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LIF measurements of radiative lifetimes of the C2(B'1Σ+g) state
CHEMICAL PHYSICS LETTERS
Volume 2 17, number 3
LIF measurements Mengxiong
14 January 1994
of radiative lifetimes of the C2 (B’ ‘Xi ) state
Gong, Yihan Bao, Randall S. Urdahl and William M. Jackson
Department of Chemistry, University of California, Davis, CA 95616, USA
Received 30 September 1993; in final form 8 November 1993
The 193 nm photolysis of acetylene has been used as a source of &(B ‘Z: ) radicals, which are subsequently detected by laserinduced fluorescence technique. The pressure-dependent collisional lifetimes of this radical are experimentally determined by delaying the probe laser with respect to the photolysis laser, thus allowing extraction of the pseudo-first-order rate constants. Stem-Volmer plots of these rate constants versus pressure yield the natural radiative lifetimes of the state. Three different rotational levels of the C2(B’ ‘8: ) state were studied. The natural radiative lifetimes were 11.6 f 1.4 us and 10.4 k 1.9 us for the D’=0, J’= 8 and J’= 14 levels, respectively, and 8.3 f 1.9 us for the II’= 1, J’= 8 level. These values are in reasonable agreement with the recent theoretical calculations. In addition, the second-order rate constants for the excited state quenching by Ar have also been calculated from the data.
1. Introduction The natural radiative lifetime for many of the electronic states of CZ has been either theoretically calculated and/or experimentally measured [ 11. For the b ?Zg state (T,=6434.27 cm-‘), which is the upper state of the Ballik-Ramsay bands, the experimental lifetime, 7, of 17.2 p (v=O) is in good agreement with theory [ 2,3]. By contrast, two experimental measurements of 7(v) for Cz(A ill,) yielded values of 18.5 us for v= 0 and 11.4 us for v= 3 in one study and 13.4 us for v= 0 and 12.0 us for v= 3, which are in reasonable agreement with each other [ 4,5]. These values are typically 30%-50% larger than those predicted by theory [ 6,7]. Numerous experimental studies of the familiar visible transitions in the Swan system (d ‘$+a ‘II,) give lifetimes of x 100 ns for both the v= 0 and v= 1 levels of the d “l-l, state (T,=20022.5 cm-‘) [2,8], but there have been no theoretical calculations to compare with these experimental values. In the case of the most common ultraviolet transitions, radiative lifetime measurements of the upper levels of the C ilIp and D ‘Z: states of the Deslandres-d’Azambuja and Mulliken systems yield values of 7(C ‘II,, v=O) = 65 ns [ I] andr(D1C,+,v=0)=15.6ns [9], 18.1 ns [lO],but 210
only the latter values are in modest agreement with theory [2]. Theoretical lifetime calculations have recently been performed on the infrared transitions of two newly detected electronic states of CZ, namely the B ‘4 (T,=12082 cm-‘) and B”Xl (T,=15409 cm-‘), for which no experimental lifetime data currently exists [ 11,12 1. In addition to the intrinsic value of this information, knowledge of the CZ(B’ ‘X: ) radiative lifetime would be useful in determining the contribution of cascade processes to the measured lifetime oftheA’II,state [ll]. In the present experiments, the radiative lifetimes of the B’ ‘Ep’, v= 0 and 1 states of CZ have been determined by photolyzing CzH2 with a focused ArF excimer laser and using a tunable dye laser for LIF detection of individual rotational levels of these states. The lifetimes are measured by delaying the probe laser with respect to the photolysis laser, which yields pseudo-first-order rate constants. StemVolmer plots of these rate constants yield the lifetime of this state, as well as the rate constants for electronic quenching by Ar. The lifetimes of three different rotational levels were studied, namely the J= 8 and J= 14 levels of the v= 0 vibrational level, and the 5~8 level of the v= 1 vibrational level.
