2497
J. Phys. Chem. 1986, 90,2497-2501
Simulation of Bromate-Driven Oscillations in the Presence of Excess Silver Ions Using the Oregonator Model Bengt Schwitterst and Peter Ruoff* Department of Chemistry, Rogaland Regional College, Ullandhaug, 4001 Stavanger, Norway (Received: November 19, 1985)
Using the Oregonator model and taking into account the kinetic behavior of a bromide-selective electrode when silver ions are present in excess, we are able to model the observations of Noszticzius that, when silver ions are added to a Belousov-Zhabotinsky reaction, the oscillations at the bromideselectiveelectrode are almost completely suppressed while the potential of a platinum electrode continues to oscillate with an increased frequency compared to the correspondingnon-silver ion perturbed system. Thus, we confirm our previous assumptions that the suppression of oscillations at the bromide-selective electrode is a second-order effect due to the electrode's response and has nothing to do with the oscillations in the bulk solution which are still bromide ion controlled. Therefore, the concept of non-bromide control in Ag+-perturbed Belousov-Zhabotinsky systems as first introduced by Noszticzius and then adopted by other authors is incorrect.
Introduction The prototype of bromate-driven chemical oscillators' is the metal ion catalyzed bromination of malonic acid using bromate ions in aqueous acidic media.2 The oscillator was discovered by Bel0u~0v~ using citric acid as organic substrate while Zhabotinskf continued the study. In 1972, Field, Korbs, and Noyes (FKN)S proposed a detailed mechanism in which bromide ions play the important role of a control intermediate. Today, the bromide control for the classical6 bromate-driven oscillators is generally accepted and a recent controversy about this question appears ~ettled.~ Another class of bromate-driven oscillators which was difficult to rationalize within the framework of the FKN mechanism is the so-called non-bromide-controlled oscillations where silver ions are present in ex~ess.8-~ Noszticzius8 in 1979 perturbed a classic malonic acid bromate-driven oscillator with silver ions and observed high-frequency oscillations at the platinum electrode while the bromide ion selective electrode showed.an almost monotonic behavior. Noszticzius' interpretation of the results was that the bromide concentration was forced to very low values by the silver ions, and that no oscillations in bromide ion concentration occurred. The whole situation was termed as non-bromide-controlled (Figure 1).8
Ganapathisubramanian and Noyes repeated Noszticzius' experiments in a flow reactor, agreed in the non-bromide ion control, and postulated an alternative mechanism based on bromine-atom control.1° Field9 even asks the question of whether these %onbromide-controlled" oscillations could be related to the heterogeneous halate-driven oscillations recently discovered by Orban and Epstein." However, results analogous to those described by Noszticzius for the oscillatory system have also been found by Ruoff12 when the system is in its excitable mode. When silver ions are added to an excitable Belousov-Zhabotinsky (BZ) reaction single excitation spikes may be observed, or when silver ions are used in excess, oscillations are induced ("repetitive firing") due to the excitability property of the system.13 Excitability and silver ion induced oscillations have been observed in other classical bromate-driven oscillators and seem independent of both the organic substrate and the cata1y~t.l~For excitable BZ systems, RuoffI6 and Ruoff and Schwitters17 were able to simulate semiquantitatively silver ion induced frequencies, excitation thresholds and amplitudes by using the OregonatorI8 model extended by a bromide ion removing term with a finite rate constant of about lo4 M-' s-l. Although Ruoff and SchwittersI7 were not able to model the sometimes monotonic behavior of the bromide ion selective electrode,I2 they concluded on the basis of the otherwise good agreement with the FKN theory that the nonoscillatory 'Permanent address: Fagerh~yveien22, 1324 Lysaker, Norway.
