The Role of .@owS y s t e w Irving R. E w e i n Brandeis University, Waltham, MA 02254 As the previous papers in this Symposium have demonstrated, the last decade has witnessed the discovery of a wide range of fascinating dynamical phenomena in chemistry. Many of these advances could not have been made without an experimental tool that we chemists have borrowed from our intellectual cousins, the chemical engineers. In this article, I discuss how this instrument, the continuous-flow, stirred tank reactor, or CSTR, works, and I summarize some of the many exotic modes of behavior that have been seen in CSTR's. Why Do We Need a CSTR? Undergraduate chemistry students are taught, quite properly, that any closed system must come to equilibrium, and that the equilibrium state is stable and unique. Further, there are auantities, like the Gibbs free enerw ... a t constant temperature and pressure, that must change monotonically. Are these obser\.ations incompatible with the existence of such interesting forms of behavior as periodic oscillation or chaos in chemical systems? For quite a long time, most chemists helieved that they were. The first, accidental, discoveries of chemical oscillation ( I , 2) were met with considerable ske~ticism(3). . . Fortunatelv for those interested in pursuing the study of complex dynamical phenomena, during the middle of thiscentury theoristsdeveloped a rheory of non~quilibriumthermodynamics ( 4 ) and showed that sufficiently far from eauilihrium, things like chemical oiicillatim, chaos; or spatial pattern formation are perfectly consistent with physical law.
Noneauilibrium thermodvnamics made the study of exotic chemiial dynamics an int&ectuallg respecrable endeavor. In the early 1970's, Field. Knros, and Noyes r51 at the University of Oregon went further and showed that a mechanism consisting of chemically plausible uni- and bimolecular steps could indeed generate the oscillations observed in the Belousov-Zhabotinskii reaction. However, if one works in a closed system like a beaker, any oscillations, in fact any behavior except for homogeneous equilibrium, must necessarily he transient. This has two consequences. First, if one does succeed in finding interesting dynamical behavior, like oscillation, that behavior must be studied on the run. One has to get the data before the oscillations cease, and there's always the inexorable approach toward equilibrium, though with a well-chosen system like the Belousov-Zhabotinskii reaction the approach can be quite slow. Secondly, i t is very hard to find oscillating reactions in a closed system, because most reactions simply approach equilibrium too quickly. T o get around this problem, one uses a flow reactor to maintain the system far from equilibrium. How Does a CSTR Work? How do you get around the problems associated with working in a closed system? Obviously you work with an open one. Living things do this quite successfully. They regularly take in high-free-energy reactants, or food, carry out chemicalreactions, and then excrete the low-free-energy waste products. As long as the reactant supply is main-
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tained, the machinery keeps functioning, and the outflow continues, we observe the oscillatory hehavior that we recognize as life. In a sense, the CSTR represents a minimal approximation to those aspects of a living organism that maintain its various periodicities. In addition to solving the problem of how to maintain a system far from equilibrium, the CSTR also provides a convenient way of monitoring what's going on and of keeping the system well mixed, perhaps even homogeneous. I t is desirable to have a homogeneous system, because then, if one attempts t o model the hehavior, one only has to deal with the temporal changes, i.e., with ordinary differential equations, and not with spatial variations and diffusion, which would require partial differential equations for their description. For example, consider the simple reaction scheme A+B-C C-P
k, k2
in a CSTR. The rate equations in a CSTR are given by: dAIdt = -k,AB + k,(Ao - A) + D,VZA dBldt = -k,AB k,(Bo - B) D,vZB dCldt = kIAB - k2C+ kQ(CQ - C) + DCvzC
+
+
