Further studies of induction periods in mixtures of H2, O2 and NO2

FURTHER

STUDIES

OF I N D U C T I O N OF H a , 0 2 A N D

P. G. A S H M O R E

IN M I X T U R E S

NO 2

a n d B. P. L E V I T T

INTRODUCTION

as solved at this time. It is not even clear what the relative roles of N O a n d N O 2 m i g h t be, both of which m a y be present more or less in e q u i l i b r i u m with oxygen.' Since then, a good deal of indirect 7 a n d direct s evidence has b e e n presented which shows that the i n d u c t i o n periods represent the time taken for the nitrogen dioxide to react with hydrogen to yield nitric oxide 9. For example, Figure 1 is typical of results o b t a i n e d in a prelimin a r y photometric study s of the changes of Pzr d u r i n g the induction periods before ignitions. T h e pressure of nitrogen dioxide fell from 0.6 m m on admission to less t h a n 0-1 m m at the e n d of six seconds. This extensive decomposition (,-~80 p e r cent) c a n n o t be due to the bimolecular reaction 2 N O z -~ 2 N O § 0 2 , which would lead to only 0.06 per cent decomposition in six seconds I~ A t the e n d of the i n d u c t i o n period, the trace takes a s h a r p d o w n w a r d kick due to the ignition flash. Experiments with mixtures of the same composition showed t h a t the c o n c e n t r a t i o n of nitrogen dioxide immediately before this d o w n w a r d kick is reproducible from r u n to run, a n d it was suggested s that the a t t a i n m e n t of this limiting pressure, Pc, could be taken as a condition for ignition appropriate to the original mixture. It was expected t h a t the relationship between Pe a n d the corresponding values ofpNo, Prt 2, po 2, etc., would give information a b o u t the relative roles of nitric oxide a n d nitrogen dioxide in b r a n c h i n g a n d t e r m i n a t i n g steps, a n d could be used to test various theories of the b r a n c h i n g m e c h a n i s m w h i c h h a v e been proposedT, n . T h e work described in this p a p e r set out to investigate h o w p e is influenced by the initial pressure of the sensitizer, the total pressure of a stoichiometric mixture, the partial pressure of hydrogen or oxygen, the temperature, a n d the pressure of inert gas added. T h e p h o t o m e t e r described previously 12 was modified to follow lower concentrations of nitrogen dioxide a n d to allow better time resolution. T h e significant observation was m a d e that a rapid (but continuous )increase in the rate of removal of nitrogen dioxide occurs at the end of the induction period w h e n P e is reached. T h e bearing of this observation a n d the other results upon the conditions postulated for the end of the induction period a n d the occurrence of ignition or slow reaction is discussed in detail.

I n 1928, H. B. Dixon found t h a t traces of n i t r o g e n dioxide could lower the ignition t e m p e r a t u r e of certain mixtures of h y d r o g e n a n d oxygen b y more t h a n 200~ a n d so initiated a long series of researches by various investigators z-5 u p o n the 'sensitization' of ignitions b y nitrogen dioxide. By 1941, these careful investigations h a d established the principal conditions of temperature, vessel size, a n d concentrations of reactants a n d sensitizer which lead, after a n induction period w h i c h m a y last tens of seconds, to slow reaction or ignition. Ignition occurs only if the pressure of n i t r o g e n dioxide lies between a lower a n d a n u p p e r sensitizer limit of ignition; these limits change w i t h total pressure so as .to enclose a n ignition region a. Several suggestions a b o u t the kinetic mechanisms of the sensitization h a d b e e n proposed, b u t n o n e was completely satisfactory. T h u s in t 951, Lewis a n d yon Elbe wrote 6 ' T h e suggestion t h a t T I ~ StALl i S E ~

~020.6-o,5

PERIODS

i ~

O'4 0"$ O'2 0"1

Figure 1. The concentration 0 f N O 2 against time during the induction period of a sensitized ignition. 376~ 0-6 mm NO2, 100 mm H2, 50 mm 0 2 initially. Photographofpen recorder trace of photometer output the N O e sensitization is due to the d e v e l o p m e n t of b r a n c h e d chains is generally accepted, b u t its i m p l e m e n t a t i o n by a specific m e c h a n i s m is a m a t t e r of great difficulty a n d c a n n o t be r e g a r d e d 45

