J. Phys. Chem. 1987, 91, 1707-1709
I
12.2,u.m H, = 9 0 0 G
TIME (nsecl
Figure 4. Na polarization grating. The sodium cell is placed in a static magnetic field of 900 G in the x direction. The field splits the degenerate hyperfine states, giving rise to additional frequency components in the grating signal. The temperature and fringe spacing are similar to that in Figure 2b.
ulation grating decay demonstrate that multiple interactions with the excitation field resulting in multilevel coherent superpositions is not sufficient to produce oscillations in the grating signal. The oscillations in the polarization grating signal are caused by the time variation in the absorption probabilities experienced by the rcp and Icp components of the probe. This type of timedependent absorption probability from a coherent superposition of states has been seen by Ducas et al.15 in excited-state absorption experiments. The spatial separation of the rcp and lcp grating regions gives rise to spatially separated regions of rcp and Icp superposition states of Na. It can be shown that the phase relationships among the states involved in the superpositions result in oscillations in the diffracted signal.18 On the other hand, the excitation conditions for the population grating produce only linearly polarized grating regions. These regions have different coherent superpositions with different phase relations than the rcp and lcp regions of the polarization grating. For the phase relationships which occur in the population grating, the oscillations in the signal can be shown to cancel.I8 As will be demonstrated in detail theoretically,18 the overall result is that the observation of the coherence among the N a hyperfine levels is dependent upon
1707
the spatial separation of the lcp and rcp excitation regions in the polarization grating. An interesting result occurs when the Na sample is placed in a magnetic field. The field has no effect on the population grating signal but significantly distorts the polarization grating oscillations (see Figure 4). In the absence of the field the hyperfine levels are (2F + 1)-fold degenerate. When the field is applied, the states are no longer degenerate due to the Zeeman effect. The additional splittings add extra frequency components to the grating signal, thereby complicating the appearance of the decay. In this Letter we have demonstrated some aspects of the application of picosecond transient grating experiments to problems in gas-phase systems. The decay of the population grating is related to the Fourier transform of the velocity distribution of particles in the gas. The measurement can be used to study nonequilibrium systems as well as the thermal equilibrium situation presented here. For example, in a photofragmentation of a molecule AB to A + B, the probe could be tuned into one of the fragments and its velocity distribution directly measured. The polarization grating results demonstrate that high-resolution spectroscopic information can be obtained in situations where a AM = f l selection rule occurs. Thus, examination of the dynamics of molecular rotational angular momentum states23should be possible with this approach. The information obtainable from grating experiments of this type, combined with the gratings spatial resolution and the coherent nature of the signal, will make this type of experiment useful in studying a variety of gas-phase problems including plasmas, flames,24and combustion.
Acknowledgment. This work was supported by the National Science Foundation, Division of Materials Research (Grant No. DMR 84-16343), and by the Office of Naval Research (Grant No. NOOO14-85-K-0409). Todd S. Rose thanks IBM for a graduate fellowship, William L. Wilson thanks AT&T Bell Laboratories for a graduate fellowship, and Gerhard Wackerle thanks the Deutsche Forschungsgemeinschaft for partial support. We also thank Professor Sune Svanberg for very interesting conversations pertaining to this work. (23) (a) Felker, P. M.; Baskin, J. S.; Zewail, A. H. J . Phys. Chem. 1986, 90, 724. (b) Felker, P. M.; Zewail, A. H., submitted for publication in J . Chem. Phys. (24) Pender, .I. Hesselink, ; L. Opt. Lett. 1985, 10, 264.
Traveling Waves in the Acidic Hydrogen Peroxide-Iodine System Stanley Furrow The Pennsylvania State University, Berks Campus, Reading, Pennsylvania 19608 (Received: December 9, 1986)
One- and two-dimensional traveling wave fronts have been observed in acidic mixtures of iodine, hydrogen peroxide, and starch. The passage of the wave front marks the oxidation of iodine to iodate. The wave velocities are increased with increasing acid and iodine concentration and are decreased with increasing hydrogen peroxide and starch concentration.
Introduction Traveling wave fronts have been observed in several reaction mixtures in which metastable reactants are converted to equilibrium products during the passage of the wave. The systems ferroin-bromate,' ar~enite-iodate,~,~ iron(I1)-nitric acid,4 io(1) Showalter, K. J . Phys. Chem. 1981, 85, 440. (2) Hanna, A.; Saul, A.; Showalter, K. J . Am. Chem. Soc. 1982,104,3838. (3) Rastogi, R. P.; Singh, A. R. J . Non-Equilib. Thermodyn. 1985, 10, 193.