where A, B, and Care the concentrations in the reactor, and AQ,Bo. and Co are the concentrations in the input flow (reservoir concentration/numher of feed streams). The reciprocal residence time ko, sometimes referred to as the flow rate, is the reciprocal of the average time that a molecule spends in the reactor. I t is given hy the volume of liquid that flows through the reactor inunit time divided by the volume of the reactor. In most experiments, i t is this parameter that is varied, since i t can be changed easily and continuously by twisting a dial on the peristaltic pump. The D's are diffusion coefficients, while V2 is the Laplacian operator, Wax2 a2/ ay2 az/az2. If the reactor is well mixed, the diffusion terms vanish, leaving us with the standard rate equations for a closed system supplemented by the flow terms proportional to kQ. A typical CSTR is shown schematically in Figure 1. The key elements are the reactor itself, really no more than a temperature-jacketed beaker, the input and output tubes, the pump, and the prohes. The prohes are generally either
Deslgnlng a Chemlcal Oscillator One of the most important contributions of the CSTR to chemical dynamics has been its central role in the design of chemical oscillators. Before 1980, all chemical (as distinct from biological) oscillators had either been discovered accidentally or were minor variants of the two accidentally discovered oscillators (I,2). Since that time, nearly three dozen new oscillating chemical reactions have heen discovered, most using a systematic design technique (6) that I describe briefly below. In order to oscillate, a chemical system must contain some kind of feedback; the concentration of some species must affect the rate of its own production. From looking at the known chemical oscillators, we conclude that the most promising kind of feedback is autocatalysis. Autocatalytic behavior is, of course.. uhiauitous in bioloev. . -.. hut i t is much less common in chemistry. Nevertheless, one can find autocatalvtic reactions. often in collections of lecture demonstrations, since many iutocatalytic systems make excellent clock reactions. The trick tomaking an oscillator is to find a way of resetting the clock, and that is where the CSTR comes in.
+
+
Figure 1. Schematicdrawingof aCSTR. M = monochromator.R = reactor. PM = photmuitiplier. PP = peristaltic pump.
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potentiometric-redox, pH, or ion-selective electrodes--or spectrophotometric-a light source, monochromator, and photomultiplier will suffice, though one can easily build a CSTR into the sample compartment of many commercial spectrophotometers.
Journal of Chemical Education
Fiaure 2. Exoerimentallv determined bistabilitv and hvsteresis in the absorbaiceat460nm([i21)andin 11.1 t o r t h e c h l o r i t e - i o d d e r e a c t # o n i n a ~ ~ ~ ~ ( ~ ) The npfflmncsnlration ol I- s varlet wh~lsthemhsrnputs. [CI02-1. = 2 5 X lo-' M and pH = 3 35, are heia fixed at a flow rate ko = 5 4 X s-' Steady-state concentrations are shown. Dashed arrows indicate spomaneous transitions between states.
One mode of hehavior that can be shown by a chemical reaction in an open system like a CSTR, but not in a closed system like a beaker, is bistability, the existence of two different stable steady states under the same experimental conditions. Which state is actually achieved depends upon the past history of the system, i.e., there is a memory effect. The notion of bistability is familiar to physicists, who encounter this behavior and the accompanying hysteresis loops in studying low temperature magnetic phenomena. However, many autocatalytic chemical reactions when studied in the CSTRdisplay bistability and hysteresis. An example, the chlorite-iodide reaction (7), is illustrated in Figure 2. A simple mathematical model proposed by Boissonade and De Kepper (8) suggests that a bistable chemical system can he converted to an oscillatory one by adding an appropriate feedback species. This additional reactant must have two properties: i t must react with one or more species present in the initial bistable system to a much greater extent on one of the steady state branches than on the other, and its reactions with the bistable system must be slower
than the reactions of that system's constituents with each s be found. then the model oredicts other. If sucha s ~ e c i ecan that adding it tothe bistable systemwill give rise to acharacteristic "cross-sha~ed ohase diaeram" of the sort shown in . . Figure 3. The narrowing of the bistable region as more of the feedback substance is added enables one to desien a ssstematic search procedure t o find the cross point P beyond which oscillations arise. Exotlc Dynamlcs in the CSTR
