818
J. Phys. Chem. 1082, 86,818-824
Chemical Oscillations and Instabilities. 46.1a Iodide Ion Measurements on the Osciliatory Iodate-Peroxide System J. Adeola Odutoia,‘b Catherlne A. Bohlander, and Richard M. Noyes’ Deparlment of Chemistry, University of Oregon, Eugene, Oregon 97403 (Received:April 6, 1981; I n Final Form: May 20, 1981)
If hydrogen peroxide is added to a moderately acidic (0.065 < [H+]< 0.075 M) solution of iodate, there is a very narrow range of concentrations within which the first induction period of iodate reduction is followed by rapid small oscillations in [I-] that first decrease and then increase in amplitude before conventional larger amplitude oscillations begin. A t still larger acid concentrations ([H+] 0.08 M), there is a convergence of the maximum and minimum hydrogen peroxide concentrations at which oscillations are possible. If both iodate and iodine are present when peroxide is added, [I-] decreases initially in the approximate range 0.02 < [H+] < 0.10 M and increases either above or below that range; direction of change may then reverse after an induction period. These initial directions of change differ systematically from effects observed if iodine is not present initially but is subsequently generated. If [H+]> 0.07 M, streams of O2 and N2 exert identical rather small effects on the character of the oscillations; if [H+]< 0.05 M, Sharma and Noyes reported extreme sensitivity to concentration of dissolved oxygen, while streams of O2 and N2 affected behavior greatly and in opposite directions. These new observationsdemonstrate that the mechanism for oscillations proposed by Sharma and Noyes cannot be valid in all details. However, we still believe that iodide ion exerts a major control over switching the system between a radical regime during which iodine is oxidized to iodate and a nonradical regime during which iodate is reduced to iodine.
Introduction The iodate-catalyzed disproportionation of hydrogen peroxide was the first entirely inorganic homogeneous solution chemical oscillator to be discovered. Oscillations were reported by Bray2 and were studied extensively by Liebhafsky and co-~orkers.~ A large body of information now exists about this system, and several mechanisms have been proposed. In this manuscript, we report still more observations and reach the conclusion that none of the previously proposed mechanisms, including that of Sharma and Noyes4 (SN), can be correct in detail. However, these same observations provide strong support for a modification of that mechanism. Experimental Procedures Reagent-grade KI and KI03 were used without further purification. A few experiments with NaI03 gave identical results. Stock solutions about 2 M in HC104 and H202 were prepared by dilution of commercial reagents and were analyzed by standard procedures. Triply distilled water was used for preparing all solutions. Potentiometric measurements were conducted with an Orion Model 94-95 iodide ion specific electrode and an Orion Model 90-00-00 double junction reference electrode. Potentiometric traces were obtained with a Leeds and Northrop Speedomax recorder. Optical measurements were made at 525 nm with conventional cells in a Cary 15 spectrophotometer. Results Limiting Conditions for Oscillations. Figure 1illustrates various types of behavior that may be observed at 50 “C with an iodide ion specific electrode when hydrogen per(1) (a) Paper No. 45 is: Noyes, R. M. Proc. Natl. Acod. Sci. U S A . 1981, 78,7248-9. (b) Department of Chemistry, University of Ife, Ile-Ife, Nigeria. (2) Bray, W. C. J. Am. Chem. SOC.1921, 43, 1262-7. (3) See ref 4-23 from ref 4 below. Also see: (a) Liebhafsky, H. A.; McGavock, W. C.; Reyes, R. J.; Roe, G. M.; Wu, L. S. J. A m . Chem. SOC. 1978, IW,87-91. (b) Liebhafsky, H.A.; Roe, G. M. Int. J.Chem. Kinet. 1979,II, 693-703. (c) Liebhafsky, H.A.; Furuichi, F.; Roe, G. M. J.A m . Chem. SOC.1981,103, 51-6. (4) Sharma, K.R.; Noyes, R. M. J.Am. Chem. SOC.1976,98,4345-61.