0022-365418712091-1707$01.50/0
date-s~bstrate-catalyst,~ and chlorite-thiosulfate6 are among those studied recently. The wave fronts are rather sharp boundaries between essentially unreacted material and products. In some cases the reacting zone is wide enough to be called a band. (4) Bazsa, G.; Epstein, I. R. J . Phys. Chem. 1985, 89, 3050. (5) Rastogi, R. P.; Varma, M. K.; Yadava, R. J . Chem. SOC.,Faraday Trans. 1985, 81, 751. (6) Nagypal, I.; Bazsa, G.; Epstein, I. R. J . Am. Chem. SOC.1986, 108, 3635.
0 1987 American Chemical Society
Letters
1708 The Journal of Physical Chemistry, Vol. 91, No. 7 , 1987 TABLE I: Effect of Concentration on Wave Velocity"
M x 104
[I,-Io,* M X IO'
[H+Io,
6.5 3.3
3.2 1.9
0.101 0.101
0.004 63 0.004 63
0.050 0.050
velocity, mm/s X lo3 4.14 2.22
6.5 5.7
3.1 2.5
0.101 0.050
0.018 3 0.0180
0.050 0.050
2.5 1.67
0.101 0.101 0.101
0.005 01 0.005 01 0.005 01
0.080 0.040 0.020
2.7 3.4 5.8
[I210,
M
6.1 6.1 6.1
[HZ02103
M
[starch], ?i
[13-10/[13-1
at final readind
time at final reading, s
8780 9960
5.8 16 215 45
11000 17400 4000 3600 4650
a In all cases, 1 .O X lo-, M KI was present initially (not corrected for 13-). Temperature was 25.0 OC. At the final reading, the mixture ahead of the wave was still blue. bMeasured on parallel runs without starch
Saul and Showalter' have presented an excellent theoretical treatment for the arsenite-iodate system. The acidic hydrogen peroxide-iodine system also exhibits traveling wave front behavior. A thin capillary tube filled with acidic solution of hydrogen peroxide, iodine, a small amount of iodide, and starch will remain blue for hours. When the wave is initiated with silver nitrate solution, oxidation of the iodine to iodate occurs, and the solution behind the wave front turns colorless. This system is analogous to the acidic ferroin-bromate system where an oxidized ferriin region advances into a reduced ferroin region (and in which the wave is inhibited by bromide ion). Like that system, the metastable hydrogen peroxideiodine mixture ahead of the wave changes composition very slowly. Experimental Procedure Stock solutions of potassium iodide, saturated iodine water, starch, and perchloric acid were prepared from reagent grade materials and double-distilled water. Perchloric acid was standardized by titration against sodium carbonate. Hydrogen peroxide, Fisher stabilizer-free, was diluted with double-distilled water and analyzed by a standard iodometric procedure.* Wave velocity measurements were carried out in a 1.45-mm Pyrex capillary tube, closed at one end with a Teflon plug. The tube was placed in a horizontal position beside a scale inside a thermostated condenser. The temperature for all runs was 25.0 "C. The condenser was covered with aluminum foil, and the room was darkened except for brief times when the position of the front was observed relative to the scale. The wave was initiated by touching the end of the tube with a thin probe which had been dipped in 0.010 M AgNO, solution. Two-dimensional waves can be observed in a thin layer of solution in a Petri dish. This method was not used for wave velocity measurements because of the high volatility of iodine. Spectrophotometric measurements were made on similar solutions without starch using a Hewlett-Packard 845 1A diode array spectrophotometer to follow absorbance at 352 and 460 nm (for triiodide and iodine concentrations). Results There is a long induction period for oxidation of iodine by hydrogen peroxide in acidic solutions. A steady state is eventually reached where the following reactions are balanced: H + + IHOI
+ H202
+ H202
+
-
+ H2O H+ + I- + 0 2 + HzO HOI
(U1) (D1)
The net result is 2H202
+
2H2O
+0 2
(A)
The I- concentration continues to drop very slowly, however, during this "steady state". Eventually, when 11-1 becomes low enough, iodine is oxidized to iodate. In the capillary tube in the presence of starch, the blue color occasionally cleared spontane(7) Saul, A,; Showalter, K. Oscillations and Travelling Waues in Chemical Systems; Field, R . , Burger, M., Eds.; Wiley: New York, 1985; p 419. (8) Kolthoff, I . M.; Sandell, E. B. Textbook of Quantitatioe Inorganic Analysis, 3rd ed.; Macmillan: New York, 1952; p 600.