0009-2614/94/$ 07.00 0 1994 Elsevier Science B.V. All rights reserved. SSDI OOOOS-2614(93)E1374-P
Volume 2 17, number
3
CHEMICAL
PHYSICS
2. Experimental
The experimental conditions were similar to those described earlier [ 8 1, so that only the few changes that were made will be described. The output from an ArF excimer laser (Lambda Physik EMG 101 MSC) was apertured and focused with a 38 cm UV fused-silica lens into the 130 liter stainless steel vacuum chamber used for the static cell experiments. Typically, laser energies of =4 mJ/pulse were focused to a 0.3 mmX 1.5 mm rectangular spot, yielding fluences of zz 1 J/cm’. Excitation of the C2( B’ El > radical was performed with a XeCl extimer-pumped tunable dye laser (Lambda Physik EMG 101 +MSC/FL2002) operated with BMQ in dioxane, where the wavelength was tuned into a given rotational line of the D ‘Ef tB’ ‘Ez, Au=0 transition. The Mulliken band emission was collected with a Dynasil-1100 lens, isolated with a 25 nm fwhm interference filter (Corion) centered at 239 nm and focused onto the cathode of an EM1 9789QB photomultiplier tube (PMT). The output from the PMT was integrated by an Evans 4130 gate integrator and then fed into a Laser Interface LI-1000 series data acquisition system for signal averaging and analysis. The data acquisition system can be used to scan the delay time between the photolysis and probe lasers without affecting the delay time of the gate after the probe laser. At each pressure, care was taken to ensure that the PMT was not saturated. The acetylene (Matheson, 99.6% purity) was purified using a dry ice/acetone slush trap. The purity of Ar (Spectra Gases) was 99.999W.
3. Results and discussion Recently we have shown that the C2(B’ ‘Ez ) radicals are produced in the photolysis of C2H2 via the following reaction scheme [ 13,14 ] : W-b +ha,m+H+GH, CZH+~h93nm
+H+C2(B”C,+,
(1)
v,J) .
(2)
Transitions between the B’ ‘El state and the ground X ‘EC state of C2 are forbidden, thus any C2 radical produced in the B’ ‘Ez state will radiatively decay to the A ‘IIu state or be quenched. The radiative decay
LETTERS
14 January
1994
process creates infrared fluorescence, which is more difficult to measure than ultraviolet or visible radiation. Therefore, the probe laser was used to excite the D ‘Cz (v’, J’)+-B’ ‘E,‘( v”, Y’) transition at z 356 nm. The actual lifetime of the B’ ‘2: state was measured by determining the intensity of the emission from the D ‘E: (v’, J’) state as the probe laser was delayed with respect to the photolysis laser. Signal loss due to mass transport effects has to be taken into account, since the time evolution of the LIF signal depends not only on the radiative decay and quenching process, but also on the diffusion of excited radicals out of the probe laser volume, Bialkowski et al. [ 151 have derived the mass transport equations appropriate for a cylindrically symmetric, collinear or perpendicular pump-probe experiment. Their equations were used to estimate the minimum pressure of Ar (2 Torr) that needs to be added to insure that the loss of signal due to diffusion is less than 10% of what the signal would be without diffusion. The rotational relaxation within the same electronic and vibrational state could affect the measured quenching and radiative lifetimes. In our laboratory, we have measured the nascent rotational distributions of this fragment in the 193 nm photolysis of acetylene. Our results indicate that the nascent rotational distributions of the C2(B’ ‘Ep’ ) fragment can be approximately respected by the Boltzmann-like distributions with a rotational temperature of 670 K for the v=O level and 500 K for the v= 1 level [ 141. Using Ar as the buffer gas not only reduced the diffusion, but also quenched the rotational excitation in the nascent C2(B’ ‘El ) before any experimental data were collected. The range of Ar pressures used in the experiments is about 2 to 40 Torr, and the minimum delay time between the photolysis laser and probe laser is 0.5 ps. With the minimum Ar pressure we used, at the time for collecting the first data point (0.5 ~LSdelay time), there were already about 10 collisions between C2(B’ ‘Ez ) and Ar, which is sufficient to quench the rotational excitation in the nascent C2(B’ ‘Eg’ ) radicals formed in the photolysis of acetylene. Since the FranckCondon factors for the D ‘E,’ +-B’ ‘Ez transition are not available yet, we are unable to calculate the relative vibrational populations of the nascent C2( B’ ‘Cl ) radicals. Since the vibrational relaxation 211