oxide is added to a solution of potassium iodate and perchloric acid. At sufficiently low acid concentrations, type I behavior corresponds to monotonic increase in [I-]. The value of [I,] also increases monotonically, and solid iodine may eventually precipitate. As acid concentration increases, there is a sharp transition to type 11. Such a system suddenly switches briefly to a situation in which [I-] is reduced by about a factor of 10 and [I,] is decreasing. In about 1min, [I-] switches back almost to its previous maximum and [I2]begins to increase again. During each period, [I-] reaches its maximum only shortly before its rapid but brief transition to the smaller value. As the acid concentration increases, the character of the oscillations changes continuously from type I1 to type 111. Maxima in [I-] are now more rounded, the amplitude is less, times spent in high and low [I-] conditions are more comparable, and the switching between those conditions is less sharp. At still higher concentrations of acid and peroxide, behavior of type V is attained. The value of [I-] rises to a rounded maximum and then decreases sharply. The system then passes with perhaps a few damped oscillations to a condition called “smooth catalysis” by Liebhafsky5~~~ and “second induction period” by Sharma and no ye^.^ The hydrogen peroxide disproportionates to water and oxygen, and the concentration of iodine decreases slowly so that [12]/[H202]remains essentially constant. If the concentration of acid is not too great, the system eventually begins very small amplitude oscillations that grow rapidly until a typical type I11 condition is attained. The greater the initial concentration of hydrogen peroxide, the longer is the second induction period before oscillations commence. Type IV behavior, which has not previously been reported, is intermediate between types I11 and v. After the first induction period, there are a few minutes during which small, frequent oscillations first decrease and then increase in amplitude before the type I11 condition is attained. (5) Liebhafsky, H.A,; Wu, L. S. J. Am. Chem. SOC.1974,96,7180-7.
0022-3654/82/2086-0818$01.25/00 1982 American Chemical Society
The Journal of Physical Chemlstry, Vol. 86, No.
Chemical Oscillations and Instabilities
5, 1982 819
00754
0
i
[H*Io = 0 0545 M
[H,O,]o
01
03
02
04
05
= 0 446 M
-_1
Flgure 2. Initial conditions leading to behavior at 50 OC resembling that of curve I V in Figure 1. Curve A is for [IO,-],= 0.432 M, and curve B is for [IO,-],= 0.10 M. Above and to the right of each curve, behavior was of type V, while below and to the left it was of type 111. Insets show representative behaviors of types 111-V.
4
M
I
b
t
c
. . [H]',
= 0 0764 M
H [O , ;],
0,0818 M
d
Flgure 1. Traces of potential obtained at 50 OC with an iodide ion specific electrode for five different acidified iodate solutions to which hydrogen peroxkle was added at the times indlcated with arrows. Each solution then became 0.432 M in IO3-in a volume of 110 mL. Other initial concentrations are indlcated for each curve. Increasing potential corresponds to increasing [I-].
As has been pointed out before: behavior in this system is strongly dependent upon acidity. At 50 "C and iodate concentrations of a few tenths molar, the transition between types I and I1 takes place at values of [H+] very near to 0.05 M. Types I11 to V are observed when [H+] is between about 0.065 and 0.075 M. For any specific acidity in this region, behavior obviously depends upon instantaneous hydrogen peroxide concentration. At sufficiently small [H202], type I11 oscillations begin immediately after the first induction period. At sufficiently large [H202], smoothly catalyzed disproportionation takes place during a long second induction period before oscillations finally commence. The transition between the two regions is not a discontinuity, and there is a narrow intermediate zone, type IV, in which oscillations begin immediately after the first induction period but the initial small amplitude decreases before it increases. At a particular concentration of acid, type IV behavior was observed over only a very limited range of initial hydrogen peroxide concentrations. Figure 2 shows plots of [H+], against [H2O2I0 to obtain type IV behavior for two different values of initial iodate concentration, For an initial peroxide concentration to the left of the curve, the system went into full amplitude oscillations immediately after the iodine production of the induction period was completed. To the right of the curve, peroxide was
e
Flgure 3. Trace of potential obtained at 50 O C with an iodide ion specific electrode for a solution that initially contained [H'], = 0.0773 M, [IO3-], = 0.432 M, [H202]0= 0.1114 M in 110 mL. At the time indicated by an arrow between periods d and e, the solutiin was diluted to 140 mL. Regions of time are designated a-e. Here a is the first induction period, b is the second induction period, c is the period of type 111 oscillations, d is the period after cessation of oscillations, and e is the period of type I1 oscillations after dilution. (There was no break in time between the segments shown.)
destroyed during a second induction period before oscillations could commence. It should have been possible similarly to determine [H+l0 and [H20210for the transition between behavior of types I and 11. We did not attempt to do so because the observations of Sharma and Noyes4indicate that oscillations at low acidity are more sensitive to factors like light, stirring rate, etc. Dilution of an Exhausted Oscillator. Figure 3 illustrates an interesting trace. The initial acid concentration was rather large, and comparatively few oscillations occurred after a rather long second induction period. After those oscillations ceased, the solution was diluted from 110 to 140 mL. Type I1 oscillations commenced immediately. The effect of dilution was to reduce [H+] from 0.0773 to 0.0607 M, and the change in character of the oscillations is consistent with that change in acidity. However, the resumption of oscillation demonstrates that the cessation during period d could not have been because hydrogen peroxide was completely consumed.6 (6) Although the evolving oxygen would scrub some iodine with it, the fourfold excess of [IOa-]O over [H202]0 indicates that oscillations in the initial system stopped because [H202] rather than [IO,] had fallen below a critical value.
