J. Phys. Chem. 1993,97, 5-9
Oscillating Chemiluminescence in the System Methyl Radical plus 0 2 plus Helium Denis J. Bogan,* Dong-Heon Lee,? Michelle Galanti,* and Maria Tricia Pelalosat Department of Chemistry, The Catholic University of America, Washington, D.C. 20064 Received: August 5, 1992; In Final Form: September 30, 1992
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Oscillating formaldehyde (SI SO)chemiluminescence has been observed in slow laminar flows of methyl 2 plus helium a t a pressure of 1 atm and temperatures of 508-825 K. All volume elements in radical plus 0 the reactor were observed to oscillate synchronously on a 0.01 -s time scale, although they had a distribution of residence times on the order of seconds. Period-doubling and period-halving cascades were observed. The oscillatory conditions have been mapped, and a mechanism based upon autocatalytic self-heating is postulated.
Introduction Hydrocarbon cool flames, known and studied for many years,'-5 are ideal systems in which to search for oscillations and deterministic cha0s,4,~subjects of great contemporary The cool flame is the first and lowest temperature luminous stage in spontaneous combustion. It is a self-inhibiting phenomenon. A modest increase in temperature will extinguish the cool flame, and a subsequent decrease will reignite it. There are published reports that a dozen or more repeated pulses in light and temperature have been observed in static vessels and attributed to multiple cool Simpler chemistry that appears to capture the essence of the cool flame occurs when di-tert-butyl peroxide (DTBP) is thermally decomposed in the presence of o~ygen.~ The . ~ DTBP decomposition products are methyl radical and a ~ e t o n e .The ~ subsequent chemistry, that of interest here, can be considered as the chemistry of methyl radical plus 0 2 . The above facts motivated us to search for oscillating chemiluminescence (CL) in heated mixtures of DTBP, oxygen, and helium in a flow reactor. We have observed C L in steady state and in richly detailed oscillatory wave forms. The purpose of this report is to present and interpret these wave forms, map the conditions under which they occur, and postulate a chemical mechanism.
Experimental Section
1/e time constant of the flask (V/Fr)was 2 0 0 4 0 0 sunder typical conditions, and a single data scan duration was 1 s so that concentrations changed slowly during a single scan. (See supplementary material.) Helium was bubbled through liquid DTBP, and oxygen was added to the combined stream in the mixing flask. The liquid volume used per unit time was measured; gas flows were measured by ball flowmeters. The flow rates of H e and DTBP were constant 2 was at 7.4 and 0.18 (STP) cm3/s, respectively, while that of 0 varied from 0 to 7 cm3/s. All experiments tookplace a t a pressure of 1 atm. The reactor exhaust was vented to a hood through a 2-m-long tube of the same 2.2-cm inside diameter as the reactor itself. The reactor flow velocities were 5-20 cm/s, and the Reynolds number was I 10 at all times. Average temperature was measured between the outside wall of the reactor and the heat pipe, Figure 1. C L was viewed on the reactor axis with a photomultiplier and glass filter. Photon counts were captured in a 1024-channel array with a dwell time of (in most cases) 0.001 s/channel. Typically 99 data scans were taken with a dead time of about 2.5 s between scans. During the dead time, the computer named and stored the last scan and zeroed the array.
Results and Discussion
A unique and effective experimental apparatus was assembled for this work. It consists of a heated cylindrical flow reactor and a flask that premixed the reagents, as shown in Figure 1. In effect, it resembles a continuously stirred tank reactor, but the stirring occurred upstream of the laminar flow reactor. This eliminated competition between turbulent mixing and reaction in the observation zone, a possible cause of oscillations. The exponential dilution flask gave precise knowledge of concentration as a function of time according to the equations.
where subscripts i and f denote initial and final, F is the total gas flow rate in cm3/s, Vis the flask volume in cm3, and t is time in s measured from the time when the oxygen flow was changed. Using these equations, data scans as functions of time were converted to data scans as functions of 0 2 concentration. The Present address: Department of Chemistry, Johns Hopkins University, Baltimore, MD 21218. Undergraduate Senior Research Student, 1991-1992.
