1988
J. Phys. Chem. 1995,99, 1988-1994
New Measurements on the Chlorite-Iodide Reaction and Deduction of Roles of Species and Categorization Janet D. Stemwedel and John Ross* Department of Chemistry, Stanford University, Stanford, Califomia 94305 Received: September 22, 1994; In Final Form: November 28, 1994@
We present the results of new experiments on the chlorite-iodide reaction and use these results to determine the roles of various chemical species in the reaction mechanism. We simultaneously monitor three species, I-, ClOz-, and 12, and detennine the relative phases of oscillations in these species. We use perturbations in these species and the additional species NaOC1, IQ-, C1-, HI02, and HzOI+ to perform qualitative pulsedspecies response, concentration shift regulation, and concentration shift destabilization experiments. Within a scheme of categorization of oscillatory reaction mechanisms, we determine that the chlorite-iodide system is a category 1CX or 1CW oscillator. Further, we distinguish essential and nonessential species and identify C102- as a type Z essential species, I- as a type Y essential species, and HOC1 as an essential species of type X or W. HOI and H I 0 2 are essential species whose roles we were unable to identify from these measurements. I2 and 1 0 3 - are identified as nonessential species of type B, while C l is a nonessential species of type C. Our assignments of the mechanistic roles of the essential species show complete agreement with those predicted by the Citri-Epstein mechanism. However, that model mechanism predicts that I2 is a nonessential species of type C and ;hat C1- is a nonessential species of type B.
I. Introduction The chlorite-iodide reaction, which was f i s t reported in 1982,' has been found to exhibit complex phenomena such as sustained oscillations and bistability between multiple steady states, when run in a continuous-flow stirred tank reactor (CSTR).1$2The overall stoichiometry of the reaction is given by C10,-
+ 41- + 4H'
-
21,
+ C1- + 2H20
(1)
Chlorite participates in a further reaction with iodine which has the stoichiometry
3210,-
+ 21, + 2H,O
5C1-
+ 410,- + 4H+
(2)
In 1985, Epstein and Kustin3proposed a 13-step mechanism containing 14 species (nine of them independent) which accounted for both batch (clock) behavior and CSTR behavior (specifically bistability and periodic oscillation). In 1987, Citri and Epstein4 gave a simplified mechanism for the chloriteiodide reaction which involved only eight elementary steps and 10 chemical species. Systematic methods have been proposed for studying oscillatory dynamics which identify the roles of and connectivity among the essential species in a s y ~ t e m . ~These ? ~ methods suggest a number of useful tests to be performed on experimental systems, which have been summarized in ref 7. Some of these methods have already been applied to theoretical8 and experimental9 studies of the chlorite-iodide reaction. Recently, such methods have been applied successfully to the study of other experimental systems.'0," In this study, we apply experimentally some categorization tests to the chlonte-iodide system in order to assign the roles of the three detectable species in the system (I-, C102-, and 12) and of the additional species which can be used to perturb the system (NaOCl, 103-, C1-, HI02, and H201f). The tests applied ~~~
~
@Abstractpublished in Advance ACS Absrracfs, February 1, 1995.
