C. P.FENIMORE AND G. W. JONES
1834
VOl. 66
CONSUMPTION OF OXYGEN MOLECULES IN HYDROCARBON FLAMES CHIEFLY BY REACTION WITH HYDROGEN ATOMS BY C. P. FENIMORE AND G. W. JONES General Electric Research Laboratory, Schenectady, N . Y. Received March 91, 1969
The rate of consumption of 0 2 is measured by probe sampling through low pressure, flat, premixed flames of CHI, 02, A or through flames with C ~ Hor P CaHa fuels, all burnt on cooled porous burners with flame temperatures of 1300 to 1950'K. [HI is also measured in the same flames by the rate of formation of H D from added DP or DzO, and turns out to be the concentration required, within 30y0 to account for the observed -d[Oz]/dt accordin to the known rate of the reaction, Oz + OH 0. It is concluded that 02 is consumed chiefly by reaction with atoms in either lean or rich hydroH carbon flames.
+
8
+
Introduction TABLE I The rate constant for the reaction H 0 2 --t OH RATE CONSTANTS IN L. MOLE-^ S E C . - ~AT FLAME TEMPERA0 is fairly well known,l-a so by measuring [HI, TURES IO,] and -d[02]/dt in hydrocarbon flames, one kfanard kbaokwsrd (a) H + H ~ O= I x I O ~ ~ ~ - ~ ~ 2~. 6OxO1 0~ 1 ~1 ~T- 1~0 ~ ~*0 ' ~ ~ can tell whether this reaction is of major imporHz + OH tance for the observed decay of 0 2 . In the flames (b) H + cop= 3 101ze-aa,aooi~~g 2 . 3 x 101Oe-lo,mo/m reported in this paper, with CH4, C2H2 or C3Hs CO + OH fuels, O2is consumed much more by reaction with H H + oz = 1 . 5 x 10s at IIOOOK.: atoms than in any other way. OH + 0 E: = 18 3 kcal.
+
+
(d) H
Experimental
+ NzO
Ns
Water-cooled, flat-flame burners4 were used at reduced pressures to obtain moderately thick, flat flames. Any rich flames used were free from soot. Temperature traverses were made with quartz-coated thermocouples corrected for radiation,' s a m p h g was through h e quartz Probes, and analyses were carried out on a mass spectrometer. The composition traverses were recast as reaction rates through the flame already described.* Briefly, the mole fraction of each species was plotted US. distance from the surface of the burner, Xi v;. Z . Using approximate binary diffusion coefficients,s the diffusion velocity of the ith species was calculated through the flame, VI = -(Di/Xd dXd&' and then the fraction of mass flow due to the 1th species
u* = M average lnthese formulas, D, = diffusion coefficient, M molecular weight, M~ = molecular weight of the jth species, = gas velocity as calculated from the known mass flow pv Finally, the rate of appearance of the ith and the density species due to chemical reaction was obtained, it is equal to ( p v / M i ) dGi/dz. The concentrations of radicals were estimated by 'in& cator*#reactions as aheady described. The estimates of [HI are accurate to d t h i n a factor of two at least, because in&pendent estimates by other methods have been found to agree at least this we11.8 A few estimates of [O] must be viewed more skeptically because the method used for this radical has not been checked against other methods. The rate constants used to interpret the data are listed in Table I. The reverse constants for reactions (a) and (b) were calculated from the forward constants and from a tabulation of equilibria over the temperature range of interest.' IC. is known from measurements of the rate of consumption of Oz in the early parts of three Hz, 01 flames, with simultaneous measurements of [HI via the formation of HD from added heavy water.* The value of Table I lies between an estimate by Semenov'; 6.7 X lo6 a t 793' which would become 1.8 X 108at 1100'K. if one accepts his activation energx of 18.5 kcal;. and Baldwin's%estimate of 2.7 X 108 at 793 , which would become 0.7 x lOBat 1100'K. on the same basis. 8
(1) N. N. Semenov. Acta Physicochim., 20, 290 (1945). (2) R.R.Baldwin, Trans. Faraday SOC.,62,1344 (1956). (3) c. P. Fenimore and G. W. Jones, THIS JOURNAL, 63, 1154 (1959). (4) W. E. Kaskan. "6th Symposium on Combustion," Reinhold Publ. Corp., New York, N. Y.,1957, p. 134. (5) A. A. Westenberg, Combustion & Flame, 1, 346 (1957). (6) B. Lewis and G. von Elbe, "Combustion. Flames and Explosions of Gases," Academic Press, New York, N. Y.,1951.
