shock tube study of carbon disulfide oxidation

SHOCK TUBE STUDY OF CARBON D I S U L F I D E OXIDATION

JAMES HARDY AND W. C. GARDINER, JR.

Dept. of Chemistrt3, University1 of Texas, Austin, Texas 78712

The induction zone of shock-initiated explosions of carbon disulfide-oxygen-argon mixtures was studied using the reflected wave end-on method. Profiles of chemiluminescence at 490 nnr, attributed to SO2", and infrared emission at 5 Ixm, attributed to CS 2 and CO, were analyzed to determine the characteristic branched-chain growth rates and ignition delay times over the temperature range 1400-2100 K for CS2:O 2 ratios varying from 1:9 to 3:10 with various dilutions in argon. Computer modelling in terms of a conventional mechanism for the CS2-O 2 reaction was able to account for the ignition delay times under a variety of assumptions about the high temperature rate constants, but no adjustments of the mechanism or the rate constants were found that were capable of giving satisfactorily correct models of the qualitative forms of the visible emission profiles or the mixture dependence of the growth rates.

Introduction

The low-temperature CS2-O 2 reaction has long attracted experimental interest because of the unusual behavior of the explosion limits and the prominent intermittent cool flame phenomena.1 In recent years the high- temperature CS2-O 2 flame has been shown to hold promise as a chemical pump for the CO infrared laser. 2 Attempts to unders tand and optimize the mechanism of CO populat ion inversion in a CS2-O 2 flame are limited, however, by the lack of rate constant information on the key elementary reactions in the flame temperature range. 3 Shock-tube studies of the relevant dissociat ion-recombination reactions 4 were mostly done in temperature ranges well above the CS2-O 2 flame temperature, while flow-reactor studies of the principal atom-molecule and free-radical steps were done at lower temperatures and may also have been significantly inf luenced by wall reactions. 5 Except for some early experiments that were not analysed for chemical information 6,7 there has been only a single shock-tube investigation of the CS2-O 2 reaction. 8 A recent investigation of the closely-related COS-O 2 reaction has appeared. 9

The goal of the investigation reported here was to define as well as possible the initiation, branching and recombinat ion rates of the

high-temperature CS2-O ~ explosion and by means of computer simulations to derive elementary reaction rate constant expressions capable of describing our observations as well as those of earlier investigators of closely related reactions. 1~ In order to maximize our observational capabili ty in the earliest stages of reaction, the shock-tube technique em- ployed was an extension of the reflected-wave end-on method developed by Gutman and coworkers, a233 As in previous applications of this method, light emitted from the reacting gas was viewed through a window in the shock tube end plate with appropriate detectors and wavelength filters. For the CS2-O 2 reaction, the most useful emission signals are expected to be the visible chemiluminescence, attributed by Sheen s to the reaction SO + O + M = SO2" + M, and thermal infrared emission from CO. We extended the end-on technique in two ways. First, the chemiluminescence signal was integrated electronically dur ing each experiment in order to enhance the S / N ratio. Second, the absolute sensitivity of the detector to chemiluminescent SOz* emission was calibrated from the known SO2" chemiluminescence rate 14,15 by determining the post- combust ion emission intensi ty in shock-heated Hz-O2-SO2-Ar mixtures, where the concentra- t ion product [SOl[O] rapidly equilibrates. These extensions proved to be rather important

985

986 KINETICS OF ELEMENTARY REACTIONS

for this study, for in contrast to the familiar exponential growth of chain center concentrations characteristic of H2-Oz 16 or hydrocar- bon-O~z 17 explosions under shock-tube conditions, the CS2-O 2 explosion appears to be a b lend of straight-chain, branched-chain, and termination reactions over the range of conditions studied. Data processing in terms of exponential growth constants and igni t ion delays is insufficient to characterize the observations.

TABLE I Experimental mixtures*

Number % CS 2 % O 2 % Ar symbol?

1 1.0 3.0 96.0 �9 2 1.0 4.0 95.0 A 3 1.0 9.0 90.0 [] 4 0.4 1.2 98.4 5 0.4 3.6 96.0 C) 6 3.0 10.0 87.0 V

Experimental Aspects

The shock tube was a Monel tube with a 7.62 cm i.d., 9.4 m long mirror-honed test section and a 15 cm i.d., 1.9 m long driver section. All velocity gauges, observation windows, and valves on the experimental section were flush to +_0.025 mm. The diaphragms were of scored soft a luminum, pressure-burst to initiate the experiments. Shock temperatures were varied by changing the H2 /N z ratio of the driver gas. Test gases were prepared at high pressure (usually about 140 kPa total) in 25 dm a stainless steel tanks in an all-metal vacuum system. Leak and outgassing rates were below 40 ~xPa s 1. The shock tube was evacuated to at least 1.0 dPa before admit t ing test gas and periodically cleaned of diaphragm fragments and polymeric reaction products as required.