0022-365419512099-1988$09.00/0
include qualitative pulsed-species response experiments, concentration shift regulation and destabilization experiments, and a comparison of the phase shifts of the oscillatory wave forms of the detectable species. Detailed discussions of these and other categorization methods are given in ref 7. We present brief descriptions of the tests and their utility in assigning species before presenting our experimental results. 11. Experimental Section The chlorite-iodide reaction was run in a continuous-flow stirred tank reactor (CSTR) in which we control inflows of solutions of chlorite, iodide, and a buffering solution as described el~ewhere.~ A schematic diagram of the experimental apparatus is given in Figure 1. The reactant solutions are prepared in deionized water. Potassium iodide and anhydrous sodium sulfate were obtained from J. T. Baker (Phillipsburg, NJ), anhydrous sodium chlorite from Kodak (Rochester, NY), sodium hydroxide from Mallinckrodt (Paris, KY), and 5.0 M sulfuric acid from Fisher (Fair Lawn, NJ). All chemicals were used without further purification. The reactant solutions have the following concentrations: iodide, 0.0177 M IU;buffer, 0.184 M Na2S04 and 0.0295 M H2S04; and chlorite, 0.0127 M NaC102 and 0.001 M NaOH, where the NaOH stabilizes the chlorite. Iodine, potassium iodate, and sodium chloride were obtained from J. T. Baker, and sodium hypochlorite was obtained from Sigma (St. Louis, MO), for use as perturbants. Three feedstreams are used to flow the reactant solutions into the CSTR. The chlorite solution is flowed into the CSTR via a peristaltic pump, and the iodide and buffer solutions are flowed into the CSTR via two computer-controlled magnetically coupled metering gear pumps (Micropump, Concord, CA). In order to maintain pH 2.05, the sulfate buffer solution flow rate is set at 26.52% of the total inflow rate in all experiments. Waste is removed from the CSTR by vacuum suction. For all experiments, the CSTR is thermostated at 24.0 & 0.2 "C, and the stirring speed is adjusted to 350 & 20 rpm. The iodide potential of the system is measured with a solid state iodide ion-selective electrode (Orion Model 94-53, Cam1995 American Chemical Society
J. Phys. Chem., Vol. 99, No. 7, 1995 1989
New Measurements on the Chlorite-Iodide Reaction n
PERISTALTIC I
I
I '
WATER BATH
I AMPLIFIER
-
BJARD*
IEM
AID
PC-XT
a b C Figure 2. Trace of iodide potential versus time for typical pulsedspecies response experiments. Pulses of species are added to the system at a stable steady state. ko = 9.8 x s-I. [ClO~-ld[1-]0 = 0.41. (a) Pulse perturbation in I- of strength M. (b) Pulse perturbation in C102- of strength M. (c) Pulse perturbation in C1- of strength M. For each of these perturbations one to three oscillatory peaks are observed before the system returns to the steady state.
BOARD+
Figure 1. Schematic diagram of experimental apparatus. TABLE 1: Typical Standards for the Spectrophotometric Measurement of Chlorite and Iodine standard no. 1 2 3 4 5 6
I
d-8
[C102-1 (mM) 0.0127 0.0254 2.54 1.27 0.254 0.127
[I21
(d)
0.525 0.2625 0.0263 0.0525 0.1313 0.1313
bridge, MA) against a double-junction reference electrode (Orion Model 90-02). The potential is followed by a Fisher Accumet Model 805 MP pH meter (Santa Clara, CA), whose output signal is filtered by a 2 Hz low-bandpass Butterworth filter and amplified by a factor of 14.1. This filtered signal is then sent to a Houston Instruments Microscribe strip-chart recorder (Houston, TX) and to an IBM PC-XT with PCLAB routines via a Data Translation DT2805 12-bit digital-to-analog and analog-to-digital board (Marlboro, MA). The chlorite and iodine concentrations are measured by pumping the reactor contents, at a flow rate equal to the total rate of throughput, into a quartz flow-through cuvette with a path length of 0.3 cm in a photodiode-array ultraviolet-visible spectrophotometer (Beckman Model DU-7500, Fullerton, CA). We utilize the Beckman Multicomponent Analysis (MCA) software to track the concentrations of C102- and 1 2 from fullscale spectral measurements. In order to use this method, we collect a set of standard measurements of the full-scale absorbance spectra of various mixtures of C102- and 12; a typical set of standard mixtures is given in Table 1. Since these two species react via eq 2, the C102- and 12 are mixed quickly in the cuvette, and the absorbance is scanned immediately. To collect continuous measurements of [ClOz-1 and [I21 during an experiment, we utilize an extemal triggering device set to make measurement every 8 s (the minimum amount of time required for MCA calculations between data points). The cuvette and tubing connecting the cuvette to the CSTR are rinsed with deionized water between measurements to prevent clogging.