820
T25mr
7
Odutola et al.
The Journal of Physical Chemistry, Vol. 86, No. 5, 7982
-
IO min t
--
Figure 4. Part of trace obtained for potential of an iodide ion specific electrode with a solution at 50 O C whose initial composition was [H'], = 0.0727 M, [H,O,lo = 0.146 M, [IO,-],= 0.432 M in 110 mL. During time periods a and c, no gas flowed. During period b, nitrogen gas flowed through the solution at 100 bubbles in 31 s. During period d, oxygen flowed at 100 bubbles in 28.5 s.
This experiment suggests that at acidities as high as 0.077 M there are both maximum and minimum concentrations of hydrogen peroxide at which oscillations are possible. As acidity is reduced, there is a decrease in the minimum hydrogen peroxide concentration for oscillations. The curves in Figure 2 indicate approximate maximum concentrations of hydrogen peroxide at which oscillations are possible at any acidity. There must certainly also be minimum concentrations at which oscillations are possible, although they may lie close to the ordinate in Figure 2. The observation in Figure 3 suggests that the curve separating oscillatory and nonoscillatory behavior goes through a rounded maximum at acidity somewhat above 0.077 M. Effects of Gases. The mechanism of Sharma and Noyes4 assumed that elementary oxygen was not an inert product but was chemically involved when hydrogen peroxide was oxidizing iodine to iodate and when the rate of production of oxygen was simultaneously at its maximum. The strongest evidence for this conclusion7 involved experiments at 50 " C with [H+] < 0.05 M and with [IO,] N 0.1 M. Such solutions were very sensitive to the pressure of the gas above the solution, which of course affected the concentration of the dissolved oxygen product. Both light and increased oxygen concentration promoted oscillations, while bubbling nitrogen through the solution drove the system from curve I1 to curve I in Figure 1. If the acidity was increased to 0.059 M, the sensitivity of the system was much reduced. However, streams of oxygen and nitrogen still affected behavior in opposite directions. Oxygen favored oscillations and reduced the fraction of a period spent in the regime of larger [I-]. Figure 4 illustrates a trace at still greater acidity with [H+]> 0.07 M and [IO,] E 0.4 M. Streams of oxygen and nitrogen now have small but virtually identical effects. Both gases decrease the frequency of oscillations and increase the fraction of a period in the regime of larger [I-]. The gas flows in Figure 4 were equated by the crude procedure of counting bubbles. The experiments were repeated with a flowmeter based on a ball in a vertical tube. Gas streams of about 100 mL/min were probably at least 10 times the rate at which oxygen was being produced by the reaction itself. The results were the same as in Figure 4 in that for a given rate of gas flow we could not detect any consistent difference in oscillation frequency whether the gas was oxygen or nitrogen. A t the same reading of the flowmeter, helium stopped the oscillations completely. However, the meter essentially measured flow in mass per unit time, and equal measured flow rates of helium and nitrogen corresponded to many more moles of helium that could entrain iodine. We could not use the (7) Microfilm edition of ref 4 above.
flowmeter reliably with helium readings one-seventh of those used with nitrogen, but we are convinced that the difference in behavior of these two gases was due to physical rather than chemical effects. Although these new observations superficially appear to contradict those of Sharma and Noyes? the discrepancy is rationalized in the Discussion. Transient Effects with Solutions Initially Containing Both Iodate and Iodine. In the experiments reported above, hydrogen peroxide was added to an acidified solution of iodate, and there was an initial induction period during which some of the iodate was reduced to iodine by process A. 2103-
+ 5H202 f
2H+ -.+I2
+ 502 + 6H20
(A)
We thought that the effects of that induction period could be eliminated by adding the hydrogen peroxide to a solution in which iodine had already been generated. In most of our experiments, process B was used to prepare 103- + 51-
+ 6H+
4
312 + 3H20
(B)
a solution such that, when hydrogen peroxide was added, the system would be 0.125 M in IO3-and 6.0 x lo-* M in 12. The experiments were conducted at 25 O C rather than at 50 " C because Liebhafskf has shown that even at the lower temperature the half-life is only about 1 min for oxidation of iodine by process C. We do not believe that
-
I2 + 5H2O2
210,-
+ 4H20 + 2H+
(C)
the temperature difference was of major importance for the qualitative effects reported here. In most of our experiments, the initial transients were followed potentiometrically with an electrode specific to iodide ion. Because Iz was already present at time zero, we believe electrode response was rapid enough that we could measure the direction of change of [I-] immediately after the few seconds necessary for addition of peroxide. In some separate experiments, particularly at low acidity, we followed [Iz] spectrophotometrically. Initial transients were a little harder to identify in this way because the solution could not be placed in a cell and observed until about 0.5 min after the peroxide had been added. However, we could identify whether iodine subsequently increased or decreased. Because IO3-and Iz were present at much greater concentrations than any other known iodine-containing species, spectrophotometricallymonitored decrease in [Iz] unequivocally indicated oxidation to iodate while increase indicated net reduction of iodate. Potentiometric measurements were more equivocal because changes in [I-] could reflect changes in the [I-]/[HOI] ratio without any necessary correlation to change in [I2]. Figure 5 illustrates some of the variety of transient potentiometric behavior observed. At concentrations of acid below about 0.02 M and with [H,O2] > 0.01 M, [I-] increased immediately after addition of peroxide as illustrated by curve i. At acidities only a little above 0.02 M, [I-] initially decreased; curves ii-iv illustrate varieties of subsequent behavior dependent upon the concentration of added peroxide. The spectrophotometricmeasurements also established that [Iz] increased for [H+]below about 0.02 M and decreased for [H+]somewhat above that value. Figure 6 resembles Figure 2 in that it attempts to locate the boundary between regions of composition within which particular types of behavior were observed. The boundary (8) Liebhafsky, H. A. J. A m . Chem. SOC.1931. 53, 2074-90.