: 'I = I
0
0
0
0
ok
' 0.62 ' 0.04 ' 0.06 (H202)
0.08 ' 0;lO
(MI
Figure 1. Wave speed as a function of hydrogen peroxide concentration M; ([HCIO,] = 0.10 M; [I2J0= 6.5 X lo-, M; [I-], = 1.0 X temperature 25.0 "C).
ously before the passage of the wave front. To inhibit this spontaneous oxidation of iodine, a small amount of iodide ion was added to the mixtures. Within the limits studied here, the iodide concentration seemed to have little influence on the wave velocity. So far as could be determined in these studies, wave velocities were constant for a given mixture. There was some nonlinearity occasionally during the first 1000 s or so. These effects were attributed to temperature and concentration transients introduced during wave initiation. The boundary of the wave between blue and colorless was neither vertical nor sharp, especially at first. The sharpness usually improved after the first centimeter or so of travel; part of this difficulty at the beginning is certainly associated with the method of starting. Hydrodynamic effects can play a large role in wave behavior.6 Under the conditions here hydrodynamics are not expected to be dominant. The tube diameter is near the size where previous studies found independence from tube size.6 The reaction is slightly exothermic, but the temperature change is less than 0.1 deg in an insulated container with a mixture which requires approximately 8 min to react to completion in bulk. The influence of major concentration variables is shown in Figure 1 and Table I. Typical wave speeds found here are about 10-100 times lower than those reported for most other systems. Hydrogen peroxide has an inverse effect on wave velocity. The effect is similar to the effect on rate of oxidation of iodine in bulk mixtures. Although hydrogen peroxide is the oxidizing agent, higher concentrations decrease the reaction rate and wave speed. Hydrogen peroxide concentration was kept fairly low to avoid oxygen bubbles from unwanted catalytic decomposition. Increased iodine concentration leads to increased wave speeds. This trend also correlates with reaction rates in bulk, where speed of iodine oxidation increases with increasing iodine concentration. Increased acid concentration results in slightly increased wave velocity. As with peroxide and iodine, this trend is the same as the trend in reaction in batch mixtures.
The Journal of Physical Chemistry, Vol. 91, No. 7, 1987
Letters Within the limits tried here, neither iodide nor triiodide concentration seems to have much effect on the velocity. In the blue mixture, iodide ion is slowly oxidized to iodine by hydrogen perioxide. The reactions are
H+ + I-
- + -+ -+
+ Hz02 H+ + I- + HOI
resulting in 2H+
+ 21- + H202
HOI I2
12
H20
(U1)
H20
2H20
In parallel runs in the spectrophotometer, both iodide and triiodide concentrations in the unoxidized mixture decreased by 1 or 2 orders of magnitude while wave front velocity remained constant. (See Table I.) Iodine concentration, in large excess, remained essentially constant. The wave front velocity was strongly inversely dependent on starch concentration. Starch has been used by other investigators to visualize iodine in wave velocity s t u d i e ~ , ~ . but ~ - ~starch ’ dependence has either been small’, or not reported. A starch concentration of 0.02% is near the lower limit of observation with the above experimental setup because the blue color is very light. Reaction mixtures were kept in darkness as much as possible. Wave fronts in mixtures exposed continuously to room light traveled about 25-30% slower than mixtures kept in the dark (except for readings).