TABLE 2: Results of Qualitative Species Response Experiments Monitoring Iodide Potential perturbing species response Idamped oscillations c102damped oscillations c1small amplitude damped oscillations 103no response I2 H201t HI02
no response
damped oscillations damped oscillations
111. Results
A. Qualitative Pulsed-SpeciesResponse Experiments. In these experiments, a pulsed perturbation of one species at a time is applied to a system at a steady state near a supercritical Hopf bifurcation. The relaxation to the stable steady state is measured, and the behavior during this relaxation is characterized as oscillatory response, monotonic decay, or no response. The results of these experiments give information toward the assignment of species as essential or nonessential and the determination of the types of the nonessential species.6 We adjusted the system to the steady state side of a supercritical Hopf bifurcation. The reciprocal residence time used was 9.8 x SKI;the ratio of input concentrations [C102-]d[I-]o was set to 0.41. Pulsed perturbations of strength M in I-, ClOz-, 12, and Io3-; of strength M in C1-; and of unknown strength in HI02 and H20I+ were added to the reaction mixture by syringe. HI02 was synthesized as detailed in ref 12. H201f (the protonated form of HOI) was synthesized as described in ref 13. Aliquots (5 mL) of each of these unstable compounds were added as perturbants immediately at the conclusion of each synthesis. The observed responses of the I- evolution are shown in Table 2 . A trace of the iodide potential over time for a typical experiment is shown in Figure 2. Pulse perturbations in I- and C102- are seen in the trace to cause one to three oscillatory peaks before the system retums to the steady state, while the addition of C1- is seen to produce a number of small amplitude peaks. B. Concentration Shift Regulation Experiments. In this experiment, a constant inflow of one species at a time is added
Stemwedel and Ross
1990 J. Phys. Chem., Vol. 99, No. 7, 1995 TABLE 3: Results of Concentration Shift Regulation Experiments Obtained by Monitoring Iodide Potential and Chlorite Absorbance" response of increase in flow of species sDecies
c102-
c102I-
-
-
c10-
18 16
14
I-
+ +
o The experiments are performed on the stationary state side of a supercritical Hopf bifurcation: the steady state of iodide is at intermediate concentration. A (+) indicates that a perturbation causes an increase in the steady state concentration of the monitored species, while (-) indicates a decrease in the steady state concentration of the monitored species.
to the system at steady state near a supercritical Hopf bifurcation. This additional inflow should not be large enough to shift the system from one dynamic region to another, for example, from a stationary state to an oscillatory state. The response of the concentrations of as many species as possible is determined after the addition of each species and compared to the steady state concentrations of the unperturbed system. These measurements allow the construction of an experimental shift matrix, which is directly related to the Jacobian matrix.6 Moreover, qualitative assignment of the inflows as increasing (+) or decreasing (-) the steady state concentrations of each species suffices to give the signs of the elements of J-', the inverse of the Jacobian matrix; from this information it is possible to distinguish roles of essential species and to assign the category of oscillator. Experiments are performed at the middle iodide steady state near the supercritical Hopf bifurcation at total flow rates of 7.75-8.00 mL/min. Then, a constant perturbing inflow is applied to the system in such a manner that the total flow rate of reactant solutions through the CSTR remains constant. To perturb [Cl02-]0 or [I-]o, it is simply necessary to increase the concentration of C102- or I- in the bottle serving as the pump reservoir. Adding perturbing inflows of species not normally flowed into the reactor (Le., 12 and NaOCl) without changing the other input concentrations or the total flow rate into the CSTR requires that one of the inflowed species, C102- or I-, be pumped on two channels in the unperturbed system. To add the perturbation, one of these two channels is used to inflow the additional species, and the bottle concentration of C102- or I- is increased so that the original bottle concentration times the original influx rate due to both channels equals the new bottle concentration times the new influx rate on a single pumping channel. The perturbation strengths of NaOC1, 12, C102- , and I- used are not sufficient to displace the system from the steady state. Comparison is made between the iodide potential of the middle iodide steady state in the unperturbed system and the iodide potential of the system with the additional perturbing inflow to determine whether [I-] increases (+) or decreases (-). The results of these experiments are summarized in Table 3. A typical set of spectrophotometric data for this experiment is shown in Figure 3. C. Concentration Shift Destabilization Experiments. A constant inflow of species is added to a system near a supercritical Hopf bifurcation (on either the steady state or the oscillatory side). It is noted whether or not a transition occurs across the bifurcation and, if so, whether the transition is from oscillations to a steady state or vice versa. The procedure is continued on both sides of the bifurcation with increasing inflow concentrations of perturbant until either a shift away from the bifurcation or a shift toward the bifurcation is observed. The shift in stability is assigned as stabilizing (s) for oscillatory to steady state and destabilizing (d) for steady state to oscillatory.