-
Chemical Oscillations and Instabilities
I mm
00188M
[H,0,]o=0.0457M
= 00206 M [H202]0=0.137 M
1z5mv
A
!25mv
1
,
.,,,..
Figure 5. Traces of potential obtained at 25 "C with an iodide ion specific electrode for several acidified solutions of iodate and iodine to which hydrogen peroxide was added at the times indicated with arrows. Each solution then became 0.125M in 10,- and 6.04 X lo4 M in I,. Other initial concentrations are indicated for each curve. Increasing potential corresponds to increasing [I-].
was rather poorly defined at these low acidities and [H+] values up to 0.002 M from the curve sometimes exhibited behavior opposite to that anticipated. SN4also noted that reproducibility was most difficult in solutions at low acidity. Within the uncertainties encountered, we could not assign a significant difference to our results whether [I-] or [Iz] was used as a criterion for direction of initial change. The curve in Figure 6 is qualitatively consistent with the previous observation^^^^ that at low acidities iodate is reduced smoothly by peroxide without any oscillations in the parameters measured, while at higher acidities the system goes to a smooth catalysis of peroxide disproportionation accompanied by slow oxidation of iodine to iodate. However, two quantitative features of Figure 6 appear superficially inconsistent with previous reports. In the first place, Liebhafskp observed that, at iodate and acid concentrations comparable to those in Figure 6, Iz was rapidly oxidized at 0 "C and [HZO2]C 0.01 M. Our contrary behavior at higher temperature and peroxide concentration illustrates the remarkable sensitivity of this system to small changes in conditions. The dashed portion of the curve at very low peroxide concentrations would permit our observations to be consistent with those of Liebhafsky.* In the second place, SN4observed that at 50 "C and with no initial iodine, [Iz] increased monotonically unless [H+]
The Journal of Physical Chemistry, Vol. 86, No. 5, 1982 821
was at least about 0.05 M. Therefore, between acidities of about 0.02 and 0.05 M, [Iz]decreases if it is present at the start of an experiment; yet if only IO3- is present initially, then [Iz] increases monotonically right through the same range! This remarkable contrast is consistent with the potential of the system for oscillatory behavior. There must be two possible pseudostationary states having identical compositions of all major species yet in one of which [I2]increases while in the other it decreases. Initial presence or absence of I2 determines which of those pseudostationary states is attained first. Curves ii-iv permit a rationalization of these peculiar differences. At 0.05 M peroxide (curve ii), [I-] is depressed for about 15 min after the start, but it then increases by a factor of about 10 during an interval of less than 1min; the subsequent slow increase of [I-] and presumably also of [I2] is consistent with the SN4 observations when no It was present initially. At 0.09 M peroxide (curve iii), the sudden increase in [I-] occurs after only about 6 min. At 0.14 M peroxide (curve iv), the sharp initial decrease in [I-] is followed immediately by an increase without any intervening induction period. We conclude that, when peroxide is added to iodate at acidities between about 0.02 and 0.05 M, the initial presence of Iz causes a rapid decrease in [I-] that is eventually followed by an increase which starts sooner if the concentration of peroxide is greater. If no Iz is present initially, increase in [I-] begins immediately after peroxide is added. In curve v at 0.04 M acid, the transient decrease in [I-] is followed by a very slow increase, while in curve vi at 0.06 M the long-term behavior is also a decrease. These differences in long-term behavior are consistent with the SN4 observations at comparable acidities without initial iodine present. Finally, curve v i shows that at still greater acidities the initial transient in [I-] is again positive! The break between behaviors of types vi and vii occurred at about [H+l0= 0.10 M. This observation is unanticipated because this acidity correspondsto the region of smooth catalysis5 in which [I2] decreases monotonically after it has attained a single maximum. Curve vii shows that [I-] decreases after its transient increase, and it is not clear that [I2]ever exhibits even a transient increase at these acidities if it is already present at the time peroxide is added.
