A Study of the Chemiluminescence of the Pb + O3 Reactions*

The chemiluminescent reaction of Pb + O3 has been studied using both “cold” and vibrationally excited O3. Emission from new states a and b has been observed in addition to the A and B states. The reaction of vibrationally excited O3 with Pb to yield PbO(A) appears to be faster than that using “cold” O3.


Introduction
Th e res ults of our rece nt s tudi es on lase r e nh a nce d reac ti ons have s how n th a t vibra ti onal e ne rgy in a reac ta nt molec ule can rea ppear as exc itati on in a produ c t s pec ies. F or e xa mple, e mi ss ions fro m both NOt and SOt produ ced in th e reac ti ons of NO a nd SO with 0 3 were o bse rv ed to shift to s horte r wa vele ngth wh e n the 0 :1 was vibrati onally exc ited us in g a C O~ laser [1 , 2].1 Beca use of the s pec trosco pi c co mplexiti es of the tri atomi c molec ul es, N0 2 a nd S O~, our int e ntion in th e prese nt stud y was to inv es ti gate a c he miluminesce nt reacti on produc in g a di ato mi c produ c t whic h would be, in principle, easie r to c harac terize s pec troscopically. The met al ato m-oxidant syste ms re present a class of suc h reac ti ons. A signifi cant numb er of these hav e been investigated to da te beca use of their potenti al as c he mical lasers. W e re port herein some obs ervations on the reac ti on (1) While the information obtain ed fro m s tudying th e infrared laser-e nhan ced reactio n co mpone nt is minimi ze d by th e overall reac ti on complexity, it does neve rth eless pro vide so me additi onal in sight into thi s reac ti on sys te m. This information coupled with ne w hi gh press ure spectrosco pi c res ults co mple me nt th e d e tail ed low press ure inv es ti gation by Olde nborg, Di ckson , a nd Zare (ODZ) [3].

. Experimental Detail
Th e furn ace, reacti on ce ll , fas t Row pumpin g syste m , CO 2 lase r, a nd s pec tro me ter a re s hown sc hema ti call y in fi gure 1. Lead vapor, produced from a res istive ly heated c ru cible containing le ad metal e nte rs th e glass reac ti on c ha mber in an AI' dilu e nt stream . Th e e fflu e nt from a co mm e rcial 0 3 ge ne rator, co nsis tin g of 4 pe rce nt 0 3 in O~ is mix ed with Ar and Rows pas t the cell wind o ws (to eliminate window de pos its) into th e cell. Th ere it diffu siv ely mix es with the lead-argon Row. Th e te mpe rature of th e cru c ibl e (as me as ured by a th erm oco uple prob e) ran ges from 900-1000 K whil e the te mperature in th e fl a me re action zone vari es from 500-600 K. The to tal press ure in th e cell varies from 1 to 5 torr (1 torr = 133.3 Pal with the flow through the furnace be in g an ywhe re from 20 to 50 percent of the total Row. The 0.5 cm diameter beam from a CO 2 laser tuned to the 9.6 J.Lm P(30) transition is square wave chopped and traverses the flame exciting /)3, the asymmetric stretchin g mode of 0 3 (1043 cm -1). The chemiluminescence from the Pb + 0 3 reaction is monitored through a spectrometer-photomultiplier asse mbly. The photomultiplier output is fed through a seri es of pulse amplifiers and voltage di scriminator into a du al counter, one chann el of whi c h record s the " laser-on" signal and the oth e r th e "laser-off". A print.o ut from th ese counters is sync hronized with the s pec trom e ter wavele ngth-sc an-dri ve th e re by facilitatin g the recordin g of th e modulati on s pectrum vs wavele ngth. Th e normal spec tral ("lase r-off") e mi ss ion is a utomati c ally obtain ed fro m th e " lase r-off" co unter.