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0022-3654/58/2097-0005$04.00/0
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Spectral Identification. C L spectra were identified as formaldehyde (A1A2 Z A I ) (SI-So)and were the same regardless of whether the system was in steady state or oscillating (see supplementary material). The region 300-600 nm was scanned, and no other emissions were present. The same spectrum has been observed by Sheinson and Williams in cool flames'O and is due to bimolecular disproportionation of methoxy radicals,' I reaction 6*, in the mechanism to be postulated. Synchronous Oscillation. The design of the reactor allows only axial viewing by the photomultiplier; viewing on a diameter is prevented by the heaters and insulation. The observed signal at a given instant in time is proportional to an integration of all light emitted within the full reactor volume. Remarkably, the observed data scans showed that all volume element8 in the reactor oscillated synchronously on a 0.01-s time scale although they had a distribution of residence times on the order of seconds! This observation was subjected to experimental tests and withstood all attempts to disprove it. We first tested for the possibility that light emission might be concentrated in a small fraction of the total reactor volume. A Teflon baffle was constructed with a hole drilled in the center that passed one-fourth of an incident beam of diffuse light and was machined to fit snugly inside the reactor. Regular oscillations were established, and then the baffle was inserted at the midpoint Q 1993 American Chemical Society
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The Journal of Physical Chemistry, Vol. 97, No. 1, 1993
Letters
MpoNENTlAL FLASK CURVE 0 2 f X O W STEPPED UP 2,
LT Y
t
He + DTBP
(I U REACTOR
\\
1,
02
/.
LP
TIME OR SCAN NO. CAPILLARY TIP
Figure 1. Schematicdiagram of the experimental apparatus. The symbols used in the figure are LT = Wood's horn light trap, C = copper heat pipe, H = heaters, I = insulation, T = thermocouple position, W = quartz window, 1-4 = gas inlets and outlets as labeled. The drawing is not to scale.
of the reactor. This attenuated the light peaks reaching the detector to 60 f 5% of their unbaffled value, consistent with synchronous light emission in the entire reactor. If the CL were confined to the volumeupstreamof the baffle, the fraction reaching the detector would have been I/4. If it were confined to the downstream side of the baffle, the fraction would have been 1. If the emitted photons filled the reactor homogeneously and were detected with equal efficiency from all points, the fraction would be ' / 2 + '/2('/4) = '/8The peak shape was preserved upon introducing the baffle, evidence that traveling waves were absent. The typical halfheight width of our peaks was 0.01 s. Therefore, traveling waves that traversed the entire reactor in less than 0.01 s would not have been recognized as waves. Other peak-shape experiments were done without the baffle. Unsymmetrical peaks, fitting the definition of relaxation oscillations,2' were observed under some conditions (see next section and supplementary material). The experimentalapparatus itself (Figure 1) has asymmetry with respect to reversing the direction of gas flow. In normal operation, the gas entered far from the detector and flowed toward it. When the flow was reversed, gas entered closeto thedetector and flowed away from it. Experiments with reversed flow left the unsymmetrical peaks unchanged. If traveling waves were present, flow reversal would reverse the direction of the waves with respect to the detector. This would cause the peaks to be reflected in time so that peak shapes in forward-flow and reverse-flow experiments would be mirror images. Detection efficiency has a 1/ r 2dependence on distance ( r ) from the light source to the detector. Therefore, a moving source of constant intensity will give a peak shape that reveals whether it is moving toward or away from the detector. The shapes of the unsymmetrical peaks in the system are apparently governed by the time evolution of species concentrations. Mapping the Oscillatory Region. Data from many series of data scans were combined to obtain the map of the oscillatory region shown in Figure 2. Each plotted symbol represents the point when the signal changed from oscillating to steady state. Crossing the boundary in this direction and late in a series of scans ensured that [02] was on the slowly changing part of the exponential flask curve shown in the inset of Figure 1. The accuracy to which [ 0 2 ] is known is a strong function of location on this curve. The mole fraction of oxygen, X(02),entering the reactor at any given time is known only to 1-2 decimal places,
MOLE FRACTION (02) Figure 2. Map of oscillatory region as a function of temperature and
