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Kinetic studies of ionization and recombination processes of metallic additives to flames
KINETIC STUDIES OF IONIZATION AND RECOMBINATION PROCESSES OF METALLIC ADDITIVES TO FLAMES D. E. JENSEN* AND P. J. PADLEYt
Department of Physical Chemistry, University of Cambridge, Cambridge, England Values of the recombination constants of alkali metal ions with electrons in H2-O2-N2 flames are calculated from measured rate constants for the reverse ionization step. These values are compared with similar, but measured recombination constants for certain other metals in the same H2-O2-N2 flames (to which have been added 1% proportions of acetylene). The good correlation obtained lends strong support to the view that the processes under study are those represented by the two reactions
Me + -1- e- --}-M ~ Me* "-I- M, where Me* represents an electronically excited metal atom and M a bulk flame-gas molecule. For chromium, an additional heterogeneous process ivolving involatile oxide particles may also be involved.
The ionization of alkali metals A in the burned gases of pre-mixed H2-N2-O2 flames at atmospheric pressure has recently received further attention? ,2 Detailed data obtained for all five metals 1 have been shown to be consistent only with a "slow" (rl/2 ~ 0.1 to 1 msec under the experimental conditions used) thermal ionization represented b y the reaction
discrepancy can be explained in terms of participation of excited electronic states of A in the ionization process. Such information as is available on the reverse of Process (I) has been inferred from measurements made on flames containing hydrocarbon additives; in such flames, species in the reaction zone can make significant contributions to production of A+, apparently through chargeexchange processes such as 2.5.
A q- M---~ A+ q- e - -q- M,
A -t- S+---+ A+ nt- S (or fragments).
Introduction
(I)
where M is a general (and, therefore, almost always a polyatomic and neutral) flame-gas molecule, and not with a process involving A and one of the species e-, OH and H20. The activation energies of Process (I) for A = Na, K, Rb, and Cs, were found to be very close to the corresponding ionization potentials, within the limits of experimental error, and the associated cross sections were found to be nearly 1000 times larger than those predicted on the basis of "simple" bimolecular collision theory. These findings are in agreement with those of Hollander, Kalff, and Alkemade, ~ who have studied ionization of Na, K, and Cs in C0-02-N2 flames. Hollander4 has suggested t h a t the cross-section Present addresses: * AeroChem Research Lab. Inc., P. O. Box 12, Princeton, N. J. t Department of Chemistry, University College,
Swansea.
Here S+ is a "natural" flame ion. In this way, an above-equilibrium concentration of A + (which persists into that region of the burned gases in which ionization of additives can be studied kinetically) may be produced, but the effect is rather too small to make practicable the reliable measurement of the rate constant for the recombination step. However, for certain other metals, with higher ionization potentials, ratios of observed to equilibrium ion concentrations higher than tenfold can be obtained, 2,5-~ and over-all rates of processes such as Pb + -q- e----~ Pb
(III)
can be measured. I t is thus possible to compare directly measured pseudo-second-order rate constants kr of processes like ( I I I ) with the corresponding constants kr of the process A+'q- e-'--~A,
351
(II)
CHARGED SPECIES IN COMBUSTION PROCESSES
352
TABLE I Comparison of recombination constants
T, ~
Metal
kr (HS)
k, (SW)
Li Li Na K Rb Cs Pb Pb Mn Mn Cr Cr
--X X -)< X ------
1 . 4 X 10 -s
2368 2475
2250 2250 2250 2250 2250 2368 2250 2368 2250 2368
6.4 3.5 4.5 6.0
------9.0 X 10-9 -2.4 X 10-* -1.8 X 10-8
10-9 10-9 10-9 10-~
E in kcal/mole, kr in cm* molecule-1 sec-'.
M i c r o w a v e Cavity R e s o n a n c e T h e o r y The theory of the microwave cavity resonance method of measuring electron concentrations in flames was discussed briefly in a previous paper) The value of re-~ provided b y flame additives was related to the currents I and I0 (taken from the output loop of the cavity and rectified), measured in the presence and absence, respectively, of additive, through the equation :/2 - -
1 =
Cre-],
(1)
where C is the "cavity constant." The validity of this equation in these systems has recently been questioned, and two implied assumptions made in previous work should perhaps be pointed out here. The Q factor of a resonance cavity is defined by the equation
Q
=
wW,/PL,
E (this work)
--
9.0 8.5 6.5 5.5 8.5 6.5
X X X X X X -7.5 X --
10-9 10-9 10-9 10-~ 10-9 10-g
--7• --64-4 --44-4 --34-5 --84-4
10-9
--6~-4
* 2 . 6 X 10 -s
--
* Rough guide only--kr is slightly composition dependent.
calculated from the known ionization rate constants for Process (I) and the corresponding Saha equilibrium constant. Selected values of these calculated rate constants for the alkali metals are shown in Table I. Those found experimentally for certain other metals were obtained as described below.
([o/I)
k, (this work)
(2)
where W, is the peak energy storage in the electromagnetic field of the resonator and Pz the time-
averaged power loss in the resonator at its resonance frequency r Gc/sec). If Q0 and Q are the Q factors of the resonator in the absence and presence of electrons in the flame, respectively, it can be shown7 that
Q o / Q - 1 = E(a~o/oo):/~ - 1-] "F (GaQe/w), (3) where ~ is the conductivity of the flame (assumed uniform in the section of flame gases sampled) and G is a constant dependent upon the material and shape of the cavity. Measurements made by means of a 10-cm-band wavemeter revealed that, when Qo/Q ~ 5, the frequency shift (wo -- o:) was ~ 3 Mc/sec, and that (3) may therefore be reduced without appreciable error to
( G o / Q - 1) = GaQo/wo.
(4)
This analysis justifies the first implicit assumption. Since ~ is directly proportional to Ee-3, Eq. (4) becomes
Q o / Q - 1 = C['e-].
(5)
Provided that the coupling into and out of the cavity is light (a condition satisfied in the present work, 7 and implicitly assumed in Ref. 5), I is proportional to Q2, and Eq. (5) thus reduces to (1). The constant C, a function of electron-neutral molecule collision frequency, is determined through the usual practice of seeding flames with known quantities of caesium. 5,7
KINETIC STUDIES
353
Measurement of Electron Concentrations [e-] Both apparatus and procedure have been described in detail before.~,5,~ Observations were made on [ e - ] when about 1013 atoms/cm3 (free and combined) of Pb, Mn, or Cr were introduced into atmospheric pressure I-Iz-O-N2 flames to which 1%-by-volume proportions of acetylene had been added. For each metal, ['e-] was studied in the height range 1.0-3.0 cm above the reaction zone (in which range the temperature is effectively constant) in flames with final temperatures in the range 1815~ to 2385~ At 1815~ and 2385~ a height-difference of 1 cm corresponded to a time-difference of 0.6 and 0.34 msec, respectively.