Aside from bistability and "simple" periodic oscillation, what else does one see in a CSTR? Multistability need not he limited to histahility between a pair of steady states. Tristability of three steady states (9) in the arsenite-iodate-chlorite-iodide svstem is illustrated in Fieure 4. while bistahilitv between twdoscil~atorystates, or hirhythmicity (10) in t h i bromate-chlorite-iodide reaction (11).is shown in Fieure 5. Oscillatory hehwior is not always either simple or Figure 6 is an X-Y plot from the "zoo" of comolex ~eriodic behavior found in-the bromate-chlorite-iodide ieaction (121, while Figure 7 demonstrates complex aperiodic behavior (chemical chaos) in the reaction of chlorite with thiosulfate (13). Note the irregular alternation of the large and small amplitude peaks. More Elaborate Flow Systems
Flgure 3. "Crossahaped phase diapam" typical of behavior seen in bistable SvStemS wkh feedback i n s CSTR. The svstem shown is Hao-SZ-. Note the wo dllleren steady state regions (A and r I. the r e g m ol blrtab~lltybetween them (0).and. where mls region narrows to a pomt. the regoon of ore latmon
Finally, is the CSTR as described above the last word on how to studv noneauilihrium ohenomena in chemical svstems? The answer is clearly no. Experiments show that the CSTR is not perfectly well mixed-the rate of stirring, even a t several hundred rpm, affects significantly both bistable (14) and oscillatory behavior (15). An example is shown in Figure 8. Chemical engineers have conducted detailed studies on mixing in CSTR's and have developed very useful guidelines for how to improve reactor design (16). These include the use of baffles to break up the flow, special shapes of stirrers, preferred locations for the input streams, and the use of syringe pumps in place of the more common (and less expensive) peristaltic pumps. Alternatively, one might want to design more elaborate CSTR's to study more complex phenomena. For example, as illustrated in Figure 9, one can couple two CSTR's by mass flow in order to investigate the hehavior of two coupled chemical oscillators. One such study (17), in which the two
..
Time
Figure 4. Trlslabillty In lhe chlnite-iodide-iodate-anenit.
system in s CSTR
(91. Input Concentrations of arsenne and iodide are varied, while olher canstrainta are held fixed. There are three differem steadv states. SSI. SSll and SSlll (not shown on this phase diagram), three diflerem 0-regions ol bistabili among these. and a single central T-region of tristabiiity.
(in.
Figure 5. Blmyihmiclty in Me bromte-chlorite-iodide reaction in a CSTR Flow rate in each time segment is shown at lhe top. At times indicated by mows, flow rate is changed. Note that lhe oscillatory nates A am3 B are both stableat ko = 7.14 X SO.T = 25 'C. = 6.5 X 1 0 P M . [BrOo-Io = 2.5 X M. [ClOl-]a = 1.0 X 10-'M. [H2SO& = 0.75 M.
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oscillators were Belousov-Zhahotinskii reactions with slightly different input concentrations, found a variety of interesting phenomena including phase locking, in which the two subsystems oscillate at a common frequency, and "phase death", in which the oscillators appear to interfere destructively, leaving the coupled system in a nonoscillatory steady state.
One can also design unstirred flow reactors to study nontransient spatialstructures. One approach (18)is a system in which the reaction occurs in an annular section of a gel that is continuously fed a t its inner and outer boundaries with fresh reactants. Another technique (19)utilizes the phenomenon of Couette flow. The reactor consists of two concentric cylinders, one of which can rotate about its axis. Two CSTR's feed in reactants a t either end. When the rotating cylinder turns fast enough, bulk motion of the fluid begins, producing mixing of the reactants. In effect, by varying the rotation rate one can tune the diffusion constant of the system. Although even more elaborate arrangements are sure to emerge, one of the most attractive features of CSTR methods is that a basic apparatus, suitable for the study of most dynamical phenomena, is relatively inexpensive. The reactor can he constructed by most machine shops out of Plexiglas for under $200. All that is then required is a monitoring device (potentiometric methods are simplest and cheapest) and a means of achieving a constant flow. While peristaltic pumps (cost: about $1,500 for a four-channel pump) are most often used, a simple gravity flow system can he both inexpensive and effective.
