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D. Indritz, H. A. Rabitz, and F. W. Williams
comDarisons with Dr. Westbrook's methane oxidation ca1c;lations and Dr. Dryer's assistance in evaluating rate constants. Informal discussions with other colleagues, too to mention, have helped to clarify the concepts presented here. References and Notes C. T. Bowman, Symp. (Int.) Combust. [Proc.], 75th, 869 (1974). C. Westbrook, J. Creighton, C. Lund, and F. L. Dryer, J. Phys. Chem. manuscript In this issue. D. B. Olson and W. C. Gardiner, Jr., J . Phys. Chem., manuscript in this issue. V. S. Englemcun, V. J. Saminsky, W. Bartok, US. Government Report EPA-600/7-76-009b (1976). G. B. Skinner, A. Lifshltz, K. Scheller, and A. Burcat, J. Chem. Phys., 56, 3853 (1972). W. C. Gardiner, Jr., J. H. Owen, T. C. Clark, J. E. Dove, S. H. Bauer, J. A. Miller, W. J. McLean, Symp. (Int.) Combust. [Proc.], 75th, 857 (1974). T. Tsuboi, Jpn. J . Appl. Phys., 15, 159 (1976). F. L. Dryer, and I. Glassman, Symp. (Int.) Combust. [Proc.], 14th 987 (1972). T. Tsuboi and H. Gg.Wagner, Symp. (Int.) Combust. [Proc.], 75th, 883 (1974). J. Peeters and G. Mahnen, Symp. (Int.) Combust. [Proc.], 1 4 7 , 133 (1972). R. S. Brokaw, Symp. (Int.) Combust. [Proc.], I l t h , 269 (196?), has analyzed CO oxidation using reactions 1, 2, 4, and 5. T. A. Brabbs and R. S. Brokaw, Symp. (Int.) Combust. [Proc.],693 (1974).
Discussion D. B. OLSON(University of Texas). You said that you used basically the mechanismof Bowman (symp, (znt,) combust. IProc.l,15th, 869 (1974)). I find that his rate constant for H + 0, = OH + 0 is about five times the recent value obtained by Schott. I suggest that you carefully evaluate the rate of this reaction. J. R. CREIGTON.Following Bowman, we used the Leeds rate constant k4 = 2.2 X 1014exp(-8450/T) Schott's rate constant (Combust.Flame, 21, 357 (1973))
K4 = 1.22 X 10'7T-0*w7 exp(-8390/T) has a value about ode third of the Leeds constant at 1000 K. The analysis presented in this paper indicates that the exact value of k4 should be unimportant during the induction period and the oxidation of CO. Computer calculations showed variations of about 10% during induction and CO oxidation when k4 was reduced a factor of 3 by using Schott's rate constant. Unexpectedly, the rate of energy release was linearly proportional to k4 during the energy release phase of a simulation of Tsuboi and Wagner's shock tube experiments (0.2% methane, 2 % oxygen in 1.8 X mol/cm3of argon at 1620 K). Under conditions similar to an internal combustion engine, the exact value of k4 was unimportant at all times.
Use of Modeling to Design Experiments. Doping Radicals into Complex Combustion Systems Doren Indritr,
Herschel A. Rabitz,
Frick Chemistry Laboratory, Princeton University, Princeton, New Jersey 08540
and Frederick W. Williams Chemistry Division, Naval Research Laboratory, Washington,D.C. 20375 (Received May 5, 7977) Publication costs assisted by the Na Val Research Laboratory
Numerical modeling can be used to suggest what key experiments should be performed to elucidate complex kinetic systems. In addition, the modeling can be quite useful in the design of such experiments. As an example of such an experimental design we chose a complex combustion system. To elucidate the source of chemiluminescent (A 'A2 X 'Al) formaldehyde in the gas phase oxidative decomposition of di-tert-butyl peroxide an incremental concentration of selected precursor radicals can be added into the reactive system. Numerical modeling has suggested the design of experiments to add the radicals in the desired concentrations at the desired location of the reaction zone. Modeling of this system has indicated that elaborate doping probes with their concomittant problems are unnecessary. Further, premixing dimethyl peroxide, azomethane, and methyl hydroperoxide yields suitable sources of methoxy, methylperoxy, and hydroxy radicals, respectively. The inability to directly scale model-calculations is indicated. In addition, the relative (doped to undoped) nature of the calculation ameliorates any uncertainty in the rate constants.
