8346
J. Phys. Chem. A 2000, 104, 8346-8352
Mechanisms and Relative Rates of MX2* Chemiluminescence in the Reactions of Ca, Sr, and Ba(1S) Atoms with Dihalogen Molecules P. Kierzkowski and A. Kowalski* Institute of Experimental Physics, UniVersity of Gdansk, ul. Wita Stwosza 57, PL-80-952 Gdansk, Poland
D. Wren and M. Menzinger Department of Chemistry, UniVersity of Toronto, Toronto, Ontario M5S 1A1, Canada ReceiVed: April 18, 2000
Chemiluminescent reactions of ground state (Ca, Sr, and Ba) atoms with (Cl2, Br2, I2, ICl, and IBr) were studied in a beam-gas arrangement. The MX2* pseudo-continua were measured as a function of target gas pressure in the 0.0001-0.25 Pa range. To identify the main reaction channels that contribute to MX2* formation and to obtain their relative contributions, kinetic models were fitted to the data. The following channels were considered: (1) radiative two-body recombination (R2BR), (2) radiative three-body recombination (R3BR), (3) two consecutive harpooning steps involving MX† intermediate (two-step chemiluminescent reaction TSCR), and (4) combinations of the above. On their own, none of the mechanisms (1-3) provide satisfactory data fits. The best agreement is obtained by a model involving both R2BR and TSCR. The branching ratios of these channels were determined for p ) 0-0.25 Pa. At 0.16 Pa these R2BR fractions vary from 7% (for Ca, Sr + ICl) to 79% (for Ba + IBr). Absolute CL cross sections and lower limits of photon yields were estimated by cross-calibrations. Photon yields for R2BR varied from 0.0004% to 0.037%, depending on the collision partners.
1. Introduction The pseudo-continua arising from the M(1S0) + X2 reactions of alkaline earth atoms with halogen molecules, first observed by Jonah and Zare,1 are generally believed1-18 to arise from metal dihalides MX2*, whose electronic states remain a matter of speculation. The kinetics of emitter formation is interesting, complex, and controversial. On the basis of the pressure dependence of the MX2* spectrum, the pseudo-continuum was originally attributed to the radiatiVe two-body recombination (R2BR) process:1
M(1S0) + X2 f MX2* f MX2 + hν
(1)
If spectrally resolved at sufficiently low pressure, this emission would constitute a spectroscopy of the transition state.19 More detailed studies2-6,9 in the 0.1-5 mPa range showed that, in addition to a second-order process with a linear pressure dependence at the lowest pressures (called microTorr range; 1 Torr ) 133 Pa), a quadratic, third-order process began to dominate in the mPa region (this can be clearly seen in Figure 2 of ref 6). Originally it was proposed3,5,9 that this third order process involves the very fast collisional stabilization of a vibronically excited collision complex, followed by its radiative decaysa sequence called radiatiVe three-body recombination (R3BR): * Corresponding author: Institute of Experimental Physics, University of Gdansk, ul.Wita Stwosza 57, PL-80-952 Gdansk, Poland. Fax: (00-48)(58)341-3175. E-mail:
[email protected].
M + X2 T MX2*†
(2)
MX2*† + X2 f MX2* + X2
(3)
MX2* f MX2 + hν
(4)
where the dagger denotes vibrational-rotational excitation. A rationalization of this mechanism requires extremely large stabilization cross sections σs g 3000 × 10-20 m2 with a range of energy transfer rET > 5 × 10-9 m. Failing this, the complex lifetime would have to be unreasonably long (“immortal” complex). These facts stand against the R3BR mechanism.15 However, R3BR was recently revived in the work of Gole et al.12-14 to explain newly measured (purely quadratic in the 0.1-5 mPa range) pressure dependences of the chemiluminescence (CL) intensity and the appearance (or absence) of selected spectral features of MX2* obtained under well-defined multiple collision conditions. An alternative “pseudo-third-order” mechanism3,5,9 involves two sequential harpooning steps,15 also called a two-step chemiluminescent reaction (TSCR):
M + X2 f MX† + X
(5)
MX† + X2 f MX2* + X
(6)
MX2* f MX2 + hν
(7)
In contrast to R3BR, where stabilization of the complex (3) must occur immediately after its formation (2), due to its short lifetime, in TSCR a long time may elapse before the MX† radical
10.1021/jp001465e CCC: $19.00 © 2000 American Chemical Society Published on Web 08/12/2000
MX2* Chemiluminescence
J. Phys. Chem. A, Vol. 104, No. 36, 2000 8347
undergoes the second harpooning step (6). Furthermore, the ionization potential of vibrationally excited MX† radicals is lower than that of M atoms. Hence the second harpooning step (6) is expected to be even faster than the first one. Both facts make the TSCR mechanism somewhat more plausible a priori than the competing R3BR mechanism. The principal goal of the present work is therefore to settle the issue of competing reaction mechanisms in 15 reactions M + X2, XY by a careful kinetic analysis of new detailed experiments. The dependence of the MX2* emission intensity ICL on the number density n of target molecules is different for each of the three mechanisms considered above. For R2BR it is1
ICLR2BR ∼ An exp(-nxσM)
(8)
ICLR3BR ∼ Bn2 exp(-nxσM)
(9)
for R3BR it is6,12
and for TSCR, in the experimental arrangement used, it is11
ICLTSCR ∼ Cn[exp(-nxσM) - exp(-nxσMX)]
(10)