Test gas mixtures were prepared manometri- eally with calibrated diaphragm-type pressure gauges or mercury manometers. The CS 2 was Matheson, Coleman and Bell Spectroquality grade, shielded from light at all times and purified in a clean vacuum system by nu- merous freeze-pump-thaw cycles at 77 K before being distilled at 273 K to make test gas mixtures. The O 2 was Matheson Research Pu- rity (99.99%) and the Ar was Matheson Ultra- High Purity (99.999%) grade, used without further purification. The compositions of the test gases are given in Table I.

Reflected shock condit ions were computed in the conventional way from incident shock velocities, corrected for 2 % / i n attenuation to give state 5 properties at the end wall, us ing JANAF thermochemical properties. Experi- mental profiles were recorded photogra- phically from a Tektronix 7633 storage oscilloscope and hand-digit ized for computer processing.

The intensity of the visible chemiluminescence s was monitored through an interference filter with 50% maximum transmission and 7.2 nm (FWHM) triangular bandpass centered

*Several mixtures used in preliminary experiments and sensitivity calibrations are not listed here. No data from these mixtures is reported in this paper. Mixtures 1, 3, and 6 were actually prepared in several different batches for the experiments, with no apparent systematic differences being found in the data from the different batches.

?The starting pressure is indicated by modifying each symbol according to the following code: [] = 1.3 kPa; ~ = 2.0 kPa; [~ = 2.7 kPa; [~ = 3.a kPa; [2-= 4.0 kPa;qD-= 4.7 kPa;-(2 = 5.3 kPa; �9 = 6.7 kPa.

at 488 nm. The photomult ipl ier sensitivity was calibrated by appropriate shock waves in H 2 / O ~ / S O J A r mixtures. To increase the S / N ratio the photomult ipl ier current was integrated electronically prior to oscilloscope display. Infrared emission was monitored with an InSb photovoltaic cell and a 4.5 t~m high-pass filter, giving a 4.5-5.4 ~m total bandpass. The geom- etry of the detectors and observation windows was adjusted in each setup to give an undis- turbed depth of view of 40 era.13

The visible bandpass was selected to remove interferences from atomic lines which are emitted from all strong shocks in this shock tube. As pointed out by a reviewer, this bandpass happens to include two bands observed in CS2-O 2 flames and attributed to $2.18 Neither the growth constant nor the ignit ion delay data would be distorted by S 2 emission for our experimental conditions, the former because both SO2" and $2" formation must be two-chain-center processes 13 and the latter because the concentrat ion product [SO] [O] has to be many orders of magnitude greater than [S] z near the end of the induct ion period in fuel-lean mixtures.

The IR bandpass was originally selected to observe the CO fundamental with the only spectral interference apparently possible being from the 4.8-4.9 ~m band of COS, which should be of negligible intensity for our conditions. 19 However, it turned out that the v 3 band of CS 2 expands to emit strongly

C A R B O N D I S U L F I D E O X I D A T I O N S T U D Y 9 8 7

T A B L E I I

R a t e - c o n s t a n t e x p r e s s i o n s ~

R a t e c o n s t a n t (s -1, c m 3 s - l ,

R e a c t i o n A H ~ (kJ) 2 o r c m 6 s -1 u n i t s ) F o o t n o t e

O + C S 2 = C S + S O - 1 2 9 A i x 8 . 3 x 10 - n e x p ( - 9 5 6 / T ) a O + C S 2 = C O S + S - 2 2 5 A i x 2 .8 x 10 -12 e x p ( - 6 0 4 / T ) b

O + C S 2 = C O + S 2 - 3 4 8 2 .8 x I 0 X 2 e x p ( - 6 0 4 / T ) c

O + C O S = C O + S O - 2 1 5 1 .0 x 1 0 - a 0 e x p ( - 2 7 7 0 / T ) d

O + C O S = C O z + S - 2 2 4 2 . 0 x 10 l ~ e

O + C O 2 = C O + O a + 3 2 1.8 x 10 1 2 e x p ( - 2 0 6 0 0 / T ) f

O + S~ = S O + S - 9 2 6 . 6 x 10 - l~ g

O + C S = C O + S - 3 1 1 4 . 0 x 1 0 - 1 0 e x p ( - 1 0 1 0 / T ) h

S + O z = S O + O - 2 3 2 . 0 x 10 l~ i

S + C S z = C S + S 2 - 3 7 A i x 2 . 5 x 10 - l i j

S + C O S = C O + S 2 - 1 2 3 1 .5 x 10 1 2 e x p ( - 1 2 6 O / T ) k

S O + O z = S O 2 + O - 5 4 A i x 5 . 8 x 10 1 3 e x p ( - 3 2 7 0 / T ) 1

S O + S O = S O 2 + S - 3 1 8 . 3 x 1 0 - 1 3 e x p ( - 1 6 6 0 / T ) m

S O + C O S = C O g + S 2 - ' 1 3 2 1 .7 x I 0 16 n

C S + 0 2 = C O + S O - 3 3 4 A i x 9 .1 x 1 0 - 1 7 e x p ( - 1 0 1 0 / T ) o

C S + O z = C O S + O - 1 1 9 A i x 5 .1 x 10 l % x p ( - 4 7 8 O / T ) o C S + S O = C O + S z - 2 1 9 A t x 1.7 • 10 -11 p