Results Plots of 1/[-e-J versus time after leaving the reaction zone are all satisfactory straight lines for Pb, Mn, and Cr; typical results for manganese are shown in Fig. 1. Sample values of k~ for these metals, obtained from the slopes of such plots, are shown in Table I. Also shown in Table I are values of k~ measured by Soundy and Williams6 ['k~(SW)-], who used a probe technique in otherwise similar systems, and values of b,
2D
I
/8
I
I
I
/.4 2"2 3.0 /-/eight obove re~cfion z o n e Fro. 1. Second-order electron decay; typical results for Mn, in three flames. Unb~ned Hr-Oz-N2 volume ratios are indicated against each plot.
,,.
9
o./t-
^-L~
0.21
o
o.5
SoCbm. 9
I 4"0
I 4.5
I
/
5"0
/0 4 T -t
Fro. 2. Variation of k,/~Yl] with flame temperature for Na, K, Rb, and Cs. O, calculated from "optical" experimental data (Ref. 1); Q, calculated from "cavity" experimental data (Ref. 1). The slightly different slope for Cs should be ignored.
obtained by Hayhurst and Sugden 2 ['k,(HS)]. The temperature variation of kr being small (see below), it is evident not only that the agreement between the independent sets of results is satisfactory, but also that values of kr for the alkali metals inferred from measurements on Process (I) are strikingly similar to values of k, measured directly for chromium, lead, and manganese. This comparison of rate constants measured with and without 1% of acetylene added to a flame is fair, for addition of this proportion of acetylene to the unburned gases of a fuel-rich H~0~-N~ flame has little effect upon the temperature and composition of the burned gases, s The temperature dependence of k~/['M-] for the alkali metals is depicted in one of several possible ways in Fig. 2. If straight lines are drawn through the sets of points for Cs, Rb, K, and Na, the slopes of these particular plots then correspond to "activation energies" E o f - - 3 4 - 5, 7 - 4 4 - 4 , - - 6 4 - 4 a n d - - 7 4 - 4 kcal/mole, respectively {where E is defined to be -- Rd/d(T -1) In k,/[M~; all M are taken to be equally efficient in causing ionization of A }. Corresponding plots for Pb and Mn are very similar [-see Fig. 3(b) for Pb-], the values of E being --8 4- 4 and --6 4- 4 kcal/mole, respectively. For none of these metals is there any measurable dependence of k, upon flame-gas composition at a given temperature. Figure 3(a) shows an alternative way of depicting the temperature dependence of k,/['M]. For all the alkali metals, and for Pb and Mn, k~/[M'] is proportional to T -1"~:1, within the limits of experimental error. (Computed factors for the alkali metals, T-~-35, T -2.5~, T -1"~4, and T +~ for Na, Rb, and Ca, respectively.)
354
CHARGED SPECIES IN COMBUSTION PROCESSES as[
,
,
,]
,
important st lower temperatures cannot, h o w be ruled out, but even in this event it would not be possible to account for the observed variation of k, with ECr]~.
,
ever,
o.2s
o.~2
Ioq~o (Io-' r)
o.3e
4-e
5.2
~-8
Io" r"
FIG. 3. Variation of k,/[M'] with flame temperature for Pb; direct experimental data.
Results
for C h r o m i u m
Although plots of 1/[e-J versus time for chromium are satisfactory straight lines, there is for this metal a small but definite variation of kr with isothermal composition. This is illustrated in Fig. 4, which shows that k~ is greater in flames of near-stoichiometric composition than in those which are fuel-rich but have the same temperature. Moreover,/c~ for Cr seems to be dependent upon the total (combined, ionized or free) concentration of Cr, I-Crib, introduced into the flame; for example, when [CrJr in a flame of unburned gas volume ratios H~/O~/N2 3.5/1/3 was reduced from 1.5 X 10la atoms/cm 8 to 6 X 10~e atoms/cm 3, the value of kr fell by a factor of approximately 2. This behavior is again in contrast to that observed with Pb or Mn. The following explanations have been considered: =
(1) Formation of CrOH+
(2) Influence of Solid Particles In the temperature range under consideration, atomic Cr accounts for only a small proportion ( < 1 0 % ) of the total chromium added; the behavior of the free Cr-atom concentration as flame temperature and composition are changed indicates that the bulk of the chromium added is present in the form of oxide, s When [Cr]~ takes the comparatively high value of 10I3 atoms/cm 3, the flames are clearly streaked with heavy involatile particles which must consist of many molecular units, and the variation of the intensity of emission from these particles with flame temperature and composition s suggests not only that these particles consist of chromium oxide, but also that the bulk of the chromium added is in fact precipitated. When [ C r ~ is increased, or when the isothermal flame composition is changed from fuel-rich to near-stoichiometric, there will be more of these particles. It is under just these circumstances that the value of It, for Cr is increased, and heterogeneous contributions to kr are therefore to be considered. The rate of electron removal may be represented by
dEe-Vdt
=
Ee--I{ECr+-I(k,EM']+ ks
If the equilibrium Cr+ ~ H20 ~ - CrOH + -~ H were established, then
(6)
+
d[e-]/dt = --k/['Cr+][e - ] - kr"[CrOH+][-e-~.
[
With [-Cr+-] q- rCrOH +'] --- [e-l, and ['e--] = ['e-]0 at time t = 0 (i.e., in the reaction zone), kr in this event will be given by
.tpl%
o
, ,
(kr' -4- k/'~bo)/(1 + ~o),
where 4,0 = [-CrOH+]/[-Cr+] in the reaction zone. However, through use of a quadrupole mass spectrometer (kindly made available by Dr. A. N. Hayhurst), it was shown that ~bQis only 1/800 in a flame of composition 4/1/4 (2020~ Thus, the improbably high value of kr" ~ 10-5 em3 molecule-1 sec-1 would have to be adopted in order for CrOH + to be kinetically important in the recombination process. (Similar considerations applied to manganese and lead also lead to the conclusion that only the atomic ion is important.) The possibility of contributions from other ions (e.g., hydrated ions~) being
0.2 I
I
4,2
/04
I 4 "6 T -/
I
I 5"0
FIG. 4. Variation of k, with flame temperature and composition for Cr. Lines are drawn through points obtained from flames with the same O2/N~ ratio (1/3 or 1/4); along each line, H2/O~ varies from 2.8 to 4.0.
