J . Phys. Chem. 1986, 90, 5124-5126
5724
ratios decrease, deviations from linearity become large, and oscillatory behavior is observed. Fortunately, from the oscillatory behavior, information regarding the geometry of the fractal structure under study can be obtained. In principle, the results obtained for the cases of small D / d , for different acceptor concentrations and/or for different interaction parameters should enable experimentalists to test whether the anomalous decay is due to a real fractal space or to a regular structure with excluded volume. For fractal structure, it is possible, at least in principle, to characterize the fractal dilation symmetry experimentally by determining the value of No 2nd b from the oscillatory, temporal behavior of donor intensity. Unfortunately, the ranges of time and concentration which can be studied ex-
perimentally in enegy-transfer processes do not allow the observation of full oscillation. Instead, a part of the oscillation could only introduce errors in eq 7 when used to determine D. Furthermore, the value of D determined could depend on the time interval plotted (i.e., on a different portion of the oscillation used). Thus, due to the experimental limitation imposed by the lifetime of the donor excited state, and the short range of the transfer of the exchange interaction mechanism, the determination of the real fractal dimension from one-step exchange energy transfer might be met with uncertainty.
Acknowledgment. We thank the Office of Naval Research for financial support.
Chemical and Physical Exit Channels In the Quenchlng of Cd(5s5p 'P1) by Several Molecules W. H. Breckenridge,*t W. L. Nikolai,' and D. Oba* Department of Chemistry, University of Utah, Salt Lake City, Utah 841 12 (Received: April 11, 1986)
Chemical as well as physical product channels in the collisional quenching of Cd(5s5p IP1)by several simple molecules have been characterized by using the laser pump-and-probe technique under single-collision conditions. Branching ratios as well as initial J-state distributions for the spin-forbidden production of the lower lying Cd(5sSp 3PJ) states were determined for H2, D2, and CO and compared to similar data for other molecules. Branching ratios were also determined for CdH formation for the quenching molecules H2, CH,, C3Hs, and I'-C4H10.Possible mechanistic explanations of the results are discussed.
In order to understand collisional quenching of electronically excited species at the molecular level, it is often valuable to determine the initial quantum-state distributions of energy in the products.',2 For those cases in which there are two or more exit channels, it is also important (but often surprisingly difficult) to determine the branching ratios for each exit channel as well. For instance, even though it may be possible to detect one set of products easily (because a product fluoresces, for example), one cannot really claim to have characterized the quenching process if the branching ratio for that exit channel is extremely small. Particularly interesting are those situations in which the electronic energy can be dissipated physically (e.g., by E-to-v,R energy transfer) or chemically (by chemical reaction).',* In our laboratories, we have previously studied the excited state Cd(5sSp 'PI), where just such competitive chemical vs. physical quenching is observed,'-' Cd(5s5p IP,)
+ RH
Cd(5s5p 3P,2)
+ CdH(v,N) + R * Cd + H + R**
+ RH*
(la)
Cd(5s2 'So) R H * *
(1b)
-
(2a)
-
-+
-
(2b)
where R = alkyl or H. The electronic energy of the Cd('PI) state (125.0 kcal/mol) can be dissipated physically by forming either ground-state Cd('So) and vibrotationally excited R H * * (with a large amount of energy necessarily going into relative translation, since R-H bond energies are only 91-104 kcal/mol) or the lower lying (86-91 kcal) Cd(3Ph2) states with the rest of the energy in vibrotationally excited RH' (and relative translation). Two chemical exit channels are also available, either complete scission of the R-H bond or abstraction of an H-atom to form CdH (R* and R** represent vibrotationally excited species for the cases where R = alkyl radical).