C S 2 + O 2 = C S + S O 2 - 1 8 3 A i x 1 .7 x 10 l Z e x p ( - 2 1 6 0 0 / T ) q

C S + S + M = C S 2 + M - 3 8 8 1 .4 x 1 0 - a Z T 3 r

C S + S + C S 2 = C S 2 + C S 2 - 3 8 8 2 .8 x 10 ZZT-3 s C O + S + M = C O S + M - 3 0 2 8 .1 • 1 0 - 2 3 T 36 t

C O + O + M = C O 2 + M - 5 2 6 3 .1 x 1 0 - 1 2 T -6v u

O + O + M = O z + M - 4 9 4 1 .2 x 1 0 - 3 6 T 2 4 e x p ( 7 1 0 4 / T ) v

S + O + M = S O + M - 5 1 7 2 . 8 x 1 0 - 2 3 T - ~ w S + S + M = S 2 + M - 4 2 5 6 . 0 x 1 0 - 2 9 T 1 x

S O + O + M = S O 2 " + M - 1 4 8 3 . 2 x 1 0 - a 6 T 184 y

S O 2 " + M = S O z + M - 4 0 0 5 .3 x 1 0 - 1 1 T - Z 4 z

S O 2 " = S O 2 + h v 0 5 x 103 z

1. T h e m u l t i p l i e r s A i a r e u n i t y u n l e s s s p e c i f i e d o t h e r w i s e b e l o w . F o r t h e v a r i a t i o n s o n t h e s t a n d a r d

m e c h a n i s m t h e y h a v e t h e v a l u e s l i s t e d , w h e r e i = 1 f o r t h e m e c h a n i s m w i t h o u t C S + O= p a r t i c i p a t i o n

b u t w i t h i n c r e a s e d r a t e s f o r t h e k e y c o n v e n t i o n a l r e a c t i o n s , i = 2 fo r t h e m e c h a n i s m s p e e d e d b y t h e

a d d i t i o n o f C S + 0 2 r e a c t i o n s , a n d i = 3 f o r t h e m e c h a n i s m w i t h r a p i d i n i t i a t i o n .

2. D . R. S t u l l a n d H . P r o p h e t , J A N A F T h e r m o c h e m i c a l P r o p e r t i e s , S e c o n d E d i t i o n , N S R D S - N B S 37 ,

N a t i o n a l B u r e a u o f S t a n d a r d s , W a s h i n g t o n , 1971 .

a. Ref . 5. A 1 = A 3 = 2 . b . C o m b i n a t i o n o f t h e 1 1 0 0 K v a l u e o f Ref . 5 w i t h t h e 3 0 0 K v a l u e o f Ref . 2 0 i n A r r h e n i u s f o r m .

A 1 = A 3 = 8. c. Ref . 20 .

d . Refs . 5 a n d 21.

e . Ref . 22 .

f. T a k e n f r o m t h e e x p r e s s i o n fo r t h e r a t e c o n s t a n t f o r t h e r e v e r s e r e a c t i o n g i v e n i n Ref . 23 .

g. T h i s is t h e 1 1 0 0 K e s t i m a t e i n Ref . 5. h . Ref . 3.

i. C o n s e n s u s of n u m e r o u s r o o m - t e m p e r a t u r e e x p e r i m e n t s . Cf . Ref . 24.

j. R o o m - t e m p e r a t u r e r e s u l t o f Ref . 25. A 1 = A 3 = .001 .

k. U p p e r l i m i t o f Ref . 11.

1. Ref . 5. A t = 4, A 3 = 0 . 2 5 . m . C o m b i n a t i o n o f t h e 1 0 0 0 K u p p e r l i m i t f r o m Ref . 5 w i t h t h e 3 0 0 K u p p e r l i m i t o f Ref . 26 . n. Ref . 9.

o. E x p r e s s i o n o f Ref . 3 m u l t i p l i e d b y 10 3. A2 = 1 0 0 0 , A 3 = .001.

P. S u g g e s t i o n o f Ref . 3


TABLE II (continued)

q. Suggestion of Ref. 3. A 3 = 4000. r. Taken from the expression for the rate constant of the reverse reaction given in Ref. 27, using

JANAF thermoehemical data. s. This combines the factor 21 increase in third-body effectiveness for CS 2 compared with Ar, as

found in Ref. 28, with the rate constant for dissociation of CS 2 dilute in Ar given in Ref. 27. t. Taken from the expression for the rate constant of the reverse reaction given in Ref. 29, using

JANAF thermochemical data. u. q~aken from the expression for the rate constant of the reverse reaction given in Ref. 30. v. Taken from the expression for the rate constant of the reverse reaction given in Ref. 31. w. Guess from the rates of the preceding and succeeding recombination reactions. x. The 2500 K estimate of Ref. 32, with T -1 temperature dependence assigned. y. This is the combination of the room temperature measurement of Ref. 26 with the dissociation

rate data of Ref. 33, for ground-state SO, z. For convenience we assume that all recombination proceeds through the emitting state of SOz*. (Cf. Footnote z) Thermochemical data for SOz* were generated from SO z data by increasing the heat of formation by 400 kJ/mol.

z. This combination of quenching and radiative decay rates accomplishes the purpose of achieving the steady-state rate of Ref. 15 with the radiative lifetime of Ref. 14. The formation of ground-state SO z proceeds at the correct rate (footnote y) also, and thermal emission (although insignificant at these temperatures) is automatically included through equilibration of the quenching reaction.

throughout the 4.5-5.4 ixm region at the temperatures of these experiments, prevent ing the acquisit ion of early exponential growth and calibrated induct ion time data from the IR experiments.