KINETIC STUDIES In Eq. (6), Pn represents a neutral solid particle and P~ an ionized one. The second term on the right-hand side of this equation is probably negligible, for, although the cross section in k2 will be larger than that in/c~, [-P,] ~ [M.]. The last term allows for the possibility of P being charged and might in some circumstances be comparable in magnitude with the first term. The electron concentration may also be reduced if the work function of P is high. Evidence which has so far been obtained on the nature of any charge on P (through application of high, ~ 1 kV/cm, electric fields 9) has not yet proved conclusive. Also the "brightness temperature" of the particles is almost certainly not constant s in the region of kinetic study. Investigations are being continued at Swansea, with the viewpoint of establishing the dissociation energy, size, and "work function" of the particles.
Mechanical Scheme for Ionization and Recombination For three-body electron-ion recombination with polyatomic molecules as third bodies, modified J. J. Thomson theory 1~expresses k~ as kr -~ (8kT/zcme)l/2( 47rro3) (3y)-lk.
(7)
Here r0 = 2e~(3kT) -1 and y ,,~ (NQd) -1, where m~ and e are the electronic mass and charge, respectively, N is the number density of the gas and Qd the diffusion cross section for electrons in the gas. With Qd ~ 30 A.U. 2 (Ref. 11), and k~ ---- 6 X 10-9 cm3 mo]ecule-1 sec-1, the value of k (a parameter which reflects the efficiency of exchange of energy between electron and third body, and which is greater than the "elastic" term [-2 X mass of electron/mass of third body) is calculated to be about 0.02. This value is of the same order of magnitude as values obtained from experiments on low-energy electrons in drifttubes when polyatomic molecules are present? ~ The observed variation of /c, with temperature (k, oo T-~.%t=l) is also not inconsistent with Eq. (7), in view of the large experimental uncertainties. Derivation of Eq. (7) involves the assumption that energy ~ k T is transferred from electron to third body on collision. The recombination step suggested is therefore Me + + e- + M ----)Me* + M
(IV)
where Me* represents any metal to which Process (IV) applies, electronically excited to an energy level between (V -- kT) and V, the
355
ionization potential. The reverse of (IV) has a rate constant k* which can be written in the form k* = ~'a2Me*_M(SkT/~Me--M) 1/2, where is a factor rather less than unity. A large number of bound electronic states do have energies between V -- k T and V, and ionization of atoms in these states should occur at most collisions with bulk gas molecules. The measured second-order rate constant k~ for the ionization process (I) will then be given approximately by k*[Me*]/[Me]tot~l. Since k~ was obviously measured under conditions where [Me +] < [-Me+]eq, the ionization "leak" must cause [Me*] • [ ' M e * ~ . Thus l~ <<,k * ( A / f ) exp ( - - V / R T ) ,
(8)
where A is the sum of statistical weights over levels in the energy band (V -- kT) to V, and f is the statistical weight of the ground electronic state. The apparently high cross sections for the ionization step predicted by applications of simple collision theory to the ground state alone might therefore be interpreted in terms of Eq. (8), through appropriate selection of A (cf. also Ref. 4). Three general points arise from the above considerations. In the first place, in order to express the above argument in a detailed theory (which could be developed on lines similar to those along which theoretical studies of diatemic molecule dissociation/atom recombination are proceeding13), knowledge of specific interactions between particular excited atomic states and molecular vibration states would be necessary. Second, caution should be exercised when use is made of rate constants given for Processes (I} and ( I I I ) at reduced pressures, where radiation depopulation of excited electronic states of atoms is likely to produce changes in ionization rates. Third, no results so far obtained have suggeste d any departures from the rate-quotient law; indeed, the self-consistency and simplicity of the ionization and recombination data imply steadystate population of electronic levels of Me in the region of kinetic measurements from whichever side equilibrium is approached, and therefore indicate that this law is in fact satisfied in the height range in which kinetic measurements were made.
ACKNOWLEDGMENTS
The authors wish to thank Prof. T. M. Sugden, Dr. E. M. Bulewicz, Dr. A. N. Hayhurst, Mr. N. Telford and Mr. H. Williams for helpful comments during the course of this work.
356
CHARGED SPECIES IN COMBUSTION PROCESSES REFERENCES
1. 2.
3. 4. 5.
6.
JENSEN, D. E. AND PADI~EY, P. J.: Trans. Faraday Soc. 62, 2132, 2140 (1966). HXYHURST,A. N. AND SUGDEN,T. M.: IUPAC Meeting on Plasmas, (two papers), Moscow, 1965. ALKEMADE, C. T. J., HOLLANDER, T., AND KALFF, P. F.: J. Chem. Phys. 39, 2558 (1963). HOLLANDER, T. : Thesis, Utrecht, 1964. PADL~Y,P. J. AND SUODEN,T. M. : Eighth Symposium (International) on Combustion, Williams and Wilkins, p. 164, 1962. SGUNDY,R. C. ANDWILLIAMS,H., 26th Meeting
7. 8. 9. 10.
11. 12.
13.
of Propulsion and Energetics Panel, AGARD, Pisa, Italy, September 6-9, 1965. JENSEN, D. n.: Thesis, Cambridge, 1965. PADLEY, P. J.: Thesis, Cambridge, 1959. KELLY, R. ANDPADLEY, P. J. : Unpublished data. MASSEY, H. S. W. AND BURHOP, E. H. S.: Electronic and Ionic Impact Phenomena, Chaps. IV, X, Clarendon Press, 1952. BULEWlCZ, E. M.: J. Chem. Phys. 36, 385 (1962). SCHOFIELD, K.: Tenth Symposium (International) on Combustion, p. 603, The Combustion Institute, 1965. KOLKER, H. J.: J. Chem. Phys./e~, 582 (1966).
