J . Phys. Chem. 1992,96, 9104-9106
9104
4719. Geusic, M. E.; McIlrath, T. J.; Jarrold, M. F.; Bloomfield. L. A.; Freeman, R. R.; Brown, W. L. Ibid. 1986, 84, 2421. Raghavachari, K.; Binkky, J. S. Ibid. 1987, 87, 2191. (16) Jarrold, M.F.; Honea, E. C. J . Phys. Chem. 1991, 95, 9181. (17) One model of delayed, or activated, electron emission rata yielding an Arrhenius expression has ken derived by: Klots, C. E. Chem. Phys. Lett. 1991, 186, 73. However, it is not clear that the assumptions used in this derivation are applicable to finite negative ions, where there may be only a
few or no bound excited states. The first example of a negative ion excited state is that of Cz-:Lineberger, W. C.; Patterson, T. A. Chem. Phys. k t r . 1972,13,40.
(1 8) Exo-electrons from hyperthermal cluster impact have been described by: Even, U.; delange, P. J.; Jonkman, H. T.; Kommandcur,J. Phys. Rev. Lett. 1986, 56, 965. (19) Rtithlibergcr, U.; Andreoni, W.; Giannozzi, P. J. Chem. Phys. 1992, 96, 1248.
Chaos In Batch Belousov-Zhabotinsky Systems Peter Ruoff Department of Chemistry, Rogaland University Center, Box 2557, Ullandhaug, 4004 Stavanger, Norway (Received: August 4, 1992; In Final Form: September 17, 1992)
Chaos in the oscillatory Belousov'-ZhabotinskyZ (BZ) reaction is exclusively studied in open flow systems and interpreted as determinktic." Here we show experimentally the occurre- of chaotic oscillations in batch BZ systems and theii simulation by incorporating concentration fluctuations (related to the stirring process) in the original Oregonator model.
ExcitabilitP-'O in the BZ reaction is, in analogy to excitability in biological systems,I1 an all-or-none respond2 that occurs when the concentration of bromide ion ([Br-1; Br- is a control intermediate in the BZ reaction)I0 is forced below or above a critical value, [Br-Iht. It results in a sudden pulse of oxidations*9or red~ction.'~Due to this excitability, BZ systems may become extremely sensitive to small variations in bromide ion when its From closed BZ system it is known concentration is near [Br],. that irregular oscillations can sometimes be observed at the end of the oscillatory region when oscillations stop with undiminished amplitude and when the system enters an excitable steady-state transit."J5 These early experiments did not exclude atmospheric oxygen, which is now known to have a considerable influence on the chemistry of the BZ reaction'6 and may lead to a nonoecillatory excitable steady state.17 To avoid any interfering oxygen effects, all the experiments reported here were conducted in an inert atmosphere of argon. Figure 1 shows chaotic oscillations of a batch BZ system. In batch, chaotic oscillations are found as a transition phenomenon when the BZ reaction is near or slowly approaches the region of a nonoscillatory excitable steady state. Because [Br-] in this excitable steady state is slightly above [Br-],t, fluctuations or perturbations that drive [Br-] below [Br-Iht (for example, adding small amounts of silver ions17or reducing the sped of stirring15) will induce (generally higher frequent) oxidation pikes.^ The model used in the simulations shown below is the original Oregonator'" with the Field-Fiirsterling rate constant valuesI9 (Table I). To account for local concentration variations (due to stirring) inside the reactor, the reacting solution is divided into N fluid cells, each cell having a lifetime 7 , During the cells' lifetime, contents of different cells do not mix, but chemical reactions proceed within each cell as described by the rate equations of the model. At the end of cell lifetimes, the contents of all cells are mixed and the average concentration for each reacting species "I"' within the whole reactor ((q))is determined. Then, a new concentrationof chemical component 'I"' in cell 'f' is calculated (q), where cii. is allowed to fluctuate around (4) according to the relationship
TABLE I: Thc Oregonator18Model" A+Y-.X+P X+Y--.2P A X- 2X Z 2X-A+P
+
+
z-fy
(1) (2)
(3) (4) (5)
"Rate constants:19 k, = 1.3 M-' s-I, k2 = 2.4 X lo6 M-I s-I, k3 = 34 M-I PI, k, = 3 X lo3 M-I s-', k5 = 0.02 s-';f= 1.0. A = BrO; = 0.1 M,X = HBr02, Y = Br-, Z = 2Ce(IV), P = HOBr. Kinetic active components: X, Y, and Z.