f
J. S. Guggenheim Memorial Fellow, 1984-1985. Present address: Hercules, Inc., Aerospace Division, Magna, UT 84044.
0022-3654/86/2090-5724$01.50/0
Earlier experiment^^*'-^ have shown that for R H = CH,, C3Hs, and C4HI0exit channel l a dominates, with branching ratios $la = 0.9 f 0.1. This is remarkable, in that spin-forbidden processes occur with a high cross section (essentially every gas-kinetic collision) despite the fact that there are two highly exothermic chemical exit channels available, (2a) and (2b), in all cases. The initial quantum-state distributions of Cd(3Ph2) multiplets also vary continuously with RH; Cd(3P2) is favored for CHI and is progressively less favored for C2H6and C3H8, and the populations are statistical (5:3:1) for i-C4HIo.On the other hand, when R H is H2, qualitative observations4~8~10~11 indicate that (2a) and (2b) are more important exit channels and perhaps even dominate the quenching process. We present new results here in which the branching ratios $2a for exit channel 2a, CdH formation, have been determined for R H = H2, CH,, C3H8,and i-C4H10. In addition, the branching ratios & a for exit channel la, as well as the 3Ph2 initial quantum-state distributions, have been determined for H2, D2,and the unreactive quencher CO. The data are consistent with our earlier work, and it has been shown that in the case of R H = H2, physical and chemical exit channels are quite competitive. (1) Breckenridge, W.H.; Umemoto, H. The Dynamics of the Excited State; Lawley, K., Ed.; Advances in Chemical Physics 5 0 Wiley: New York, 1982. (2) Breckenridge, W. H. Reactions ofSmall Transient Species; Clyne, M., Fontijn, A., E&.; Academic: New York, 1983. (3) Breckenridge, W.H.; Renlund, A. M. J. Phys. Chem. 1978,82, 1474. (4) Breckenridge, W.H.; Renlund, A. M. J . Phys. Chem. 1978,82, 1484. ( 5 ) Breckenridge, W. H.; Malmin, 0.Kim; Nikolai, W. L.; Oba, D. Chem. Phys. Lett. 1978, 59, 38. (6) Breckenridge, W. H.; Donovan, R. J.; Malmin, 0. Kim Chem. Phys. Lett. 62, 608 (1978). (7) Breckenridae. - W. H.: and Malmin, 0. Kim Chem. Phvs. Letf. 1979, 68, '34 1. (8) Breckenridge, W.H.; Oba, D. Chem. Phys. Lett. 1980, 72, 455. (9) Breckenridge, W. H.; Malmin, 0. Kim J. Chem. Phys. 1981, 74, 3307. (10) Nikolai, W. L. Ph.D. Thesis, University of Utah, 1981. (11) Oba, D. Ph.D. Thesis, University of Utah, 1986. Copies of the relevant section of the thesis are available on request from W. H. Breckenridge.
0 1986 American Chemical Society
The Journal of Physical Chemistry, Vol. 90, No. 22, 1986 5125
Quenching of Cd(5sSp 'PI) TABLE I: Relative Initial Populations of Cd(%,) Process l a (in Percent)
auencher molecule ~~~~
Formed in
3P7
'PI
'Po
80f3 55f2 56f2 61f3 62f2 76f2 65f1 56f1 56
16f2 34f2 32f2 36f2 35f2 19f2 27f1 33f1 33
4f1 11f1 12f1 3 f l 3 f 1 5 f l 8 f l 1 1 f 1 11
TABLE 11: Absolute Branching Ratios for Processes la and 2a quencher molecule (CdOP,) formation) 4% (CdH formation) H2 D2
~
Ar4 N2"
c04 H2 D2 CH4" C3H8' i-C4H,04
electronically statistical (5:3:1) Reference 9. Experimental Section
The experimental apparatus has been described in detail elsewhere,'-]' and only a brief summary will be provided here. To a stream of cadmium vapor in helium carrier gas (- 15 Torr) is added a small pressure (0.01-1.0 Torr) of quencher gas. The frequency-doubled output of one dye laser is tuned to the Cd(5s2 'So 5s5p 'PI) transition a t 2288 A. The output of a second dye laser, delayed a few nanoseconds, illuminates the pump-laser/cadmium interaction region for state-selected laser-induced fluorescence (LIF) detection of products of Cd('P1) collisional deactivation. The CdCP, ) products are detected via transitions all to the 5s6s 3Slupper state. The a t 4679,4801, and 5087 product CdH(X2Z+;u,N)is detected by L I F via the transitions to CdH(A2111/2).8,1'
-
A,
Results
Exit Channel l a . ( i ) Determination of Initial Cd(3P,2) Quantum-State Distributions. A procedure identical with that described previously9was used to determine the initial distribution of Cd(3P,2) quantum states for R H = H2 and D2. The results are shown in Table I, along with some earlier results for comparison. N o differences in Cd(3P,2) distributions were observed when the Hz and D2 pressures were varied from 0.05 to 0.5 Torr, showing that secondary collisional intramultiplet relaxation was negligible. (ii) Determination of $la Earlier careful measurements of $la = 0.85 f O.1S6s9for N2 as a quencher were performed by comparing the total fluorescence from the long-lived product Cd(3Pl) to the diminution of total fluorescence from Cd('Pl) when a certain pressure of N2 was added. Such a determination of $la is formally a lower limit, since any net quenching of Cd(3Po_2) would result in fewer fluorescence photons from Cd(3P1). Such a measurement is not possible for H2 or DZ,since both species quench Cd(3Po,l)quite efficient1y.'v2 Instead, we have compared the total Cd('Ps2) yields by LIF when a known, small pressure of N 2 is alternately replaced by a known, small pressure of another quenching gas under identical laser excitation and flow conditions. Details may be found elsewhere.I0 Absolute quenching rates of Cd('PI) by N2 and the other quenching gases are required for accurate measurements, but these were determined earlier in the same a p p a r a t u ~ . ' , ~Loss ,~ of Cd(3Po-2)by quenching is negligible during the very short time between "pump" and "probe" laser pulses. The results for H2, D2, and C O are shown in Table 11, along with other values determined p r e v i o ~ s l ywith ~ ~ ~the same technique. The only other previous determinations of $la by this3 and otherI2 research groups are not reliable. They involved indirect measurements of Cd(3PJ) by Cd(3Pl)fluorescence or absorption which was not time-resolved, and also corrections for Cd(3P,2) secondary quenching which are bound to be uncertain, since quenching rates for Cd('P2), now known to be the dominant product, are unknown. In this regard, such measurements are in qualitative agreement with the data in Table I1 for quenchers such as N2 and alkanes, where secondary quenching of all Cd(3PJ) states is apparently inefficient but yield values which are much (12) Czajkowski, M.; Walentynowicz, E.; Krause, L. J. Quant. Spectrosc. Radkat. Transfer 1983,29, 113, and references therein.