(e)
+ OH
4 X 1011"'6sa'O/RTa
+ Nzo
2N0 or approximate 0.9 values only
lolls-az'ooo~Rrlo
x 1011e-*7,soo/nT
k. in Table I is the unchecked constant used to determine 101. The first value is the approximate estimate from our
own work; the second is obtained from the assumption that NO decays a t moderate temperatures via the reverse process,
and from Kaufman and Kelso's accurate determination of this decay rate.7 For the rough estimates of [O] made in this paper, it does notmatterwhich expression is used. It should be pointed out that a ercentage comparison of + ~~0 = HD + OD, [HI measured via reaction (a), with [HI re uired to destroy 02 ma reaction (c) depends on the ratio rather than on the absolute value of either constant. This is all to the good, for kb, IC, and kd of Table I were determined relative to k, and while these constants are only claimed to be correct to within a factor of two, their ratios are correct to perhaps 30%. This estimate is suggested because we find a 3O% discrepancy between Our data and a conclusion which we believe to be consistent with them. It would be very difficult to estimate separately the errors resulting from approximate diffusion corrections, sampling errors, etc.; but an earlier comparison of reaction rate ratios, k a h b with the reverse constants, gave about the same discrepancy'a
Results from a Typical Run.-Some analyses and derived ratesof reaction in CH( flames are plotted in Figs. 1 to 3, and numerical data are listed in Table 11. The flame described by Fig. 1 is discussed in detail as an example. This had the reactant composition CH( + 1.87 o2+ 8~ + H ~ , and was burnt with a mass flow of 8.65 x g./Cm.', Sec. a t a pressure of 7 cm. Small concentrations of C2 hydrocarbons and perhaps HzCO were formed in the strongly luminous zone, but did not persist into the post flame gas. The concentration of H atoms was estimated by two different methods. First, heavy water was added to the reactants and the rate of formation of HD measured just beyond the main reaction zone.* At 0.4to 0.55 cm. from the burner surface, (7) F. Kaufman and J. Kelso, J . Chem. Phys., 2 3 , 1709 (1956). (8) C. P. Fenimore and G . W. Jones, THISJOURNAL, 62, 693 (1958). (9) C. P. Fenimore and G . W. Jones, ibid., 62, 1678 (1958). (IO) C. P.Fenimore and G. W. Jones, ibid., 62, 178 (1958).
CONSUMPTION
Nov., 1959
OF
OXYGEN MOLECULES IN HYDROCARBON FLAMES BY HYDROGEN 1835
-
this method gave [HI = 50 X mole/l. in the post flame gas at 1780°K. Second, part of the Hz in the fuel was replaced by Dz and the rate of formation of H D measured early in the flame.3 I n this second method, one must correct for the fact that the gross rate of formation of HD is larger than [HD] observed because H D undergoes simultaneous oxidation a t a rate which is approximated by
iHD1
hml
--
TEMPERATURt
500'K. Y
H2A
-'
3
z!