0022-3654/86/2090-2497$01.50/0
TABLE I: Numerical Values of Rate Constants, f, and Initial Concentrations
parameter
value
kol = k l * [ H + ] 2M-3 , s-I ko2 = k , * [ H + ] ,M-2 S-' ko3 = k,*[H+], M-2 s-'
k,* = 2.094 k2* = 2.0 X IO9 4.0 k,* x= 107 103-104 0.25-1.0 104 1.O-2.5
0.1 1.o
response of the bromide ion selective electrode seems related more to the response kinetics of the electrode than to the actual bulk bromide ion concentration. In this paper we show that including the response of the bromide ion selective electrode to silver ion in the Oregonator, we are able to model Noszticzius' 1979 observation^.^*^ Based on results presented by us in this and p r e v i o u ~work '~~~~~~~~ and in a recent Oregonator study by Varga et al.I9 of the thallium(II1)-perturbed BZ reaction, it appears that there is no non-bromide ion controlled class8-I0of bromate-driven oscillators.
Model and Method of Calculation The Model. The model used in our calculations is the original Oregonator of Field and Noyes,I8 extended by the reversible (1) Reviews and references can be found in: Oscillations and Traveling Waves in Chemical Systems; Field, R. J., Burger, M., Fils.; Wiley: New York, 1985. (2) Field, R. J. In Theoretical Chemistry; Eyring, H., Henderson, D., Eds.; Academic: New York, 1978; Vol. 4. (3) Belousov, B. P. Ref.Radiats. Med., Moscow 1959, 145. (4) Zhabotinsky, A. M. Dokl. Akad. Nauk SSSR 1964, 157, 392. (5) Field, R. J.; KBros, E.; Noyes, R. M. J . Am. Chem. SOC.1972, 94, 8649. (6) Noyes, R. M. J . Am. Chem. SOC.1980, 102, 4644. (7) (a) Ruoff, P. J . Phys. Chem. 1984, 88, 2851. (b) Noszticzius, 2.; Gaspar, V.;Forsterling, H.-D. J . Am. Chem. SOC.1985, 107, 2314. (8) Noszticzius, Z. J . Am. Chem. SOC.1979, 101, 3660. (9) Field, R. J., ref 1, p 73. (10) Ganapathisubramanian, N.; Noyes, R. M. J. Phys. Chem. 1982,86, 5155. (11) Orbin, M.; Epstein, I. R. J . Am. Chem. SOC.1981, 103, 3723. (12) (a) Ruoff, P. Chem. Phys. Lett. 1982, 90, 76. (b) Ruoff, P. Chem. Phys. Lett. 1982, 92, 239. (13) Field, R. J.; Noyes, R. M. Faraday Symp. Chem. SOC.1974, 9, 21. (14) Ruoff, P.; Schwitters, B. Z . Phys. Chem. (Frankfurt am Main) 1983, 135. 171. -(l5) Ruoff, P., unpublished results. (16) Ruoff, P. Z. Naturforsch., A 1983, 38a, 974. (17) Ruoff, P.; Schwitters, B. J . Phys. Chem. 1984, 88, 6424. (18) Field, R. J.; Noyes, R. M. J . Chem. Phys. 1974, 60, 1877. (19) Varga, M.; Gyorgyi, L.; Koros, E. J . Phys. Chem. 1985,89, 1019.