Data interpretation was accomplished with the aid of numerical integrations of the kinetic equations and the conservation equations appropriate either to constant area reflected shock flow or constant density, both models giving essentially identical results for present purposes. The reaction mechanism and rate constant expressions are given in Table II.

Detailed descriptions of the apparatus and computational procedures may be found else- where. 34

Results

Typical records of integrated SO2" emission intensity and IR emission intensity are shown in Fig. 1. The exponential growth of SOz* emission intensity that is characteristic of branched-chain explosions ~2 is evident as expected in the intermediate stage of the induction zone, (Fig. lb) while more rapid rates of growth precede and succeed it. The intermediate exponential growth stage of the integrated SO2" emission intensity was taken to characterize that part of the explosion where branched-chain kinetics predominate. The lin- ear increase in IR emission intensity, as the column of emit t ing CS 2 lengthens, is so strong that product IR emiss ion- -mos t ly if not en-

tirely attributable to C O - - o n l y appears briefly as an exponential increase at the very end of the induction period. In Figs. 2 and 3 the exponential growth constants for the two types of emission are shown as functions of temperature for various compositions. It can be seen that the IR growth constants are larger than the SO2" growth constants by factors - e 2 at 1500 K and - e at 2000 K. Based upon either the later stages of the SO2" emission records or the computer simulations, these differences can be fully explained as due to the late times at which the IR growth constants had to be measured. In Figs. 4 and 5 are shown the times required for at tainment of a value of SO2" emission intensity integrated over optical depth (i.e. column density) of 4.6 x 1014 quanta cm 2s ~ and for appearance of product IR emission, as measures of the ignition delay time. In each Figure, a normalization with [02] 5 was used to suppress part of the density and composi t ion dependence without pre- suppositions about any mechanist ic reason therefor. The computed lines refer to profiles generated by computer simulations using the Table II mechanism and rate constant expressions as indicated.

Discussion

One can begin to understand the mechanist ic implications of our observations only by re- ducing the large catalog of reactions in Table II to a comprehensible form. Fol lowing the

CARBON DISULFIDE OXIDATION STUDY 989

z O I o ~

h i

r n

> - F -

Z

-25 Z

Z o

" ' - 3 0 i.a.l

c n

u ' )

; >

_3 -35

c

. h

~ f

z o U')

i , i

13g

..Q

_ 5 x l O 11 quanta crn -2

Shock Ar r i vo l

- - . ,oo Ss -

I i

!

i i I i

I!

",":7"- ~'1 ,I __1 1

/" / ' /J" ! I , I I i ! /

Arr ivo l X I I

i / , / , i l , , , H,00 s -

/ k - -

h--IOOl~s

I / j

I J 1 L

bas ic ideas d e v e l o p e d by L i f sh i t z e t al . 9 and Cul l i s and M u l c a h y l~ we first i den t i fy those steps r equ i r ed to in terpre t the chemis t ry pr ior to the t ime where in t e rmed ia te - in te rmed ia te , i n t e rmed ia te -p roduc t , and r e c o m b i n a t i o n reac t ions beg in to be impor tan t , and then con- s ider the f low of reac t ion w i t h i n the resul t ing ne twork shown in Fig. 6.

As in any explos ion, some reaction(s) of the s tar t ing mater ia ls or impur i t i e s mus t p rov ide an ini t ial i npu t of cha in carriers. S ince it is un l ike ly that the iden t i ty of these first species is impor tan t , we as sume the obv ious , that S a toms f rom thermal d i s soc ia t ion of CS2, possi- b ly s u p p l e m e n t e d by an add i t iona l react ion i n v o l v i n g bo th CS 2 and 0 2 , start the chain. T h e rap id react ion of an S atom w i t h an O z m o l e c u l e generates one O a tom, and the s lower reac t ion of the SO radica l also p r o d u c e d in this step wi th ano ther Oe mo lecu l e forms a s econd O atom. These O atoms can then u n d e r g o three types of reac t ion w i t h CS2, l e ad ing in the major c h a n n e l to CS and SO and in the mino r channe l s to C O and S 2 or C O S and S. 2~ The c o m m o n a s sumpt ion is that CS, C O S and S 2 are un reac t ive and can not con t r ibu te fur ther to the m e c h a n i s m unt i l later stages of react ion, w h i l e t he S atoms p r o d u c e d in the th i rd channe l are ava i lab le to react again in the rap id b r a n c h i n g reac t ion w i t h O z . We re turn in a m o m e n t to the ques t i on of whe the r this a s sump t ion is l ike ly to be true. T h e f inal reac t ion of poss ib le impor t ance in the conven- t ional m e c h a n i s m w o u l d be a se l f - inh ib i t ion reac t ion of S atoms w i t h CS z. T h i s is then the ful l set of k n o w n react ions a m o n g the

