equation may be caused by the nonequilibrium behavior of the chemical reaction or may be explained by mixed potentials.10 Other species like the oxybromine species have less influence on the measured redox potential although they are very important in the chemical mechanism. Due to variations in the sensitivity of commercial redox electrodes, the redox potentials are given in arbitrary units. The absolute value of the Ce4+ concentration may be determined by spectroscopic means (absorption of Ce4+ at 350 nm).11,12 At the surface of the Pt working electrodes redox processes occur involving Ce4+, Ce3+, and the oxybromine species. The response of the MB system to the electrical current will be described in the three parameter regions A (thermodynamic branch), B (region of bistability), and C (kinetic branch) (Figure 2). Thermodynamic Branch A. When an electric current is applied to the system at a low flow rate of 0.0032 s-1, close to the region of bistability, a shift of the measured redox potential to lower values in both reactors, anodic and cathodic, is observed up to a value of 55 µA at an applied potential of 0.4 V (Figure 3a). Surprisingly, the shift in the anodic reactor is larger than in the cathodic reactor. When a threshold value of 60 µA (0.45 V) is exceeded, the behavior in the anodic reactor changes significantly: oscillations appear (Figure 3b). After switching off the current the system returns to its original steady state. An increase of the applied current above a value of 150 µA (0.65 V) leads to larger amplitude oscillations in the cathodic reactor whereas the redox potential in the anodic reactor drops to a lower value, becoming aperiodic (Figure 3c). The applied current oscillates with a low amplitude (about 10 µA) since it depends on the concentrations of the oscillating species. The aperiodic behavior in the anodic reactor may be caused by these perturbations. A further increase of the current up to 190 µA (0.7 V) leads to a drop of the redox potential to lower values in both reactors (Figure 3d). After switching off the electric current, the potentials return to their original value with an overshoot in the cathodic reactor. Region of Bistability B. At a flow rate of 0.005 s-1 (region B of the hysteresis diagram, Figure 2), application of an electric current of 50 µA (0.40 V) causes a transition from the thermodynamic branch to the kinetic branch in the anodic reactor whereas the potential in the cathodic reactor is only slightly lowered (Figure 4a). After turning off the electric current, the system in the anodic reactor remains on the kinetic branch while the system in the cathodic reactor returns to its initial state. An increase of the current to 160 µA at a potential of 0.65 V leads to a transition from the thermodynamic branch to the kinetic branch in the anodic and cathodic reactor (Figure 4b). The transition time in the cathodic reactor is shorter than in the anodic reactor. After turning off the electric current, the system remains on the kinetic branch in both reactors. In the MB system it is not possible to switch from the kinetic branch to the thermodynamic branch by the application of an electric current of either polarity. Starting the experiment on the kinetic branch a small shift of the redox potential is observed when a current of 750 µA at a potential of 1.0 V is applied (Figure 4c). The redox potential in the anodic reactor is shifted to higher values whereas the potential in the cathodic reactor remains almost constant. When the electric current is switched off, the redox potentials return to their initial values. Kinetic Branch C. At a flow rate of 0.0075 s-1 in region C (Figure 2), the behavior of the system on the kinetic branch is similar to the behavior of the kinetic branch inside the bistability region. The redox potential in the anodic reactor is shifted to higher values while the potential in the cathodic reactor is shifted
3224 J. Phys. Chem., Vol. 100, No. 8, 1996
Hohmann et al.
Figure 5. Measured redox potential in the anodic and cathodic reactor at a flow rate of 0.0075 s-1 (region C) and an applied potential of 1.0 V (750 µA). The arrows a and b indicate the switching on and off of the applied current. On the kinetic branch the potential in the anodic reactor is shifted to slightly higher values whereas in the cathodic reactor the system is shifted to lower values.