0 1986 American Chemical Society
2498
The Journal of Physical Chemistry, Vol. 90, No. 11, 1986
Schwitters and Ruoff
> E Y, 0
eI
\
The Journal of Physical Chemistry, Vol, 90, No. 11, 1986 2499
Simulation of Bromate-Driven Oscillations precipitation reaction 0 6 where A = Br03-, X = HBr02, Y = ko1
A+Y-X+P
(01)
k%
X+Y-2P A
+ X 22X + Z
(03)
2X%A+P
(04)
kc6
D + Y Z Q
(06)
kos
Br-, Z = 2Ce(IV), P = HOBr, D = Ag’, and Q = AgBr(s). The variables that are treated as time dependent are A, D, X,Y, and Z. Table I shows the parametrization used in the calculations reported here. As described in a previous paper,I7 reversibility of step 0 6 leads to the following contribution to the rate of D and Y: (1) [Yl = [Dl = k06(LAgBr - ID] LY1) The Bromide-Detecting Electrode. Most of the commercially available electrodes (Philips IS 550, Orion 94-35A, or Methrom EA 306-Br) consist of a mixed matrix of silver bromide and silver sulfide. The electrode has a Nernstian response to both bromide and silver ions. Ganapathisubramanian and Noyes20have studied the effects on such an electrode of silver ions, elementary bromine, and acidic bromate under equilibrium or almost equilibrium conditions. They concluded that simple extrapolation by means of the Nernst equation provides a satisfactory measure of bromide concentrations and generates even better consistency than before between experimental observations and attempts to model the reaction numerically. However, here we are concerned with bromate-driven oscillators when silver ion is in excess; Le., the system is not in equilibrium and [Ag+][Br-] > LAgBr. We first describe the response of a bromide ion selective electrode when both bromide and silver ions are present under equilibrium condition and then we derive kinetic expressions used in the calculations when silver ions are added in excess to a BZ system under nonequilibrium conditions. Response of a Bromide Ion Selective Electrode in the Presence of Silver and Bromide Ions under Equilibrium Condition. When both silver and bromide ions are present, and the system including the electrode has equilibrated, the potential of the bromide ion selective electrode is expressed by2’~22 E A g + = E o A g + + (RT/F) In QAg+ (2) or EBr- = E’sr- - (RT/F) In QBr-
(3)
where QAg+
= %([Ag+l + ([&+I2
+ ~ L A ~ B I ) ” ~ ) (4)
Figure 2. Schematic representation of the bromide-selective electrode (Br-SE) and its environment. In the presence of excess silver ions in the bulk solution (BL) we have precipitation of AgBr. During the precipitation we always have [Ag’] [Br-] > LAgBr. Only directly at the electrode’s interface between the AgBr matrix and bulk (stagnant layer, SL) the solubility product of AgBr must be fulfilled in order to get a single well-defined potential.
also with the platinum e l e ~ t r o d e . Although ~ ~ ~ ~ ~ this interference may be of some quantitative importance, for example, to reproduce the form of experimental phase plotsi6 in the malonic acid BZ reaction or the shape of the redox oscillations in the bromate ion driven oxalic acid o ~ c i l l a t o r the , ~ ~ calculations presented here neglect the influence of possible interfering species both on the platinum and on the bromide-selective electrode. Response of the Bromide-Selective Electrode in the Presence of Excess Silver Ions in a Classical Bromate-Driven Oscillator. As has been shown in previous work,iZb,14*’6,17 the essence to understand classical silver ion perturbed bromate-driven oscillators is that bromide ion has to be removed by silver ions at a rate considerably less than for diffusion-controlled processes. Both simple qualitative calculations’2band c a l c ~ l a t i o n s ’using ~ the Oregonator showed that a rate constant for the AgBr precipitation in the malonic acid BZ system of about lo4 M-’ s-I provides best agreement with experiments. The experimental rate constant for this process is still unknown; nevertheless, we consider it of importance to show that at this stage of development the 1979 results by Noszticzius* can be understood using a model of the FKN mechanism with the incorporation of the electrode’s behavior. Due to the slowness of AgBr precipitation in the presence of excess of silver ion, it takes a certain time for AgBr to precipitate. During that time we must always have
where [ ]BL denotes bulk concentrations. Only directly at the interface of the electrode to the solution must the solubility product be satisfied. Otherwise the electrode’s potential would not be well-defined. The situation is shown schematically in Figure 2. Because directly at the electrode-solution interface (“stagnant layer”, SL) the solubility product is obeyed, while in the bulk eq 6 is fulfilled, we must have
or QB,- =
YAW1
([W’
4L~g~r)”’)
(5)
Solving for x and inserting [&-IBL - x into the Nernst equation (8) for the bromide-selective electrode
These equations were deduced by Meites21 for the more general situation when an ion-selective electrode acts as an indicator in precipitation or complexometric titrations.” The BZ reaction, however, contains several species which might interfere with the bromide ion selective e l e ~ t r o d e ’ ~and - ~ ~probably (20) Ganapathisubramanian,N.; Noyes, R. M. J . Phys. Chem. 1982,86, 3217. (21) (a) Meites, L.; Goldman, J. A. Anal. Chim. Acta 1964, 30, 18. (b) Meites, L.; Meites, T. Anal. Chim. Acta 1961, 37, 1 . (22) Vesely, J.; Weiss, D.; Stulik, K. Analysis with Ion-Selective Electrodes; Ellis H o r w d : Chichester, U.K., 1978. (23) Noszticzius, Z. Acta Chim. Acad Sci. Hung. 1981, 106, 347. (24) Noszticzius, Z.; Noszticzius, E.; Schelly, Z . A. J . Am. Chem. SOC. 1982, 104, 6194. (25) Noszticzius, 2.;Noszticzius, E.; Schelly, Z . A. J . Phys. Chem. 1983, 87, 510.