M E C H A N I S M OF COMBUSTION REACTIONS EXPERIMENTAL T h e gases were p r e p a r e d a n d stored as described elsewhere 9. R e a c t a n t mixtures were p r e p a r e d in mixing vessels, a n d then delivered t h r o u g h a conventional Pyrex glass v a c u u m system to a Pyrex or quartz reaction vessel h e a t e d in a n electric furnace. T h e bulk of this work was carried out in a q u a r t z reaction vessel, a p l a n e - e n d e d cylinder of length 2 0 c m a n d d i a m e t e r 3 . 5 c m . Pressure changes were m e a s u r e d with a B o u r d o n gauge. T h e concentration of nitrogen dioxide in the reaction vessel was followed continuously with a modification of a p h o t o m e t e r described previously 12. A tungsten l a m p was viewed by two separate logarithmic photometers 12, using photomultiplier tubes w h i c h are m a t c h e d as nearly as possible in sensitivity. T h e reaction vessel lies between the source a n d one photomultiplier ('measure') a n d a n adjustable slit between the source a n d the other ( ' d u m m y ' ) . T h e difference in potential between the p h o t o m u l t i p l i e r cathodes is directly proportional to the c o n c e n t r a t i o n of nitrogen dioxide in the vessel; it was m e a s u r e d on a microammeter, or amplified to operate a short period ' R e c o r d ' p e n recorder, a K e l v i n - H u g h e s high-speed p e n recorder, or a n oscilloscope. T h e double b e a m circuit reduced drift due to variations in light intensity by a factor of 40; the overall drift of the p h o t o m e t e r was reduced by a factor of 5; the sensitivity was d o u b l e d ; a n d the 50 cycle noise considerably reduced. T h e detailed study of the changes of concentration of nitrogen dioxide n e a r the e n d of the induction periods was started, using the oscilloscope. A device was constructed to trigger the oscilloscope time base for a single sweep (1.5 or 0-5 seconds) w h e n the concentration of nitrogen dioxide fell to a selected level. By choosing this level just above Pc, p h o t o g r a p h s could thus be taken of the oscilloscope trace n e a r the end of the induction periods.

were taken d u r i n g the last second of the induction period. A typical trace is shown in Figure 2. After pe is reached, the rate of removal of nitrogen dioxide increases rapidly, a n d ignition occurs only after the pressure of nitrogen dioxide has

Figure 2. Photograph of oscilloscope trace near the end of an inductionperiod fallen to a lower b u t definite concentration, Pi. T h e rate of disappearance of nitrogen dioxide accelerates thirtyfold for a fall in p ~ o 2 of only 10 p e r cent.

(b) Above the upper sensitizer limit--Immediately above the u p p e r sensitizer limit the same r a p i d acceleration is observed w h e n Pe is attained. However, the acceleration falls off rapidly, a n d instead of reaching a very low value, p ~ o 2 falls to a nearly stationary value, Ps. T h e onset of the slow h y d r o g e n - o x y g e n reaction was followed by the pressure change o n a B o u r d o n gauge. I t occurred, as closely as could be j u d g e d , immediately after Pe was a t t a i n e d w h e n PNo2 fell rapidly; the coincidence was within a small fraction of a second after a n i n d u c t i o n period of a m i n u t e or more. As P0 was increased further in successive runs, P8 rises rapidly, a n d the acceleration of the removal

/Is

MM 2"0

/

RESULTS

Variation of pNo~ near Pe (a) Before ignition--Although the rate of removal of nitrogen dioxide d u r i n g the induction period would be expected 9 to fall as the first power of the concentration, a n d traces like those in Figure 1 show some decrease in the rate as nitrogen dioxide disappears, some traces taken a t low total pressures showed a n increasing rate towards the e n d of the induction period (see below). Closer examination of traces like those in Figure 1 showed t h a t there was a clear increase in the rate of disappearance of nitrogen dioxide after the a t t a i n m e n t of pc a n d immediately before the ignition flash. T o make sure t h a t this was not due to the finite time response of the recorder, p h o t o g r a p h s of a n oscilloscope trace of the o u t p u t from the p h o t o m e t e r

7~

I-0

l

~/~"/ I/7

"

I

PoM~ Figure 3. Pseudo-stationaryconcentrationof nitrogen dioxide in mixtures with initial concentrationsof 33-3 ram O2, 66.7 ram H 2 andpo ram NO2 at 370~ plotted againstPo 46

I N D U C T I O N PERIODS IN M I X T U R E S OF H~, O 2 AND NO~ of N O 2 becomes less a n d less pronounced. Eventually, with high P0, PNo2 falls smoothly to Ps a n d there is no observable onset of the h y d r o g e n oxygen reaction. T h e points in Figure 3 show h o w Ps varies with Po' !

h u n d r e d t h s of a second, leads to ignition or slow reaction of the reactants. T h u s the time at which Pe is reached virtually determines the e n d of the induction period. A l t h o u g h the ignition is detected when pN02 reaches Pi, a n d n o t Pe as was previously t h o u g h t s, Pe as the point of c o m m e n c e m e n t of the acceleration is of great importance. T h e

O-~O

o'~5

m i

0"05

IaNITION ~ l

l 2

l ~

Time See

PNO 2 5

~'05

0"05

2

50

6

100 150 Total P,-egauz~ m

Time SeQa.