Fro. 1. a) Record of temporally and spatially integrated SO2* emission in CS2:O2:Ar = 3:10:87, T 5 = 1540 K, PI = 4 kPa. "rig is the visible ~mission induction time as defined in the text. The ordinate scale is based on the calibration experiments in H2-O2-SO2-Ar mixtures, b) Semilogarithmic pre- sentation of the same record, c) Record of spatially integrated IR emission in CS2:O2:Ar = 1:3:96, T 5 = I845 K, PI = 2.7 kPa. The calculated ignition delays to [CS 2] = 0.9 [CS2] s are 1000 gs for the A o rates, 250 ixs for the A l rates, 190 Ixs for the Az rates, and 30 its for the A a rates, teorresponds in the calculated profiles to 1 x 10 .6 mol cm -2 CO column density . . . . . . . . . . . . Simulation with standard set of rate constant expressions (Ao) (on baseline) . . . . . . Simulation with A 1 modifications (speedup of standard set) . . . . . . Simulation with A 2 modifications (speedup with C8 + 02 reactions) . . . . . . . Simulation with A a modifications (fast initiation)


T 5 26

'~ 25

c~ 24

~ 23:

22!

- 20

~ - " " ~ - 21 ~ ~ ' . - - . ,?, -.. -...>.... "--.C.~......... E

o ~ - 2 4 ~

I ~ ~ A qA .o. ' - 'A [] s ~ -25

I I I I I 1 -'~ 5 6 7 - 26

10 4 K /T

Flc. 2. Growth constants (base e) for SO2" emission, divided by [O2] 5. The symbols for test gas compositions are given in Table I. Results of simulations for CS 2:02 :Ar = 1:3:96, 1:9:90, and 3:10:87, P1 = 1.3-4.0 kPa, are denoted as in Fig, 1, and can be compared directly with the data points. (The spread of the calculated values normalized in this way is worse than the data scatter. The systematic trend with composition actually implies a [02 ] -1/2 [CS2 ] -1/2 dependence rather than the [O~] t pre- sumed by the normalization. See text.)

-27

. . . . -"A0 FicJII0 - ~ . . . . []'- [I]/A, 3

5 I I I I

6 7

10 4. K /T

Fxc. 4. Ignition delay for attainment of column intensity o{ SO2" emission 4.6 x 1014 quanta cm -2 s - l , multiplied by [02] 5. Symbols and lines as in Fig. 2.

'o, 26 7

0

E "& 25

' ~ 2 4 .ca.

2- 23

~ 22

= 21 _.J

A0

t I I I t I 5 6 7

10 4 K / T

Fic. 3. Growth constants (base e) for CO emission, divided by [02] 5 . Symbols and lines as in Fig. 2. (The experimental values are for the difference between the emission during the onset of ignition and the level of CS~ emission extrapolated from before the upturn of the total emission signal. The calculated values are for the CO exponential growth rate when [CS2] = 0.9 [CS2]~.)

-20 . .-A 0

E -22 A2

E -23 "'"" . "

o

' ~ _25 ( /

=, -26 /

-27 " / ~ ~ ~ i I I 5 6 7

10 4 K /T

Fic. 5. Ignition delay, multiplied by [02 ] 5, from IR emission experiments. Symbols and lines as in Fig. 2. (Ignition is defined as [CS2] = 0.9 [CS2] 5 in the simulations and as the appearance of product emission in the experiments.)


CS z § M 0 ( CSz * 02?

TO / A \ TO

INHIBIT ~, J BRANCH

FIG. 6. Seussian network describing the flow of reaction during the induction zone of the CS2-O 2 explosion. Chain centers are denoted by circles, bulk reagents by triangles, and (relatively) unreactive products by rectangles. Arrows denote the exothermic reaction directions, except for CS 2 + M ~ CS + S + M. All bimolecular reactions involving CS 2 or O z are included. The sum reaction of the branch route is CS 2 + 202 = COS + SO 2 + O, AH ~ = -302 kJ. The sum reaction of the straight chain route is CS 2 + 02 = CS + SOz, AH ~ = -183 kJ.

starting materials and the species S, O, and SO.

The main induct ion zone chemistry com- prises in this model two coupled chains. The CS + SO output channel of O + CS 2 provides a straight exothermal chain (net AH~ = _ 183 kJ) that would eventually, even in these highly diluted mixtures, lead to a thermal explosion, while the COS + S output channel gives an even more exothermal (AH ~ = - 3 2 0 kJ) branched chain. We now inquire whether this induction zone mechanism can, with appropriate choices of rate constants for the several elementary reactions, account for the observed emission profiles and ignit ion delays. The answer is that it can not. T h e essential reason, which emerged in the usual process of trial simulations with variations in the rate constant expressions, is illustrated by the computed curves in Fig. 1. If the rate constants are adjusted to give correct ignit ion delays, then the exponential growth is much faster than observed in the SO2" emission profiles; if the exponential growth rate is adjusted to give

agreement with the visible emission experiments, then the mixture never ignites soon enough. While either one of these objectives can be met with fairly small adjustments of literature rate constant expressions (Cf. Table II and the Figures for an adjustment, the A 1 modifications, that matches the calculdted SO~ profiles with the visible emission ignition delays in the middle of the temperature range investigated), it became clear in the trial simulations that no reasonable combinat ion of rate constants for this mechanism could ever gen- erate the quali tat ive shapes of the observed visible emission profiles.