Previous Mechanistic Proposals Although there have been a few other attempts to explain this fascinating reaction,+" only two3*g4have been developed in enough detail to permit even approximate comparison with experiment. Liebhafsky et al.3aformulate detailed chemical steps. They have attempted to avoid radical species but have invoked an I+ that reacts with hydrogen peroxide as a 2-equiv reducing agent while HOI reacts with peroxide as a 2-equiv oxidizing agent. Moreover, I+ and HOI can be interconverted only by first reacting with I- to generate I* We consider such an I+ species to be highly implausible. We are also unsure that a linear stability analysis of the Liebhafsk? mechanism would even generate an unstable steady state. The other mechanistic proposal was by Sharma and no ye^.^ They observed' that at low acidities the system was very sensitive to operations that affected the concentration of dissolved oxygen. They also observed12 that, (9) Peard, M. G.; Cullis, C. F. Trans. Faraday SOC.1951,47,616-30. (10)Degn, H.Acta Chem. Scand. 1967,21,1057-66. (11)Matsuzaki, I.; Nakajima, T.; Liebhafsky, H. A. Faraday S y m p . Chem. SOC.1974,9, 55-65.
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The Journal of Physical Chemistty, Vol. 86, No. 5, 1982
when iodine was being oxidized and the rate of evolution of gas was simultaneously greatest, the solution became supersaturated with oxygen to a concentration about 1.5 times the equilibrium value. They proposed that oxygen was not an inert product of hydrogen peroxide disproportionation but was an essential intermediate during oxidation of iodine by process C. They also invoked radical species and developed a mechanism that did indeed generate an unstable steady state. However, the SN4 mechanism was cumbersome a t best. Although modeling computations by Edelson and NoyesL3generated oscillations, they did so only by the tour de force of maintaining a constant concentration of hydrogen peroxide. In addition, the shape of modeled oxygen pulses differed considerably from that observed experimentally. Furthermore, studies by Furrow and Noyes14of the oscillatory Briggs-Raus~her'~ oscillating reaction have shown that SN4must have misassigned the reduction potentials of some oxyiodine species. Finally, the observations illustrated in Figure 4 demonstrate that a t sufficiently high acidity streams of oxygen and nitrogen have almost identical effects on the oscillatory system. It seems to be impossible to reconcile Figure 4 with the original SN4 proposal that elementary oxygen plays an important chemical role in oscillations under all conditions.
Requirements for a Satisfactory Mechanism The discrepancy between Figure 4 and the oxygen effects of SN7provides merely another example of the contradictory conclusions that can be reached by studying this fascinating reaction under slightly different conditions. Thus, it has previously been reportedL2that light can initiate oscillations when [H+] = 0.047 M and can inhibit them when [H+] = 0.059 M! There must be a molecular mechanism consistent with the large body of apparently contradictory information. We still believe that many features of the original SN4mechanism must be valid and can provide a basis for a more complete explanation. The following discussion summarizes features that must be satisfied by any mechanism that is finally accepted. The major reactant species H20, H202,H+, and IO3- do not change concentrations by significant fractions during a single period. Although the product O2exerts a chemical influence at low acidity, it does not do so at high acidity. In order to define the phase during an oscillation, the concentrations of a t least two intermediates must be specified. SN4originally selected I2and O2as those species. We now find that O2does not always exert a major chemical influence and instead select I2 and I- as these phasedefining intermediates. The data of SN4 are unequivocal that when d[12]/dt > 0 then [I-] has a comparatively large value, and when d[I,]/dt C 0 then [I-] has a comparatively small value. SN4never observed [I-] to change by much more than a factor of about 20 between its extremes during a single period, and that range is consistent with curve I1 in Figure 1. Our experience with other halate oscillatorsL6leads us to believe that there is another intermediate whose concentration switches by orders of magnitude when d[12]l d t changes sign. That switching occurs because of a competition between the first-order autocatalytic formation of the switched intermediate and its first-order destruction. We believe that HIOz is the best candidate for the switched intermediate. If -IOz is subsequently reduced by some (12) Sharma, K. R.; Noyes, R. M. J. Am. Chem. SOC.1975, 97,202-4. (13) Edelson, D.; Noyes, R. M. J. Phys. Chem. 1979, 83, 212-20. (14) Furrow, S. D.; Noyes, R. M. J . Am Chem. SOC.,in press. (15) Briggs, T. S.; Rauscher, W. J. J. Chem. Educ. 1973, 50, 496. (16) Noyes, R. M. J. Am. Chem. SOC.1980, 102, 4644-9.