COMMENTS Dr. T. Hollander (State University of Utrecht): P. J. Kalff, C. T. J. Alkemade and I have measured ionization and recombination rate coefficients for the alkali metals in CO/02/N2 and CO/O2/Ar flames at atmospheric pressure.~.~ The temperatures ranged from 2100~ to 2500~ We proposed as an ionization and recombination mechanism the following reaction kl MeWM~Me I0-1
+~e-
WM,
(I)
Me = metal atom; M = flame-gas molecule. Other reaction mechanisms were ruled out: a. Electron collisions leading to ionization were unimportant for when [e-] was varied by a factor of I000, no influence on the reaction rate was found. (I-A] means content or concentration of species A.) Afterward, calculations showed that this could be understood completely. b. Reaction involving hydrates Me -t- H~O ~- (Me + H20) ~ e --* Me + W e W H20 (II) could be ruled out, since we have flames almost without H~O ("dry" CO flames). The reaction now suggested and affirmed by Padley rEq. (1)] is likely the predominant one. We made certain that formation of metal hydroxides played no part under our flame conditions. We found with Na, K, and Cs, activation energies which correspond within a few per cent to the ionization energies. We are pleased that Padley and Jensen found the same result now, and that they derived additional chemical evidence for this outcome. It should be noted that the ionization rates found
by us are independent of Me, but are directly proportional to M. Diatomic molecules proved to be very effective in ionizing the metals, atoms (like At) being almost not effective. Padley and Jensen report the same result now, making certain that Reaction (I) will be the predominant one. Recent measurements performed in our group by Dr. P. J. Kalff revealed that the activation energy for the ionization of Sr in the CO flame again equals the ionization energy. The ionization rates found are about a factor of 10 lower than those attained with sodium. The question of the large cross sections for ionization derived from our work and Padley's can be further investigated according to our suggestion that the ionization also takes place from excited atomic levels and not only from the ground state of the atom. We are starting measurements for confirming this mechanism in further detail. We note that our results (rate coefficients, etc.) obtained with Na and K agree fairly well with those obtained by Schofield, Sugden, and Jensen and Padley. Finally, we are initiating ionization measurements in H2/O2/N2 flames, in order to be able to compare these results with our CO results and the results in the H2 flames obtained by Sugden, Padley, et al.
References 1. Kalff, P. J., Alkemade, C. T. J., and Hollander, T.: J. Chem. Phys. 39, 2558 (1963). 2. Hollander, T.: Thesis, Utrecht, 1964.
Mr. B. Brown (Hercules Inc.): How can the ionization rate be 1000 times higher from excited states, yet the activation energy is the same as that from the ground state?
KINETIC STUDIES Dr. P. J. Padley: I t should first be observed that the experimental evidence for the reality of the discrepancy alluded to is now very strong. Its precise extent is not known, because we had to assume that all bulk flame-gas molecules are equally efficient in causing ionization of the alkali metal. This may not be the case, and indeed very recent work ~ shows that the quenching cross sections of sodium D-line radiation (for example) by H20, H2, and N2 are 0.5 A ~, 2.9 A 2, and 7.0 A ~, respectively, may point in this direction. However, provided at least H2 and N2 are approximately equally efficient, and the effect of H20 not entirely negligible, none of our principal calculations will be affected, since the slopes of the smooth, Arrhenius-type plots can still be interpreted in terms of the ionization potential of the metal. It should, perhaps, not go unnoticed that, according to us, the measured cross sections for all five alkali metals are, to within a factor of 2, the same. 2 A question which our paper poses rather than answers, as does Hollander's thesis (Utrecht, 1964), is how best to allow for participation of excited electronic states of the alkali metal atom. The answer to Brown's question might be that atoms in a large number of effectively thermally populated, lower electronic levels (those ca. k T below the ionization potential) are being elevated to the ionization potential by collision with flame-gas molecules, which themselves possess effectively thermally distributed energy. There is little available experimental evidence which can usefully comment on this, but it should perhaps be observed that the upper states of the first resonance doublets, at least, are known to be thermally populated for all five alkali metals. Also, for sodium at least, this same critical upper state does not appear to be a population bottleneck for ionization, for if sodium D-line radiation is focussed onto a flame containing sodium vapor, under conditions such that the upper state is thereby overpopulated, then there is no detectable effect on the rate of ionization, a All this evidence, it should be emphasized, is in atmospheric-pressure flames, in which radiation depopulation problems can be ignored. References 1. Jenkins, D. R.: Proc. Roy. See. (London) A293, 493 (1966). 2. Jensen, D. E. and Padley, P. J.: Trans. Faraday Soe. 62, 2140 (1966). 3. Padley, P. J.: 26th A G A R D meeting, Pisa, Italy, 1965. Dr. D. E. Jensen: One might further discuss Brown's question by writing down two extreme situations. In the first, represented according to
357
the notation of the paper by Me (ground electronic state) K* k* ~- M e * ~ M e + + e - ,
(i)
each excited electronic-state population is governed by the Boltzmann equation. In the second, represented by Me (ground and lower excited electronic states) k' K' --* Me* ~- Me + + e-
(II)
(where k' is a compound coefficient containing contributions from many states), the rate of ionization is governed entirely by the rate of population of excited electronic states close to the ionization potential. In (I), the high pre-exponential factor in the ionization rate constants is represented as arising from a high statistical weight of the species Me*. In (II), this factor arises from summation of statistical weights of ground and lower (energy < V - kT) excited electronic states. The treatment of Me* as a distinct chemical species is, of course, quite artifical, and is introduced only for the sake of argument. In practice, the ionization process must be represented by a scheme intermediate between (I) and (II), for the colllsional rates of population of excited electronic levels close to the ionization potential will clearly be of the same order of magnitude as collisional rates of ionization of species in these levels. The comments mad~ in the paper simply suggest that scheme (I) is a closer approximation to the true situation than (II) at atmospheric pressure. A proper theory would take into account the detailed rates of population and depopulation of each excited electronic state occurring through radiative as well as through collisional processes. Comparison with the theory of dissociationrecombination reactions for diatomic molecule-free atom systems suggests that different conditions of pressure and temperature probably result in quite different distributions of atoms in electronic levels, both close to and far from equilibrium; energy differences between possible "population bottlenecks" and ionization potentials, for example, may vary rather widely.
Dr. L. F. Phillips (University of Canterbury, Christchurch): Has Dr. Padley considered using a lamp emitting resonance lines of Cs + to follow (Cs +) by light adsorption?
358
C H A R G E D S P E C I E S IN C O M B U S T I O N PROCESSES
Dr. P. J. Padley: Insofar as cesium is nearly fully ionized in the flames we have been using, measurements on ECs +] would suffer from the same limitation as measurements on r e - ] from t h e viewpoint of measuring rate constants of ionization of cesium. On the other hand, with a Cs + resonance lamp, it should be possible to make measurements m u c h nearer the reaction zone t h a n is possible b y t h e cavity method, and this might therefore be of value if more precise values of the
ionization rate constant of cesium t h a n those reported b y us are required.
Dr. L. F. Phillips: W h a t are the values obtained for the dissociation energies of alkali hydroxides? Dr. P. J. Padley: The values of AH0~ for the process AOH(g) --~ A(g) A- OH(g) axe 101 ~ 2, 77 =t= 4, 81 =i= 2, 83 =t= 2, and 91 =i= 3 kcal/mole for A = Li, Na, K, Rb, and Cs, respectively.