Figure 4. The concentration of nitrogen dioxide during the induction period of the sensitized hydrogen-oxygen reaction. Photograph of pen recorder trace; 372~ Trace A: 34 mm (2H 2 + O2) , 0.13 m m NO~ initially; Trace B: 16 mm (2H 2 + O2), 0-07 mm NO 2 initially (c) Below the lower sensitizer l i m i t ~ A t 370~ a n d m o d e r a t e pressures, the induction periods b e c o m e very short n e a r the lower sensitizer limit. I t was found to be convenient to cross the limit b y successive runs with mixtures of constant composition b u t lower a n d lower total pressure. Figure 4 shows p h o t o g r a p h s of pen recorder traces for two runs in a series of this type; the p e n recorder used here is of longer period t h a n that used for Figure 1. M i x t u r e A lies above the limit of ignition. At these low pressures the rate of removal of nitrogen dioxide appears to increase almost continuously, t h o u g h this a p p e a r a n c e is in part d u e to the finite radius of the p e n recorder. M i x t u r e B lies below the ignition limit. Here the c o n c e n t r a t i o n of nitrogen dioxide fails steadily until the rate suddenly accelerates. T h e concentration at w h i c h the rate accelerates can be identified with Pc" Figure 5 shows Pe a n d the induction period plotted against total pressure for the whole series. Both are continuous across the limit. T h e p h e n o m e n a continue, as the initial pressure is reduced, to the lowest p o i n t at which p h o t o m e t r y is possible. T h e experiments detailed above show t h a t each i n d u c t i o n period c a n be divided into two very u n e q u a l portions. I n the longer initial part, often lasting tens of seconds, PNo~ falls steadily to the critical value Pe at which a substantial acceleration in -dpl~oJdt occurs; this acceleration, over a few

Figure 5. Plots showing the variation of: (i) the concentration of nitrogen dioxide, Pc, at the end of the induction period (R.H. scale, triangles), (ii) the length of the induction period (L.H. scale, cbrles) against total pressure of a mixture of the composition : H 2 : O 3 : NO~ = 167 : 83 : 1 in each run initially, 372~ Induction period measured to the sensitized ignition or to the rapid disappearance of nitrogen dioxide where no ignition Occurs

observed d e p e n d e n c e of pc u p o n certain variables will therefore be described.

Variation of p e with Po and with PT T h e variation of pc with the initial pressure P0 of nitrogen dioxide was investigated for three different total pressures PT of a 2 : 1 m i x t u r e of hydrogen a n d oxygen at 370~ using the high-speed pen recorder. T h e results are s h o w n in Figure 6. For most of the ignition region, Pe falls linearly as P0 is increased, particularly at the higher pressures; the slope -(dpe[dPo)p ~ appears larger at higher values of PT. For all the plots, Pe is greater the higher the total pressure, a n d dPe/dpT decreases somewhat as P0 increases b u t is a p p r o x i m a t e l y constant for each value of p0. T o w a r d s the u p p e r sensitizer limit of ignition, the curve of pc against P0 flattens b u t is continuous across the limit. Eventually p, is replaced by Ps as explained earlier. T h e induction period % the time p~To2 takes to fall from P0 to pc, increases rapidly as P0 approaches a n d crosses the u p p e r limit as found by other investigators a-5.

Variation of p, with ptl 2 and with Po~ Figure 7 shows the variation of Pe a n d of ~- for constant P0 w h e n the partial pressure of h y d r o g e n 47

M E C H A N I S M OF COMBUSTION REACTIONS Pl-I~ is altered, a n d Figure 8 shows the changes w h e n the partial pressure of oxygen po 2 is altered. I n both cases Pe rises rapidly as the concentration of a d d e d gas rises t h r o u g h the stoichiometric ratio, but well above this it becomes nearly constant. T h e b e h a v i o u r of the induction periods, however, are in m a r k e d contrast : those for a d d e d hydrogen decrease steadily even w h e n Pe is nearly constant, whereas those for a d d e d oxygen fall sharply until the stoichiometric p o i n t is reached a n d then rise slowly. T h e m i x t u r e X containing 0.4 m m NO2, 33.3 m m 0 2 a n d 66.7 m m H 2 is c o m m o n to Figures 6-8. Ifdpe/dP~, is constant forP0 = 0.4 m m , the identity