Tl,e next stage of data interpretation was to consider whether these difficulties indicate that additional reactions of the species shown in Fig. 6 may play important roles in the induct ion zone. The most likely of these would be reactions of CS, which has long been suspected of reacting with 0 2 at high temperature even though these species coexist for long times at low (near room) tempera ture) ~ Trial simulations (for example, the A 2 modifications


as in Table II and the Figures) again showed the same qualitative disagreement with experimental profiles. The degree of agreement that can be achieved by adjusting the rate constant expressions for the first mechanism (CS s and O 2 react only with S, O, and SO) and for the second (O 2 also reacts with CS) turns out in fact to be about the same.

Next one considers whether reactive species or additional reactions have been overlooked. The most likely candidates for reactive species would be other oxides of sulfur. Our search for such species that would perhaps react in a helpful way led to no success. While many additional reactions can and do participate at the end of the induct ion period and thereafter (as seen by not ing the computed rates of the remaining reactions in Table II at late times), we could find no supplementary reactions capable of generating the observed profiles even with major modifications of the rate constant expressions.

Our major effort in this direction was as follows. Clearly igni t ion should be postponed if reactions among chain carriers lead to unreaetive products. To test whether any such reactions would really have the desired overall effects, the test reaction CS + SO = CO + S 2 was given arbitrarily large rate constants until the growth was stopped at the needed level. Ignit ion could indeed be regulated in this way (with k ~ 1.7 • 10 -7 emas 1 the ignition delays were about right), but the computed SO2" emission profiles could not be made to resemble the experiments at all.

A final attempt to design a successful model was based upon general experience with the H,2-O s explosion, a5 There the slopes of semilogarithmic graphs of chain carrier concentrations versus time are determined solely by chain-carrier-plus-reactant rates during the induction zone, while their "intercepts" are determined solely by initiation rates. To solve the present difficulties with calculated SO2 ~ profiles in CSs-O 2 explosions, we thus investigated how far the init iat ion rate would have to be increased, while decreasing the chain reaction rates, to achieve simultaneous agreement with growth constants and igni t ion delays. As can be seen from the results of the A a modifications shown in Table II and the Figures, this approach also fails. It is possible that an assumption about dissociation of impurities could improve the situation.

A characteristic feature of the calculated parameters that permitted the simulations to be accurately represented in Figs. 3-5 by single lines is the dependence upon composit ion according to [02] - i [CSs ] -o. Calculated val-

ues for the SO2 ~ appearance induct ion times, the CS 2 disappearance induct ion times, and the CO exponential growth constants could each be normalized to within 15% with [O] 1 [CS2 ] o. This held over the temperature range 1400-2000K for all three mixtures (1:3:96, 1:9:90, 3:10:87) and starting pressures (1.3 kPa, 2.7 kPa, 4.0 kPa) used, and was essentially the same for all of the mechanisms considered. The different mixture dependence found for the calculated SO2" exponential growth rates may be attributed to the procedure by which the times for evaluating those rates were chosen, which was according to a formula with a [O~] --61 dependence. This procedure was required in order to obtain consistent data over a wide range of condit ions when the exponential growth rate changed during the course of each experiment, as can be seen in Fig. lb .

The IR emission data considered indepen- dently do not present any severe interpreta- tional difficulties. The literature (Ao) set of rate constant expressions already gives a reasonably good representation of the ignit ion delays (Fig. 5) up to about 1800 K; adding speedup reactions, such as the A 2 incorporation of CS + 02 reactions, with appropriate rate constant expressions would readily permit one to compute the necessary additional accelera- tion at higher temperatures. The inhibi t ion by CS 2 that is suggested by the longer ignit ion delays of the richer mixtures could be account- ed for by taking the rate of S + CS 2 = S, 2 + CS to be larger than snggested in Table II. Since our computed profiles invariably show substantially larger growth rates at the end of the induct ion period, the factors of 2 to 3 discrepancy between the data and the A 0 growth constants in Fig. 3 is altogether expected.

One then questions the validity of our identification of the observed visible emission traces with profiles of [SO2 ~ ], or the mechanism used to calculate [SO2" ] profiles. While there is reasonably good evidence that this is a fairly straightforward chemiluminescence situation in shock-heated SO s and in simpler reactive environments ~4,~s it is possible that there are other sources of 490 nm emission in the induct ion zone of the CS,~-O s explosion. Our assnmption to the contrary is based en- tirely upon the results of Sheen. s In view of the complicated excited electronic states of the SO,~ molecule, it is also quite possible that the relationship between emission intensity and molecular concentrations is more subtle than was suggested by the spectroscopic in- vestigations. A similar difficulty with SO s spectroscopy may exist in SO s dissociation


experiments, where a major discrepancy exists between laser-schlieren 33 and spectroscopic 36 measurelnents-.(cf, also our earlier remarks concerning S 2 emission.)