Department of Physical Chemistry, University of Cambridge, Cambridge, England Values of the recombination constants of alkali metal ions with electrons in H2-O2-N2 flames are calculated from measured rate constants for the reverse ionization step. These values are compared with similar, but measured recombination constants for certain other metals in the same H2-O2-N2 flames (to which have been added 1% proportions of acetylene). The good correlation obtained lends strong support to the view that the processes under study are those represented by the two reactions
Me + -1- e- --}-M ~ Me* "-I- M, where Me* represents an electronically excited metal atom and M a bulk flame-gas molecule. For chromium, an additional heterogeneous process ivolving involatile oxide particles may also be involved.
The ionization of alkali metals A in the burned gases of pre-mixed H2-N2-O2 flames at atmospheric pressure has recently received further attention? ,2 Detailed data obtained for all five metals 1 have been shown to be consistent only with a "slow" (rl/2 ~ 0.1 to 1 msec under the experimental conditions used) thermal ionization represented b y the reaction
discrepancy can be explained in terms of participation of excited electronic states of A in the ionization process. Such information as is available on the reverse of Process (I) has been inferred from measurements made on flames containing hydrocarbon additives; in such flames, species in the reaction zone can make significant contributions to production of A+, apparently through chargeexchange processes such as 2.5.
A q- M---~ A+ q- e - -q- M,
A -t- S+---+ A+ nt- S (or fragments).
Introduction
(I)
where M is a general (and, therefore, almost always a polyatomic and neutral) flame-gas molecule, and not with a process involving A and one of the species e-, OH and H20. The activation energies of Process (I) for A = Na, K, Rb, and Cs, were found to be very close to the corresponding ionization potentials, within the limits of experimental error, and the associated cross sections were found to be nearly 1000 times larger than those predicted on the basis of "simple" bimolecular collision theory. These findings are in agreement with those of Hollander, Kalff, and Alkemade, ~ who have studied ionization of Na, K, and Cs in C0-02-N2 flames. Hollander4 has suggested t h a t the cross-section Present addresses: * AeroChem Research Lab. Inc., P. O. Box 12, Princeton, N. J. t Department of Chemistry, University College,
Swansea.
Here S+ is a "natural" flame ion. In this way, an above-equilibrium concentration of A + (which persists into that region of the burned gases in which ionization of additives can be studied kinetically) may be produced, but the effect is rather too small to make practicable the reliable measurement of the rate constant for the recombination step. However, for certain other metals, with higher ionization potentials, ratios of observed to equilibrium ion concentrations higher than tenfold can be obtained, 2,5-~ and over-all rates of processes such as Pb + -q- e----~ Pb
(III)
can be measured. I t is thus possible to compare directly measured pseudo-second-order rate constants kr of processes like ( I I I ) with the corresponding constants kr of the process A+'q- e-'--~A,
351
(II)
CHARGED SPECIES IN COMBUSTION PROCESSES
352
TABLE I Comparison of recombination constants
T, ~
Metal
kr (HS)
k, (SW)
Li Li Na K Rb Cs Pb Pb Mn Mn Cr Cr
--X X -)< X ------
1 . 4 X 10 -s
2368 2475
2250 2250 2250 2250 2250 2368 2250 2368 2250 2368
6.4 3.5 4.5 6.0
------9.0 X 10-9 -2.4 X 10-* -1.8 X 10-8
10-9 10-9 10-9 10-~
E in kcal/mole, kr in cm* molecule-1 sec-'.
M i c r o w a v e Cavity R e s o n a n c e T h e o r y The theory of the microwave cavity resonance method of measuring electron concentrations in flames was discussed briefly in a previous paper) The value of re-~ provided b y flame additives was related to the currents I and I0 (taken from the output loop of the cavity and rectified), measured in the presence and absence, respectively, of additive, through the equation :/2 - -
1 =
Cre-],
(1)
where C is the "cavity constant." The validity of this equation in these systems has recently been questioned, and two implied assumptions made in previous work should perhaps be pointed out here. The Q factor of a resonance cavity is defined by the equation
Q
=
wW,/PL,
E (this work)
--
9.0 8.5 6.5 5.5 8.5 6.5
X X X X X X -7.5 X --
10-9 10-9 10-9 10-~ 10-9 10-g
--7• --64-4 --44-4 --34-5 --84-4
10-9
--6~-4
* 2 . 6 X 10 -s
--
* Rough guide only--kr is slightly composition dependent.
calculated from the known ionization rate constants for Process (I) and the corresponding Saha equilibrium constant. Selected values of these calculated rate constants for the alkali metals are shown in Table I. Those found experimentally for certain other metals were obtained as described below.
([o/I)
k, (this work)
(2)
where W, is the peak energy storage in the electromagnetic field of the resonator and Pz the time-
averaged power loss in the resonator at its resonance frequency r Gc/sec). If Q0 and Q are the Q factors of the resonator in the absence and presence of electrons in the flame, respectively, it can be shown7 that
Q o / Q - 1 = E(a~o/oo):/~ - 1-] "F (GaQe/w), (3) where ~ is the conductivity of the flame (assumed uniform in the section of flame gases sampled) and G is a constant dependent upon the material and shape of the cavity. Measurements made by means of a 10-cm-band wavemeter revealed that, when Qo/Q ~ 5, the frequency shift (wo -- o:) was ~ 3 Mc/sec, and that (3) may therefore be reduced without appreciable error to
( G o / Q - 1) = GaQo/wo.
(4)
This analysis justifies the first implicit assumption. Since ~ is directly proportional to Ee-3, Eq. (4) becomes
Q o / Q - 1 = C['e-].
(5)
Provided that the coupling into and out of the cavity is light (a condition satisfied in the present work, 7 and implicitly assumed in Ref. 5), I is proportional to Q2, and Eq. (5) thus reduces to (1). The constant C, a function of electron-neutral molecule collision frequency, is determined through the usual practice of seeding flames with known quantities of caesium. 5,7
KINETIC STUDIES
353
Measurement of Electron Concentrations [e-] Both apparatus and procedure have been described in detail before.~,5,~ Observations were made on [ e - ] when about 1013 atoms/cm3 (free and combined) of Pb, Mn, or Cr were introduced into atmospheric pressure I-Iz-O-N2 flames to which 1%-by-volume proportions of acetylene had been added. For each metal, ['e-] was studied in the height range 1.0-3.0 cm above the reaction zone (in which range the temperature is effectively constant) in flames with final temperatures in the range 1815~ to 2385~ At 1815~ and 2385~ a height-difference of 1 cm corresponded to a time-difference of 0.6 and 0.34 msec, respectively.