co N2 CH4 C3H8 i-C4HI0
0.26 f 0.05 0.33 f 0.10 0.94 f 0.18 0.85 f 0.15" 0.84 0.16' 0.89 f 0.13" 0.96 f 0.14"
0.20 f 0.05
*
0.04 f 0.02 0.05 f 0.01 0.04 f 0.01
References 6 and 9. too low for CO, probably because Cd(3P2)is efficiently quenched to ground-state Cd('So) by CO. Exit Channel 2a. Determination of It had been shown previously8 that CdH(u = 0) is produced in good yield in the quenching of Cd('P1) by H2and that the rotational quantum-state distribution was characterized approximately by a Boltzmann-type distribution with a "temperature" of 5000 f 1500 K. Experiments performed much earlier, utilizing resonance-radiation flash photolysis, had shown that $2a for H2 was 10.5.4 We have determined the absolute branching ratio for production of CdH(v = 0) in reaction 2a for R H = Hz by measuring the ratio of L I F signals for CdH(u = 0) vs. those for Cd(3P,2) under identical conditions in the apparatus and for the same pressure of H2. From this ratio, given the absolute branching ratio $la for H2of 0.26 f 0.06 determined in this study, the absolute branching ratio for CdH(v = 0) production can be calculated. Although it was not possible to make accurate LIF measurements of CdH(u = 1-4) because of much weaker signals and spectral interferences, the yield of CdH(u = 1) is roughly one-half that of CdH(v = 0), and the yields of CdH(v = 2-4) are all less than 10% of the CdH(u = 0) yield. A semiquantitative determination of can therefore be made for R H = H2. Similar estimates can also be made of the very low 4%values for R H = CH4, C3H8, and i-C4HI0. These determinations are shown in Table 11. Details of the procedures and calculations for determination of the values are given in detail elsewhere." Individual transition probabilities for all the Cd(3PJ 3Sl)and CdH(XZZ+ A2111,2)transitions must be known, and ratios of total laserinduced fluorescence intensities for selected pairs of transitions were measured accurately. Lifetimes of the upper Cd(3S,) and CdH(A2111/2)states were taken to be 9 f 1 and 70 f 7 ns, respectively for calculation of Einstein B coefficient^.'^^'^ Honl-London factors were calculated with the formulae of Earls,'5 and the CdH(A-X) Franck-Condon factors utilized were those calculated by Branch and Be11.I6 Kinetic estimates indicated that during the very short time delay between pump and probe laser pulses, production of CdH by secondary reaction of Cd(3P,2) produced in process l a should be negligible. This was confirmed experimentally by showing that the amounts of CdH(u = 0) produced were linear functions of R H pressure in the low-pressure range where quantitative data were taken. Large amounts of CdH from secondary reaction of Cd(3PJ) would have shown a dependence on the square of the R H pressure."
-
-
Discussion
Ar. Since for most of the quenching species discussed here, exit channel l a , formation of Cd(3P24), dominates, let us first discuss those quenchers for which channels 2a and 2b, chemical reaction, are impossible. The argon case is interesting, since theoretical calculations of the relevant CdAr excited-state potential curves have recently appeared." As can be seen from Table I, quenching of Cd('PI) by Ar results in preferential formation of higher lying Cd(3P2) vs. Cd(3Pl) or particularly Cd(3Po). This (13) Kerkhoff, H.; Schmidt, M.; Teppner, U.; Zimmerman, P. J. Phys. B. 1988. -~--, 13. 3969. -- - ~ (14) Jourdan, A.;Negre, J. M.;Dufayard, J.; Nedelec, 0. J . de Phys. 1976, 37, L29. (15) Earls, L. T. Phys. Rev. 1935,48, 423. (16) Bell, R.A.;Branch, D., private communication. (17) Czuchaj, E.; Sienkiewicz, J. J . Phys. B. 1984, 17, 2251.
--.
5726 The Journal of Physical Chemistry, Vol. 90, No. 22, 1986
Breckenridge et al.
is consistent with the theoretical calculations, which show that of the five CdAr triplet states which correlate with the Cd(3P2+) multiplets, the most repulsive state by far is the degenerate 30+,31 state (Hund's case "c" coupling notation; 3Z+in case "a" notation), since it has entirely u p-orbital character. This state should undergo a crossing with the least-repulsive (In)of the two CdAr Ar('So), facilitating states which correlate with Cd('P,) deactivation. Since the 30+,31state correlates asymptotically with Cd(3P2) + Ar('So), it is not surprising that Cd(3P2)is populated preferentially. The cross section for quenching of Cd('PI) by Ar is small (