-
Introduction Numerical modeling has become a valuable tool in unraveling complex kinetic schemes, such as those found in gas phase oxidation systems. Careful examination of a model can help to suggest what further key experiments should be performed to elucidate any problem areas. However, we explicitly demonstrate how modeling can also be useful in designing future experiments. Doping chemical species into reactive systems is a useful technique to determine the incremental importance of the added species. Free radicals are important in the reactions yielding electronically excited formaldehyde. Radicals, however, are very reactive and short-lived and thus present The Journal of Physical Chemistry, Vol. 87, No. 25, 1977
an experimental problem if one wishes to have them in specific concentrations, at specific locations and at specific times. Modeling the unperturbed system, the stable molecules which decompose to the radicals of interest and the system plus the dopant can suggest to the experimenter where and how much to add of the radical precursor. Thus, computer modeling preexperiment can tremendously augment chemical kinetic intuition in the design of experiments. Method The oxidative decomposition of di-tert-butyl peroxide ( (CH3)3COOC(CH3)3,DTBP) has been examined and
Use of Modeling to Design Experiments
2527
TABLE I: Reactions with Sufficient Exothermicity to Produce ‘A, H,CO* (80.6 kcal/mol) AH,
kcal/mol CH,O, t CH,O, H,CO + CH,OH CH,O + CH,O -. H,CO + CH,OH CH,O + OH- H,CO + H,O CH,O + CH, H,CO + CH, -+
-
-+
+ 0,
(4) (5) (6) (7)
-89.1 -82.7 -98.4 -83.1
formaldehyde (A lA2 X lAl) chemiluminescence has been 0bserved.l The observed spectrum is characteristically the same as that observed in the cool flames of hydrocarbons.2 Based on the energy of the ’A2 state of formaldehyde, 28 188 cm-l, thermochemistry indicates that radical-radical reactions are involved. Table I indicates the reactions which could conceivably yield the excited ‘A2 formaldehyde3based on thermochemistry (AH values are listed). Two types of reaction are possible: (i) the reaction of two methylperoxy radicals: reaction 4;and (ii) hydrogen abstraction from a methoxy radical by another radical, reactions 5-7. Each reaction involves either methylperoxy (CH302)or methoxy (CH30) radicals. The obvious experiment suggested is to add methoxy or methylperoxy radicals to the DTBP system and monitor changes in chemiluminescence. For example, if reaction 5 were the key reaction, addition of methoxy should produce a second-order increase in luminescence. If reaction 6 or 7 were key, a first-order increase in luminescence would be expected, etc. Additionally, deuterated radicals could be added and the D2CO* emission could be observed. D&O* emission is sufficiently shifted from H2CO* emission5that it can be monitored with a simple band pass filter. The question remains: How can radicals as reactive as methoxy or methylperoxy be added in situ in the DTBP oxidative decomposition? The experimental system used in our work’ is the vertical tube reactor (VTR) developed at the Naval Research Laboratory.6 The VTR can maintain a thoroughly premixed reaction system at precisely controlled low flow rates (ca. 5 cm/s) and low temperatures (ca. 550 K). Provisions exist for adding radical producing species through a doping probe in a sidearm window, which can be either upstream or downstream of the chemiluminescent zone. However, a probe has many undesirable
‘ T I M E I N SECGNDS 1 Figure 1. Di-tert-butyl peroxide oxidative decomposition with flow rate of approximately 5 cm/s and temperature of approximately 550 K. 0.65% di-fert-butyl peroxide in 4.81 % oxygen.