0 oO ,~q~xz I . ~ x ~ x o s ~mx~ xs s~oo~s xs snoQ Aoal~

0-10 ~ ~ ~ ~

~ c ~ ~c~

.~

005

dpe] I

o2

I

I

I

o.4

o.6

oo

I

dp2lp,

~-o PoMM

Figure 6. Plots of p e againstpo for ignitions of hydrogen and oxygen sensitized by Po mm nitrogen dioxide, total pressure of stoichiometrk mixture shown in mm against eachplot, 370~ Open circles, ignition; filled circles, no ignition

~o

iNPEnl DIJCT~ON O90

olo

,

s~)

+ \dpr

I \dpoJpu2

provides a useful check on the experimental technique. I t is found to hold within the error of measuring the slopes. A t first sight, the plots in Figures 7 a n d 8, with the above identity, suggest t h a t (dPe/dP~,)p~ tends to zero at higher values of PT; b u t further consideration shows t h a t this is n o t a correct inference from the curves; dpe/dpo 2 m a y be very large w h e n dpe[dPtt 2 is close to zero, a n d vice versa.

20

T h e v a r i a t i o n of Pe w i t h t e m p e r a t u r e has not been extensively investigated because it is difficult to find mixtures which r e m a i n within the ignition region, a n d have a finite i n d u c t i o n period, over a wide r a n g e of temperature. However, it is clear that, other things b e i n g constant, Pe rises rapidly with increasing temperature. TABLE 1 Values ofp~ and ~-for 2H 2 -t- 03 = I00 mm for Various Values of p0

41

3:1

I \dPlt2/~ O

[ dPe 1

Pe and temperature

~oo, i

2:1

\ dpr

[dP~

4 0 sEc

MM

i:l

= [dPH2][ aPe ]

Figure 7. Plots of p, and induction period against partial pressure of hydrogen for sensitized ignitions at 370~ 33.3 mm 02 and 0-4 mm NO 2 initially in each run

~, o 040

~jyf

370~ (Quartz vessel) 2H2+O2 = 100 mm

Po p~

0"4 0-07 17

0"6 0"04 29

0"8 iTlm

412~ (Pyrex vessel) 2 H 2 + O 2 = 100 mm

Po p~

0.5 0.12 4

1"0 0"06 15

2"0 mm

0"02 mm 46 sec

0.04 m m 49 sec

Cross checks available for 150 m m of reactants at 370~ show t h a t Pe does not change m u c h w i t h the n a t u r e of the vessel surface.

Pe and added inert gas ,oo 21

,I,

~

,!,

,~o '

L

I f inert gas is adde d to the mixture X, the effect is similar to t h a t observed w h e n P0 is raised. As nitrogen is addedPe falls steadily; 125 m m reduces it by 50 per cent a n d just suppresses ignition. T h e acceleration is still observed w h e n Pe is reached,

,] ,3

"a%

Figure 8. Plots of Pe and induction period against partial pressure of oxygenfor sensitized ignitions at 370~ : 66.7 mm H 2 and 0-4 mm NO2 initially in each run 48

I N D U C T I O N PERIODS IN M I X T U R E S OF H2, O2 AND NO2 a n d Pe is continuous across the ignition limit. If more nitrogen is added, the acceleration disappears (175 m m ) , a n d PNO, falls steadily to a nearly stationary value. This sequence shows a r e m a r k able similarity to that observed when P0 is increased above the u p p e r sensitizer limit.

induction periods with values calculated from the kinetics of the hydrogen + nitrogen dioxide mixture is fairly good at h i g h total pressures. For example, at 370~ the rate of fall of N O z with 0.6 m m N O 2 a n d 100 m m H 2 can be calculated from published results 9 to be 1/11 mm/sec; the effect of 50 m m oxygen on this ratio is small, so that PN02 would be reduced from 0-6 to 0.1 m m in 0.5 • 11 or 5.5 seconds if the rate r e m a i n e d constant. As it falls slightly (Figure 1) the calculation is in excellent a g r e e m e n t with the observed value of 5.8 seconds. However, the kinetics of the N O z / H 2 r e a c t i o n h a v e not been investigated at very low pressures, a n d it is not possible to account quantitatively for results like those shown in Figure 4. It appears, therefore, t h a t most of the investigations of induction periods in these systems can be explained in terms of the reaction between nitrogen dioxide a n d hydrogen. T h e r e is, however, one feature reported in the literatureS, 4 which c a n n o t be explained by our present interpretation. This is the substantial increase in ~- reported at lower sensitizer concentrations, below the lower sensitizer limit of ignition, with constant pressure of hydrogen a n d oxygen. (The effect is not the same as that shown in Figure 5, w h i c h can be explained by the fall inptt~.) All o u r work suggests a n increase r a t h e r t h a n a decrease in the rate of removal of N O 2 at very low concentrations, which would lead to shorter induction periods as P0 --~ 0. At present, we c a n only suggest t h a t w h a t was taken at lowP0 to be the end of an i n d u c t i o n period was actually the a t t a i n m e n t of a finite pressure change due to a n extremely slow reaction which b e g a n upon admission of the mixtures to the reaction vessel (@ DaintonlS). This point requires further investigation.