Odutola et al.
species in the solution, step I5 can initiate autocatalytic
+ I- + H+ F-! I2 + H 2 0 HIOz + I- + H+ 2HOI IO3- + I- + 2H+ HIOz + HOI HOI
2HI02
-
-
IO3-
-
+ HOI + H+
IO3- + HIOz + H+ 2 2102 + H 2 0
(11) (12) (13) (14)
(15)
formation of HI02. This species can be destroyed by several first-order processes, but step I2 can lead to direct control of switching by the phase-defining intermediate I-. Step I3 is one of the possible nonautocatalytic ways by which HI02 can be formed, and step I4 provides the necessary higher-order destruction so that step I5 does not generate indefinite autocatalytic build up of [HI02]. HOI is the only other plausible species that contains a single iodine atom and an even number of electrons. Eigen and KustinL7have shown that equilibrium I1 is established with a relaxation time of the order of 1 s. Therefore, [HOI] can be treated as always coupled to [Iz]and [I-] and is not an independent parameter for defining the state of the system. The system may also contain radical species having odd numbers of electrons. We believe that .IO2,.IO, -1,HO., and H02. are all essential to a detailed mechanism. However, rate constants for radical-radical reactions are so large that no single chain is likely to last more than about 1 s if radical concentrations are large enough for their reactions to contribute significantly to chemical change. Therefore, radical concentrations are not independent parameters but are coupled stiffly to those of the even-electron reactants and intermediates discussed above. The system may also conceivably contain small amounts of Is- and of other species containing more than one atom of iodine. The chemistry of aqueous oxyiodine species is not sufficiently understood to identify all possibilities. As proposed by William of Occam,18we shall not invoke any polyiodine species as mechanistically significant unless it becomes impossible to explain the behavior of the system without it. Within the framework of the above assumptions, oscillations occur when the system switches repeatedly between regimes dominated by radical and by nonradical processes. When the system is in the nonradical regime, d[12]/dt > 0, [I-] is large, and [HOI] and [HI02]are small. In the radical regime, d[12]/dt C 0, [I-] is small, and [HOI] and [HIO2]are large.
Significance of the Present Observations Although the experiments reported here do not provide definitive proof of mechanism, we believe that they are entirely consistent with the model developed above. Studies without Initial Iodine. If only IO3- is present initially, d[I,] /dt must necessarily be positive immediately after peroxide is added. The curves in Figure 1 all start in the nonradical regime, and [Iz]increases until its value and that of [I-] are such as to switch the system to the radical regime. At [H+]less than about 0.05 M, curve I shows that [I-] increases monotonically and the system becomes saturated with I2 before reduction of iodate initiated by step I5 is able to compete with step 12. A t slightly greater acidity, (17) Eigen, M.; Kustin, K. J . Am. Chem. SOC.1962, 84, 1355-61. (18) "Plurality is not to be assumed without necessity", William of Occam, ca. 1285-1349.
The Journal of Physical Chemistry, Vol. 86, No. 5, 1982
Chemical Oscillations and Instabilities 0033
0
02
01
03
04
[H2O2IolM
Flgure 6. Initial conditions separating directions of initial transients as illustrated in Figure 5. Solld circles use direction of initial change of potential of an iodide ion specific electrode, and open circles use direction of initial change of absorbance by I,. Below the curve, behavior resembled curve i in Figure 5, and immediately above it resembled curves ii-iv. The dashed extension of curve A at very small [H2O,lo Is roposed to attain consistency with the measurements of Liebhafsky under somewhat dlfferent conditions.
