electronic quenching of bi2 a

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Electronic Quenching of Bi2 A(0u+) v’= 18-23 by Rare Gases and Nitrogen

for submission to Chemical Physics

5 July 2007

Joeseph L. Cox, Dean T. Cherer, and Glen P. Perram1

Deprtament of Engineering Physics

Air Force Institute of Technology

2950 Hobson WayWright-Patterson AFB, OH 45433-7765

1 Corresponding author: Glen P. Perram, AFIT/ENP, 2950 Hobson Way, WPAFB, OH

45433-7765, [email protected], (937)-255-3636 x 4504, FAX (937)-656-6000.



Abstract

The rates for electronic quenching of the A(0u+) state of Bi2 by rare gases and nitrogen near

the onset of predissociation, v’=18-23, have been measured using pulsed laser induced

fluorescence. The rate coefficient for helium is 2.2 ± 0.1 x 10-11 cm3/molecule-s for v’=18

– 22, and increases to 1.0 ± 0.1 x 10-10 cm3/molecule-s for v’=23. The probability of

quenching per collision for v’=22 by rare gases ranges from 0.03 - .44 and for v’=23 from

0.15 – 0.80. The quenching probabilities for nitrogen are slightly larger than those for

argon. Despite the onset of rotationally dependent predissociation at v’=21, no significant

dependence of quenching rates on rotational state J’< 117 was observed. Electronic

quenching of higher vibrational levels, v’>23, was not temporally resolvable in the current

experiments, due to the very rapid predisocciation.

Keywords: Bismuth dimer, electronic quenching, laser induced fluorescence, lifetimes,

predissociation.



1. Introduction

The A(0u+) electronically excited state of the bismuth dimmer, Bi2, is well characterized

spectroscopically,[1-11] and exhibits a predissociation beginning at v’= 21 which becomes

quite strong above v’=22. [4-5,7] However, the ro-vibrational dependence of the

quenching of Bi2(A) is uncertain. The early lifetime studies indicate nearly gas kinetic

quenching rates. [4-5] Quenching by argon was studied for v’=1-34 and J’=10-255 with

rate coefficients of k qAr = 2.1 – 5.8 x 10-10 cm3/molecule-s. [4] However, nonlinear Stern-

Volmer plots were observed for pressures above 1 Torr, and the corresponding collisionless

decay rates exhibited a (v’, J’) dependence in disagreement with the recent systematic

study of predissociation. [7] More recently, an upper bound for the quenching of the low

lying v’=1-4 states by neon of 0.9 – 3.3 x 10 -12 cm3/molecule-s was reported from cw laser

induced fluorescence studies of vibrational energy transfer. [12]

The rates for collisional deactivation of electronic states with strong predissociation often

exhibit a dependence on ro-vibrational state, due to energy transfer to the unstable states or

collision induced predissociation. For example, the ro-vibrational dependence

of the collisional deactivation rates in Br 2 B3Π(0u+) have been examined in detail.

Collisional deactivation in Br 2(B) is very rapid and has been attributed to a variety of

mechanisms, including ( 1) collision induced predissociation involving the 0u

-

(3

Π) state,

[13] (2) energy transfer followed by spontaneous predissociation, [14-16] (3) pure

electronic quenching, [17] and (4) collisional release. [18] In the present work, we seek to



determine the ro-vibrational dependence of the electronic quenching rates for Bi2 A(0u+)

near the onset of predissociation , v’=18-23, to interpret the quenching mechanism.

2. Experimental

The pulsed laser induced fluorescence apparatus has previously been described in detail.

[12] Briefly, a Spectra Physics Quanta Ray DCR-3G pulsed Nd:YAG was used to pump a

Spectra Physics Quanta Ray PDL-3G tunable pulsed dye laser with Coumarin-480 and 500

dyes to produce 10 - 15 mJ in a 17 ns FWHM pulse. The bismuth fluorescence cell heated

granular bismuth to ~ 900 C via a tungsten basket heater to produce significant populations

of both Bi and Bi2. The six-way cross vacuum chamber was evacuated to as low as 0.01

mTorr with an oil diffusion pump. The side fluorescence was focused through a 600 nm

long pass filter onto a Burle C31034 photo multiplier tube (PMT), amplified by an EG&G

Model 5185 preamplifier, and monitored with a LeCroy 9450A Dual 300MHz

oscilloscope. [19] Multiple fluorescence decays (5000 waveforms for helium and 2000

waveforms for all other gases) were averaged for each static buffer gas pressure condition.

The assignment of laser pumped ro-vibrational states were assessed from laser excitation

spectra. [12] Due to the dense absorption spectrum, the near overlap of P(J) and R(J+8)

lines, and the 0.07 cm-1 linewidth of the pump laser, there is a blending of pumped

rotational levels with a range of ∆J ≅ 8.