Results Plots of 1/[-e-J versus time after leaving the reaction zone are all satisfactory straight lines for Pb, Mn, and Cr; typical results for manganese are shown in Fig. 1. Sample values of k~ for these metals, obtained from the slopes of such plots, are shown in Table I. Also shown in Table I are values of k~ measured by Soundy and Williams6 ['k~(SW)-], who used a probe technique in otherwise similar systems, and values of b,
2D
I
/8
I
I
I
/.4 2"2 3.0 /-/eight obove re~cfion z o n e Fro. 1. Second-order electron decay; typical results for Mn, in three flames. Unb~ned Hr-Oz-N2 volume ratios are indicated against each plot.
,,.
9
o./t-
^-L~
0.21
o
o.5
SoCbm. 9
I 4"0
I 4.5
I
/
5"0
/0 4 T -t
Fro. 2. Variation of k,/~Yl] with flame temperature for Na, K, Rb, and Cs. O, calculated from "optical" experimental data (Ref. 1); Q, calculated from "cavity" experimental data (Ref. 1). The slightly different slope for Cs should be ignored.
obtained by Hayhurst and Sugden 2 ['k,(HS)]. The temperature variation of kr being small (see below), it is evident not only that the agreement between the independent sets of results is satisfactory, but also that values of kr for the alkali metals inferred from measurements on Process (I) are strikingly similar to values of k, measured directly for chromium, lead, and manganese. This comparison of rate constants measured with and without 1% of acetylene added to a flame is fair, for addition of this proportion of acetylene to the unburned gases of a fuel-rich H~0~-N~ flame has little effect upon the temperature and composition of the burned gases, s The temperature dependence of k~/['M-] for the alkali metals is depicted in one of several possible ways in Fig. 2. If straight lines are drawn through the sets of points for Cs, Rb, K, and Na, the slopes of these particular plots then correspond to "activation energies" E o f - - 3 4 - 5, 7 - 4 4 - 4 , - - 6 4 - 4 a n d - - 7 4 - 4 kcal/mole, respectively {where E is defined to be -- Rd/d(T -1) In k,/[M~; all M are taken to be equally efficient in causing ionization of A }. Corresponding plots for Pb and Mn are very similar [-see Fig. 3(b) for Pb-], the values of E being --8 4- 4 and --6 4- 4 kcal/mole, respectively. For none of these metals is there any measurable dependence of k, upon flame-gas composition at a given temperature. Figure 3(a) shows an alternative way of depicting the temperature dependence of k,/['M]. For all the alkali metals, and for Pb and Mn, k~/[M'] is proportional to T -1"~:1, within the limits of experimental error. (Computed factors for the alkali metals, T-~-35, T -2.5~, T -1"~4, and T +~ for Na, Rb, and Ca, respectively.)
354
CHARGED SPECIES IN COMBUSTION PROCESSES as[
,
,
,]
,
important st lower temperatures cannot, h o w be ruled out, but even in this event it would not be possible to account for the observed variation of k, with ECr]~.
,
ever,
o.2s
o.~2
Ioq~o (Io-' r)
o.3e
4-e
5.2
~-8
Io" r"
FIG. 3. Variation of k,/[M'] with flame temperature for Pb; direct experimental data.
Results
for C h r o m i u m
Although plots of 1/[e-J versus time for chromium are satisfactory straight lines, there is for this metal a small but definite variation of kr with isothermal composition. This is illustrated in Fig. 4, which shows that k~ is greater in flames of near-stoichiometric composition than in those which are fuel-rich but have the same temperature. Moreover,/c~ for Cr seems to be dependent upon the total (combined, ionized or free) concentration of Cr, I-Crib, introduced into the flame; for example, when [CrJr in a flame of unburned gas volume ratios H~/O~/N2 3.5/1/3 was reduced from 1.5 X 10la atoms/cm 8 to 6 X 10~e atoms/cm 3, the value of kr fell by a factor of approximately 2. This behavior is again in contrast to that observed with Pb or Mn. The following explanations have been considered: =
(1) Formation of CrOH+
(2) Influence of Solid Particles In the temperature range under consideration, atomic Cr accounts for only a small proportion ( < 1 0 % ) of the total chromium added; the behavior of the free Cr-atom concentration as flame temperature and composition are changed indicates that the bulk of the chromium added is present in the form of oxide, s When [Cr]~ takes the comparatively high value of 10I3 atoms/cm 3, the flames are clearly streaked with heavy involatile particles which must consist of many molecular units, and the variation of the intensity of emission from these particles with flame temperature and composition s suggests not only that these particles consist of chromium oxide, but also that the bulk of the chromium added is in fact precipitated. When [ C r ~ is increased, or when the isothermal flame composition is changed from fuel-rich to near-stoichiometric, there will be more of these particles. It is under just these circumstances that the value of It, for Cr is increased, and heterogeneous contributions to kr are therefore to be considered. The rate of electron removal may be represented by
dEe-Vdt
=
Ee--I{ECr+-I(k,EM']+ ks
If the equilibrium Cr+ ~ H20 ~ - CrOH + -~ H were established, then
(6)
+
d[e-]/dt = --k/['Cr+][e - ] - kr"[CrOH+][-e-~.
[
With [-Cr+-] q- rCrOH +'] --- [e-l, and ['e--] = ['e-]0 at time t = 0 (i.e., in the reaction zone), kr in this event will be given by
.tpl%
o
, ,
(kr' -4- k/'~bo)/(1 + ~o),
where 4,0 = [-CrOH+]/[-Cr+] in the reaction zone. However, through use of a quadrupole mass spectrometer (kindly made available by Dr. A. N. Hayhurst), it was shown that ~bQis only 1/800 in a flame of composition 4/1/4 (2020~ Thus, the improbably high value of kr" ~ 10-5 em3 molecule-1 sec-1 would have to be adopted in order for CrOH + to be kinetically important in the recombination process. (Similar considerations applied to manganese and lead also lead to the conclusion that only the atomic ion is important.) The possibility of contributions from other ions (e.g., hydrated ions~) being
0.2 I
I
4,2
/04
I 4 "6 T -/
I
I 5"0
FIG. 4. Variation of k, with flame temperature and composition for Cr. Lines are drawn through points obtained from flames with the same O2/N~ ratio (1/3 or 1/4); along each line, H2/O~ varies from 2.8 to 4.0.
