J. Phys. Chem. 1984,88, 2243-2241 spectra quickly revert to those of unpurifed solutions. Methods. Samples were prepared as described above in a sealed cell consisting of two arms: a larger reservoir for the bulk solution, and a 3 mm i.d. quartz optical arm. The concentration of the solution in the optical arm was adjusted by vacuum transfer of the solvent into or out of the optical arm, as desired. With this arrangement the complete range of concentrations can be studied on a single sample without exposing it to the atmosphere. In these sealed cells the concentration was determined by comparing the tautomer fluorescence intensity at room temperature to that of a standard solution in the same solvent. The fluorescence intensity at room temperature was found to vary linearly with concentration over the range investigated. Minor deviations in the tube diameter introduce a slight degree of error into this procedure; such deviations are not significant to this work. Because the observed solvation and aggregation effects are found to be strongly cooling-rate dependent, all 77 K spectra are reported for quick-frozen samples which were plunged directly into liquid nitrogen. Consistently reproducible results were obtained in this manner. Water was added to the purified hydrocarbon solutions in a stepwise fashion by allowing atmospheric moisture to condense into the momentarily unstoppered sample cells (at 77 K) for various periods of time. Then upon warming in the closed system and refreezing, the curves of Figure 2 were obtained. Watersaturated solutions were prepared either by the addition of a drop
2243
of water, allowing sufficient time for mixing (cf. Figure 2, top), or by bubbling water-saturated Nz gas through the solution (cf. Figure 8, bottom). Analogous results were obtained by each method. Apparatus. All absorption spectra were measured on a Cary 15 spectrophotometer. The 77 K and variable-temperature measurements were made in a specially designed Dewar. All luminescence measurements were obtained on a spectrometer array which consisted of the following: a 150-W xenon lamp excitation source, a 'l4-rn Jarrell-Ash excitation monochromator, an adjustable stage capable of mounting the liquid-nitrogen Dewars, and a 1-m Spex 1704 monochromator equipped with a 1P28 photomultiplier tube. The output of the photomultiplier tube was amplified by means of a Keathly picoammeter and plotted by a Hewlett-Packard X-Y recorder. Both monochromators were calibrated with the spectral lines of a low-pressure mercury lamp. In addition to the monochromators mentioned, various liquidz4 and glass optical filters (Corning) were utilized in both excitation and detection paths whenever low-level emissions were interfered with by stray or scattered light. All spectra reported are uncorrected for instrumental response. Registry No. 3-Hydroxyflavone,577-85-5.
(24) M. Kasha, J. Opt. SOC.Am., 38,929 (1948).
I ntramultiplet-Mlxlng Collisions of I n 5p *P, with Molecules. Absolute Cross Sections and Collision Energy Dependence J. M. Parson Chemistry Department, The Ohio State University, Columbus, Ohio 43210 (Received: September 14, 1983)
Experiments using CW laser-induced fluorescence of an atomic beam have been performed which show efficient transfer from the 2P3/2 state to the zP1/2state in collisions with CO, 02,NH3, CH4, C2H4,and CzH6. Upper and lower bounds on cross sections for this process were obtained by observing the populations of both In states as the gas pressure was varied. Vibrational excitation of these molecules is energetically allowed and likely to occur. Cross sections were too small to be determined accurately for scattering by He, Ar, H2, and N2. A time-of-flight (TOF) method was used to obtain the dependence of the cross sections on the average collision energy. For the gases with larger cross sections, a decrease with increasing collision energy was observed, suggesting that attractive interactions occur up to the region of nonadiabaticity.
Introduction Numerous measurements have been made of rates of collisional transfer between atomic spin-orbit levels arising from the same L-S term.' Most frequently these have involved excited atomic terms, which means that the intramultiplet-mixing transitions compete with other processes such as chemical reaction or quenching to lower atomic terms possibly accompanied by electronic excitation or dissociation of the collision partner. In order to test models for nonadiabatic processes, it is convenient to identify systems which involve a small number of potential energy surfaces, as is possible for intramultiplet-mixing transitions within the lowest atomic term in collisions with an atom or molecule restricted to a single electronic state. Collisional transfer between the lowest np 2P1/2and 'P3/2 states of group 3A atoms represents such a case, and we report here measurements of cross sections for the process
for X = CO, 0 2 , NH3, CH4, C2H4, and C2H6. The absolute values (1) S:e, for example, L. Krause, Adv. Chem. Phys. 28, 267 (1975); H. Okabe, Photochemistry of Small Molecules", Wiley, New York, 1978, pp 139-161.