(26) Carnman, K. Das Arbeiten mit ionenselektiven Elektroden; Springer-Verlag: West Berlin, 1973; Chapter 1.5. (27) Field, R. J.; Boyd, P. M. J . Phys. Chem. 1985, 89, 3707.
The Journal of Physical Chemistry, Vol. 90, No. 11, 1986
2500
Schwitters and Ruoff
I A{lp:10.2M
lniZl
I -8 -10 .12 - 14
-16
InlYl -9 -13
- 17 -221,
I
1
I
.
,
',
,
,
,
I
*
, ,
,
,
,
>
I
rnV
w
mY
C
250-
300-
LOO0
time
io
io
io > i o ' 6 0 ' io ' l o ' d o ' Figure 3. Calculated effect of perturbing an oscillatory Oregonator by M of silver ions. The potential difference between a bromide ion selective electrode and a standard calomel reference electrode is shown in part C (k3* = 1.0 X lo4 M-* s d , kos = 1.0 s - ' , f = 1.0). I
;@'
'
tirnlS)
350(51
6
'
40
80
120
160
200
240
280
320
360
T
Note that when [Ag+IBL= 0 eq 9 reduces to eq 3. On the other hand, when equality is assumed in eq 6, Le., equilibrium condition, then x = 0, and eq 9 reduces to eq 3 or 8b. The subscript SL can then be replaced by the subscript BL. When silver ion is in excess compared to bromide ion, eq 9 is dominated by the [ A g + l B ~ term. In this case EBr-can be shown to be approximately constant, indicating the flat response of the bromide ion selective electrode under these conditions. Finally the potential difference between EBr- and a standard calomel electrode is computed
where Eocalomel = 0.2680 V. Equation 11 is the electrode response used in the present calculations. The remaining parameters have the following nuM2, EOA~+ = merical values: T = 298 K, L A g ~=r 7.7 x 0.7994 V, and ( R T / F ) = 0.0257 V. The liquid junction potential at the reference electrode is neglected. Numerical Integration. Numerical integration of the differential equations generated by the Oregonator model was performed on a HP85 microcomputer using a BASIC version of the Gear algorithm.2*
Figure 4. Calculated effect of perturbing an oscillatory Oregonator by 1.25 X lo-) M of silver ions. The potential difference between a bromide ion selective electrode and a standard calomel reference electrode is shown in part C ( k , = 1.25 X lo4 M-' s-I , ko5 = 0.25 s-I, f = 1.0). In121 1
mV
C
Results and Discussion Figure 3 shows the effect when silver ions are added to an oscillatory Oregonator where the bromide ion selective electrode responds to Ag+ and Br- according to eq 9 and 11. Concentration oscillations in both the catalyst and bromide ion are observed, but the behavior of the bromide ion selective electrode is almost monotonic as observed by Noszticzius.8 The parametrization to obtain Figure 4 yields far better quantitative agreement with observationss than the one used to obtain Figure 3. This is achieved by reducing k3* and ko5 to respectively 0.125 and 0.25 of their original'* values (Table I). The primary effect of a reduction of k3* in the simulations is a general reduction of [Br-] and [Ce4+].17 For instance, the maximum and critical values of [Br-] in an oscillation in the Ag+-free regions of Figures 3 and 4 are 1.6 X and 6.0 X IO-'