12 10
8
6 100 200 300 400 500 600 700 800 900 Time (seconds)
Figure 3. Trace of chlorite concentration for a typical concentration shift regulation experiment. Initially, the system is on an unperturbed s-I, [Cl02-]d[I-]o = 0.55). At 480 s, steady state (h= 2.167 x [ClOz-l~is increased from 4.05 x to 4.21 x 10-3 M. TABLE 4: Results of Concentration Shift Destabilization Experiments Obtained by Monitoring Iodide Potential" perturbing species assignment Idestabilizing stabilizing c102NaOCl stabilizing stabilizing I2 The experiments are performed either on the stationary state or on the oscillatory side of a supercritical Hopf bifurcation; the steady state of iodide is at intermediate concentration. An (s) indicates that the added inflow is stabilizing, while (d) indicates that the added inflow is destabilizing. This test may also be performed on either side of a saddlenode infinite period bifurcation. Concentration shift destabilization experiments were performed near the supercritical Hopf bifurcation as in the concentration shift regulation experiments. The ratio of input concentrations [C102-]d[I-]o was adjusted to give smallamplitude oscillations (oscillatory side of supercritical Hopf bifurcation) or the middle iodide steady state (steady state side of Hopf bifurcation). Upon addition of a constant perturbing inflow, the system relaxes to either a stable steady state or stable oscillations. Given a sufficient perturbation (but one small enough to keep the system in the linearized regime), the perturbing species shifts the stability of the system either from steady state to oscillations (destabilizing, d) or from oscillations to the steady state (stabilizing, s). Note that it is sufficient to measure the response of a single species to assign all the species used as perturbants as stabilizing or destabilizing. Results of concentration shift destabilization experiments are summarized in Table 4. Figure 4 shows typical stabilizing and destabilizing shifts from the steady state. Figure 5 shows typical stabilizing and destabilizing shifts from the oscillatory region. Upon addition of constant perturbing inflows of C102-, NaOC1, and 12, either to the stable steady state side of the bifurcation (Le., the middle iodide state) or to the oscillatory side of the bifurcation, the system relaxes to a stable steady state (s). Depending on the size of the perturbation, the system relaxes to either the middle iodide steady state or to the low iodide steady state, even further from the supercritical Hopf bifurcation. Addition of a constant perturbing inflow of I- to either the steady state or the oscillatory side of the bifurcation point causes the system to relax to stable oscillations (d). For relatively large I- perturbation strength, the amplitude of the oscillations increases, indicating that the system has been shifted away from
J. Phys. Chem., Vol. 99, No. 7, I995 1991
New Measurements on the Chlorite-Iodide Reaction 30
25
2
'3 15 "
f
0
10 5
0
a b Figure 4. Trace of iodide potential versus time for typical concentration
0
200
400
600
800
1000 1200 1400
Time (seconds)
shift destabilization experiments. ko = 2.59 x 10-3 SKI. [ClOz-]d[I-]o = 0.528. (a) Stabilizing shift from the steady state. Perturbation in [NaOClIo = 8.28 x M. (b) Destabilizing shift from the steady state. Perturbation in [I-]o = 1.50 x 10-3 M.
Figure 6. Spectrophotometric measurement of oscillations in chlorite
a b Figure 5. Trace of iodide potential versus time for typical concentration
(mi d Figure 7. Measurement (ref 1) of iodine absorbance (proportional to [Iz]) and of iodide potential (proportional to -log[I-1) versus time. The maximum in the iodide potential represents a minimum in iodide concentrations. Therefore, the concentration oscillations in iodide and iodine are nearly antiphase, with [I-] advancing [I21 slightly.
shift destabilization experiments. ko = 2.60 x s-I. [ClOz-]d[I-]o = 0.497. (a) Stabilizing shift from the oscillatory region. Perturbation in [NaOClIo = 3.13 x M. (b) Destabilizing shift from the oscillatory region. Perturbation in [I-]o = 1.54 x 10-3 M.
the supercritical Hopf bifurcation and toward the center of the oscillatory region. D. Phase Shifts of Oscillations. The relative phases of oscillations of essential species may provide useful information about the roles of the species in the categorization scheme. For the chlorite-iodide reaction, we find that the maximum amplitude of the [C102-] and [I21 oscillations are in phase, as shown in Figure 6. Our simultaneous measurement of [C102-] and [I21 is slightly offset from our measurement of I- potential. However, Dateo et al.' report simultaneous measurement of [I21 and I- potential, shown in Figure 7, from which it can be seen that the maximum 12 concentration occurs slightly ahead of the maximum I- potential. Since a low I- potential corresponds to a high I- concentration, the [I21 maximum occurs after the [I-] maximum. As seen in Figure 6, the [I21 and [C102-I maxima are in phase with each other. Hence, the [I-] maxima are followed by the [C102-] maxima, which are less than 180" after them. These phase relations are summarized in Table 5 .