0022-3654/84/2088-2243$01 .50/0
and energy dependence of the cross sections have been found by using a beamscattering gas configuration and a C W tunable dye laser to monitor the atomic states. Because the exoergicity for process 1 (2213 crn-')' is large compared to the average relative collision energy ((ET)= 440-580 cm-'), we may neglect the reverse process under our experimental conditions. Experimental Arrangement The 'P3/2 state of In was prepared in an effusive source operated at 1300 K, at which the vapor pressure is -0.05 torr and 15% of the beam is in this state. The radiative oven heating arrangement has been described previ~usly.~A tantalum oven with an alumina crucible and a 1.6-mm-diameter orifice was used. The oven chamber was pumped by a 6-in. diffusion pump, and the scattering-gas chamber by a baffled 4-in. diffusion pump. The scattering gas was introduced by a needle valve at a large distance from the In beam, and the pressure was determined by a capacitance manometer (Datametrics Model 573). The pressure rise
-
-
(2) C. E. Moore, NBS Handb. (US.), No.35 (1971). (3) J. M. Parson, L. C. Geiger, and T. J. Conway, J . Chem. Phys., 74,5595
(1981).
0 1984 American Chemical Society
2244
The Journal of Physical Chemistry, Vol. 88, No. 11, 1984
in the oven chamber when the scattering gas was introduced was too low to affect the beam. In principle, process 1 may be detected by monitoring either a loss of the zP3/2state or a gain of the 2Pl/2state. The former is preferred because the fractional change in the 2P312state will be much larger as it is a small fraction of the beam initially. It is useful, however, to be able to monitor the 2Pi/2state in order to test for the presence of elastic scattering of the In prior to the detection region. Elastic scattering is expected to be limited to a small cone about the In beam for the collision partners used, which are all much lighter than In. Also, the scattering cell and detection geometry were chosen so as to minimize the extent of elastic scattering. The output of a CW dye laser was passed perpendicular to the In beam at a close distance (6.3 mm) to a 1.1-mm-diameter orifice which allowed the In beam to enter the scattering-gas chamber. Elastically scattered In atoms were expected to lie in the path of the laser and hence to be detectable. For monitoring the 2P3/2state the dye laser (Spectra Physics Model 380A), pumped by the UV output of an Ar ion laser (Spectra Physics Model 171-19), was operated with stilbene 3 laser dye and a three-plate birefringent filter, producing light at 451 1 A with a bandwidth of -0.5 cm-' for excitation to the 2S state. For the 2P112state the dye laser was operated with stilbene 1 laser dye and a one-plate birefringent filter, producing light at 4105 A with a bandwidth of - 5 cm-I, also for excitation to the 2Sstate. The stability of the excitation was enhanced by rapidly modulating the frequency of the dye laser over -0.1 cm-I by means of a sine wave oscillation (150 Hz) imposed upon the angle of orientation of two intracavity galvonometer plates which varied the cavity length. The laser at the intersection region had a circular profile with a diameter of - 4 mm. Fluorescence of the ' S state was detected free of scattered laser light by employing an interference filter which passed emission only to the 2PJstate not being probed by the laser. Light was collected at 90' to the laser beam with a 50-mm-diameter aspheric lens with a focal length of 33 mm positioned -50 mm from the In beam and focused on the cathode of a photomultiplier tube (EM1 Model 97894 B). Standard photon counting methods were used. Care was taken to avoid significant optical pumping from one spin-orbit state to the other by attenuating the dye laser output with neutral density filters until the fluorescence signal was proportional to laser power. were found by measuring Absolute cross sections for loss of 2P312 the ratio of fluorescence signals with gas off and on for pressures state population was also monitored up to 100 mtorr. The 2P112 over this pressure range. The collision energy dependence of the cross section for loss of 'P3/2 was measured by detecting the fluorescence as a function of In flight time from a chopper close to the oven orifice to the detection region. The chopper was a 13.3-cm-diameter aluminum wheel with four 2-mm-wide slots which was rotated at 190 H z by an asynchronous motor and was located 20.8 cm before the detection zone. Fluorescence pulses were counted by a 100-channel analyzer (Honeywell Model SAI-42A) with 10-k~dwell time per channel. The trigger pulse for the analyzer was taken from a lamp and photodiode combination located at 180' to the beam axis. The TOF data were transferred to a Hewlett-Packard desk calculator for storage and analysis. TOF spectra were accumulated with the scattering gas off, on, and then off again. The two gas-off curves were averaged to correct for drift in the laser intensity or frequency. The spectra reported here were obtained with a 1 X 10 mm slit located 11.4 mm from the detection region rather than the geometry described above. Both geometries gave similar absolute attenuation cross sections, agreement being within 20%. Absolute Cross Section Since transitions from 2P to 'P3/2 are forbidden at the collision energies sampled here, the 'I' P312 population is expected to follow the simple form4
N3/, = N"3/2e-*anJ
(2)
(4) See, for example, R. D. Levine and R. B. Bernstein, "Molecular Re-
action Dynamics", Oxford University Press, New York, 1974, p 18.