Results
In contrast to the spatially sharp diffusion flame observed for the Ba + 0 3 (or N 20) reaction, the Pb + 0 3 flame is quite diffuse (apparently reaction limited). It is brightest in the high temperature zone at the furnace nozzle, diminishes with decreasing temperature (increasing distance from the nozzle), and persists for some two to three feet into the pumping system. These observations suggest a reaction rate for Pb + 0 3 which is considerably slower than gas kinetic.
The spectrum which we observe at several torr total pressure partly resembles the low pressure spectrum obtained by ODZ and reproduced by us in a similar quasi-beam apparatus_ The short wavelength end of the more complete spectrum ( fig. 2  the low (submicron) pressure spectrum in that it is less diffuse. The long wavelength portion between 480 nm and 595 nm is almost entirely the new a state recently characterized by ODZ_ At still longer wavelengths, our spectrum differs from that of ODZ in that we observe a series of strong lines which do not agree with a ~ X, A ~ X, or B ~ X, but rather appear to originate from a new state observed via six weak lines by ODZ and identified as b by them. This b state is seen more intensely in our high pressure spectrum. This series oflines in our spectrum can be fit to the expression: where the lower state constants have been taken from Rosen's compendium [4]_ The spectral constants given here and in tables 1 and 2 for the a, A, and B state are not as well determined as previous values given in references [1] and [4].
The calculated v have been generated from a least-squares treatment of the observed data using Rosen's constants for the X state. The generating equations are: Th e calc ulated v have bee n generated from a least·squares treat· men t of th e data us ing Rose n's constants for the X state. Th e ge n· erating equation is: A definite vibrational assignment for an electronic state, for which a rotational analysis has not been observed, requires the measurement of a vibrational isotope shift. Lacking data of this type one tries to assign band heads such that both (0, v'') and (v', 0) levels are observed. Th e assignment hypothesized by ODZ on the basis of six observed transitions in a (v', 0) tran sition has placed Too of the b state about one vibrational quanta above Too of the a state. In this study 20 band heads have been observed that can be assigned to b state. In addition to th e (v', 0) band heads, other bands have been observed with v" = 1, 2, 3, 4, 5. The hypothesis regarding the separation of the a and B states is supported by arguments give n later.
Although considerable inte nsity is observed for B -X transition, the zeroth level of this state lies very close to the thermodynamic thres hold for the reaction Pb (j = 0) + 0 3 ~ PbO(B) + O 2 • The dissociation energy (D~) of PbO is given by Rosen [4] as 30,920 ±500 cm -I • Using !:J.Hr(298 K) of 0 3 and 0 as 34.1 and 59.5 kcal/mol as recommended by Wagman et al. [5], one computes 22036 cm -I for the exo thermicity of the re action.
This to be compared to 22174 cm -I of th e V(O , O) level of the B state. Oldenborg and Zare have suggested that production of this state res ults from reac tion of Pb (j = 1) present in their experiments due to an electric discharge in their furnace. The strong B ~ X e mission observed in our high press ure experiment was found to vary mark edly with the oven te mperature . The observed B ~ X emis sion increase over that emission from either a or b ~ X with increasing temperature obeyed an Arrhenius-type formulation with an activation energy of so me 10 kcal (i.e. nearly equal to th e e nergy difference between) = 0 and} = 1 multiplet compon e nts ofPb). This observation s ugges ts that Pb (j = 1) is produced thermally in our furnace as opposed to its possible production via secondary processes, e . g.

PbO*+Pb (j=O)~PbO+Pb (j=I).