-
7-
nL Absorbance
Flgure 8. X-Y (480 nm absorbance-Pt electrode potential) plots of complex pariodlc oscillations In the bromate-chlorite-iadide reaction In a CSTR (12). [ClOs-10 = 1.0 X 10-'M. [I-10 = 4.0 X 10-'M:(a) [BrO3-Io = 2.5 X 10-SM, = 0.1 M, ko = 3.0 X [HISO& sCt; (b) [Ef03-]0 = 3.0 X M, [H2SO& = 0.04 M: ko = 5.8 X 10-'s-'. Figure 8. Elfed of stlrrlng rate on oscillations in the chlwlie-Iodide reactlon (15). At point A. the stlning rate Is Increasedfrom about 700 toabout 850 rpm. causing the large amplitude oscillations to give way to lower amplitude irregular flucIuationS.
Flgvre 7. Chemlcal chaw in tns chlcrlte-lhiosblfate reactlon in a CSTR (IS). [ClO2-I0 = 5 X 10-'M, [Snl2-lo = 3 X lOPM, pH 4. Resicence t mes: (a) 6.8 mln. (bl 10.5 mln, lc) 23.6 mi".
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Journal of Chemical Education
Flgure 9. Schematic diagram 01an apparatus (17) for studying coupled chemical OSCillatOrS. The two CSTR's are Identical and are connected lhrough an opening whose size can be varied with lhe needle valve
Acknowledgment
I thank Patrick De Kepper of the Paul Pascal Research Center, for me to the many tages of using CSTR's. I am grateful to the National Science of the work de&bed F&dation for its support if here. 1. Bray, W. C. J. Am. Chem. Sm. 1921,43.1262. 2. Belomw, B. P. Sb.Rof. Rodiofs. Med.; Megdix Mama.. 1958.p 145. 3. Winfree, A. T. J. Chem.Educ. 1984,61,661. 4. Glendorff P.: Prknrrine. I. T h e r m o d v ~ m i rTheow 01structure. Stab2
6. ~ i d dR. , J.; K6.b. E.; NWB. R. M. J. A ~cham. . sac.1 9 7 2 , ~ , 8 ~ 9 . 6. Ewtein, I. R;Kmtin. K.; De Keppr.P.; O r b , M. Sci. Am. 1983.248(3). 112. 7. D ~ ~ ~ ~ , c . E . ; o ~ ~ ~ ~ , M . ; I.DR.~JK. .A ~~chem.soc. ~ ~ , P .1982,104,504. :E~~~~, 8. Boissonade, J.; De Keppr,P. J. Phya. Chem. 1980,84,501. 9. Orbln, M.; Dateo. C. E.; DB KBPPSI.P.; Epatein, I. R.J Am. Chem Soc. 1982.104, 5911. 10. Decmly, 0.; Goldbster, A.F%c.Norl. Acad. Sci. USA 1982,79,6917. 11. Aiamgir.M.:Epstein,I.R. J.Am.Chem. Sac. 1983,105,2500. 12. i\larndr. M.:Eatein.l.RLPhv#. them 1 9 ~ d . m . 2 ~ 1 ~ . -~ J. Phys. Chem. 1982,86.3907. P.: Roimnade.. J. Phva. Lett. 1981.. A97.16S. . Chrm. Phya. 1986.85.5733. 16. Villemaux, J, ACSSymp. Ser, l383,226,135. 17, Crmley, M. F.: Epatein, I. R. J. Phys. Chem, 1989.93.WO. 18. Naszfieziua, 2.; Horathemke, W.; MeComiek, W. D.; Swinney. H. L.: Tam, W. Y. ~~~
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