Parson
-1
-- I
I
oo
0 IO
O2
82 0
310
Number Density, IOf4 c m 3
Figure 1. Dependence of the J = 3 / 2 (circles) and J = (squares) populations on the O2number density. The lines are least-squaresfits to the data.
'
-Oat
-' 8
10
20
30
C H 4 Number Density, 10'4cm3
Figure 2. Same as Figure 1 for CHI.
where N O 3 1 2 is the In number density entering the collision chamber, n, is the scattering-gas number density, 1 is the flight path, and ua = u1 a,{ is the sum of the cross section for process 1 and an effective cross section associated with deflection of 2P312 from the detection zone. Thus, we have used plots of In (N312/ p 3 l 2 )vs. n, to determine 6,. Figures 1 and 2 show such plots obtained for X = 0, and CH4. The 2P1/2state, on the other hand, will be filled by process 1 and depleted by elastic scattering leading to the rate equation
+
dNl/2/d1
=
ul'N3/2nx
- uel"Nl/2nx
(3)
where ueyis the effective elastic cross section for deflection of 2P1/2from the detection zone and ul' is the cross section for only those inelastic events which yield the 2Pi/2product within the detection zone. Hence, ul' 5 ul and we also expect u,,' 5 u,," since small impact parameter collisions which elastically deflect 2Pi42may instead lead to process 1 rather than elastic scattering of P3j2. If one uses eq 2 for N3~2,eq 3 has the solution Nll2
=
Clearly, there are too many unknowns here to be found: ul,ul', and ue,". However, we may obtain an upper limit on a', by assuming that u,' = u,," and u1 = uI'. Then eq 4 reduces to
,:,u
N 1 1 2 / N 0 i 1=2 (1
+ @3/2/N"I/2)e-b~l'nx' - (~3/2/N"I/Z)e-aan~' (5)
The latter term is known from the N 3 / 2fit, and we have varied u,' using a nonlinear least-squares fitting program to match the experimental values for N l j 2 / N " las ~ 2a function of n,. Inclusion
The Journal of Physical Chemistry, Vol. 88, No. 11, 1984 2245
Collisions of In 5p 2PJwith Molecules TABLE I: Upper and Lower Bounds on the Cross Sections for Process 1 at the Average Collision Energies Shown (T,= 300 K)
= ~i(max), ffa
(ET), kJ/mol 6.9 6.2 6.2 6.4 5.4 5.3 6.2 6.3
scattering gas Ar N2
co 0 2
3"
CH4 C2H4 C2H6
ua - ue{
I
I
\
I
I
I
I
I
I
\
i
=
u1(min),
A2
A2
8.4 9.8 24.3 35.1 85.8 23.6 44.4 40.2
2.5 1.6 15.5 31.9 81.4 17.0 38.3 35.0
1
0
I
I
I
5
I 10
1
I
15
(ET) , kJ/mol
Figure 4. Dependence of the u, cross sections for scattering by O2on the
*I" 1 .
.........../02
am
-
off
" L
i
I
..... 1..
E
,
. ...... . .*. ..*. . . . . ...... ............ ................... .......................
5
e
0
a, = (2kTx/m,)1/2, the distribution of relative collision energy ET is given by5
*. * a *
-
d
I
00
average collision energy. The circles are experimental points, the solid line is the best fit using u, ET-'"(& - EO)q convoluted over the distributionof collision energies, and the dashed line is the unconvoluted energy dependence of the cross sections. Error bars represent 95% confidence limits based on counting statistics.
02
04
In
06
08
Flight Tirne,rnsec
Figure 3. TOF distributions for In *P3i2 with and without scattering by 02. Note the larger depletion of slower In atoms by scattering.