E
COIA
I c W
CO2IA
300'
x
(rate of formation of water from H ~ )
The quantity (rate of formation of water from Hz) is about 8 [COz][Hz]/[CO], see below, and then the gross rate of formation of H D a t 1100°K. turned out to be 4 times the [HD] observed. Equating this to k'[H][Dz] where k' is the rate constant Dz+ H D D,3J1[HI = 80 X lo-' at for H l l O O o , z = 0.137 em. Thus [HI by the two methods agreed to &25%. The [HI found above is of the right order to account for the observed rate of consumption of 02.If O2 is consumed only via reaction (c), - [O,] = k , [ 0 2 ][HI. Introducing the measured [OZ] and [OZ]a t 110O0K., and taking k, from Table I, we get [HI = 60 X mole/l. This agrees very well with [HI as measured directly. It can 0.3 c i CMS DISTANCE FROM BURNER SURFACE. be shown that reaction (c) accounts for - [ 0 2 ] not only a t 1100" but up to 1600"; for a plot of Fig. 1.-Analyses and derived reaction rates through a moderately rich C&, Hz, 0 2 , A flame. ] 1/T is linear and possesses a log - [ 0 2 ] / [ O z us. slope corresponding to 17 kcal. which is about the STRONGLY activation energy of reaction (c). At temperatures -2000°K much above 16OO0K., toward the end of the reREGION decreases because the action zone, - [OZJ/[OZJ reverse of reaction (c) increases rapidly.l2 Some additional information can be obtained from Fig. 1. Until CHh has fallen below 10%. of - 150O0: w its initial value, [CO] is 70 to 85% of -[CHI]. w s This agrees with the common belief that CO is the only carbon oxide formed directly from CHI, and that COz is formed only from the intermediate CO. Now if the last sentence is accepted, it can be -1000' shown that H20 is not formed directly from CHI either, but only from the Hz present a t any time. We have found previously that in the early parts m'0 I I of flames of mixed H2 and CO fuel, a situation in which COz is surely formed only from CO, [H;O]. e- 120[CO]/[COZ][Hzl = 8; and this was considered 0 fair agreement with the ratio ka/k-b = 12 which would be expected if HzO were formed from Hz 5u' 60only via the reverse of reaction (a), and C02 from 5c CO only via the reverse of reaction (b).a There2 fore, if HzO were formed from CH, in the present flame as well as from Hz, but C02 still formed only DISTANCE FROM BURNER SURFACE. from CO, one must have [Hi0I [COI/ [COzJ [Hzj > Fig. 2.-Results through a very rich CHI, 02,A flame. 8. But over the region z = 0.125 to 0.3 cm., we find this ratio only 5 I 1; that is, the observed rate of H2O formation relative to COz formation (11) G. Boato, G. Cared, A. Cimino, E. Molinari and G. G. Volpi, is surely no greater and probably even less than we J . C h e n . Phgs., 24, 783 (1956). expect only from the Hzpresent. I n other flames, (12) The inhibition of (0) toward the end of the reaction zone cannot be a temperature effect because the reverse of (c) has practically [Hi01[CO]/[C02][H2] is sometimes larger, but zero activation energy. Rather, the build u p of radicals by reaction never significantly greater than 8, and this rules (c) ultimately limits their own formation. The inhibition sets in out CH, OH + CHa H20 as an important rather sharply; possibly because (c) is a branching reaction, possibly reaction in CHI flames; or at least admits it only in part because H atoms can diffuse upstream more readily than 0 or OH. if H 2 0 is consumed in some other step so that the
+
+
W'
3
0
VI
2
L
+
+
1836
C. P. FENIMORE AND G. W. JONES
- 1500°K Y 3 c
z 0
B - 1000'