It is of interest to test the Fig. 6 topology and the Table II rate constant expressions against the results of previous workers. We reanalysed the ignit ion delay data of Sheen s to suppress the mixture dependence evident in his Fig. 4, obtaining by the same basic procedure used by Lifshitz et al. 9 the expression Tg = 2.28 x 10 -m exp( l1750/T)[O2] -.61 (fAr] [CS2])-(n s (Sheen's mixtures all had the same percentage of CS2, and so it was impossi- ble for us to separate the CS 2 and Ar dependence). It was readily possible to compute ignit ion delays in reasonable agreement with this fit to his data with the mechanisms that succeeded in fitting our ignit ion delay data. The calculated composit ion dependence was always somewhat stronger, the ignit ion delays be ing roughly proportional to [O2] 1. Simi- larly, the set of rate constants for the A 0 mechanism gave reasonable agreement with the COS-O 2 ignit ion delay data of Lifshitz et al. 9 Our simulations clearly showed that the growth rates reported by Sheen were measured in such late parts of the induct ion zone that many reactions among the products of the main chain(s) of the induct ion zone must have be- come prominent, and so we did not attempt to explore the degree of agreement that could be found with this data.

We are thus left with quanti tat ive charac- terizations of the kinetics of the CSa-O 2 explosion that can not, for the present, be interpreted satisfactorily in the conventional mechanistic framework. Additional experimental charac- terization of the simpler COS-O 2 reaction, a different measure of the early growth rates, and ideas about alternate reaction paths may clarify the situation. Unti l the existing data base on the principal combust ion reactions can be understood, it would appear to be futile to attempt elaboration of the mechanism to model the more complicated situation pertain- ing to CS2-O 2 flame lasers.

Acknowledgment

This research was supported by the U.S. Army Research Office and the Robert A. Welch Founda- tion.

REFERENCES

1. GREWER, Tin: Low Temperature Oxidation, W. Jost., Ed., p. 107, Gordon and Breach, New York, 1965.

2. SUART, R. D., DAWSON, P. H., AND KIMBELL, G. H.: J. Appl. Phys. 43, 1022 (1972).

3. HOWGATE, D. W. AND BARR, Z. A., JR.: J. Chem. Phys. 59, 2815 (1973).

4. TROE, J. AND WAGNER, H. Go.: Physical Chemist~ of Fast Reactions, Vol. 1, B. P. Levitt, Ed., p. 1, Plenum Press, London, 1973.

5. HOMANN, K. H., KROME, G.: AND WAGNER, H. Gr Ber. Bunsengesellschaft 72, 998 (1968).

6. ZEL'DOVICH, YA. B. AND SCHLYAPINTOKH, I. YA.: Doklady Akad. Nauk S.S.S.R. 65, 871 (1949).

7. GERSHA~IK, YA. T., ZEL'DOVlCH, YA. B.: AND ROZ- LOVSKII, A. I.: Zhur. Fiz. Khim. 24, 85 (1950).

8. SHEEN, D. B.: J. Chem. Phys. 52, 648 (1970). 9. LIFSHITZ, A., FRENKLACH, M., SCHECHNER, P., AND

CARROLL, H. F.; Int. J. Chem. Kin. 7, 753 (1975). 10. CULLIS, C. F. AND MULCAHY, M. F. R.: Combust.

Flame 18, 225 (1972). 11. SCHOFmLD, K.: J. Phys. Chem. Ref. Data 2, 25

(1973). 12. GUTMAN, D. AND SCHOTT, G. L.: J. Chem. Phys.

46, 4576 (1967). 13. GUTMAX, D. AND MATSUDA, S.: Rev. Sci. Inst. 42,

1231 (1971). 14. LEVITT, B. P., AND SHEEN, D. B.: Trans. Farad.

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50, 3119 (1969). 16. SCHOT-r, G. L. AND GETZlNGER, R. W.: Physical

Chemistry of Fast Reactions, Vol. 1, B. P. Levitt, Ed., p. 81, Plenum Press, London, 1973.

17. BPaBBS, T. A. AND BRor, aw, R. S.: Fifteenth S!r (International) on Combustion, p. 893, The Combustion Institute, 1975.

18. PEASE, R. W. B., AND GAYDON, A. G., The Identi- fication of Molecular Spectra, 3rd Ed., p. 266, J. Wiley & Sons, 1963.

19. HANCOCK, G., AND SMITH, I. W. M.: Trans. Faraday Soc. 67, 2586 (1971).

20. SLAGLE, I. R., GILBERT, J. R., AND GUTMAN, D.: J. Chem. Phys. 61, 704 (t974).

21. HOYERMANN, K., WAGNER, H. GG., AND V~OLFRUM, J.: Ber. Bunsengesellschaft 71, 603 (1967).

r22. HOMANN, K. H., KaOME, G., AND WAGNER, H. GG.: Ber. Bunsengesellschaft 73, 967 (1969).