of more parameters to represent NIl2,as in eq 4,is not justified because of the good fit provided by varying only Q'. It may appear from eq 5 that N112/A@112 should increase with n, for the case of small ue{. This behavior was noticed for X = NH3 which has the was nearly largest value for a,, but for the other gases Nl/2/A@112 constant or decreased slightly because of greater removal by elastic scattering than formation from the 'P3/2 state, whose population is much smaller initially. A lower bound on ul may be obtained by subtracting this ae,' from a,. An upper bound on crl is of course ua. Because of our choice of beam and detection geometry, a,,' is often much less than a,, making the upper and lower limits on aI close to each other. Table I presents the limits on a1obtained in this way for X = Ar, N2, CO, 0 2 , NH3, CH4, CzH4, and CzH6. Uncertainties in these limits arise from a number of sources: absolute pressure uncertainties of -*lo%, scattering path length uncertainty of --f15%, and the effect of random fluctuations in pressure and laser frequency of -&lo%. Thus, the upper and lower limits on ul are generally known to within --f30%, except for Ar and N2, where the lower limit of ul may be as small as zero. Relative cross sections are more accurately known because of cancellation of absolute errors in the pressure and scattering path length. For H e and H2 as scattering partners, no attenuation of the 2P3/2population was observed, and hence ul was too small to measure by using this experimental arrangement. Energy Dependence of Cross Sections Figure 3 shows N312and N o 3 1 2 obtained for scattering by O2 as a function of the In flight time. The shift of N3/2 to shorter times indicates that slower In atoms are preferentially lost in collisions with 02.Since eq 2 for N3/2 holds for each In velocity, the dependence of a, upon the In velocity may be found simply by plotting - In (N3/2/A@3/2).For all of the scattering partners listed in Table I except Ar and N2, ul makes the major contribution to ua, and the velocity dependence of al will be approximately the same as that for u,. Of primary interest is how a, depends on the relative collision energy, which has a distribution of values for each In velocity because of the motion of the scattering gas. For an In velocity of u l , a reduced mass N, and
Additional spread in ET values for a given flight time due to the finite shutter open time and detection zone size is negligible compared with this spread and will be neglected. From eq 6 it is readily shown that the average value for ET is given by
(7) In Figure 4 the relative values for a, for collisions with O2 are plotted vs. ( E T ) . Only points for which N3/2is greater than 1 / 4 of its maximum value have been used in this plot. In order to compare model predictions of how a1 depends on ET with experiment, it is necessary to convolute the model form with the distribution given by eq 6. We have investigated the following general form for the dependence of cross sections on ET: U,
-
ET-P(ET - E0)q
(8)
This reduces to the hard-sphere line-of-centers form when p = q = 1 and to a modified close-collision energy dependence for a long range r-s potential when p = 1 and q = 1 - 2/s, as discussed by Menzinger and Yokozeki.6 Eo is the potential barrier for the process. Withp = 1 and q = 1/2 eq 8 can also be used to represent a perturbation theory model for the Hg fine structure transition 3P1-3P0 in collisions with N2, which has been proposed by Bykhovskii and N i k i t h 7 In addition, the Born approximation for atom-diatom collisions follows this form with p = 3/2, q = 5 / 2 , and Eo the endoergicity for the process.8 Menzinger and Yokozeki6 have suggested that this Born approximation form may be applicable to other molecular systems if q is adjusted to take account of different densities of product states. We have used a weighted nonlinear least-squares fitting program to vary parameters in eq 8 so as to match the convoluted cross sections to the experimental results. Two ways of constraining the parameters were employed: (i) the close-collision model for which q = 0 and p was varied and (ii) the Born model for which p = 3 / 2 and Eo and q were varied. Data points were weighted by l/a2, where a is the standard deviation based on uncertainties in the counts used to compute the cross section via eq 2. Results are given in ( 5 ) L. Pasternack, and P. J. Dagdigian, J . Chem. Phys., 67, 3861 (1977). (6) M. Menzinger and A. Yokozeki, Chem. Phys., 22, 273 (1977). (7) V. K. Bykhovskii and E. E. Nikitin, Opt. Spectrosc. (Engl. Transl.), 16, 1 1 1 (1964). (8) B. C . Eu,Chem. Phys., 5 , 95 (1974).
2246 The Journal of Physical Chemistry, Vol, 88, No. 11, 1984
Parson
TABLE 11: Fits Obtained for the Relative Collision Energy Dependence of 2P3/2 Attenuation Cross Sections' scattering gas
co 0, 3"
CH4 C2H4 C2H6
ua
-
g
N
E,-3/2,
(ET - EO)'
ET-P
P
X:
0.80 (4) 0.60 (2) 0.73 (2) 0.64 (4) 0.84 (2) 0.73 (2)
3.3 3.0 4.3 6.9 3.6 4.3
-Eo,kJ/mol 2.0 3.4 3.0 1.2 1.9 4.6
(2) (3) (2)
(I) (1) (4)
q 1.35 (6) 1.97 (8) 1.79 (5) 1.40 (6) 1.27 (4) 2.08 (8)
XrZ 3.0
1.9 5.8 6.8 2.6 3.0
I
5
lo
0
a Numbers in parentheses give changes in the least-significantdigits which change x ~ Z by 1.
Table I1 along with the reduced x squared (x:). Approach (ii) gave somewhat better fits, but deviations were still apparent at low energies where the experimental points generally exceeded the calculated points. Figure 4 compares the calculated curve by using this approach with the experimental points for 0,.The solid curve is the convoluted cross section, and the dashed curve is the unconvoluted cross section. The difference between these two curves emphasizes the importance of convoluting the cross section in beam-gas experiments.
Discussion Extensive experimental and theoretical studies of intramultiplet mixing in 2PJalkali atom-rare gas collisions have shown that the cross sections decrease very rapidly with increasing energy gap.g The In-rare gas potential curves have the same symmetries, and the models which explain the alkali transitions9 should also be applicable here. These models predict very small (