KINETIC STUDIES In Eq. (6), Pn represents a neutral solid particle and P~ an ionized one. The second term on the right-hand side of this equation is probably negligible, for, although the cross section in k2 will be larger than that in/c~, [-P,] ~ [M.]. The last term allows for the possibility of P being charged and might in some circumstances be comparable in magnitude with the first term. The electron concentration may also be reduced if the work function of P is high. Evidence which has so far been obtained on the nature of any charge on P (through application of high, ~ 1 kV/cm, electric fields 9) has not yet proved conclusive. Also the "brightness temperature" of the particles is almost certainly not constant s in the region of kinetic study. Investigations are being continued at Swansea, with the viewpoint of establishing the dissociation energy, size, and "work function" of the particles.
Mechanical Scheme for Ionization and Recombination For three-body electron-ion recombination with polyatomic molecules as third bodies, modified J. J. Thomson theory 1~expresses k~ as kr -~ (8kT/zcme)l/2( 47rro3) (3y)-lk.
(7)
Here r0 = 2e~(3kT) -1 and y ,,~ (NQd) -1, where m~ and e are the electronic mass and charge, respectively, N is the number density of the gas and Qd the diffusion cross section for electrons in the gas. With Qd ~ 30 A.U. 2 (Ref. 11), and k~ ---- 6 X 10-9 cm3 mo]ecule-1 sec-1, the value of k (a parameter which reflects the efficiency of exchange of energy between electron and third body, and which is greater than the "elastic" term [-2 X mass of electron/mass of third body) is calculated to be about 0.02. This value is of the same order of magnitude as values obtained from experiments on low-energy electrons in drifttubes when polyatomic molecules are present? ~ The observed variation of /c, with temperature (k, oo T-~.%t=l) is also not inconsistent with Eq. (7), in view of the large experimental uncertainties. Derivation of Eq. (7) involves the assumption that energy ~ k T is transferred from electron to third body on collision. The recombination step suggested is therefore Me + + e- + M ----)Me* + M
(IV)
where Me* represents any metal to which Process (IV) applies, electronically excited to an energy level between (V -- kT) and V, the
355
ionization potential. The reverse of (IV) has a rate constant k* which can be written in the form k* = ~'a2Me*_M(SkT/~Me--M) 1/2, where is a factor rather less than unity. A large number of bound electronic states do have energies between V -- k T and V, and ionization of atoms in these states should occur at most collisions with bulk gas molecules. The measured second-order rate constant k~ for the ionization process (I) will then be given approximately by k*[Me*]/[Me]tot~l. Since k~ was obviously measured under conditions where [Me +] < [-Me+]eq, the ionization "leak" must cause [Me*] • [ ' M e * ~ . Thus l~ <<,k * ( A / f ) exp ( - - V / R T ) ,
(8)
where A is the sum of statistical weights over levels in the energy band (V -- kT) to V, and f is the statistical weight of the ground electronic state. The apparently high cross sections for the ionization step predicted by applications of simple collision theory to the ground state alone might therefore be interpreted in terms of Eq. (8), through appropriate selection of A (cf. also Ref. 4). Three general points arise from the above considerations. In the first place, in order to express the above argument in a detailed theory (which could be developed on lines similar to those along which theoretical studies of diatemic molecule dissociation/atom recombination are proceeding13), knowledge of specific interactions between particular excited atomic states and molecular vibration states would be necessary. Second, caution should be exercised when use is made of rate constants given for Processes (I} and ( I I I ) at reduced pressures, where radiation depopulation of excited electronic states of atoms is likely to produce changes in ionization rates. Third, no results so far obtained have suggeste d any departures from the rate-quotient law; indeed, the self-consistency and simplicity of the ionization and recombination data imply steadystate population of electronic levels of Me in the region of kinetic measurements from whichever side equilibrium is approached, and therefore indicate that this law is in fact satisfied in the height range in which kinetic measurements were made.
ACKNOWLEDGMENTS
The authors wish to thank Prof. T. M. Sugden, Dr. E. M. Bulewicz, Dr. A. N. Hayhurst, Mr. N. Telford and Mr. H. Williams for helpful comments during the course of this work.
356
CHARGED SPECIES IN COMBUSTION PROCESSES REFERENCES
1. 2.
3. 4. 5.
6.
JENSEN, D. E. AND PADI~EY, P. J.: Trans. Faraday Soc. 62, 2132, 2140 (1966). HXYHURST,A. N. AND SUGDEN,T. M.: IUPAC Meeting on Plasmas, (two papers), Moscow, 1965. ALKEMADE, C. T. J., HOLLANDER, T., AND KALFF, P. F.: J. Chem. Phys. 39, 2558 (1963). HOLLANDER, T. : Thesis, Utrecht, 1964. PADL~Y,P. J. AND SUODEN,T. M. : Eighth Symposium (International) on Combustion, Williams and Wilkins, p. 164, 1962. SGUNDY,R. C. ANDWILLIAMS,H., 26th Meeting
7. 8. 9. 10.
11. 12.
13.
of Propulsion and Energetics Panel, AGARD, Pisa, Italy, September 6-9, 1965. JENSEN, D. n.: Thesis, Cambridge, 1965. PADLEY, P. J.: Thesis, Cambridge, 1959. KELLY, R. ANDPADLEY, P. J. : Unpublished data. MASSEY, H. S. W. AND BURHOP, E. H. S.: Electronic and Ionic Impact Phenomena, Chaps. IV, X, Clarendon Press, 1952. BULEWlCZ, E. M.: J. Chem. Phys. 36, 385 (1962). SCHOFIELD, K.: Tenth Symposium (International) on Combustion, p. 603, The Combustion Institute, 1965. KOLKER, H. J.: J. Chem. Phys./e~, 582 (1966).