mole fraction of oxygen. The unshaded region gives steady-state chemiluminescence. The plot symbols are experimental measurements of the locationsof extinction; see text. Different plot symbols are used for the upper and lower boundaries. but the difference in X(02) over the full width of a scan is known to 3-4 decimal places. The location of the boundary was the same regardless of the direction of crossing. When the X ( 0 2 ) parameter change was very slow, all of the changes between the steady-state and oscillatory regions appeared to occur by supercritical Hopf b i f u r c a t i ~ n . " * ~ The - ~ ~ *absence ~~ of hysteresis argues against subcritical Hopf bifurcation.22 With faster parameter changes and at temperatures below about 560 K, state changes occurred by hard excitation or hard extincti~n.~Large well-spaced relaxation oscillations8*2i predominated for most of the middle of the oscillatory range (Figure 2) at temperatures below 560 K. Examples are given in the supplementary material. Wave Form Analysis. A typical example of the onset of oscillation is shown in Figure 3. The left panel shows the smoothed data scan, and the right panel shows the reconstructed phase portrait obtained using the time delay technique.I2 The optimum time delays were about one-half of the half-height width of a peak; in this case, T = 17 channels = 0.017 s. The outward spiraling of the time trajectory in the phase portrait is characteristic of supercritical Hopf bifurcation, as is the parabolic opening of the envelopedefining theoscillations in thedata can.^^^ Figure 4 shows selected data scans from a series of 99 scans taken at T = 658 K. Each scan spans 1.024 s. The values of X(02)were obtained from the time using the exponential flask equation. Chronologically, the scan at the bottom occurred first,
Letters ONSET OF OSCILLATION AT 658 K
1000
5 8 4-
800 600
5
400
ig
200
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The Journal of Physical Chemistry, Vol. 97, No. 1, 1993 7
PHASE PORTRAIT
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7
0
CH,'
+ 0, + M = CH,OO' + M 2CH,OO'
Figure 3. Onset of oscillation at T = 658 K. The left panel shows the data scan itself, and the right panel shows the reconstructed time-delay phase portrait of the data scan. The scan consists of 1024 channels. Each channel represents 0.001 s, and X(02)was calculated from the time; see Experimental Section. The transition appears to be a supercritical Hopf
bifurcation. so this was a period-halving sequence. The halving points cannot be assigned unambiguously. The wave forms change subtly and continuously in accord with theory.I3 In the period 2 scan, for example, the steady growth of the small middle peak is evident as the wave form smoothly approaches period 1. The period 16 scan assignment is persuasive but not certain because it does not show two complete periods. The simplification of the wave forms, from period 16 to period 1, by a period-halving cascade is clear despite the presence of noise and the slow continuous change of parameters. The fundamental frequency in all scans was constant at 26-28 Hz and is believed to be mode locked by the interaction of the apparatus' geometry, heat capacity, cooling rate, and average temperature with the chemical mechanism. The middle column of Figure 4 shows the reconstructed timedelay phase portraits of the data scans.I2 The delay was six channels (or T = 0.006s) for all portraits. The period 2 and period 4 portraits show clean separation of the different sized loops representing different peaks in the repeating units of their respective scans. The period 1,2, and 4 portraits show that the trajectory is attracted to a well-defined repeating orbit, known - ~ attractors are more as a limit cycle or a t t r a ~ t o r . ~ The " ~ t r a n g e ~in~the - ~ period 8 and 16 scans. The rightmost column of Figure 4 shows the spectral power distributions of the data scans obtained from their fast Fourier transform^.'^ The fundamental frequency is the strongest in all cases. As the repeating unit of the wave formgrows morecomplex, subharmonic frequencies appear below the fundamental. Higher overtones of the fundamental are also needed to represent the wave form. We have observed other period-halving sequences and period-doubling sequences, but this is the best one. Period doubling (or halving) is strong evidence that a system Deterministic chaos requires is capable of deterministic that there be, among the equations that govern the system, at least three differential equations with at least one nonlinear feedback coupling term.I5 In the mechanism below, we propose that feedback occurs through the shifting of the positions of three equilibrium steps as a function of temperature. Postulated Mechanism. Griffiths and co-workerss reported large temperature oscillations (AT 100 K) when DTBP was thermally decomposed in a continuously stirred tank reactor in the presence of N2 and 02. The experiments were done at temperatures of 46&540 K and pressures of about 100 Torr. They proposed that feedback coupling to drive the oscillation came from autocatalytic self-heating.8 The present conditions are similar to those studied by Griffiths and co-workers,s and we postulate a similar mechanism, believed to be chemically reasonable and capable of explaining the oscillations. It is not intended (or claimed) to be complete.
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AH = -32 kcal/mol16 (3/-3) 2CH,O'
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CH,OH
2CH30' 2CH,O'
(5)
+ H,C=O
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AH = -82 kcal/mol" (6) CH,OH
+ H,C=O * (S,)
(6*)
+ M * CH,OOCH, + M CH,O' CH,OO'
CH,O'
(4)
+ 0,+ H,C=O
2CH300* CH,OH 2CH,O*
+ 0,
+ 0,
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+ HOO'
AH = -38 kcal/molg917(7/-7) H,C=O
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+ HOO'
CH,OOH
(8)
+ 0,
(9)
+ HO' + M F= CH,OOH + M AH = -44 k c a l / m 0 1 ~ " ~(lo/-10) HO'
+ RH
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H,O
+ R'
(11)
The Arrhenius activation energies for steps 1 and 2 are 389and 1718kcal/mol,respectively. SinceE2