f
curve I1 shows that [I-] continues to increase almost until the point that it is rapidly depleted by the switch to the radical regime. Finally, at still greater acidities, curves 111-V show that [I-] has been decreasing for an appreciable time before the system switches to the radical regime. During that decrease, d[12]/dt is still positive, and the equilibrium of step I1 requires that d In [HOI]/dt > d In [Izlldt. We are convinced that the above observations can all be rationalized by considering the effect of acidity'on the equilibrium of step I1 and the effect of low oxidation states of iodine on the efficiency with which step I5 initiates the autocatalytic production of HIOp The detailed mechanistic treatment is left for a future publication. Systems Containing Iodine Initially. If an oxyiodine solution initially contains both IO3- and 1, in appreciable amounts, [I-] is quite small. Sudden addition of H202to such a solution will create a system in the radical regime even if the acidity is so low that Figure 1predicts dominance of the nonradical regime. Figure 5 illustrates a range of transient effects that are then possible. If the composition is in the region below the curve in Figure 6, the system switches to the nonradical regime more rapidly than we can measure, and both [I,] and [I-] begin to increase as shown in curve i. At slightly larger acidity, curves ii and iii show that the system persists in the radical regime for an appreciable induction period before a rapid increase of [I-] by about a factor of 10 signals the switch to the nonradical regime. That switch is initiated by a sufficient concentration of I-, and this species is generated by step D1. Therefore, HOI
+ HzO,
-+
I-
+ 02 + H+ + HzO
(Dl)
increasing [H20,] decreases the length of the induction period just as is observed. Curves iii-v exhibit rapid initial decreases in [I-] that are bigger the larger the amount of peroxide that is added. We believe that these transients indicate that at least some of the radicals oxidize I- directly. Not all mechanistic implications are yet appreciated. As [H+] increases to about 0.06 M, curve vi shows the anticipated radical disproportionation of hydrogen peroxide like the second induction period in curve V of Figure 1.
Finally, for still larger acidities, curve vii shows that [I-]
823
may actually increase even though the system is presumably in a radical regime with decreasing [I2]. In such a situation, the equilibrium of step I1 requires that d In [HOI]/d In [I2]> 1. We believe that these transient effects could also be rationalized by a mechanism like that discussed above. Such an undertaking should employ the reduction potentials and rate constants required to explainlgthe related Briggs-Rau~cher'~reaction. Effects of Gas Streams. Any mechanisitic explanation should also address the apparent discrepancy between Figure 4 and the grossly different effects of nitrogen and oxygen as reported by Sharma and no ye^.^ A t the low acidities studied by SN,7the equilibrium I1 produces more I- for a particular concentration of 1,. Such a system will tend to persist in the nonradical regime and will be particularly sensitive to influences that may even temporarily shift it to radical. Elementary oxygen is notorious for adding to organic radicals and would presumably form ,100 with iodine atoms. Any process that could then generate .IO would be a bypass of the need for HOI as an intermediate in radical process C. Small changes in dissolved oxygen could have a major influence on whether or not [I-] could be depleted enough to permit the autocatalytic processes that would switch the system to the radical regime. At the high acidities of Figure 4, [I-] is so small that the system can be switched to the radical regime by processes that do not require O2as an intermediate. The effects of Figure 4 then arise because I, is entrained by any gas stream, and it takes a longer time in the nonradical regime before [I2]becomes large enough that the system switches. The above discussion is a rationalization rather than a firm mechanistic proposal. We hope that further studies can dissect the obviously complex radical chemistry. However, the processes suggested by us keep getting closer to explaning an increasing body of complicated behavior. We see real hope that it will soon be possible to explain this complex, fascinating system that was discovered over 60 years ago.2 Possibilities for Future Experimentation. The observations reported here are far from a complete exploration of the system. Several obvious extensions suggest themselves: (a) The transients with iodine initially present should be repeated at 50 OC to determine whether temperature is a significant factor in the acidities at which behaviors change. (b) The curve in Figure 6 should be extended to very low concentrations of hydrogen peroxide to determine whether it does behave as suggested and thereby provide consistency with the Liebhafskf studies by different techniques. (c) The region of the transition between curves vi and vii in Figure 5 should be studied spectrophotometrically as well as potentiometrically to determine whether we are justified in our expectation that d[I,]/dt is always negative at these acidities regardless of the initial sign of d[I-]/dt. (d) The time scales of Figure 5 are based on periods of several seconds or more. If electrode responses are rapid enough, a stopped flow reactor could examine more rapid transients and learn more about the switch between radical and nonradical regimes. (e) The curves in Figure 1 follow the single species I- and do not permit us to follow concentrations of I,, IO3-, H+, and HzO, simultaneously throughout a cycle. Such simultaneous following of several species is possible in a continuously stirred tank reactor. Roux and VidaP have recently shown how such a reactor can elegantly charac(19)Noyes, R. M.;Furrow, S. D.J. Am. Chem. SOC.,in press. (20) Roux, J. C.; Vidal, C. N o w . J . Chim. 1979, 3, 247-53.
024
J. Phys. Chem. 1902, 86, 824-832
terize the details of a cycle of another oscillatory reaction. Some of the above studies could be done easily, while others would require additional apparatus. Any study of a system as complex as this will always leave loose ends and suggest further tests. We believe that the work reported here provides a sufficient extension of understanding to justify publication at this time.
Acknowledgment. This work was supported in part by a grant from the National Science Foundation. After the experimental work had been completed, Professor Stanley D. Furrow of the Berks Campus of The Pennsylvania State University pointed out the Liebhafskf observations that made necessary the dashed extension of the curve in Figure 6.