IV. Interpretation of Measurements with Respect to the Reaction Mechanism In undertaking to assign the mechanistic roles of species and to categorize the chlorite-iodide oscillator, we may eliminate category 1B from consideration, since the chlorite-iodide system does not exhibit sustained oscillations under batch condition^.^ Hence, we need only consider categories lCX,
(solid line) and iodine (dotted line) versus time. The maxima of these concentration oscillations are in phase.
1
Tim.
TABLE 5: Phase Relations among Oscillations of Monitored Essential Specie@ concentration maxima of species
with respect to 1c10z-
1I
+
c102I
a The symbol I denotes in phase; (-) denotes a small lag; and (+) denotes a small advance.
lCW, and 2. We consider the possible deductions about the reaction mechanism from one experiment at a time. Table 6 gives a summary of our conclusions about the assignment of the species from each experiment. First, we consider the results of the qualitative pulsed-species response experiments, which allow us to distinguish essential and nonessential species. A nonessential species of type A shows a negligible response to perturbation by any species but itself, for which it exhibits monotonic decay; this is because A acts only as a reactant in this network, never as a product. On the other hand, a perturbation by a type A species affects the responses of species connected to A as products, causing a damped oscillatory response in all essential species and in nonessential species of type B. Type B species show an oscillatory response because they are products of the participants in the autocatalytic cycle. A perturbation by a nonessential species of type B causes negligible response in all species except
Stemwedel and Ross
1992 J. Phys. Chem., Vol. 99, No. 7, 1995
TABLE 6: Summary of Deductions about the Reaction Mechanism Drawn from the Results of Various Experiment@ Ic10C102HI02 H201f 103I2 Category 1CX or 1CW qualitative pulsed-species response E E E E NEb NEb NEc Y Z concentration shift regulation concentration shift destabilization Y x, w Z Y Z relative phases E, Y E,XIW E,Z E E NEb NEb conclusion Category 1CW assignment from Citri- Epstein mechanism E, Y E, W E, Z E, X E, X NEb NEc
c1-
NEc NEb
a E indicates an essential species of indeterminant type; NE b and NE c indicate nonessential species of types B and C, respectively; X, W, Y, and Z indicate essential species of types X, W, Y, and Z, respectively. Note that none of our experimental methods are able to distinguish type X and type W species.
TABLE 7: Expected Responses to Pulsed Perturbations for Essential and Nonessential Species of Types A, B, and C in Any of the Categories of Oscillatory Reactions response of measured species perturbing species essential A B C no response no response damped oscill. essential damped oscill. no response monotonic decay damped oscill. A damped oscill. no response no response monotonic decay B no response small ampl. damped oscill. monotonic decay small ampl. damped oscill. no response C itself, for which it shows monotonic decay. This is because TABLE 8: Sign-Symbolic Concentration Shift Matrices type B species are inert products, not acting as reactants AXs,.,,,b for the Essential Species in the Prototype of Each anywhere in the network. A nonessential species of type C is Categow Category 1B in a quasi-steady state to which it retums nearly instantaneously after perturbation by any species. Since C acts as a reactant in perturbing species the reaction of the essential species of the autocatalytic cycle, measured species X Y Z a perturbation in C will cause small amplitude damped oscilX latory responses in the essential species and in nonessential Y species of type B. Finally, perturbation by essential species Z directly affects the other species involved in autocatalysis, Category 1CX leading to the damped oscillatory response of all essential species and of nonessential species of type B. These conclusions perturbing species are summarized in Table 7. measured species X Y Z Since a pulse perturbation in I- leads to a damped oscillatory X response in I-, I- is an