(28) Field, R. J. J . Chem. Educ. 1981, 58, 408
0
40
80
120
160
200
260
(SI Figure 5. Calculated effect of continuous addition of a 0.05 M silver ion solution to an excitable closed Oregonator c f = 2.5). [DIo = 5 X M, flow rate = 1 mL/min, initial volume = 150 mL, k3* = 10' M-'S-', kos = 0.25 s-'. The potential difference between a bromide ion selective electrode and a standard calomel reference electrode is shown in part C. lime
M, and 5.0 X lom5and 7.8 X lo-* M, respectively. The latter values are in far better agreement with the admittedly somewhat scarce quantitative result^^^^^ than the former. FKNS determine a value of about 3 X IO" M for [Br-Imaxin an experimental BZ system of roughly comparable composition to the one assumed in our simulations. The main effect of a reduction of ko, in the simulations is a general increase in the period length P. In the silver ion free regions of Figures 3 and 4 P is 23.5 and 34.1 s, respectively. The combined effect of reducing k3* and ko5 within the silver ion
J. Phys. Chem. 1986, 90, 2501-2505
perturbed region is now obvious. It should be noted that [Ag+]o = 1.25 X l V 3 M as used for the simulation in Figure 4 is the same as that used by Noszticziuss in his experiments (Figure 1). Even better agreement between simulations and experiment can be obtained by a fine-tuning of k3* and kos, but we leave this until an experimental determination of k a is available. Preliminary results performed by us using conductivity methods strongly indicate that ko6 will turn out to be somewhat larger than lo4 M-’ s-l, necessitating a further reduction of k3*,which in turn would decrease the difference between predicted and experimentally determined bromide ion levels. In accordance with our preliminary results, Varga and K o r o found ~ ~ ~ recently (in a malonic acid BZ system) ko6 values in the order of lo4 M-’ s-I. k l * - k a represent a subset of rate constants which describe the oxybromine chemistry in BZ systems, and the values of several of these are not known with certainty.27-30*31b,32 T y ~ o n reports ,~ a rate constant set which in the Oregonator results in a reduction of k3* from 104 to 2 X lo2 M-I s-I, but this latter value is probably too low.” However, we note that the values of k3* used here are well within this suggested range of values. Also flow experiments when silver ions are used in the feed stream of a CSTR’O or when silver ions are continuously generated by an electrochemical processs can be simulated as shown in Figures 1B and 5 . Critical readers still will find discrepancies between our calculations and expetiment. Most obvious is that in the nodperturbed oscillating regime the calculations do not show the characteristic increase of the bromide ion selective electrode’s potential (29) Varga, M.; Koros, E. J . Phys. Chem., submitted for publication. (30) Noyes, R. M. J . Chem. Phys. 1984,80, 6071. (31) (a) Tyson,J. J. J. Chem. Phys. 1984,80,6079. (b) Tyson, J. J., ref 1, Chapter 3. (32) Tyson, J. J. J. Phys. Chem. 1982, 86, 3006.