Dynamics of Protein Domain Coalescence. 2+ Gary P. Zlentara, Janlce A. Nagy, and Jack
H. Freed’
Baker Laboratory, Department of Chemistry, Cornel1 University, Ithaca, New York 14853 (Received: July 26, 1981; In Final Form: September 21, 1981)
Dynamic effects of a model pair correlation function and Oseen’s tensor hydrodynamic interactions are included in the study of the kinetics of protein domain coalescence using the numerical approach of Zientara, Nagy, and Freed [J.Chem. Phys., 73,5092 (1980)l.Modifications to the previously reported results due to hydrodynamic drag and either Debye-Huckel or Coulombic electrostatic forces are presented. A model domain pair correlation function is also incorporated to more accurately simulate the spatial and energetic aspects of hydrophobic bonding. Applying this extended model, the variation of coalescence lifetimes with ionic strength and temperature is then calculated and discussed with reference to published experimental data. A frequently observed but anomalous temperature variation in a renaturation rate constant is explained by our results.
I. Introduction An analysis of the kinetics of protein domain coalescence, an elementary step in the complex protein folding process, has previously been introduced by Karplus and Weaver’ in terms of a diffusion-reaction model. The analytic results of their model for the mean lifetime of uncoalesced domains in the limit of low coalescence probabilitylb (Le., reactivity) complement the study of Adam and Delbruck,2 who discussed the mean lifetime of reactive species confined to finite spatial domains in the limit of infinite reactivity. Recently, the first passage time approach of Szabo et al.3r4has unified previous theories by consideration of the complete range of reactivities. These studies provide an excellent mathematical basis for the study of protein domain coalescence assuming simple domain interactions. The restriction to simple interactions is due to the analytical mathematical difficulties in solving the Smoluchowski equation with a general interaction potential, V ( r ) . Model systems of protein dynamics, however, must include protein-solvent, protein-ion, and protein-protein interactions so that model results can be useful in predicting and interpreting experimental data. In order to present a method which allows an unrestricted choice of domain-domain and domain-olvent interactions, Zientara et (hereafter referred to as I) have employed numerical solutions of the Smoluchowski equation to calculate the mean lifetime of coalesced domains. The model utilized in I is based upon that of Karplus andd Weaver’ modified to include the orientation dependence of domain reactivities, interdomain electrostatic forces mediated by a solution with a finite ionic strength, and the effects of domain hydration shells. In this study we first discuss hydrodynamic effects on the simple Brownian diffusive motion of the protein do+ Supported by NIH Grant GM-25862 and NSF Grant CHE 8024124.
mains. This modification is included through Oseen’s tensor ,corrections to the diffusion tensor and is applied in the study of domains interacting through Debye-Huckel or Coulombic potentials. Also, the hydration shell structure that provides the energy barrier involved in hydrophobic bonding in protein systems is simulated by employing a model domain-domain pair correlation function within the mathematical framework of I. The ionic strength dependence of the coalescence lifetimes is then described by a Debye-Huckel interaction including hydrodynamic effects. Finally, the variation in the rate of coalescence with temperature is examined for different cases of electrostatic interactions. The discussion of the theoretical and numerical aspects of the calculations is contained in section 11. The general effects upon predicted values of mean coalescence lifetimes of hydrodynamic terms and a pair correlation function are presented in section 111. In section IV the ionic strength and temperature dependence of coalescence rates are discussed and compared with experiments. A summary of the results of this study appears in section V. 11. Theory Hydrodynamics. The calculation of the mean lifetime
of uncoalesced protein domains has been developed in I through numerical solutions of the Smoluchowski equation (1) (a) M. Karplus and D. L. Weaver, Nature (London),260, 404 (1976); (b) M. Karplus and D. L. Weaver, Biopolymers, 18,1421 (1979); (c) D. L. Weaver, Biophys. Chem., IO, 245 (1979); (d) D. L. Weaver, J. Chem. Phys., 72,3483 (1980). ( 2 ) G. Adam and M. Delbrtick, in “Structural Chemistry and Molecular Biology”, A. Rich and W. Davidson, Ed., Freeman, San Francisco, 1968. (3) A. Szabo, K. Schulten, and Z. Schulten, J . Chem. Phys., 72, 4350 (1980). (4) The fiist passage time approach is reviewed by N. S. Goel and N. Richter-Dyn,“StochasticModels in Biology”,Academic Press, New York, 1974. ( 5 ) G. P. Zientara, J. A. Nagy, and J. H. Freed, J. Chem. Phys., 73, 5092 (1980).
0022-3654/82/2086-0824$01.25/0@ 1982 American Chemical Society