essential species. The species whose Y perturbations produce no response in I-, that is, 1 0 3 - and 12, Z are then nonessential species of type B, and the one producing Category 1CW small-amplitude damped oscillatory decay, C1-, is a nonessential perturbing species species of type C. The species which are not monitored but whose perturbations cause damped oscillations in I-, that is, measured species X Y Z W ClOz-, HI02, and HOI, are either essential species or nonesX sential species of type A. Since no realistic examples of type Y A nonessential species have been given,5 we are probably Z W warranted in concluding that these species are essential. Next, we consider the results of the concentration shift Category 2 regulation experiments for the essential species. Table 8 shows perturbing species the sign-symbolic concentration shift matrices for the different measured species X Z categories of oscillators. For all categories of oscillatory systems, species Z may be distinguished from species X,Y, and X Z W by inspection of the diagonal elements of the sign-symbolic concentration shift matrix AXsymbsince it displays inverse (-) A (+) indicates that a perturbation causes an increase in the steady ~elf-regulation,'~~'~ while the other species display normal (+) state concentration of the monitored species, while (-) indicates a self-regulation. Species X, Y, and W, and the category of decrease in the steady state concentration of the monitored species. oscillator, may then be distinguished by examining the rows of the sign-symbolic concentration shift matrix. If each row has We find that I- displays normal self-regulation, while C102only elements of the same sign, the oscillator is in category 2; displays inverse self-regulation. Thus, C102- is the essential species of type Z in this reaction. Moreover, from the species X shows (+) regulation with respect to all inflows and species Z shows (-) regulation with respect to all inflows. If off-diagonal elements of the experimental sign-symbolic shift all rows have entries of both signs, the oscillator is in category matrix, in particular the fact that an increase in the inflow of I1C; species X (and W) shows (-) regulation with respect to causes an increase in the steady state concentration of ClOz-, inflow of Y, and species Y shows (+) self-regulation but (-) we deduce that the system is not a category 2 oscillator, for regulation with respect to all other inflows. Identification of which the response of the type Z species to an inflow of any the inversely self-regulated species (Z) is central to these essential species is (-). In both of the remaining categories, assignments. 1CX and lCW, the species whose inflow causes a (+) response
+ + +
+
+
+
+
+ +
+
+ +
+
+
+
+
+
+
+
New Measurements on the Chlorite-Iodide Reaction
J. Phys. Chem., Vol. 99, No. 7, 1995 1993 TABLE 9: Effect of Essential Species Influx on the Hopf Bifurcation in Oscillators of Category 1" (a) High [XI on Steady State Side of Hopf Bifurcation 1B 1cw 1cx
X
Y
Z
S
d d d
d
S S
W
S
S
S
(b) Low [XI on Steady State Side of Hopf Bifurcation 1B 1cw 1cx
X
Y
d d d
S
S
S
d d
Z
S
W d
a An (s) indicates that the added inflow is stabilizing, while (d) indicates that the added inflow is destabilizing.
TABLE 10: Sign-Symbolic Phase Shift Matrices A&,,,b for the Essential Species in the Prototype of Each Category of Oscillatory Reaction@
Ib)
Cateeorv 1B ~~~
w7 3.
phase relation of species with respect to
X
Y
X
I
-
+
I
+
Y Z
Z -
+
-
I
Category 1CX
Figure 8. Network diagrams for oscillators of type 1CW. In the network diagrams, the number of feathers at a species corresponds to the number of molecules of the species consumed in the reaction (no feathers shown when stoichiometric coefficient is 1); the number of barbs at a species corresponds to the number of molecules of the species produced in the reaction. (a) The unstable current for the Citri-Epstein model, from the analysis in ref 5. Essential species are boxed, their types indicated outside the boxes. (b) The prototype for category 1CW. The variables X, W, Y, and Z are essential species of types X, W, Y, and Z, respectively.