23. RAWLINS, W. T. AND GARDINER, W. C., JR.: J. Phys. Chem. 78, 497 (1974).

24. CLYNE, M. A. A. AND TOWNSEND, L. W.: Int. J. Chem. Kin. Symposium 1, 73 (1975).

25. BASCO, N. AND PEARSON, A. E.: Trans. Farad. Soc. 63, 2684 (1967).

26. HALSTEAD, C. J. AND TURUSH, B. A.: Proc. Roy. Soc. (London) A295, 363 (1966).

27. OLSCHEWSKI, H. A., TROE, J., AND WAGNER, H. GG.: Z. Physik. Chem. NF45, 329 (1965).

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COMMENTS

J. Troe, University of Gfttingen, West Germany. Did you observe thermal emission by CSe in the visible and near ultraviolet FT? This emission was studied in detail by Rosenkranz and Wagner (Z. Phys. Chem. NF 61, 302 1968).

Authors" Reply1. To our knowledge our visible emission profiles were not contaminated by CS 2 thermal emission. We did not observe any visible emission behind the incident shock waves in our reflected wave experiments, although the detector viewed regions as hot as 1200 K under these conditions. A few low temperature experiments in 1% CS 2 in Ar also gave negative results. However, one can imagine that visible emission with an extreme temperature dependence could combine with SO2" to give the profiles that we observe.

E. Dan Hirleman, Purdue University, USA. The authors apparently analyze a column of radiation emitted through the end wall parallel to the shock tube axis. Any ignition delay measurements would therefore reflect the emission occurring in the gas adjacent to the end wall. Could the observed dis- crepancies between experimental and analytical ignition delays have been caused by errors in interpretation and calculation of the experimental delays from the emission data due to impurities or to end wall temperature, pressure, or concentration gra- dients?

Authors" Reply. We discount the contribution of surface effects to our emission profiles for two reasons: First, experiments in pure argon, 1% 0 2 in Ar, and 1% CS 2 in Ar showed no emission. Second, the condition of the surfaces near the end wall had no apparent effect. The first experiments after clean- ing the tube were not different from those immedi- ately preceding, even if aluminium chips from the diaphragms were present near the end wall.

Richard S. Brokaw, Baldwin-Wallace College, USA. Hydrogen-free combustion systems such as

CO-Op, C2N2-O 2 and CaO2-O 2 are notoriously sensitive to traces of hydrogenous materials. What steps did you take to be certain that such factors are not influencing your results?

Authors" Reply. In order to investigate the effects of impurities, we simulated experiments with up to 1% H 2 0 in the starting CS2, using a complete mechanism for both CS 2-0 2 and H 2-0 2 combustion. The results indicated that our experimental profiles would be unaffected by such contamination.

W. Tsang, National Bureau of Standards, USA. What will be the effect of temperature inhomogenei- ties along the axis of your shock tube on the emission measurements?

Authors" Reply. Simulations indicate that our experimental parameters were measured too early in the reaction to be strongly affected by the temperature and pressure changes due to reaction. Changing the flow model from ideal, constant density to isothermal flow changed the calculated parameters by about 10%.

R. B. Klemm, Brookhaven National Laborator~l, USA. I feel obliged to call attention to several questionable values in your rate constant data base (Table II). In particular, the values for three reactions do not reflect the results of several recent studies, 1-3, i.e.,

O + O C S = C O + S O (1)

S + 0 2 = SO + 0 (2)

S + OCS = CO + S 2 (3)

where the rate constants for reactions 1-3 have been measured over a range in temperature using the flash photolysis-resonance fluorescence technique.

k 1 = (1.65 -+ 0.13) x 10 11

exp( -4305/RT) ; T = 263 -502 ~ K


k 2 = (2.24 _+ 0.27) • 10 -12

exp(0 -+ IO0/RT); T = 252 -423~

k 3 = (1.52 + 0.20) x 10 12

exp(-3630 +_ 120/RT); T = 233 -445~

Units are cm 3 molec-1 s -1

Would the use of these rate data make any significant difference in the analysis of your experiments?

REFERENCES

1. KLEMM, R. B., AND STIEIr, L. J.: J. Chem. Phys. 61, 4900 (1974).

2. DAvis, D. D., KLEMM, R. B. AND PmLINC, M.: Int.

J. Chem. Kinet. 4, 367 (1972). 3. KLEMM, R. B. AND DAvls, D. D.: J. Phys. Chem.

78, 1137 (1974).

Authors'Reply. Our mechanism reflects the dearth of good high-temperature measurements and a belief that a possibly contaminated high-temperature experiment might give a rate no worse than that obtained by extrapolating a low-temperature result which contains a small uncertainty in the activation energy. Vv'here a rate constant had been measured above 1000 K, this value was chosen for our mechanism. The effects of using the low-temperature rate data for the reactions that you mention were investigated and found not to be important for the simulation of our experiments.

shock tube study of carbon disulfide oxidation

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