If PbO(B) is indeed produced through reaction of Pb ( J = 1) with ozone, the rate of this reac tion mu st be extremely fast to co mpete with the deac tivation process Pb (j=1)+0 2 ~ Pb (j=0)+0 2 since the deactivation proceeds with a high rate constant and the O 2 pressure is twenty times that of 0 3 under our usual experime ntal conditions. Part of the modulation spectrum is reproduced in figure 3. This spectrum, which has bee n smoothed, represents only that component of the chemiluminescent emission which varies with the laser excitation of 0 3 (i.e. only that component which either increases or decreases due to a change in reaction rate with reactant vibrational excitation). Thus, if the emission originated only from a single electronic state, the modulation spectrum would appear as a quasi-continuum with possibly some small structure due to sharp changes in population of one vibrational line relative to an adjacent one. The large amount of structure in figure 3 indicates the presence of emission from at least two electronic states. One might speculate that at the longer wavelength, where the normal spectrum consists mainly of a and b emission lines, this modulation structure could reveal an increase or decrease of b emission lines relative to a emission lines (or vice versa). However, the peaks (or valleys) in the modulation spectrum do not agree well with either a or b state emission lines. More surprisingly, they agree much better with A ~ X transitions. We therefore tentatively identify the modulation spectrum as a quasi continuum due to a ~ X and b ~ X emissions at long wavelengths (possibly some-B ~ X short wavelength) with structure due to A ~ X emission lines superimposed throughout the entire wavelength range. This suggests that vibrational excitation in 0 3 increases the production of the a, b, . and possibly the B state of the PbO all to some small degree, while increasing A state production most significantly. We must emphasize, however, that the assignment of A state responsibility for structure in the modulation spectrum is tentative since the modulation data are difficult to obtain, require long integration times, and should be obtained in the low (submicron) pressure region where only the a and B states have been observed. Nevertheless, we can speculate on the production of PbO (A) in the laser excited reaction. It is possible that as a result of laser excitation of 0 3 forming 0 3 t the reaction with Pb (j = 1) now produces PbO (B) in higher vibrational levels. These can then be collision ally transferred to the A state which is seen in emission. A second equally likely possibility is that the vibrational energy in 0 3 increases the rate of A state production directly at the expense of one or more of the other reaction channels. From the numerical value of the percent modulation in the laser experiments (i.e. the continuum region assigned to a and b state enhancement) we can calculate a rate constant enhancement of approximately a factor of two. This is obtained by comparing the percent modulation of both the Pb+03 t and NO+03 t reactions in this apparatus under identical experimental conditions.
We can obtain a very rough estimate of the quantum yield of a and b state production in the following manner. First we assume the reaction of 0 3 with Pb of about 10 -5 assuming Pb (j= 0) and Pb (j= 1) reacted with 0 3 with the same rate constant. The observation of the decay of chemiluminescence over several feet in our flow tube points to a slow rate of reaction for Pb (j=0) while the fact that the reaction of Pb (j = 1) must compete favorably with its deactivation channels speaks for a very fast (collision frequency) rate of reaction for Pb (j = 1). Assuming a reaction efficiency of 10 -2 for the Pb (j = 0) reaction in the spectrometer observation zone increases the quantum yield for a + b state production by a factor of 100 to 10 -3 • We compare this to the ODZ upper limit of 10 -2 obtained under the assumption of a fast reaction rate for Pb (j = 0). A slower reaction rate would unfortunately raise their quantum yield (in greater disagreement with our 10 -3 estimate). However, our observation of a large luminescent region is not necessarily contradictory to ODZ's estimate of a fast reaction rate because of the different temperature regions of the two studies. In the quasi-beam configuration, Pb exits the furnace at very high temperature (> 1000 K) and colliaes with 0 3 with much higher kinetic energy than in our high pressure experiments (kinetic energy of 600 K at the nozzle tip and decreasing rapidly to 400 K downstream of the mixing zone).