8 generatei? a uniform random number (e E (0,l)) based on three linear c+mgruentialgenerators to assure a practically infinite period lengthzo K is a scaling factor ( K E (O,l)), and indicates the random multiplication of +1 or -1. When c,, has been determined
"*"
for all cells, a new 'lifecycle" of cells starts. Since fluctuations will also drive the bromide ion concentration below [Br],,, a certain number of cells (neJ are assumed to be in an excited (oxidized) state. Figure 2 shows simulations when local fluctuations due to mixing are included in the model. As in the experiments (Figure l), chaos is observed when the reacting system is near the border to the excitable steady state. In the computations this can be achieved by 'balancing" the influences of K and &, while keeping thef-factor (for the sake of simplicity) constant. High K and ncx values correspond to a high 'noise level" of the stirrer. Figure 2 shows that K and ne, are acting in opposite directions: while an increase of K increases the average time between two suaxssive excitations, an increase in n,decreases the average period length. Chaotic oscillations in batch BZ systems have experimentally not been recognized or simulated with the OregonatorI8model. The study of chemical chaos in batch systems has the advantage that mixing effects between inflow reagents and the bulk reaction mixture of the CSTR (which is a possible source of deterministic chaos)z2are not present. Although the originalla Oregonator is generally considered6 of being unable to model (deterministic) chaotic oscillations, the simulations presented here suggest (along with work on flow reactors)= that local fluctuations due to 'stirring noise" appear important to fully understand the chaotic response of BZ systems.
0022-365419212096-9104$03.00/0 0 1992 American Chemical Society
The Journal of Physical Chemistry, Vol. 96, No. 23, 1992 9105
Letters
Flgare 1. Chaotic batch BZ oscillations in an inert atmmphere of argon. Parts A and B show the response of a bright platinum electrode ("+" sign indicates the direction where the Pt potential gets more positive) against a Ag/AgCl double junction reference electrode (the outer electrolyte was 1 M sulfuric acid). Initial concentrations: [malonicacidlo = 0.30 M,[(NH4)2Ce(N03)6]0 = 2.1 X l(r3M, [KBr03Jo= 0.10 M,[H304Jo= 1.0 M. All chemicals were of analytical quality and uscd without further purification. Details of the reactor deign can be found in Figure 2 of ref 21. Stirring was provided by means of a magnetic stirrer. First the following reagents were mixed: 6.0 mL of 2.3 M sulfuric acid, 4.0 mL of 1.8 M malonic acid, 10.0 mL of 0.25 M KBr03. Magnetic stimng was started, and wet argon was bubbled through the mixture for approximately 5 min. The reaction was then started by adding 4.0 mL of 1.25 X M (NH4)2Ce(N03)6(dissolved in 2.3 M H s 0 4 ) . After the addition of Ce(IV), Ar bubbling was stopped, but argon gas was still allowed to flow above the surface of the reacting solution to assure that the argon pressure above the solution was higher than the pressure of the outer atmosphm. The flow rate of the argon gas was approximately 1 L/min. Escape of argon gas from the otherwise closed reactor occurred through a paper stopper. Stirring rates: (A) 1100 rpm, (B) 300 rpm. Insets show a 1-h time period of chaotic oscillations. The reSOnsc of the Pt electrode at low stirring spaad (B) is more 'noisy" compared to the same experiment at high stirring spaads (A). -11)
-23
-2.8
IA
n
-33 ,
I
1
I
12600
100
I
v) Q)
3
c
Q
> a
-11)
s
-23
Q
-2.8
u)
>
Y
E a, 0
L
-1B
-23
-2.8
-33 0
Time, s Fig" 2. Modeling of chaotic oscillations using the Oregonator (Table I). For all calculations: number of fluid cells N = 600,and lifetime of cells T = 1 .O s. To show the influence of the number of excited cells, n, decreases linearly from 60 to 30 during the first hour. After r = 3600 s, n, was kept constant at nex= 30. K (stc cq I) had the following values: (A) K = 0.85, (B) K = 0.90, (C) K = 0.92.
J. Phys. Chem. 1992,96, 9106-9111
9106
References and Notes
(12) Nicolis, G.; Prigogine, I. SelfOrganizarion in Nonequilibrium Sys-
(1) Belouaov, B. P. In Oscillations and Traveling Waves in Chemical Sysrems; Field, R. J., Burger, M., Eds.; Wiley: New York, 1985. (2) Zhnbotinsky, A. M. In Oscillations and Trawling Waves in Chemical Sysrems; Field, R. J., Burger, M., Us.; Wiley: New York, 1985. (3) Hudson. J. L.: Mankin. J. C. J . Chem. Phvs. 1981. 74.6171-6177. (4) Gybrgyi; L.; Field, R. J.;Noszticzi~~, Z.; M ~ r m i W.'D.; c ~ Swinney, H. J . Phys. Chem. 1992,96, 1228-1233. (5) R o w J.-C.; Simoyi, R. H.; Swinney, H. L. Physica 1983, A?, 257-266. (6) Gybrgyi, L.; Field, R. J. Nature 1992, 355, 808-810. (7) Schneidcr. F. W.: MIinstrr. A. F. J . Phvs. Chem.1991.95.2130-2138. (8) Field, R. J.; Noyes, R. M. Faraday Symp. Chem. Soc.' lfi4,9,21-27. (9) Ruoff, P. Chem. Phys. Lett. 1982,90, 76-80. (10) Ruoff, P.; Varga, M.; KbrBs, E. Acc. Chem. Res. 1988,21,326-332. (11) Troy, W. C. In Theorefical Chemistry; Eyring, H., Henderson, D., Eds.; Academic: New York, 1978; Vol. 4.
rems; Wiley: New York, 1977; Chapters 13.5 and 15.4.