TABLE 2 BrO3- + Br- + 2H+ f HBrO2 + HOBr HBrO2 + Br- + H+ f 2HOBr HOBr + Br- + H+ h Br2 + H2O BrO3- + HBrO2 + H+ h 2BrO2• + H2O Ce3+ + BrO2• + H+ h Ce4+ + HBrO2
(R1) (R2) (R3) (R4) (R5)
TABLE 3 k1 k2 k3 k4 k5
2.1 s-1 M-3 2.0 × 109 s-1 M-2 8.0 × 109 s-1 M-2 1.0 × 104 s-1 M-2 6.5 × 105 s-1 M-2
k-3 k-4 k-5
1.1 × 102 s-1 M-1 2.0 × 107 s-1 M-1 2.4 × 107 s-1 M-1
to lower values. Even an increase of the electric current up to 2.45 mA at a potential of 1.5 V does not change the behavior of the system significantly (Figure 5). The relative effect in the anodic reactor is stronger than in the cathodic reactor. The small shifts may be caused by oxidation of Ce3+ at the Pt electrode in the anode reactor and reduction of Ce4+ in the cathodic reactor. Effect of Electric Current on a Single MB System For two coupled reactors oscillations in one reactor lead to variations of the electric current which perturb the other
reactor (Figure 3c). In order to avoid such mutual perturbations, experiments are carried out in a two-reactor setup in which one reactor only serves as a reference. The reference reactor contains a Ce4+/Ce3+ mixture (3.0 × 10-4 M/1.0 × 10-4 M) in sulfuric acid (1.0 M). The other reactor is used as before. With this experimental setup experiments are carried out in region A with a cathodic reactor where the applied current is kept constant while the flow rate is changed. At an applied potential of 0.75 V (200 µA), the flow rate is increased from 0.0018 to 0.003 05 s-1 (Figure 6). At a flow rate of 0.0018 s-1 the first oscillations emerge. Each further increase of the flow rate (0.002 05, 0.0023, 0.002 55 s-1) leads to stable oscillations of higher amplitude. At a flow rate of 0.003 05 s-1 a transition is observed from oscillations to a steady state of low potential. The same tendencies can be observed at an applied potential of 0.7 V (current 170 µA) where the flow rate is varied from 0.0025 to 0.0033 s-1. These experiments demonstrate that the amplitude of the oscillations depends on the flow rate. The threshold current for the observation of oscillations and for the stabilization of the low potential steady state is lowered with increasing flow rate. Although the current is not constant during the experiments due to the passivation of the surface of the Pt working electrodes, the amplitude remains constant at a given flow rate. Working with the anodic reactor in region A, oscillations can be observed at flow rates higher than 0.0032 s-1 with amplitudes increasing with higher flow rates. The threshold current for oscillations is lower than in the experiments in the cathodic reactor. Model Calculations The MB reaction can be modeled with a mechanism suggested by Noyes, Field, and Thompson (NFT model).1 Numerical simulations based on this model reproduce the experimental oscillations and bistability. The agreement between experiments and simulations is almost quantitative.13-19 The original 10-variable model may be reduced according to Bar-Eli7 (stage “e”) to a seven-variable model. The reduced model shows the same dynamic features as the original model. With respect to new kinetic measurements improved sets of rate constants were suggested by Tyson20 and by Field and Fo¨rsterling.21 The new set of rate constants shifts the dynamical phenomena in parameter space, but it does not improve the agreement between simulations and experiments.22
Figure 6. Measured redox potential in the cathodic reactor at an applied potential of 0.75 V (200 µA) (region A). Increase of the flow rate leads to oscillations of larger amplitude. At a flow rate of 0.003 05 s-1 a steady state of low potential is stabilized during the application of the electric current.
Minimal Bromate Reaction
J. Phys. Chem., Vol. 100, No. 8, 1996 3225
Figure 8. Simulated electrode reactions in region A with constant current (kel ) 1.0). An increase of the flow rate leads to an increase of the amplitude of the oscillations.
