J . Phys. Chem. 1990, 94, 8866-8868
8866
TABLE I: Average Energies Transferred for All, "Down",and "Up" Collisions, the Largest Observed 'Down" and "Up" Energy Transfers ( A E , , - and AEmX,*)and Ratios of Largest to Average Energy Transfers in I5000 Collisions of CS, ( E o = 57.18 kcal/mol) with Ar, CO. HCI. and CHIa collider Ar CO HCI CH, -0.09 -0.48 0.27 -18.5 14.5 -206 161 38 54 0.32 0.25
-0.22 -0.94 0.27 -36.0 16.0 -164 73 38 59 0.63 0.28
-0.09 -0.50 0.24 -13.0 10.0 -144 Ill 26 42 0.23 0.17
-0.10 -0.78 0.22 -26.0 10.0 -260 100 33 45 0.45 0.17
"All energies are in kcal/mol. in the Ar + CS2, HCI + CS2, and CH, + CS2 systems, as shown in Figure 4, and in the He + SF, system, too.
Conclusion The calculated results show that the collisional relaxation of vibrationally hot molecules involves not only weak but also strong collisions. The probability of large energy transfer is, however, much smaller than that assumed in the "strong collision assumption" of unimolecular reaction rate theory. The Occurrence
of supercollisions is rare enough to have little influence on (A&,) and also ( A&ib)downand (A&b),,T In Table I we list the average and largest observed energies transferred in down and up collisions of hot CS2 with different colliders, as well as ratios of these quantities. The largest AE's can be as large as 200 times the average AE's. We have examined the relationship between these largest AE's and several attributes of energy transfer, including (AEvib), (AEib)down,(A&,)up, and Eo, but the results in the table do not show systematic variation with any of these quantities. Some common features, however, can be seen. The largest AE's on the down collision wing of the energy-transfer probability function are about 35 times (AEvib)dawn while on the up transition wing they are about 50 times ( A & b ) u P This shows that although the up-collision probability function is narrower, it has a relatively longer tail. It can also be seen that hEvib,Qwn, which cannot exceed E, can be as large as 63% of the initial energy in the hot molecule. Improving our statistics can only lead to an increase in this percentage. Although the classical trajectory calculations applied in the present study may have a limited accuracy at low internal energies, their applicability at high energy seems reasonable. The observation that the probability of transferring a given AE has a very long tail at large negative AE's may be of practical importance for combined RRKM + master equation models of unimolecular reactions. In addition, our characterization of large AE's may help explain a number of recent experiments that are especially sensitive to the tail of the energy-transfer distribution. Acknowledgment. This research was supported by NSF Grant CHE-9016490.
Chemical Instabilities: A Spectroscopic Study of Spatial Inhomogeneities in the CIOJI- Reaction in a Continuously Stirred Tank Reactor Ei-Ichiro Ochiait and Michael Menzinger* Department of Chemistry, University of Toronto, Toronto, Ontario M5S I A I , Canada (Received: August 16, 1990; In Final Form: November 6, 1990)
It is shown through spatially resolved absorption spectroscopicscans across a CSTR that in the chlorite/iodide system there exist substantial 13- concentration gradients d[l,-]/dx even in the vicinity of the stirrer. These noninvasive measurements confirm earlier results obtained by the use of spatial microelectrodescans and show that the imperfect macro- and micromixing are involved in the evolution of heterogeneity-induced dynamic states.
Stirring effects'J in continuously fed stirred tank reactors (CSTR) have shown that the dynamical signature (bifurcation structure) of nonlinear kinetic systems may depend in a dramatic way on inhomogeneities of the reacting medium. The latter arise frequently from incomplete mixing of reactant feedstreams and are traditionally classified by their length scale; they are frequently associated with the concepts of micro- and ma~romixing.~ In micromixing m0dels3*~ of stirring effects attention is focused on the microscale eddies arising in the cascade of turbulent energy dissipation? and it is usually assumed that macroscopic gradients are absent. Macromixing approaches, e.g., the coupled reactor model,5 on the other hand, rest on the opposite assumptions. The reality lies probably somewhere between these extremes, and it is not clear whether and to which extent the spatial scale of a reactor nonideality determines the dynamical response. The first of these issues was addressed recently by Menzinger and Dutt6 for the chlorite/iodide reaction in a CSTR. I n order to test for macroscopic concentration gradients, a Pt microelectrode
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Permanent address: Department of Chemistry, Juniata College, Huntingdon, PA 16652.