3. Results and Discussion

The decay of fluorescence after laser excitation of v’=20-23 with 0.23 – 0.28 Torr of

helium buffer gas is shown in Figure 1. For the lower vibrational levels, v’=18-22, the

decay is well represented by a single exponential:

b

t

o I e I I += Γ −(1)

where

I o = peak intensity

I b = background intensity

Γ = decay rate

The decay rate in Figure 1 for v’=20 is Γ = 1.814 ± 0.001 µs-1, or a decay time of τ = 0.55

µs, which is slightly shorter than the radiative lifetime of 0.57 ± 0.08 µs. [7] The signal-to-

noise is sufficient to track the decay over 4-5 e-folds. The decays from v’=18-21 are very

similar. The decay from v’=22 is faster, but the change is independent of pressure and is a

result of predissociation. [7] However, at v’=23, the quenching rates increase dramatically.

For v’>23, predissociation dominates and the decay rates are two rapid to measure in the

current apparatus. In all cases, the fits were applied to data sectioned beyond t ≅ 0.1 µs, to

avoid convolution with the temporal shape of the laser excitation source.

Figure 2 provides a Stern-Volmer plot for the pressure dependence of the decay rates:



][ M k M

qo +Γ =Γ (2)

where

Γ o = collisionless decay, including radiative and predissociative rates

k q M = rate coefficient for quenching by specie M

[M] = concentration of specie M

The quenching rates for helium are obtained from a linear fit of equation (2) to the data of

Figure 2 and reported in Table I. The uncertainties in the fit decay rates, Γ , at each pressure

are quite small, typically 0.1 – 1%. Systematic errors associated with pressure control lead

to somewhat larger error bound for the fit rate coefficients of 5 - 10%.

The decays from v’=22 for a variety of collision partners is illustrated in Figure 3 and the

resulting quenching rate coefficients are provided in Table II. The scatter in Figure 3 is

somewhat larger than in Figure 2, due in part to the averaging of 2000 instead of 5000

waveforms.

The quenching from v’=23 is considerably faster than v’=18-22 with a nearly gas kinetic

rate coefficient. Furthermore, single exponential fits are inadequate to describe the

pressure dependence of the decay rates. Indeed, the corresponding Stern-Volmer plot for

v’=23 exhibits a negative slope, as shown in Figure 4. Therefore, double exponential fits

were also employed:

b

t t

o I aee I I ++=Γ −Γ − )( 1 (3)



where a is the relative amplitude for component of second decay rate and Γ 1 was

constrained to the value determined for the same pressure in v’=22. Fits of the observed

decays to equation (2) are also provided in Figure 4, and do indicate a linear correlation

with pressure. The quenching rates for v’=23 as reported in Table II were determined from

these double exponential fits.

The quenching rates are large, with probabilities:

g

k

k

k P

M

M

q

M

g

M

q

σ

`

== (4)

where the gas kinetic rate coefficients, k g M are defined by the hard sphere collision cross-

sections,2

2 )( M Bi M r r += π σ and relative collision speed,2/1

2 )/8( M BikT g −= πµ . The

data for collision radii, r M , and reduced mass, µ Bi2-M , are discussed in reference [19]. The

probability of quenching per collision are high, P = 0.03 – 0.44 for v’=22 and 0.05 – 0.80

for v’=23, and scale linearly with polarizability of the collision partner, as shown in Figure

5.

The rotational dependence of the rates for quenching by helium in v’=17, 19, and 21 was

also examined during a second set of experiments and the results are summarized for J’ =

18 - 116 in Figure 6. No significant rotational dependence is observed.



4. Conclusions

Previous studies of the quenching of Bi2(A) [4-5] indicated total deactivation rate

coefficients of 2.1 – 5.8 x 10-10 cm3/molecule-s for v’=1-34, which is considerably higher

than the present results. However, these studies were focused on predissociation and

employed a grating spectrometer to limit the emission to a single vibrational level. Thus,

the deactivation rates include vibrational energy transfer, and these rates are relatively large

even for low lying vibrational levels. For example, the V-T transfer rate coefficient for

v’=4 →v’=3 for neon is 1.96 ± .31 x 10-11

cm3

/molecule-s.[12] Scaling these V-T rates to

v’=18-23 could easily explain the difference in total deactivation.

There is a strong dependence of collisionless lifetime on rotational state in v’=23 due to

predissociation [7] and one would expect a dependence of quenching rates on rotational

state if rotational energy transfer to less stable states contributed significantly to the

electronic deactivation [14-16]. Such a dependence is not observed in the present

experiments. However, the multi-exponential behavior of the quenching in v’=23 does

suggest two contributions to the quenching: (1) a component independent of vibrational

level, and (2) vibrational energy transfer up the manifold to less stable (highly

predissociated) states.

The quenching rates for all studied vibrational levels are quite large, and pure electronic

quenching, particularly to the ground electronic state appears unlikely. The electronic

structure of Bi2 near the A-state is dense. Thus, electronic quenching involving transfer of



population to the adjacent states, or possibly collision induced predissociation, appears to

be a more likely mechanism.