product of the flow rate kf and the difference between the actual concentration yi and the inflow concentrations y0i of the species i. The main electrode processes are single electron transfer reactions. Besides the Ce3+ and Ce4+ cations, the oxybromine species may also be involved in electrochemical redox processes at the Pt electrode. In the experiments inside the bistability region we observe switching from the thermodynamic to the kinetic branch by applying an electric current. Since the dynamics on the thermodynamic branch is determined by the autocatalysis (Table 2, reactions R4 and R5), the observed switching may be performed by inhibiting the autocatalytic reaction path. This may be achieved by the electrochemical consumption of the BrO2• radical. Furthermore, the experimental appearance of oscillations in region A (Figure 3b,c) requires that the rate of consumption of the latter species is higher on the thermodynamic than on the kinetic branch. The electrode reaction has to be at least first order with respect to the essential species. The bromine dioxide radical grants these requirements. Therefore, we suggest an additional chemical reaction at the Pt working electrode, which consumes the BrO2• radical in a first-order reaction. In the simulations we consider this further reaction by adding the term kely6 to the differential equation for the bromine dioxide radical turnover: Figure 7. Simulated electrode reaction in region A (kf ) 0.0035 s-1). The current is switched on at t ) 1000 s. (a) With low current (kel ) 0.55) the thermodynamic branch is preserved. Increasing the current, (b) an oscillatory state (kel ) 1.1) and (c) a kinetically determined state is obtained (kel ) 1.3).
Here we use the reduced version of the NFT model (Table 2) to explain the effects of the electrical current on the MB reaction. The rate constants are given in Table 3. The concentration of water is contained in the rate constants. The concentrations of the constant components H+ and BrO3- as well as the inflow concentrations of Ce3+ and Br- are given in Table 1. The theoretical and experimental concentrations of reactants are slightly different to improve the agreement between the experiments and calculations. From the chemical equations in Table 2 a 7-dimensional system, can be derived
dyi/dt ) fi(y) - kf(yi - y0i), i ) 1, 2, ..., 7
(1)
where y is a 7-dimensional vector containing the concentrations yi of all species i (Table 2). f represents the rate equations, while the flow through the open CSTR is modeled by the
dy6/dt ) f(y) - kf(y6 - y06) - kely6
(2)
The concentration of the bromine dioxide radical is given by y6, whereas kel is assumed to be directly proportional to the electric current as a first approximation. kel summarizes all microscopic physical and chemical processes which may take place at the electrode. With this modified system of differential equations our simulations are performed. At a flow rate of kf ) 3.5 × 10-3 s-1 the system stays on the thermodynamic branch (region A). If a small current is applied (kel ) 0.55), the Ce(IV) concentration is somewhat lowered (Figure 7a). Increasing the current strength leads to oscillations (kel ) 1.1, Figure 7b) and a state with low Ce(IV) concentration (kel ) 1.3, Figure 7c). In all cases the system recovers its original state after the current is switched off. Figure 8 shows the dependence of the amplitude on the flow rate while the current is kept constant. The calculation is started at a low flow rate (kf ) 2.9 × 10-3 s-1) and is raised stepwise up to a flow rate of kf ) 0.0035 s-1 close to the region of bistability (region B). Each increase of the flow rate leads to oscillations of higher amplitude.
3226 J. Phys. Chem., Vol. 100, No. 8, 1996
Hohmann et al. the oxidation and reduction of Ce3+ and Ce4+, respectively. Surprisingly, in the numerical simulations of the NFT model oxidation and reduction reactions involving Ce3+ to Ce4+ do not influence the dynamics of the MB system. In contrast, the Ce4+ in the BZ reaction induces transitions from the thermodynamic to the kinetic branch, and vice versa, by anodic oxidation or cathodic reduction, respectively.5 In the MB system, however, it is only possible to switch from the thermodynamic to the kinetic state; i.e., the electric current of either polarity interrupts the autocatalysis of bromous acid through the consumption of bromine dioxide radicals always leading to a state of low Ce4+ concentration. At low flow rates in region A of the bifurcation diagram (Figure 2) a continuous application of an electric current above a threshold value induces chemical oscillations. A further increase of the current leads to a newly generated steady state whose Ce4+ concentration is low (Figure 3d). The latter transition may act like a chemical switch which can be used to realize Boolean logical gates.23 Compared to flow rate perturbations the transition times are found to be shorter for electrical perturbations. Therefore, the electrical current provides a fast and convenient means to apply perturbations to nonlinear chemical reactions containing redox processes. Acknowledgment. We thank the Volkswagen Stiftung, the Deutsche Forschungsgemeinschaft, and the Fonds der Chemischen Industrie for partial support of this work. We thank G. Dechert and K.-P. Zeyer (Wallenstein) for helpful discussions. References and Notes
Figure 9. Simulated electrode reactions in region B (kf ) 0.005 (a) With low current (kel ) 0.110 012) the thermodynamic state is preserved. (b) At a higher current (kel ) 0.110 013) the kinetic branch is obtained. After switching off the electric current the system remains on the kinetic branch. s-1).