0022-36S4/90/2094-8866$02.50/0
was scanned across a cylindrical CSTR near the helical glass stirrer blade. Its potential E(r) was found to depend markedly on radial position r , suggesting a similar radial dependence of the con( I ) (a) Roux, J. C.; DeKepper, P.; Boissonade, J. Phys. Lett. 1983,97A, 168. (b) Menzinger, M.; Giraudi, A. J . Phys. Chem. 1987,91,4391. (c) Luo, Y.;Epstein, 1. R. J . Chem. Phys. 1986, 85, 5733. (d) Boukalouch, M.; boissonade, J.; DeKepper, P. J . Chim. Phys. ( L a U l k Fr.) 1987,84, 1353. (e) Dutt, A. K.;Menzinger, M. J . Phys. Chem. 1990, 94, 4867. (2) Ali, F., this laboratory, unpublished results. (3) (a) Villermaux, J. Genie de /a Reaction Chimique; Edition Tech & Doc; Lavoisier: Paris, 1972. (b) Westerterp, K. R.;VanSawaaij, W. P. M.;
Beenackers, A. A. C. M. Chemical Reactor Design and Operation; J. Wiley: New York, 1983. (4) (a) Horsthemke, W.; Hannon, L.J . Chem. Phys. 1984,81,4363. (b) Hannon, L.;tiorsthemke, W. J . Chem. Phys. 1987,81,4363. (c) Boissonade, J.; DeKepper, P. J. Chem. Phys. 1987, 87, 210. (d) Puhl, A.; Nicolis, G. J . Chem. Phys. 1987,87, 1070. (e) Fox, R. 0.; Villermaux, J. Chem. Eng. Sci., in press. ( 5 ) (a) Kumpinsky, E.; Epstein, 1. R. J . Phys. Chem. 1985, 82, 53. (b) BarEli. K.; Noyes, R. M . J . Chem. Phys. 1986,85, 3251. (c) Boukalouch, M.; Elezgaray, J.; Arneodo, A.; Boissonade, J.; DeKepper, P. J . Phys. Chem. 1987, 91, 5843. (d) Hocker, C. G.; Eptein, I. R. J . Chem. Phys. 1989. 90, 3017. (e) Gyorgyi, L.; Field, R. J. J. Phys. Chem. 1989, 93, 2865. (6) Menzinger, M.; Dutt, A. K. J. Phys. Chem. 1990, 94, 4510.
0 1990 American Chemical Society
Letters
The Journal of Physical Chemistry, Vol. 94, No. 26, 1990 8867
- -
(a)
---+x 300
500
400
600
wavelength
-7
I - collimator
light 'beam
Figure 1. Scale drawing of the CSTR (dimensions 30 X 30 X 20 mm). (a) Side view: - - -,scanning plane; x = distance (light beam - reactor axis). (b) Top view, x = IO mm.
centration c(r) in this highly turbulent region. Control experiments showed that a modification of the electric double layer9 at the electrode by the spatially dependent turbulent field could not account for the magnitude. of the observed effect, supporting the interpretation. Still, the interpretation of electrochemical measurements in turbulent flows of this kind is frought with complications and is not as convincing and unambiguous for the diagnosis of spatial distributions as the noninvasive light absorption method, even if three-dimensional resolution is no longer achieved due to spatial averaging over the absorption path. The purpose of the present work is therefore to verify the existence of macroscopic concentration gradients in a CSTR in the chlorite/iodide system by UV/vis absorption spectroscopy. A CSTR with rectangular cross section and a volume of 18 cm3, drawn to scale in Figure 1, was fitted with quartz windows separated by a 20-mm absorption path and with a Pt electrode for simultaneous electrochemical monitoring. It was mounted on a sliding track which allowed the entire CSTR to be scanned across the light beam of a H P 8452 UV/vis diode array spectrometer. Absorption spectra were taken at different distances x (where -10 < x < +IO mm) between light beam (diameter 1.5 mm) and the stirrer axis. The direction of the stirrer (glass propeller 16 mm tip to tip, S = 50-2500 rpm) could be reversed. The reactant streams A (C102-) and B (I- + buffer) entered through two 0.75-mm ports in the base of the reactor. Results and Discussion A preliminary experiment, summarized in Figure 2a,b illustrates the changes of the absorption spectrum at x = 10 mm and of the electrode potential E ( S ) as a function of stirring rate S . The bands at 288 and 352 nm belong to 13-, and the one at 460 nm belongs to 1,. Initially, the system was on the thermodynamic branch characterized by high E, [I,] and low [I-]. As the stirring (7) The magnitude of the spatial effect 1[1,-(x=+10)] - [l,-(x=-lO)] was found to peak under the conditions of the experiment (Figure 3) and to fall off slowly with higher and lower [CIO2lO. (8) (a) Dateo, C. E.; Orban, M.;DeKepper, P.; Epstein, I. R. J . Am. Chem. SOC.1982, 104, 504. (b) Epstein, I. R.; Kustin, K. J . Phys. Chem. 1985.89, 2275. (c) Citri, 0.; Epstein. I. R. J . Phys. Chem. 1987, 9/, 6034. (9) Bockris. J. O M . ; Rcddy, A. K. N. Modern Electrochemistry; Plenum Press: New York, 1970: Vol. 2.
2
4
6
8
IO
time ( m i d
Figure 2. (a) Absorption spectra taken at x = IO mm and at different indicated in the lower panel. (b) Electrode potential vs stirring rate S. Initially, the system is on the thermodynamic branch. The latter is metastable at S = 320 rpm, and transition to the flow branch occurs spontaneously near c. Constraints: [CIO;], = 3.0 X IO-' M, [I-], = 8.9 X IO4 M, pH = 1.75, ko = 0.05s-l.
times
speed was decreased in steps from 1800 to 320 rpm, absorption spectra labeled a-q were recorded a t the times marked by the arrows in Figure 2a. The potential decreases with decreasing S, reflecting the well-understood" increase of [I-] and hence of [I 1200 rpm, just as the electrochemical experiments6 have shown. The present experiments were performed at stirring rates and flow rates comparable to those in the literature,' suggesting that similar gradients were present in the earlier experiments. Although gradients may be minimized by increasing the turbulence by the use of baffles and impellerst0at even higher stirring rates, and by further decreasing the flow rate, it has to be kept in mind that complete homogeneity is reached only asymptotically. In conclusion, the present light absorption measurements have confirmed the existence of macroscopic gradients in a CSTR at low and intermediate stirring rates where many previous experiments have been performed. Acknowledgment. This work was performed under a grant from the NSERC of Canada. ~~~~~
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(10) Klein, J. P.; David, R.; Villermaux, J. Ind. Eng. Chem. Fundam. 1980, 19, 3 1 3 .