References

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6. R.E. Franklin and G.P. Perrram J Molec Spectrosc 194 1 (1999).

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8. G. Gerber, Honinger, and J. James Chem Phys Lett 85 415 (1982).

9. G. Gerber and H.P. Broida J Chem Phys 64 3423 (1976).

10. R.F. Barrow, F. Taher, J. D’Incani, C. Effantin, A.J. Ross, A. Topoizkhanian, G.Wannous, and J. Vreges Molecular Physics 87 725 (1996).

11. C. Effantin, A. Topouzkhanian, J. Figuet, J. d’Incan, R.F. Barrow, and J. Verges J Phys B 15 3829 (1982).

12. R.E. Franklin and G.P. Perram J Chem Phys 111 5757 (1999).

13. M. Kitamura. K. Nakaaawa. K. Suzuki. T. Kondow. K. Kuchitsu. T. Manakata, and T.

Kasuia, J Phys Chem 90 1589 (1986).

14. L. J. Van de Burgt and M. C. Heaven, Chem Phys 103 407 (1986).

15. M. A. A. Clyne and M. C. Heaven, J Chem Soc Faraday Tran. II 76 1992 (1978).

16. M. A. A. Clyne, M. C. Heaven, and S. J. Davis, J Chem Soc Faraday Tran. II 76 961

(1980).

17. M. A . A. Clyne M. C. Heaven, and E. Martinez, . A . A. Clyne M. C. Heaven, and E.

Martinez, J Chem Soc Faraday Tran. II 76, 405 (1980).



18. J. E. Smedley, H. K. Haugen, and S. R. Leone, J Chem Phys 86 680l (1987).

19. J.L. Cox, “Electronic Quenching of the A(0u+ ) State of Bi2”, Masters Thesis, Air Force

Institute of Technology, AFIT/GAP/ENP/01M-02 (2002).



Table I. Vibrational Dependence of Rate Coefficients for Quenching by Helium

v’ k q He ( 10-11 cm3/molecule-s)

18 2.27 ± 0.0919 2.10 ± 0.12

20 2.25 ± 0.11

21 2.23 ± 0.07

22 2.27 ± 0.16

23 10.5 ± 1.4

Table II. Quenching Rates for Rare Gases and Nitrogen

k q M ( 10-11 cm3/molecule-s)

v’ He Ne Ar Kr Xe N2

22 2.27 ±

0.16

2.8 ± 0.2 6.6 ± 0.3 6.4 ± 0.2 8.5 ± 0.6 8.0 ± 0.5

23 10.5 ± 1.4 7.4 ± 1.7 13.1 ± 2.1 ----------- 15.6 ± 1.4 15.7 ± 4.9



Figure Captions

Figure 1. Exponential decay of fluorescence after laser excitation of: ( ) v’=20 at helium

pressure of 0.23 Torr, (- ⋅ -) v’=21 at 0.23 Torr, (⋅ ⋅ ⋅ ) v’=22 at 0.28 Torr, and (---) v’=23

at 0.28 Torr.

Figure 2. Pressure dependence of decay rates with helium collisions for: (O) v’=18, ( )

v’=19, (∇ ) v’=20 and (∆) v’=21.

Figure 3. Pressure dependence of decay rates for v’=22 for collisions with: (O) He, (•) Ne,

( ) Ar, (s) Kr, ( ∆) Xe, and () N2.

Figure 4. Pressure dependence of decay rates for v’=23 for collision with helium: (•)

single exponential fit to equation (1) and (O) doube exponential fits to equation (3).

Figure 5. Scaling of the probability for quenching per collision with polarizability for

various collision partners for (O) v’=22 and ( ) v’=23.

Figure 6. Rotational dependence or helium quenching rate cofficients for (•) v’=17, (O)

v’=19, and (s) v’=21.



time, t (µs)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

l o g 1 0

( I ) ( a r b . u n i t s )

10-3

10-2

10-1

100

101



He Pressure, PHe

(Torr)

0 1 2 3 4 5 6

D e

c a y R a t e ,

Γ

( 1 0 6

s - 1 )

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5



Buffer Pressure, P (Torr)

0 1 2 3 4 5 6

D e c a y R

a t e ,

Γ

( 1 0 6

s - 1 )

2

4

6

8

10

12

14

16

18



Helium Pressure, PHe

(Torr)

0 1 2 3 4 5 6

D

e c a y R a t e ,

Γ ( 1

0 6 s - 1 )

10

15

20

25

30

35

40

45



Polarizabiity, α (A3)

0 1 2 3 4 5

P

= k

q / k

g

0.0

0.2

0.4

0.6

0.8

1.0He Ne N

2Ar Kr Xe



J'

0 20 40 60 80 100 120

k

q ( 1 0 - 1 1 c m

3 / m o l e c u l e - s )

1.8

2.0

2.2

2.4

2.6

2.8

electronic quenching of bi2 a

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