attributes including probe reactions (the radicals may never get into the reactor) and uncertain mixing properties. Ideal doping of radicals would be performed by premixed addition of a stable compound that will either thermally unimolecularly (at the temperature of the DTBP experiment, ca. 550 K) or photolytically decompose to the desired radicals. Premixing alleviates any worries about inadequate mixing, or probe reactions, or surface-catalyzed reactions on the inserted probe. Numerical modeling is used to indicate the feasibility of such premixing of a dopant. The first step, of course, is to model the undoped system. Table I1 lists the reactions of the di-tert-butyl peroxide system indicated by “b” (all except reaction 51) and Table I11 shows the rate constants used. We have tried to minimize “dead-ends” (the formation of species which do not have further reactions) in our reaction scheme. This, of course, makes for a highly coupled system. The rate constants and reactions are basically the ones used in our study of the undoped system.l The effect of rate constant error is discussed below. Gas flow in the VTR at the experimental flow rate of 5 cm/s can be considered as plug flow; therefore, a one-dimensional model is appropriate where distance up the VTR corresponds to time. The Gear
TABLE 11: Reaction Scheme for Di-tert-butyl Peroxide (b), Dimethyl Peroxide (d), Azomethane (a), and Methyl Hydroperoxide ( m ) (CH,)COOC(CH,), 2(acetone) t 2CH, CH, + 0,- CH,O, CH,O, + CH,O, CH,O + CH,O + 0, CH,OH + H,CO t 0, CH,O, + CH,O, CH,O + CH,O -+ CH,OH + H,CO CH,O + OH- H,CO + H,O CH,O + CH, H,CO + CH, CO + H,O- OH + HCO HCO + HCO- H, + CO + CO HCO t HCO -+ H,CO + CO HCO + CH, CH,CHO HCO + CH, CM, + CO HCO + CH,O CH,OH + CO HCO + CH, H,CO + CH, HCO + OH-. CO t H,O HCO + H,O H,CO + OH H,CO + CH, HCO + CH, H,CO t CH,O CH,OH + HCO H,CO + CH,O, -+ CH,OOH + HCO H,CO + OH --L HCO + H,O CH, + CH, C,H, CH, + CH,OH- CH, + CH,O CH, + CH,O, CH,O + CH,O CH, + C,H, -. CH, + C,H, CH, + C,H, -,C,H, -+
-+
-+
-
-+
-+
-+
-+
-+
-+
-+
(1)b ( 2 ) b,a ( 3 ) b,a ( 4 ) b,a (5) b,d,a,m (6) b,a,m ( 7 ) b,a (8) b,a,m ( 9 ) b,a,m (10) b,d,a,m (11) b,a (12) b,a (13) b d , m (14) b,a (15)b,a,m (16)b , a m ( 1 7 ) b,a (18)b , d m (19)b,a (20) b,a,m (21) b,a (22) b,a (23) b,a (24) b,a (25) h a
CH, + C,H, + CH, + C,H, CH, + CH,CHO CH, + CH,CO CH, + acetone CH, t C,H,O CH; + acetone-. CHiCO C,H, CH, t H,O -+ CH, + OH CH; + 0 ; H,Cd + OH CH, + 0, HCO + H,O CH,O + CH,O -. DMP CH,O + CH, CH,OH + CH, CH,OH t C,H, CH,O + C,H, CH,O + OH- CH,OOH CH,OH + OH- CH,O + H,O CH, + OH CH, + H,O CH, + C,H, CH, + C,H, CH,OOH-. CH, + OH CH,CO -. CH, + CO CH,CHO + OH- CH,CO + H,O C,H, + C,H,- C,H, + C,H, C,H, + OH- C,H, + H,O DMP-+ CH,O + CH,O C,H,O -. CH,CO + CH,O acetone CH,CO + CH, OH t OH- H, + 0, OH t OH + M-. HOOH t M HOOH + M-. OH + OH t M CH,N,CH, CH, + CH, + N,
-
-+