DISCUSSION

Length of the inductionperiod This experimental work has substantiated previous ideasT, s that the induction period represents the time ~- taken for a substantial portion of the nitrogen dioxide originally present to be r e m o v e d by reaction with hydrogen. T h e rate of this reaction is given 9 by expression 1. dPsz~ kIPNO~Pli~ (1) dt PNO + k2PNo2 T h e rate is slowed 9 by a d d i n g inert gases such as nitrogen, k 2 is close to one at temperatures n e a r 400~ T h e observed effect on the induction periods of c h a n g i n g pNo2, PIt~, Po 2 a n d pi~2 c a n be explained as follows: (1) as the initial pressure P0 of N O 2 is increased across the ignition region, ~- increases rapidly. Figure 6 shows that Pe decreases, so the extent of reaction is increased whereas e q u a t i o n 1 shows t h a t the initial rate is i n d e p e n d e n t of p0 a n d is in fact slower for e~/ch given PSTO~ the higher p0--for then P g o is higher. Hence the time taken before ignition increases, as observed, w h e n P0 is increased. (2) as PIt~ is increased, ~- falls rapidly (Figure 7). Not only does Pe increase, so reducing the extent of reaction required, b u t the rate increases, as shown by e q u a t i o n 1. (3) as Po~ is increased, the induction period first falls sharply a n d then rises slowly. T h e fall corresponds to a rapid rise in Pe (Figure 8) a n d can be a t t r i b u t e d to the greatly decreased extent of reaction necessary, for the effect of oxygen o n the rate of the nitrogen dioxide § hydrogen reaction is s l i g h t - - i t acts as an inert gas a n d slows the reaction somewhat. However, once Pe levels off, this slowing will account for the region w h e r e ~increases slowly. (4) the addition of nitrogen lowers Pe (note the contrast here with oxygen) a n d slows the rate of the h y d r o g e n § nitrogen dioxide reaction; hence the extent of decomposition required is increased, a n d the rate decreased, a n d these effects explain why nitrogen increases the induction periods m u c h more strongly t h a n does oxygen (c[~ Figure 8 of reference 4). O u r observations also agree with the e x p l a n a tions p u t forward3, 4 to a c c o u n t for the shortening of the induction periods u p o n photolysis; a n y reaction which hastens the decomposition of N O e will shorten the induction periods. T h e quantitative a g r e e m e n t of the length of the

Ignition boundaries (a) Upper sensitizer limit--The observations u p o n Pc, Pi a n d p~ described earlier allow a rational explanation of the u p p e r sensitizer limit of ignition, a n d the behaviour of mixtures of composition just above this limit. Figure 3 (points) shows that Ps increases rapidly asP0 increases; on the other h a n d Figures 6 a n d 2 show that Pe falls as P0 increases a n d that Pi lies below Pe for each value of p0. H e n c e a point will come, as P0 is increased, w h e n Pszo2 can fall to Pc, but reaches Ps before Pi; there should be a n acceleration of the removal of nitrogen dioxide a n d the hydrogen § oxygen reaction should begin, b u t there will be no ignition. T h e u p p e r sensitizer limit of ignition has been reached. A t still higher values of p0, Ps will be reached before Pe ; hence no acceleration a n d no h y d r o g e n - o x y g e n reaction should occur. This is exactly w h a t is observed. T h e m e c h a n i s m w h i c h establishes Ps seems to be extremely simple. As P0 is increased, the pressure Ps;o which is built u p as the nitrogen dioxide reacts 49