Inside the region of bistability (region B, kf ) 5.0 × 10-3 s-1) the MB system is switched from the thermodynamic to the kinetic state when the electric current exceeds a threshold value (kel ) 0.110 013, Figure 9b). The change appears only in one direction. After switching off the electric current the system retains its state. Below the threshold value for the applied current (kel ) 0.110 012) the Ce(IV) concentration is somewhat lowered, and the initial state is reached again after switching off the electric current (Figure 9a). Discussion On the basis of the good agreement between the numerical simulations and the experiments, we have assumed that the consumption of the bromine dioxide radical is the significant electrode reaction in the MB system. However, in order to switch from the thermodynamic to the kinetic branch inside the region of bistability, the turnover of electrons caused by the electrical current (5.18 × 10-7 mol L-1 s-1 at 160 µA) is much larger than the consumption of bromine dioxide radicals in our model calculation (1.56 × 10-8 mol L-1 s-1 at kel ) 0.110 013). Therefore, the postulated bromine dioxide radical consumption may be only a minor reaction while the main turnover is indeed
(1) Noyes, R. M.; Field, R. J.; Thompson, R. C. J. Am. Chem. Soc. 1971, 93, 7315. (2) (a) Crowley, M. F.; Field, R. J. In Nonlinear Phenomena in Chemical Dynamics; Vidal, C., Pacault, A., Eds.; Springer: New York, 1981. (b) Crowley, M. F.; Field, R. J. J. Phys. Chem. 1986, 90, 1907. (3) Schneider, F. W.; Hauser, M. J. B.; Reising, J. Ber. Bunsen-Ges. Phys. Chem. 1993, 97, 55. (4) Zeyer, K. P.; Mu¨nster, A. F.; Hauser, M. J. B.; Schneider, F. W. J. Chem. Phys. 1994, 101, 5126. (5) Dechert, G.; Schneider, F. W. J. Phys. Chem. 1994, 98, 3927. (6) Zeyer, K. P.; Dechert, G.; Hohmann, W.; Blittersdorf, R.; Schneider, F. W. Z. Naturforsch. A 1994, 49, 953. (7) Bar-Eli, K. J. Phys. Chem. 1985, 89, 2855. (8) Mu¨nster, A. F.; Schneider, F. W. J. Phys. Chem. 1991, 95, 2130. (9) Schmidt, V. M.; Vielstich, M. Ber. Bunsen-Ges. Phys. Chem. 1992, 96, 534. (10) Hjelmfelt, A.; Ross, J. J. Phys. Chem. 1994, 98, 9900. (11) Weiner, J.; Schneider, F. W.; Bar-Eli, K. J. Phys. Chem. 1989, 93, 2704. (12) Schneider, F. W.; Blittersdorf, R.; Fo¨rster, A.; Hauck, T.; Lebender, D.; Mu¨ller, J. J. Phys. Chem. 1993, 97, 12244. (13) Bar-Eli, K.; Noyes, R. M. J. Phys. Chem. 1976, 81, 1988. (14) Bar-Eli, K.; Noyes, R. M. J. Phys. Chem. 1978, 82, 1352. (15) Geiseler, W.; Bar-Eli, K. J. Phys. Chem. 1981, 85, 908. (16) Bar-Eli, K.; Geiseler, W. J. Phys. Chem. 1981, 85, 3461. (17) Bar-Eli, K.; Geiseler, W. J. Phys. Chem. 1983, 87, 3769. (18) Geiseler, W. Ber. Bunsen-Ges. Phys. Chem. 1982, 86, 721. (19) Geiseler, W. J. Phys. Chem. 1982, 86, 4394. (20) Tyson, J. J. In Oscillations and TraVelling WaVes in Chemical Systems; Field, R. J., Burger, M., Eds.; Wiley-Interscience: New York, 1985. (21) Field, R. J.; Fo¨rsterling, H. D. J. Phys. Chem. 1986, 90, 5400. (22) Hauser, M. Dissertation, Universita¨t Wu¨rzburg, 1993. (23) Hohmann, W. Unpublished results, Universitaet Wuerzburg, 1994.
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