COMMENTS Dr. T. Hollander (State University of Utrecht): P. J. Kalff, C. T. J. Alkemade and I have measured ionization and recombination rate coefficients for the alkali metals in CO/02/N2 and CO/O2/Ar flames at atmospheric pressure.~.~ The temperatures ranged from 2100~ to 2500~ We proposed as an ionization and recombination mechanism the following reaction kl MeWM~Me I0-1
+~e-
WM,
(I)
Me = metal atom; M = flame-gas molecule. Other reaction mechanisms were ruled out: a. Electron collisions leading to ionization were unimportant for when [e-] was varied by a factor of I000, no influence on the reaction rate was found. (I-A] means content or concentration of species A.) Afterward, calculations showed that this could be understood completely. b. Reaction involving hydrates Me -t- H~O ~- (Me + H20) ~ e --* Me + W e W H20 (II) could be ruled out, since we have flames almost without H~O ("dry" CO flames). The reaction now suggested and affirmed by Padley rEq. (1)] is likely the predominant one. We made certain that formation of metal hydroxides played no part under our flame conditions. We found with Na, K, and Cs, activation energies which correspond within a few per cent to the ionization energies. We are pleased that Padley and Jensen found the same result now, and that they derived additional chemical evidence for this outcome. It should be noted that the ionization rates found
by us are independent of Me, but are directly proportional to M. Diatomic molecules proved to be very effective in ionizing the metals, atoms (like At) being almost not effective. Padley and Jensen report the same result now, making certain that Reaction (I) will be the predominant one. Recent measurements performed in our group by Dr. P. J. Kalff revealed that the activation energy for the ionization of Sr in the CO flame again equals the ionization energy. The ionization rates found are about a factor of 10 lower than those attained with sodium. The question of the large cross sections for ionization derived from our work and Padley's can be further investigated according to our suggestion that the ionization also takes place from excited atomic levels and not only from the ground state of the atom. We are starting measurements for confirming this mechanism in further detail. We note that our results (rate coefficients, etc.) obtained with Na and K agree fairly well with those obtained by Schofield, Sugden, and Jensen and Padley. Finally, we are initiating ionization measurements in H2/O2/N2 flames, in order to be able to compare these results with our CO results and the results in the H2 flames obtained by Sugden, Padley, et al.
References 1. Kalff, P. J., Alkemade, C. T. J., and Hollander, T.: J. Chem. Phys. 39, 2558 (1963). 2. Hollander, T.: Thesis, Utrecht, 1964.
Mr. B. Brown (Hercules Inc.): How can the ionization rate be 1000 times higher from excited states, yet the activation energy is the same as that from the ground state?
KINETIC STUDIES Dr. P. J. Padley: I t should first be observed that the experimental evidence for the reality of the discrepancy alluded to is now very strong. Its precise extent is not known, because we had to assume that all bulk flame-gas molecules are equally efficient in causing ionization of the alkali metal. This may not be the case, and indeed very recent work ~ shows that the quenching cross sections of sodium D-line radiation (for example) by H20, H2, and N2 are 0.5 A ~, 2.9 A 2, and 7.0 A ~, respectively, may point in this direction. However, provided at least H2 and N2 are approximately equally efficient, and the effect of H20 not entirely negligible, none of our principal calculations will be affected, since the slopes of the smooth, Arrhenius-type plots can still be interpreted in terms of the ionization potential of the metal. It should, perhaps, not go unnoticed that, according to us, the measured cross sections for all five alkali metals are, to within a factor of 2, the same. 2 A question which our paper poses rather than answers, as does Hollander's thesis (Utrecht, 1964), is how best to allow for participation of excited electronic states of the alkali metal atom. The answer to Brown's question might be that atoms in a large number of effectively thermally populated, lower electronic levels (those ca. k T below the ionization potential) are being elevated to the ionization potential by collision with flame-gas molecules, which themselves possess effectively thermally distributed energy. There is little available experimental evidence which can usefully comment on this, but it should perhaps be observed that the upper states of the first resonance doublets, at least, are known to be thermally populated for all five alkali metals. Also, for sodium at least, this same critical upper state does not appear to be a population bottleneck for ionization, for if sodium D-line radiation is focussed onto a flame containing sodium vapor, under conditions such that the upper state is thereby overpopulated, then there is no detectable effect on the rate of ionization, a All this evidence, it should be emphasized, is in atmospheric-pressure flames, in which radiation depopulation problems can be ignored. References 1. Jenkins, D. R.: Proc. Roy. See. (London) A293, 493 (1966). 2. Jensen, D. E. and Padley, P. J.: Trans. Faraday Soe. 62, 2140 (1966). 3. Padley, P. J.: 26th A G A R D meeting, Pisa, Italy, 1965. Dr. D. E. Jensen: One might further discuss Brown's question by writing down two extreme situations. In the first, represented according to
357
the notation of the paper by Me (ground electronic state) K* k* ~- M e * ~ M e + + e - ,
(i)
each excited electronic-state population is governed by the Boltzmann equation. In the second, represented by Me (ground and lower excited electronic states) k' K' --* Me* ~- Me + + e-
(II)
(where k' is a compound coefficient containing contributions from many states), the rate of ionization is governed entirely by the rate of population of excited electronic states close to the ionization potential. In (I), the high pre-exponential factor in the ionization rate constants is represented as arising from a high statistical weight of the species Me*. In (II), this factor arises from summation of statistical weights of ground and lower (energy < V - kT) excited electronic states. The treatment of Me* as a distinct chemical species is, of course, quite artifical, and is introduced only for the sake of argument. In practice, the ionization process must be represented by a scheme intermediate between (I) and (II), for the colllsional rates of population of excited electronic levels close to the ionization potential will clearly be of the same order of magnitude as collisional rates of ionization of species in these levels. The comments mad~ in the paper simply suggest that scheme (I) is a closer approximation to the true situation than (II) at atmospheric pressure. A proper theory would take into account the detailed rates of population and depopulation of each excited electronic state occurring through radiative as well as through collisional processes. Comparison with the theory of dissociationrecombination reactions for diatomic molecule-free atom systems suggests that different conditions of pressure and temperature probably result in quite different distributions of atoms in electronic levels, both close to and far from equilibrium; energy differences between possible "population bottlenecks" and ionization potentials, for example, may vary rather widely.
Dr. L. F. Phillips (University of Canterbury, Christchurch): Has Dr. Padley considered using a lamp emitting resonance lines of Cs + to follow (Cs +) by light adsorption?
358
C H A R G E D S P E C I E S IN C O M B U S T I O N PROCESSES
Dr. P. J. Padley: Insofar as cesium is nearly fully ionized in the flames we have been using, measurements on ECs +] would suffer from the same limitation as measurements on r e - ] from t h e viewpoint of measuring rate constants of ionization of cesium. On the other hand, with a Cs + resonance lamp, it should be possible to make measurements m u c h nearer the reaction zone t h a n is possible b y t h e cavity method, and this might therefore be of value if more precise values of the
ionization rate constant of cesium t h a n those reported b y us are required.
Dr. L. F. Phillips: W h a t are the values obtained for the dissociation energies of alkali hydroxides? Dr. P. J. Padley: The values of AH0~ for the process AOH(g) --~ A(g) A- OH(g) axe 101 ~ 2, 77 =t= 4, 81 =i= 2, 83 =t= 2, and 91 =i= 3 kcal/mole for A = Li, Na, K, Rb, and Cs, respectively.