shows some results for a very rich flame in which more than 10% of the carbon fed as CH4 appears as CZhydrocarbons, mostly as C2H2. [HJ is smaller in this than in the preceding flame and near the value appropriate to the equilibrium H2 = 2H, for in the burnt gas the equilibrium [HI = 6 X lo-' mole/l. Small as it is, however, [HI is just about that required to destroy O2 via reaction (c) a t the observed rate. Figure 3 gives results of a lean flame. I n such flames, [HI cannot be determined easily in the burnt gas by adding DzO, but can be estimated roughly a t least by the residual [H,]. Because the reO2 = OH 0, 0 H2 OH H, actions H H H2O = H2 OH are generally equilibrated in the post flame gas,la the equilibrium 3H2 0 2 = 2H20 2H is also generally satisfied. This consideration, with equilibrium constants, from ref. 6, gives the approximate [HI titled "other" in Table 11. Once again [HI is just sufficient to react early in the flame with O2 at the measured rate of - [O,]. Finally, we replaced 10% of the O2 in the reactants by an equivalent amount of N20 in two flames, those described by Figs. 1 and 3, in order. to get an estimate of [O] by means of the reaction, 0 N 2 0 + 2NO. The effect of this partial replacement was to raise the final temperature by about 160°K. The general appearance of the curves for reaction rate vs. z was not greatly changed however. [HI was reduced, see Table 11, but remained the [HI required by reaction (c) to observed early in the flame. Furgive the - [02] thermore, over the temperature range 1000 to 1600"K., - [ 0 2 ] / [ 0 2 ] was within 30% the same as - [N10]/[N20]; and since N 2 0 reacts with H atoms with a rate constant, k d of Table I, about the same as k,, it is evident that N 2 0 also is destroyed chiefly by attack of H atoms. The small amount of NO formed suggests that in the region of maximum rate of reaction, [O] = 3[H] approximately in the fuel lean flame, and [O] = [HI approximately in the rich flame. In both flames, [0]decays rapidly as one moves downstream into the post flame gas. Thus [O] behaves differently from [HI which is about the same in the reaction zone and in the post flame gas. The result that [O] is comparable t o [HI in these flames means that 0 atoms might be important in the decay of CH4. Our finding that -[02] is accounted for by reaction (c), however, is not affected by [O] or [OH] because these species cannot destroy O2 molecules. Since five times out of five tries we found reaction (e) proceeding a t about the measured rate of -[02],we took the chief mechanism of 0 2 destruction in either rich or lean CHI flames as known a t this point. Flames with Other Fuels.-The remainder of Table I1 shows that O2 is destroyed chiefly by attack of H atoms in rich or lean flames of other hydrocarbon fuels also. Figures 4 and 5 will be discussed briefly.
+
rn.
0 100-
.
Y In
& 50-
-I W-
Ez
0
0-
u
= W -50-
0.3
0
Fig. 3.-Results
I
through a lean CH4, 0 2 , A flame. i I500'K
W
- 1000' c'
;
.a W
- 500'
DISTANCE FROM BURNER SURFACE,
Fig. $.-Results
+ + + +
+ +
+
+
+
0.6 CMS
DISTANCE FROM BURNER SURFACE
Vol. 63
through a lean C2H2, 0 2 , A flame.
net H 2 0 formation from decomposing CH, is zero or less than zero. We sum up the discussion of Fig. 1. It has been shown that O2 is destroyed chiefly via H atom attack just as in the Hz, O2 flame, and that no considerable net formation of COZ or of HzO occurs directly in the decay of CH4. Other CH4Flames.-Four other CH4 flames were examined and are discussed briefly. Figure 2
(13) (a) E. M . Bulewioz, C. G . James and T. M. Sugden, Proc. Roy. SOC.( L o n d o n ) ,A236,89 (1950); (b) W.E. Kaskan, Combustion d Flame, 2, 229 (1958).
Nov., 1959
CONSUMPTION O F OXYGEN MOLECULES IN HYDROCARBON FLAMES BY HYDROGEN 1837 TABL I1~
DATASHOWINQ THAT[HI I N FLAMES Is JUSTSUFFICIENT TO CONSTJME 0 2 AT THE RATEOBSERVED 2
1
Figure Reactants
3 CHI+
c
0 2
A Ha Massflow X 103,g./cm.a X sec. Flame T,O K . Pressure, cm. 107 [HI found via added D2O added Dz Other 107 [HI required by - [OZ] [&O 1 [CO 1
...
... -
...
vCzHn+--
4
...
5
...
CaHs+--
c
1.87 8 1 8.65
1.12 0.4 0 1.93
2.56 10 0 8.81
2.310 10 0 7.96
1.6V 8 1 8.4
1.88 7.5 0 5.05
4.84 17.2 0 7.26
8.33 11.33 0 3.0
3.13 4.54 0 3.2
4.50 5.56 0 4.23
1780 7
1860 14
1700 6
1860 8
1950 7
1818 6
1310 4
1500 3
1920 8
1940 3
50 80
5 4
25 20
15 10
10 6
22 33
60 5
3 5
14 8
10 7
7 5
23 7
*..
...