M E C H A N I S M OF COMBUSTION REACTIONS with hydrogen

is increased a n d

the reaction

2 N O + O 3 - ~ 2 N O 3 becomes i m p o r t a n t . W h e n its rate equals t h a t of the removal of nitrogen dioxide,

kl Pz,To,Pl/5,

- kt P}o Po2

P~O + k3p~'o2 Now k 2 ~ 1

at 300~ a n d as long as P s ~ P o , k J, ~t.5 a t's i'I-I~

P0

kt p0~ p o 2

.'. ps oC pao T h e dotted curve in Figure 3is a cubic in P0, passing through Ps = 1.3, P0 = 8.0. It is a close fit to the full curve t h r o u g h the experimental points. Moreover, absolute calculations ofps from appropriate valuesOJ ~ of k 1 a n d k t agree well with the experimental values. It m a y be concluded t h a t the u p p e r sensitizer limit occurs because a stationary state concentration of nitrogen dioxide is set u p by the reactions H e +NO 2 =NO

+H20

2N,O + 0 3 = 2 N O e We thus return to a modification of the ideas of Crist a n d Wertz 14. (b) The lower sensitizer limit--The experiments described here t h r o w little light o n the p r o b l e m of the lower sensitizer limit of ignition. Experiments v on the ignition b o u n d a r y found with nitric oxide as sensitizer suggest t h a t a m i n i m u m a m o u n t of nitric oxide is necessary, a n d t h a t this m i n i m u m corresponds with the lower sensitizer limit w i t h nitrogen dioxide. O u r experiments support this view, a n d further investigations of Pe a n d Pi at lower values of p0 m a y be helpful.

Conditionsfor ignition

present is strong, a n d it seems very likely that the net rate of b r a n c h i n g (the rate of production of centres by positive b r a n c h i n g minus the rate of removal of centres by t e r m i n a t i o n reactions) increases from some low negative value at the beginning of the i n d u c t i o n period towards zero at the end of the induction period. T h e increase in chain centre concentration inferred from Figure 2 could occur as the net rate of b r a n c h i n g approaches zero, however, a n d does not require the net rate to b e zero; most a r g u m e n t s a d v a n c e d previously o n these points have wrongly assumed a constant n e t rate of branching. U n t i l further studies ofpi h a v e been made, such as the effect 4 of a d d i n g i n e r t gases of different heat capacities a n d different t h e r m a l conductivities, it is not possible to assert t h a t the ignitions are ' t h e r m a l ' or 'isothermal' in character. O n the other h a n d , it is w o r t h while to investigate w h e t h e r a ,reasonable b r a n c h i n g c h a i n mechanism, c o m b i n e d w i t h the simple assumption t h a t the net rate of b r a n c h i n g is zero at the p o i n t PNO~ = Pc, cart explain the variations found in p~. T h e p r o b l e m of finding a n exclusive m e c h a n i s m is far from solved, b u t the one now proposed accounts for most of the observations on Pc, a n d avoids certain unsatisfactory features it of a m e c h a n i s m suggested earlier v. T h e m e c h a n i s m now proposed takes reactions 1-7 w h i c h are i m p o r t a n t in the h y d r o g e n + oxygen reaction 15 at higher temperatures, a n d those w h i c h have been postulated in studies 9 of the h y d r o g e n + nitrogen dioxide reaction (reactions 8-11). T h r e e further reaction steps 12, 13, 14 are postulated, a n d their roles are discussed briefly.

The kinetic scheme H +O 2 =OH +O O +H 2 =OH +H OH +H 2 =H20 +H H + 0 2 + M =HO 2 q M H O 2 + wall = end H + wall = end O H + wall = end H e +NO 3 =HNO e +H H +NO 3 =OH +NO OH ~ NO 3 +M =HNO 3 +M OH +NO + M =HNO 3 + M O +NO 3 =NO +O 2 HO 3 + NO = NO 2 + OH HO 3 + NO = HNO 2 + O

T h e r e are several reasons n for believing t h a t the reactions leading to ignition involve b r a n c h e d chains, a n d t h a t the p h e n o m e n a observed at the end of the induction periods c a n n o t be explained by a n increased rate of initiation (by nitric oxide) a n d reduced rate of t e r m i n a t i o n (by nitrogen dioxide). T h e b e h a v i o u r shown in Figure 2 provides the strongest support for these conclusions; the rate accelerates b y some thirtyfold over a small change of c o n c e n t r a t i o n of nitrogen dioxide. F u r t h e r strong support comes f r o m : (a) our observation t h a t the rate of reaction immediately below ignition boundaries like those shown in Figure 1 of reference 3 is very s l o w - - i n m a r k e d contrast to the b e h a v i o u r in n o n - b r a n c h i n g systems 1], (b) the very great difficulty of devising a n y rapid initiating steps with nitric oxide, (c) the evidence 9 from the hydrogen + nitrogen dioxide reaction t h a t nitric oxide is r a t h e r more effective t h a n nitrogen dioxide in terminating chains involving O H a n d H. T h e a r g u m e n t t h a t positive b r a n c h i n g reactions are