Discussion Previously studied systems of propagating wave fronts all show autocatalysis and exhibit bistability in a continuous-flow, stirred tank reactor (CSTR): CSTR studies have not been reported for this system; however, autocatalysis has been found.13 Since autocatalysis was known, this work was initiated with the expectation that wave fronts could be seen. The mechanism by which Hz02oxidizes I2 to 103-is not und e r ~ t o o d . ’HOI ~ ~ ~is~ reduced by H2O2l6(reaction Dl). The direct reaction between Hz02and Iz is very slow, if indeed it occurs at all. An iodine cation intermediate has been suggested.” A radical mechanism has been proposed’* to account for oscillations in the iodate-hydrogen peroxide system. A proposal by Schmitzl’ is attractive regarding a dimer of HOI which could undergo oxidation. Though the detailed mechanism is not known, some facts regarding iodine oxidation by hydrogen peroxide are available. These apply in solutions about 0.1 M in acid at room temperature. 1. Oxidation of iodine is strongly inhibited by iodide ion. When [I-] is high, reactions U1 and I1 produce a net change, reaction B. When [I-] is lower, reactions U1 and D1 produce reaction A. (9) Gribschaw, T. A,; Showalter, K.; Banville, D. L.; Epstein, I. R. J. Phys. Chem. 1981,85, 2152. (10) Weitz, D. M.; Epstein, I. R. J . Phys. Chem. 1984, 88, 5300. (1 1) Harrison, J.; Showalter, K. J . Phys. Chem. 1986, 90, 225. (1 2) Showalter, K., private communication, 1986. (13) Furrow, S., to be submitted for publication in J . Phys. Chem. (14) Furrow, S . Oscillations and Trawlling Waves in Chemical Systems; Field, R., Burger, M., Eds.; Wiley: New York, 1985; p 171. (15) Liebhafsky, H. A,; McGavock, W. C. J . Am. Chem. SOC.1978, 100, 87. (16) Liebhafsky, H. A. J . Am. Chem. SOC.1932, 54, 3504. (17) Liebhafsky, H. A. J . Am. Chem. SOC.1974, 96, 7180. (18) Sharma, K. R.; Noyes, R. M. J . Am. Chem. SOC.1976, 98, 4345. (19) Schmitz, G. J . Chem. Phys. 1974, 71, 689.
1709
Iodide ion must be still lower for net oxidation of iodine. 2. Net oxidation of iodine does occur at very low [I-]. The absorbance vs. time curve is sigmoid-shaped. The rate is approximately first-order in [I,] after the inflection point.I3 First-order kinetics can result if iodine hydrolysis is rate-limiting, (reaction Il), with I- and HOI being removed by rapid reactions. 3. Net oxidation of the intermediate HOI and HOIO by HzOz is fast.I3 4. Oxidation of I, is inhibited by H,02. This could be explained by a competition between net reduction processes and net oxidation processes of iodine species. The reduction of HOI is first-order in [HzOz].16The net oxidation of HOI is probably independent of [H202],so increasing [H202]favors reduction processes. 5. Superficially, oxidation of iodine seems to be autocatalyTic in [IO3-], although the active agent is probably [HOI] or [HOIO]. Any of these species can cause autocatalysis because all three species decrease iodide ion. The rate constant for reaction of IO< with I- is by far the smallest of the three. Since many individual steps are still not understood in detail, any mechanism is speculative. A mechanism similar to that proposed by SchmitzI9 whereby dimeric species of HOI + HOI or HOIO + I- or HOI HOIO undergo fast oxidation by H202, while monomeric species undergo reduction, is in accordance with the above facts. Dimers could only form when [I-] is low. Dihalogen species have been proposed as intermediates in other iodine and halogen reactions.2k22 The following sequence generates autocatalysis in HOI: I, HzO .+ H+ I- HOI
+
+
2HOI
.+
+ + + H20 HOIO + HOI
120
+ HzOz H+ + I- + HOIO
I20 The sum is 12
.+
-
+ 2HOI + HZ02
2HOI
+
4HOI
After the autocatalytic phase, during which [HOI] and [HOIO] both increase and 11-1 decreases, HOIO is oxidized to iodate. When [HOI] and [HOIO] are both “high”, HOI and I- can both be removed rapidly and iodine hydrolysis may become rate-determining. The dependence of wave front velocity on starch concentration is possibly a secondary result of starch binding iodine or triiodide, although like iodide, triiodide concentration changes by as much as 2 orders of magnitude in the mixture ahead of the wave with very little effect on wave velocity. Also, the rate of oxidation of iodine or iodide by hydrogen peroxide in bulk (in a spectrophotometer cell) is not affected appreciably by the presence of starch. Modeling the effect of concentration variables on the wave velocity in this system has not been attempted, although methods have been d e v i ~ e d . ~ Progress J ~ ~ ~ ~ on this system much await further progress in mechanistic studies involving oxidation of iodine by hydrogen peroxide. Species such as IzO may not be necessary.
Acknowledgment. Spectrophotometric studies were performed on a HP-8451A spectrophotometer purchased with a grant from the National Science Foundation. (20) Liebhafsky, H. A,; Roe, G.M . Inf. J . Chem. K i n a . 1979, 11, 693. (21) Taube, H.; Dodgen, H. J . Am. Chem. SOC.1949, 71, 3330. (22) Valdes-Aguilera, 0.;Boyd, D. W.; Epstein, I. R.; Kustin, K. J . Phys. Chem. 1986, 90, 6696. (23) Reusser, E. J.; Field, R. J. J . Am. Chem. SOC.1979, 101, 1063.