... 30 30 30 8
60 30 40 9
...
tCOzI[Hzl Also had 0.51 N20per mole CHI in reactants.
(1
...
... 44 50 35 9
...
*.. 6 10 4 8
...
...
Also had 0.40 N2O per mole CHI in reactants.
It may be interesting to compare our lean CzHz flame, Fig. 4, with a very lean C2H2, O2 flame probed by Fristrom and co-workers.14 Their flat flame was C2H2 3102 burnt at 7.5 cm. Hg P with burning velocity 71 cm./sec. and calculated final flame temperature of 1451°K. Ours is C2H2 4.8 O2 18 A a t 4 cm. Hg P, 90 cm./sec. burning velocity, measured final flame temperature 1300°K. At our lower pressure, the strongly luminous zone is a little thicker (-0.22 em. US. their -0.16 cm.). We agree in finding that the maximum CO occurs just about when CzHz has fallen to zero, and in placing this point within but toward the downstream edge of the luminous zone. Also we agree in finding that the maximum H2 occurs earlier in the luminous zone, about 0.1 cm. before the maximum CO, and when about 1/2 of the total fall of O2 has occurred. In both flames, H 2 0 is near its final value a t the downstream end of the luminous zone. The principal differences are: we find more residual Hz in the post flame region than they do, and we find a much slower formation of C02. These differences are probably reasonable since their flame was much leaner. Figure 4 also shows the course of HD formation and decay when a little Dz is added to the reactants. Since HD goes through a maximum, it is easy to estimate [HI when d [HD]/dt = 0 on the assumption3 that
+
+
+
-
k’[H] [Dz] = [HDI X (rate of formation of water from Ht) [Hal
where IC’ is the rate constant for H
D.
+ Dz
--t
HD
+
Figure 5 gives some results for a very rich C3H8 flame which resembles the flame described by Fig. 2 in that [HI is near the calculated concentration in the burnt gas appropriate to the equilibrium H2 = 2H; [ H I e q u i = 7 x lo-’. The flames described by Fig. 2 and 5 are the only ones in which the post flame gas contains hydrocarbons, and are also the only ones which contain just the equilibrium [HI in the post flame gas. CzHz or C3Hs flames resemble CHI flames in (14) R. M. Fristrom, W. H. Avery and C . Grunfelder, “7th Symposium (International) on Contbuation,” Butterwortha, London, 1959. p. 304,
I
I
3CH4/A
‘O2lA
I
DISTANCE FROM BURNER SURFACE.
Fig. 5.-A very rich C3Hs, Os, A flame.
that COZ appears to be formed only from the intermediate CO. If this is really so, then the observed value for the ratio [Hi01[COI/[CO2][Hz] requires the conclusion that little direct net formation of HzO occurs from these fuels either, but that H20is formed chiefly from the Hz present a t any time. Conclusion Ignoring the rough estimates of [HI entitled “other” in Table 11, we find that [HI determined via added D2 or D2O is the same within an average deviation of 30% as the [HI required if 0 2 decays solely by reaction (c), and this is true over a 20-fold change in [HI. There is little doubt that 0 2 is destroyed more by reaction (c) than in any other way. A de-
1838
R. W. KILB
struction of O2 entirely via (c), that is, no considerable reaction between 0 2 and any hydrocarbon or hydrocarbon radical at all, would be consistent with our results and with other observations on hydrocarbon flames. For it O2 reacts only with H atoms, the large amount of CO formed in CH2 flames would have to arise by reactions of 0, OH, H2O with species such as CHI, CH2, etc. But then all plausible reactions which form CO would also destroy free valences and the formation of CO and H2 from the hydrocarbon fuel should have to be considered a chain terminating process which was fed by free radicals generated in reaction (c). This view would account for the fact that flames rich enough to contain hydrocarbon in the products possess only about the equilibrium [HI in the post flame gas, while fuel lean hydrocarbon flames or either rich or lean H2 flames contain so many free radicals that [HI in the post flame gas is many times the concentration appropriate to the
Vol. 63