in the type Z species is type Y. Thus, I- is an essential species of type Y. Hence, from the concentration shift regulation measurements we are able not only to identify the essential species of types Z and Y but also to conclude that the oscillator is in category 1CX or 1CW. An analysis of the Citri-Epstein mechanism in ref 5 predicts that this model mechanism is a category 1CW oscillator. The network diagram for the CitriEpstein model from this analysis is given in Figure 8, along with the network diagram for the category 1CW prototype. Next, we discuss the results of the concentration shift destabilization experiments. Eiswirth et al.5 presented a way of distinguishing roles of essential species and subcategories of category 1 oscillators using s/d assignment and self-regulation information from concentration shift regulation experiments; the s/d assignments for essential species in category 1 oscillators are given in Table 9. From the concentration shift regulation experiments, we have identified C102- as an essential species of type Z; the concentration shift destabilization experiments determine that C102- is s. Having already eliminated categories 1B and 2 as possibilities, we determine that the system must have a high concentration of the autocatalytic (type X) species on the steady state side of the Hopf bifurcation, since this condition gives a type Z species with s behavior for oscillators in categories 1CX and 1CW. Thus, the species assigned as d (I-) must be a type Y species, while the other species besides the type Z species which is assigned as s (HOCl) must be a type X or W species. Finally, we examine the relative phases of oscillations of the essential species we are able to monitor. We determined that the maxima of the [I-] oscillations precede the maxima of the
phase relation of species X
Y
Z
X
I
A
Y
A
I
+-
with respect to
+
-
Z
I
Category 1CW phase relation of species X
Y
Z
X
I
Y Z W
A I
A I
+-
A
+
with respect to
+
W I A -
I
I
Category 2 phase relation of species with respect to
X
X
I -
Z
Z
+ I
a The symbol I denotes in-phase; A denotes antiphase; (-) denotes a small lag; and (+) denotes a small advance.
[C102-] oscillations. Knowing that C102- is an essential species of type Z, I- must be an essential species of type Y; if it were an essential species of type X or W, I- would have a concentration maximum which followed that of ClOz-. Comparing the partial sign-symbolic phase shift matrix obtained for I- and ClO2- with the sign-symbolic phase shift matrix for a category 1CW oscillator, shown in Table 10, we see that it is identical to the submatrix containing phase relations for Y and Z essential species.
V. Conclusion From all the experiments we deduce consistently the results summarized in Table 6 on (1) the distinction of some species as essential or nonessential; (2) the specific roles of these species; and (3) the categorization of the oscillator. This study shows that relatively simple, but purposefully designed, experiments may provide, by deduction, fundamental aspects of a complex reaction mechanism.
Stemwedel and Ross
1994 J. Phys. Chem., Vol. 99, No. 7, 1995
Acknowledgment. This work was supported in part by the Air Force Office of Scientific Research and the National Science Foundation. References and Notes (1) Dateo, C. E.; Orban, M.; DeKepper, P.; Epstein, I. R. J. Am. Chem. SOC. 1982, 104, 504.
(2) DeKepper, P.; Boissonade, J.; Epstein, I. R.J. Phys. Chem. 1990, 94, 6525. (3) Epstein, I. R.;Kustin, K. J. Phys. Chem. 1985, 89, 2275. (4) Citri, 0.;Epstein, I. R. J. Phys. Chem. 1987, 91, 6034. (5) Eiswirth, M.; Freund, A,; Ross, J. Adv. Chem. Phys. 1991,80, 127. (6) Chevalier, T.; Schreiber, I.; Ross, J. J. Phys. Chem. 1993,97,6776. (7) Stemwedel, J. D.; Schreiber, I.; Ross, J. Adv. Chem. Phys. 1995, 89, 327.
(8) Strasser, P.; Stemwedel, J. D.; Ross, J. J. Phys. Chem. 1993, 97, 2851. (9) Stemwedel, J. D.; Ross, J. J. Phys. Chem. 1993, 97, 2863. Ross, J. J. Phys. Chem., in press. (10) Hung, Y.-F.; (11) S h m e d a , L. L. Ph.D. Thesis, Stanford University, 1993. (12) Noszticzius, Z.; Noszticzius, E.; Schelly, Z. A. J. Phys. Chem. 1983, 87, 510. (13) Noszticzius, Z.; Noszticzius, E.; Schelly, Z. A. J. Am. Chem. SOC. 1982, 104, 6196. (14) DeKepper, P.; Boissonade, J. In Oscillations and Traveling Waves in Chemical Systems; Field, R. J., Burger, M., Eds.; Wiley Interscience: New York, 1983; p 223. (15) Termonia, Y.; Ross, J. Proc. Nat. Acad. Sci. U.S.A. 1982, 79,2878.
JP942564T