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14)

Reactions 12, 13, and 14 R e a c t i o n 12 is k n o w n 4 to be rapid, a n d early in the induction periods it will effectively stop b r a n c h ing b y competing with reaction 2 for oxygen atoms. R e a c t i o n 13 has been suggested before7; its i m p o r t a n c e will increase d u r i n g the induction 50

I N D U C T I O N PERIODS IN M I X T U R E S OF H~, O2 AND NO 2 period, and it will reduce the rate of termination of chains through removal of r i O 2 by 5 at a time when 4 and 5 would be competing successfully with 9 for hydrogen atoms. As has been explained, however, it is unlikely that the reduction of chain termination is sufficient to explain the observations, especially in view of the additional termination step 11. Reaction 14 provides a possible branching step, representing an attack of N O on the H O group of H O e rather than on the - O as in 13. The two transition complexes might be formulated as /,

(13)

ON

/

OH /

--O

(14)

/

--e(k 4 + k 6 + k g ) --

O N ........ O" H

which would be equivalent to reaction 4 followed by reaction 14, and would begin to be important in comparison with 4 as PsTo builds up. However, it seems better to keep the successive steps at present.

k4 k14 (k2 - ki2 ) kio + kii (k4 + k9) (k13 + k14)(k2 + kl 2) k3 The work 9 on the reaction between hydrogen and nitrogen dioxide has shown that klo ~ kn, so that kloPNo2PM + kllPl~oP M can be replaced by kaoPoPM. If the pressure of nitrogen dioxide falls to Pe when the net rate of branching becomes zero, then

Rates of terminating and of branching The net branching rate has been worked out for the full kinetic scheme, but for the present purpose a great simplification can be made by ignoring reaction 1, because this is acknowledged to be slow at these temperatures compared with reaction 4; it will therefore be assumed that branching occurs via reactions 4 and 14 followed by 2. The terminating and branching leactions can then be shown schematically as follows:

k4Po~ (keplt~ -- klePe)k14 (k2ptI 2 + k12Pe)(k13 + k14) kaoPs

k3pH (k4po2PM + k9Pe)

~ L

9 6 end

5 3

Propagation

end

kn + k 5 +k13 +k14

where ~ stands for k7 -+- kl~ + kll , and R i for the k3 rate of initiation (reaction 8). Inspection of the above equation will show that the terms after (1 + o~)Ri each contain the H atom concentration once, within k4, ks, and k9; the other rate expressions occur as ratios in which any chain centre concentrations cancel. These terms represent the net rate of branching. Now it is likely that the surface terms ks, ks, and k7 are small compared with other terminating steps; we found thatPe did not change much in going from a quartz to a Pyrex vessel, and Dainton and Norrish 4 found that the surface had little effect on the sensitizer limits if the vessel diameter was above 20 mm. There is also evidence S that e ~ 1. With these simplifications, the condition that the net rate of branching becomes zero is

=HNO 2 +O

4

k4kla k e(1 + u) --k12 + k5 + k13 + k14 k2 + k12

O

If 14 is followed by 2, the chain will have branched; of course, this is only likely when PNo2 becomes small and 12 less important. Previous estimates of the heat of formation of gaseous H N O e suggest that reaction 14 will be endothermic unless the H O 2 carries over some of the energy of reaction 4; this will often h a p p e n - - i n fact, R o b b has recently given reasons le for believing that H O e formed in the binary collision H + 0 2 can have a long life. Another possible branching step might be the ternary reaction H +O 2 +NO

This scheme leads to an expression for d H / d t which will hold up to the point where the net rate of branching becomes zero. If the velocity constants are allowed to stand for the full rate expression for each of the reaction steps, the equation can be written dH (1 + ~ ) ~ = (1 + 0 : ) R i

14 ~

Propagation

or t e r m i n a t i o n

51

2

or branching

(2)

MECHANISM OF COMBUSTION REACTIONS is the equation representing the variation of Pe with the initial pressure P0 of nitrogen dioxide, PH, of hydrogen, po 2 of oxygen, and PM the total pressure. It will be seen that the pressure of nitric oxide does not occur in the equation under the conditions postulated. Equation 2 is successful in accounting for most of the observed variations of Pc. (1) It is clear that the left-hand side of the equation could not become positive until Pe < k2ptiJkle. The need for the pressure of nitrogen dioxide to fall below a critical value is apparent, and the competition between 2 and 12 for O atoms obviously plays a vital part in the mechanism. (2) U n d e r conditions where the pressure of oxygen is high, the second term on the right-hand side becomes negligible in comparison with the first towards the end of the induction periods. Thus for a stoichiometric mixture, PI~ = 2pM/3, and it can be shown that

P.

this m a x i m u m value, and this point remains a weakness of the scheme put forward. O n the whole, however, this comparatively simple treatment seems very successful in explaining the observed variations in Pc, as well as giving a clear reason for the need for PNO~ to fall below some critical value, identified with Pc, before any branching can become effective. The powerful effect of reaction 12 in restricting branching has been noted beforee,a,4; it is now plain that it would effectively prevent branching in most mixtures of hydrogen, oxygen, and nitrogen dioxide were the nitrogen dioxide not removed by reaction with hydrogen.