Studies of the NH,
2501
when the autocatalytic oxidation of cerous ions occurs at low bromide ion concentrations. However, the electrode response in an experimental situation is due to bromide and silver ions as well as interfering specie^^^,^^ while we only consider here the response of the electrode toward Ag’ and Br-. Incorporation of other interfering species, as previously done,16 may further improve the already good agreement between calculations and experiment, but we doubt that such differences are of importance for the understanding of the mechanism and the special effect silver ions have in a BZ reaction. Our calculations suggest important experiments to be done, first of all to find the experimental rate constant of silver bromide precipitation in the BZ system. It is also desirable to find an experimental technique to follow the bromide ion concentration in the bulk solution in the presence of excess silver ions. Despite this lack of important experimental data, we have demonstrated that Noszticzius’ 1979 experimentss can be understood in terms of the FKN mechanism. The existence of silver ion induced oscillations does not invalidate the FKN mechanism and the Oregonator as recently suggested25nor do these types of oscillations appear to be non-bromide ion controlled. Varga et al.19 came to similar conclusions for the thallium(II1)-perturbed BZ reaction. Using the Oregonator model extended by complexation reactions between thallium(II1) and bromide ions they demonstrated the bromide ion control in these systems. We therefore conclude that the concept of “non-bromide ion control” as first introduced by Noszticzius* and then adopted by other authors9J0 is incorrect.
Acknowledgment. P.R. thanks Professor Richard M. Noyes for his hospitality and for financial support during a stay at the Chemistry Department, University of Oregon, when a first version of this paper was drafted. Registry No. Ag*, 14701-21-4.
+ NO Reaction by Infrared Kinetic Spectroscopy
Jeffrey L. Hall, D. Zeitz,+J. W. Stephens, J. V. V. Kasper, G. P. Glass, R. F. Curl,* and F. K. Tittel Departments of Chemistry and Electrical Engineering, Rice Quantum Institute, Rice University, Houston, Texas 77251 (Received: December 2, 1985)
Ihfrared kinetic spectroscopy using excimer laser flash photolysis and color center laser probing has been used to study the NH, + NO reaction. The amidogen radical, NH2, was produced by ArF photolysis of NH3. Infrared absorptions of OH and H 2 0 were measured to determine the absolute contributions of the OH and HzO product channels. It was found that the OH channel accounts for 13 2% of the reaction. Using two different pairs of NH, and H 2 0 lines, we measured values of 0.85 0.09 and 0.66 h 0.03 for the ratio of H 2 0 formed to NH3 photolyzed. All of the H 2 0 signals exhibit a pronounced induction period suggesting that H 2 0 is produced in very high vibrational states. The time evolution of low-lying vibrationally excited and ground vibrational state H 2 0 lines is adequately simulated by a model in which a stepwise sequential loss of vibrational energy occurs with quenching cross sections for each step proportional to excess energy.
*
*
Introduction The new powerful method of infrared kinetic spectroscopy has been applied to the investigation of the reaction between N H 2 and NO. This technique employs excimer laser flash photolysis to produce high radical concentrations, tunable infrared laser probes to provide high sensitivity and resolution, and fast infrared detectors to provide microsecond time resolution. This infrared kinetic specttoscopy combination provides a very effective and versatile technique for monitoring kinetics, determining nascent distributions, and acquiring spectra of new radicals. In previous we have examined the sensitivity and advantages of the Institut fiir Angewandte Physik, Universitlt Bonn, 5300 Bonn 1, Wegelerstrasse 8, Federal Republic of Germany.
method and have demonstrated its applicability to infrared spectroscopy. The present measurements illustrate the utility of the technique in the realm of kinetics. In a single experimental setup, the concentrations of most of the participants (OH, NH2, H 2 0 , NH,, NO) in the chemical reaction between NH2 and N O have been followed with high time resolution compared to the time scale of the reaction. (1) Hall, J.; Adams, H.; Russell, L. A,; Kasper, J. V. V.; Tittel, F. K.; Curl,
R. F. Proc. Int. Conf. Lasers ’83, 1985, 377.
(2) Adams, H.; Hall, J.; Russell, t.A,; Kasper, J. V. V.; Tittel, F. K.; Curl, R. F. J . Opt. SOC.Am. B 1985, 2, 776. (3) Hall, J.; Adams, H.; Kasper, J. V. V.; Curl, R. F.; Tittel, F. K. J . Opt. SOC.Am. B 1985, 2, 781.
0022-3654/86/2090-2501$01.50/00 1986 American Chemical Society