Analysis and Conclusions
Oldenborg et al. identify the two (0 -, 1) components of the 3 ~ + as b and a, respectively. This energy ordering is consistent with the present observations including an analysis of the relative intensities of the a and b transitions. A theoretical analysis can also be made of the spin-spin splitting constant of the 3~ state which shows that the 0component must be at a higher e nergy than the 1 component. The spin-spin splitting for a molecule containing a heavy atom is dominated by the second-order spin-orbit coupling to nearby electronic states. Spin-orbit coupling will occur for dO = 0 and couple the 0component to 37T (0 -), l~-(O-) and the 1 component to 37T (1), 3~-(1), l7T (1). Note that there is no first-order spin-orbit coupling between the 3~ +(1) and 3d(1) states. U sing a hamiltonian of the form L 1;. Si, i the spin-orbit interaction is reduced [6] to the oneelectron spin-orbit integrals given in table 3. Interaction with the 37T state shifts both components equally and can be ignored. The [7T(l) interaction is small both because the (J" and 7T orbitals are primarily localized on the oxygen atom, and there is a large energy separation between the 17T and 3~ -s tates. The spin-s pin splitting constant is dominated b y the difference between the 3~-( 1) and I ~-(O -) interaction s.
From table 3 we see that the 3~ -interaction is necessarily the largest term. This demonstrates that the 3~-(l) component is lower in enrgy than 3~-(0). Quantitative estimates of the spin-spin splitting cannot be made from molecular spin-orbit parameters since little is known for the PbO excited states. Using the atomic spin-orbit parame ter [6], assuming atomic populations by comparing calculations on PbO [7] and CO [8], and excitatipn en ergies for the perturbing states . [9], a spin-spin splitting of about 1000 cm -I is obtained: This qualitatively confirms th e analysis of the emission spec trum and the assignment of the a and b states. Assuming that the molec ular integrals will scale with the atomic spin-orbit parameters, th e s plitting in the case of SnO would be an order of magnitude less than the value for PbO while CeO is about two orders of magnitude less.
There are two mechanisms whic h could give inte nsity to th e dipole forbidden b ---'» X transition, spinrotation and electronic rotational couplin g. For large spin-spin s plitting the spin-rotation coupling be tween the a and b states is negligible even for} as large as 100 (one ex pects the most probable value of ) to be 24 for T= 500 K).
The electronic-rotation coupling matrix elements between a 3~ + and 37T state are given by Kovacs [11].
The coupling is proportional to 4B2}(J+l)/M for the Hund 's case a re presentation where I:1E is the difference in the electronic energies and B is the rotational . constant. Since I:1E -5000 c m -I and T -500 K, this coupling is significant but can only be ascertai ned quantitatively if the complete mixing be twee n 3~ + and 37T states is considered. It is likely that the b state transition probability would increase with temperature.
Since all the observed transitions to the ground state ultimately derive their intensity from spin-orbit mixing to the higher singlet excited states, it is well to remember that the transitions between 37T and 3~ + states are electric-dipole allowed and should have significant intensity even though they are in the infrared ( -5000 cm -I ).
The present results point to a slow overall reaction of Pb (J = 0) with 0 3 as well as a small quantum yield for production of PbO excited electronic states. Since the rea.ctant states can couple to only one final product state, adiabatically this must be PbO (X) and O2 (X). Excited PbO s tates are the result of a nonfldiabatic transition . The enhanced reactivity of Pb (J = 1) into the excited B state reflects the additional channels that are now available but the population yield of the various excited s ta tes remains puzzling. Our observations at high press ure are so mewhat different from those of Oldenborg et a1. In particular, we find more intensity in the b s tate th a n they did.
Their observations were mC\de before colli sio ns took place. In the present case many collisions can occ ur before the emitted light is observed. Two ge ne ral explanations can be advanced for the different observations. The effective rotational te mperatures can be very different. Pressure effects can also be important both by colli sionally deactivating other excited states into the b state or by collision ally indu cing the radiative transition.
Finally, we note that th e e nhance ment or eve n initial formation of the A state by laser exci tation of the ozone is not understood. In order to further unravel th ese questions, additional expe rime nts must be carried out in conjunctio n with a more extensive theoretical investigation of the Group IV oxides.