The authors would like to express their gratitude to the Royal Societyfor a grant which defrayedpart of the cost of the photometer, to the Director, R.A.E., M.O.S., Westcott, Jbr the temporary loan of a high speed recorder, and to the Director, E.R.D.E., M.O.S., Waltham Abbey, Jbr the temporary loan of an oscilloscope and camera.

a(1 -- bPo) 1 +bPo

where

a = 2k~pM/3ka2

and

b = 3kl~ (kls + k14)

REFERENCES 1 HINSHELWOOD,SIR CYRIL, and THOMPSON,M. S. Proc. Roy. Soc. A 124 (1929) 214 GRIFFITHS,J. G. A. and NORRISH, R. G. W. Proc. Roy. Soc. A 139 (1933) 147 a FOORD, S. G. and NORRISH, R. G. W. Proc. Roy. Soc. A 152 (1935) 196 4 DAINTON,F. S. and NORRISH,R. G. W. Proc. Roy. Soc. A 177 (1941) 393, 411 LEWIS, B. and VON ELBE, G. Combustion, Flames, and Explosions of Gases, p. 56 et seq. 1938. Cambridge Univ. Press; and or. Amer. chem. Soc. 59 (1037) 2022, a n d & Amer. chem. Soc. 61 (1939) 1350 6 LEwis, B. and v o s ELBE, G. Combustion, Flames, and Explosions of Gases, p. 71. 1951. New York; Academic Press 7 ASHMORE, P. G. Trans. Faraday Soc. 51 (1955) 1090 s ASHMORE, P. G. and LEVITT, B. P. Advances in Catalysis and Related Subjects, p. 367 Vol. IX. 1957 o ASHMORE, P. G. and LEVITT, B. P. Trans. Faraday Soc. 52 (1956) 835; 53 (1957) 945 10 BODENSTEIN, M. and LINDNER. Z. phys. Chem. 100 (1922) 106 ; ASHMOm~and LEVITT, Research, Lond. (Corresp) 9 (1956) $25; WISE and ROSSER, J. chem. Phys. 24 (1956) 493 11 ASHMORE, P. G. Chem. Soc. Spec. Publ. No. 9. In course of publication 12 ASHMORE, P. G., LEVITT, B. P. and THRUSH, B. A. Trans. Faraday Soc. 52 (1956) 830 13 DAINTON, F. S. Chain Reactions, p. 34. 1956. London; Methuen 14 CRIST, R. H. and WERTZ, J. E. J. chem. Phys. 7 (1939) 719 15 LEwis, B. and YON ELBE, G. Combustion, Flames, and Explosions of Gases, chap. 1. 1951. New York; Academic Press x6 RoBB, J. C. Chem. Soc. Spec. Publ. No. 9. In course of publication

2kak14 This equation predicts that Pe is proportional to the total pressure PM or PT, and this was found experimentally. Also, the equation predicts that Pe falls linearly with P0, provided that Po2 is not low, and that the slope will increase as PM is increased; both these predictions are correct, as shown by Figure 6. (3) The equation predicts that when Po2 is not low, the effect of adding an inert gas such as nitrogen should be the same as increasing P0, for PM and P0 occur together as the product PMPo on the right-hand side of equation 2, the other terms in PM cancelling. This is exactly what was found experimentally. (4) That Pe must be independent ofpo2 at high values of the latter is obvious from what has been said and from inspection of equation 2. However, at low values of Po,, the right-hand side may become independent of Po2; when this occurs, further decrease of Po, will have the same effect on the resulting equation as increasing Po has on equation 2--i.e. it decreases Pc" This was observed

(Figure 8). (5) It is easily seen from equation 2 that increasing PH2 will mean that Pe has not got to be so low in order to make the left-hand side positive, so thatpe will rise aspH2 is increased. This does occur at low values ofplt2 (Figure 7) but at high values Pe tends to a m a x i m u m value. Unfortunately, no manipulation of equation 2 seems to predict 52