equilibrium H2 = 2H. It would also agree with experiments on the slow CH,, O2 reaction in static systems at 900°K. or higher, where CH, inhibits its own oxidation presumably by the destruction of radi~a1s.l~A destruction of O2 only via reaction (c) would require that reactions between 0 2 and hydrocarbon or hydrocarbon radicals, such as are presumed to occur in low temperature oxidations and in cool flames, be irrelevant to the main course of the reaction in hot flames; but many persons have believed the low temperature mechanisms to be irrelevant to hot steady flames. It must be pointed out, however, that our data are not sufficiently precise to exclude some reaction of O2 in other ways than via reaction (c). All we can claim is that (c) is more important than any other way. (15) M. Vanpee and F. Grard, “5th Symposium on Combustion,” Reinhold Publ. Corp., New York, N. Y., 1955, p. 484; D. E. Hoare and A. D. Welsh, ibid., p. 474; and references cited by these authors
THE EFFECT OF SIMULTANEOUS CROSSLINKING AND DEGRADATION ON THE INTRINSIC VISCOSITY OF A POLYMER BYR. W. KILB General Electric Research Laboratory, Schenectady, New York Received March 86, 1060
The change in intrinsic viscosity [q]is studied for a process during which a polymer is simultaneous1 degraded and crosslinked. An example of such a process is irradiation of polymers. It is possible to determine the rerative amount of degradation and crosslinking by following the change of [ q ] during the process. Qualitative agreement of theory with experiment is good. Quantitatively the method is limited to the range unity to ten for the ratio of degradations to crosslinks. outside these limits the shape of the [ q ]curve is insensitive to this ratio. It is found that the best sensitivity is obtained when [ q ]is determined in e solvents. By followin the change in osmotic and li ht scattering molecular weight for silicone irradiated by an electron source, the ratio of degrafations to crosslinks was f o u n t t o be less than 0.5.
During certain processes, polymer molecules are simultaneously crosslinked and degraded. Typical examples are irradiation and oxidation. This leads to a polymer with long chain branching and either increased or decreased molecular weight, depending on the degree of degradation. We are interested here in determining the relative amount of crosslinking and degradation from a study of the change in intrinsic viscosity of the polymer. This problem has been treated in an approximate manner by Shultz, Roth and Rathmann.’ Although most of their results are qualitatively correct, their quantitative calculations are inexact because of their use of the Stockmayer and Fixman2 approximation for the effect of branching on the intrinsic viscosity of a polymer. Recently Zimm and Kilb* have shown that previous theories seriously overestimate the effect of branching on intrinsic viscosity, and proposed a new theory which is in good agreement with the available data. We propose to use this theory in the present study. The quantitative results of Shultz, et aE., also suffer to some extent from the lack of use of a definite molecular weight distribution. (1) A. R. Shultz, P. I. Roth and G. B. Rathmann, J. Polymer Sci., 22, 495 (1956). (2) W. H. Stookmayer and M. Fixrnan, Ann. N . Y . Acad. Sci., 61, 334 (1953). (3) B. H. Zimm and R. W. Kilb, J. Polymer Sci., 87, 19 (1959).
The problem of determining the relative amount of crosslinking and degradation has also been treated by C h a r l e ~ b y . ~His method involves following the amount of gel produced during the process. It has perhaps not been sufficiently forcibly pointed out in previous studies that the quantitative calculations are rather sensitive to the assumed initial molecular weight distribution. Consequently, in the application of the calculations, i t is necessary to determine if the experimental polymer actually has the assumed distribution. If this is not the case, the results must be viewed with some scepticism. I n this paper we shall make the assumptions: (1) the scissions are directly proportional to the crosslinks throughout the process and their distribution is “random”; (2) the crosslinks are tetrafunctional, i.e., four branches radiate out from the crosslinked site; (3) the initial molecular weight distribution is assumed to be the “most probable” distribution (see below), On the basis of these assumptions, we may combine the results of Zimm and Kilb with the distribution function given by Stockmayer5 to cal(4) A. Charlesby, Proc. Roy. Soc. (London), A224, 120 (1954). (5) W. H. Stookrnayer, J. Chem. Phys., 11, 45 (1943); 12, 125 (1944).