(13) Ruoff, P.; Noycs, R. M. J . Chem. Phys. 1986,84, 1413-1423. (14) Field, R. J. J . Chem. Phys. 1975, 63, 2289-2296. (15) Ruoff, P. Chem. Phys. Lrrr. 1983, 96, 374-378. (16) Ruoff, P.; Noycs, R. M. J . Phys. Chem. 1989,93, 7394-7398. (17) Ruoff, P. Chem. Phys. Lrrr. 1982, 92, 239-244. (18) Field, R. J.; Noycs, R. M. J . Chem. Phys. 1974, 60, 1877-1884. (19) Field, R. J.; Fbrsterling, H.-D. J. Phys. Chrm. 1986,W, 5400-5407. (20) Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; Vetterling, W. T. Numerical Recipes; Cambridge University h: Cambridge, 1989; Chapter 7. (21) Ruoff, P.; Vcstvik, J. J . Phys. Chem. 1989, 93, 7798-7801. (22) Gybrgyi, L.; Field, R. J. J. Chem. Phys. 1989, 91, 6131-6141. (23) Blittersdorf, R.; Mlnstcr, A. F.; Schneider, F. W. J . Phys. Chem. 1992, 96, 5893-5897.
ARTICLES Charge Transfer in the Photodissociation of Metal Ion-Benzene Complexes K.F. Willey, C.S.Yeh, D.L.Robbius, and M.A. Duncan* Department of Chemistry, University of Georgia, Athens, Georgia 30602 (Received: June 8, 1992; In Final Form: August 19, 1992) Photodiiation dynamics, spectroscopy, and binding energetics are investigated for a variety of gas-phase metal ion-benzene complexes. These complexes are produced and cooled by pulsed laser vaporization in a s d e d supersonic expansion. They are mass-selected and studied with laser photodissociation in a reflectron time-of-flight mass spectrometer. A prominent photoprocess for many of these complexes at low energy is "dissociative charge transfer", which produces the benzene cation photofragment. The relative importance of this channel depends on the energy of excitation and on the density of metal ion electronic states in the same energy region as the charge-transfer electronic state. The measurement of the appearance threshold for the charge-transfer channel establishes an upper limit for the metal ion-benzene dissociation energy. charge-transfer dissociation processes in a variety of metal ionIntroduction benzene complexes (e.g., Fe+-bz, Mg+-bz, Ag+-bz, Bi+-bz). The binding of metal atoms or metal ions to organic ligands These studies reveal previously unavailable energetic information such as benzene has been a topic of interest for many years.'+ for the bonding in these complexes. The data obtained here are The resulting complexes have bonding interactions representative compared to those from other techniques, when available, and to of those in many inorganic or organometallic systems, and they the predictions of theory. are also important as models for adsorption on bulk metal surfaces. Metal *-complexes with benzene or other unsaturated molecules Experimental Section have been studied since the early work of Mulliken.s However, Metal-bonzene ion-molecule complexes are produced by laser the detailed structures of these complexes and their binding envaporization at 532 nm (NdYAGsbcond harmonic) in a pulsed ergetics remain to be characterized. nozzle cluster source using naethodsdacribed pre~iously.'~-'~ The Recent technical developments stimulated by molecular beam complexes are mass-selected one at a time from the distribution cluster research have improved both the experimental and theoproduced by the source in a reflectron time-of-flight mass specretical capabilities for studying gas-phase complexes containing tr~meter.~'Laser excitation of selected ions takes place in the metals.622 In particular, metal-molecule complexes have been reflection field at the turning point in the ion trajectory. Phoproduced by pulsed laser vaporization sources for study with ' ~ J ~ ~ ~ products and parent ion depletion are measured with molecular beam laser and mass spectroscopy t e c I ~ n i q u e s . ~ ~ . ~ ~todissociation a second stage of time-of-flight mass analysis. The operation of These complexes have been studied with laser photodissociathe reflectron instrument for photodissociation experiments has tion9J0J3JsJ7-19 and collision-induced dissociation16in low-pressure been described previ~usly.~' The wavelength dependence of environments and with equilibrium methods in high-pressure mass photodhciation processes kimestigatcd with a NdYAG pumped spectrometry." In recent work in our laboratory, we have shown tunable dye laser (SpectraPhysics PDL2). Frapent ion intensity that photodissociation of metal ion complexes often leads to a is recorded as a function of the laser wavelength to obtain phopreviously unrecognized process known as "dissociative charge tofragment excitation spectra. transfer".I7 In this process, the complex dissociates in an excited electronic state in which the metal and its molecular ligand Results and Discussion separate with the charge remaining on the species with the higher Mssocition Ch8naels and Brrncbing Ratios. Figure 1 shows ionization potential. The observation of this process and its energy an example of metal-benzene complexes produced with our laser dependence can lead to the determination of the complex binding vaporization source. The Fe+-benzene cluster ion distribution energy. In the present report, we describe our observations of shown here is measured by pulsing the mass spectrometer acTo whom correspondence should be addressed. celeration plates to extract the cluster ions from the molecular 0022-3654/92/2096-9 106$03.00/0 0 1992 American Chemical Society