To see clearly why the pressure dependence is linear, apart from the exponential attenuation terms, despite the fact that two target molecules are involved in the successive harpooning steps, (10) is rederived and discussed in the Appendix. In (8-10) A, B, and C are constants, x is the beam path length in the scattering cell, and σM and σMX are the total attenuation cross sections for the collisions of target gas molecules with M atoms and MX† molecules, correspondingly. We investigate here whether and to which extent these competing mechanisms contribute to the observed CL. We take a similar approach as that for (Ca, Sr) + I2 reactions,11 consider explicitly R3BR as a kinetic alternative, and apply the analysis to the 15 systems (Ca, Sr, Ba) + (Cl2, Br2, I2, ICl, IBr). Measurements of the pressure dependence of pseudocontinua in the 0.0001-0.25 Pa range were least-squares fitted to (810) and to linear combinations of these expressions to provide an answer to this question. From the simulations, we derived the relative weights A, B, and C of the competing reaction paths as well as the attenuation cross sections σM for M atoms and σMX for MX† radicals. We determined also the chemiluminescence cross sections σCL for the MX2* emission, treated as if it was entirely due to a second-order process, by means of crosscalibration to the chemiluminescent reactions involving metastable alkaline earth atoms.20,21 This is done under the assumption that the emitters radiate where they are formed (i.e., their radiative lifetime is τrad < 1 µs). Given the total collision cross sections and the CL cross sections, we then estimated the (pseudo-bimolecular) photon yields. 2. Experimental Section The experimental setup is described elsewhere.11 Briefly, the atomic beam effused from a resistively heated stainless steel oven. The temperature of the oven was T ) 1080 K for Ca, T ) 1030 K for Sr, and T ) 1130 K for Ba, as measured with a chromel-alumel thermocouple. The scattering cell was heated to T ) 335 K and was mounted above the beam source. One face of the cell had a quartz window which was covered by a mask with a slit (3 mm × 40 mm), fixing the beam path length in the gas at x ) (21 ( 1.5) mm. The metals and halogens were supplied by Aldrich. The halogens, purified by repeated
freeze-pump-melt cycles, were admitted to the scattering cell through an adjustable leak. Scattering pressures were in the range 0.0001-0.25 Pa, as measured with a capacitance manometer (MKS Baratron 120AD-00001RAU). First the chemiluminescence spectra were recorded in the 300-900 nm range, using a 0.4 m Zeiss monochromator to establish the spectral regions in which the pseudo-continua are not overlapped by MX* emissions. The subsequent measurements of the MX2* pressure dependence were made in the regions free of the MX* emission, using combinations of long wave and short wavelength cutoff filters or glass filters (Andover) and a bare Burle C31034 photomultiplier (cooled to T ) 250 K), connected to a photon counting system. The target gas pressure was regulated with a Teflon needle valve, limiting flow from a back-up volume. It was always changed from high to low values. The Mg*(3PJ) + I2 reaction was used to calibrate the chemiluminescence cross sections, since the Mg(3P1-1S0) transition probability is known as internal clock, as critically discussed before.22 The Mg* atoms were produced by passing the atomic beam through an electrical discharge. For a similar source, ca. 20% of alkaline earth atoms were in the metastable 3P states23sthe value used in the present work. The number density of the metal atoms was determined under the assumption that it is proportional to the number density in the oven;24 i.e., it scales as (po/To). Since the oven temperature To was uncertain within (10 K, the metal vapor pressure po obtained from the standard formulas25 has a rather large error. This limits the accuracy of the absolute values of σCL. The resulting uncertainty of the CL cross sections does not exceed a factor of 2, when comparing the data for different metals. The uncertainty is much lower when comparing σCL values for the same metal M and different gases. The relative rates of light production in the M + (X2, XY) reactions were thus compared in a single experimental run with a fixed M, and all target gases one after another. This procedure was repeated three time. Intensities agreed within 20%. The absolute MX2* chemiluminescence cross sections were determined by cross-calibration20,21 with the known cross section for Mg* + I2 f MgI(B′-X) reaction under identical kinetic conditions. 3. Results and Discussion The CL pressure dependence was measured in the 0.00010.25 Pa range for 15 systems: (Ca, Sr, Ba) + (Cl2, Br2, I2, ICl, IBr). For each system, three to eight experimental runs were made, each producing several hundred data points, which were collected by a computer. The values of adjustable parameters A, B, and C, and σM and σMX, in (8-10) were then obtained by least-squares fits. Figure 1 shows sample fits of the Ba + I2 data to six models. Fitting attempts involving single reaction channels failed badly. R2BR alone (Figure 1a) cannot reproduce the nearly quadratic rise at low pressure and shows large deviations at higher pressures. The modeling with R3BR alone (Figure 1b) does not give the linear increase in the “microTorr regime” and fails throughout the pressure range covered, always deviating contrary to R2BR. TSCR does best, but the biggest problem with the simulation (Figure 1c) is that it does not give the observed linear increase of ICL in the microTorr (