14 January 1994
CHEMICAL PHYSICS LETTERS
Volume 2 17, number 3
takes much longer than the rotational relaxation, the measured lifetimes and rate constants could be affected by the vibrational excitation which may exist in the nascent C2(B’ ‘Ez ) radical. However, if quenching of the excited vibrational levels was a problem, the measured rate constant for Ar quenching for the v”= 1 level should be larger than that for the v” = 0 level. In fact, as we shall see later, they are about the same. The reactions controlling the intensity of LIF signal can be summarized as follows: &(B”Z,+,
v’,.Z’)-C~(A
‘I&, ~“,J”)+hy,
(3)
&(B’%B+, v’,J’)+C,H,+products,
(4)
Cz (B’ ‘Xz , Y’, S ) + Ar+ quenching ,
(5)
where k3 is the radiative decay rate constant which is equal to the reciprocal of the radiative lifetime r3, k4 is the total rate constant for the reaction and quenching of the C,(B’ ‘El ) state with CzH2, and k5 is the quenching rate constant by Ar. The time dependence of the fluorescence intensity, Zf, is given by Zr=ZOexp( -t/r)
,
Delay
Time/ps
Fig. 1. D ‘C,’ -+X ‘xi emission as a function of the delay time between the ArF photolysis laser and the D ‘Z: tB’ ‘Xl excitation laser. The experimental conditions were Pcm2= 40 mTorr and P&Z 2.5 Torr, and the measured lifetime T= 3.46 ps.
(6)
where 1/~=l/~3+k4PC2Hz+kSPAr.
(7)
the maximum value of Zfat t = 0, PCzH2and PA, are the partial pressures of CzHz and Ar, respectively, l/r is the reciprocal of the total decay rate constant, which is obtained from the slope of the In of the LIF signal versus the delay time between the photolysis laser and the probe laser. A typical decay curve of the LIF signal is shown in fig. 1. The observed lifetime, r, was then measured as a function of PA, at a,given constant PCZHl.The results, which are plotted in fig. 2, are in accord with eq. (7) and yield straight lines whose intercepts are l/ and whose slopes are k5, the quenching ~3+k4&m, rate constants for Ar. The intercepts of the lines increase with increasing PCzH2,whereas the slopes of the lines are reasonably constant. This means that the experimental results have not been influenced by diffusion. The intercepts obtained from fig. 2 are then converted to the Stem-Volmer plot shown in fig. 3. The intercept of this line is l/r3 and the slope is k4. FiIO is
212
o.oi::::;::.:;:: 0
5
10
zi:’ 15
,::::,::,..::::,t 20
25
30
35
P(Ar) / ToriFig. 2. The observed lifetime of C2(B’ ‘Z:, u‘=O, J’=8) versus
Pk at constantpressuresof &Hz ( (0 ) P,-w= 5.2 mTorr; (0 ) Pc2H2 = 10mTorr; ( A ) Pczm= 20 mTorq (W ) Pczm= 40 mTorr, (0) Pcm2= 80 mTorr) . The solid straight lines are least-square tits to the measured points. The slope of the line is k5 and the intercept gives 1/q + k4 Pcm .
nally, a least-squares fit was used to determine the radiative lifetime, r3, and the quenching rate constants for acetylene, k4. The procedure described above was used for the R8 and R14 lines of the (0,O) band, and the RS line of the ( 1, 1) band. The experimental values of k5, k,, and r3 obtained for the J’S 8, 14 levels of the v’=O vibrational level and the J’= 8 level of the v’= 1 vibrational level are summarized in tables 1, 2, and 3. The theoretical lifetimes of the C2(B’ ‘Zl ) state are also listed in table 3 for comparison. All the error
Volume 2 17, number 3
CHEMICAL PHYSICS LETTERS
14 January 1994
Table 1 The rate constants, 5, at different C2Hz pressures and the quenching cross sections, u, by Ar for different rotational levels of the C,(B’ ‘El ) state ‘) CzHz (mTorr)
k5x 10’
5.2 10.0 20.0 40.0 80.0
4.3* 1.2 4.5f0.6 3.9f 1.2 4.5f0.6 3.4f 1.2
(us-’ Torr-‘)
v=o, J=8
P
I
I
00 0
*o
20
30
40
50
60
70
80
90
100
ks=(4.1+1.4)x10-2ps-‘Torr-’ =(1.3+0.4)x10-‘* cm3 molecule-’ s-i
P(C,H,)/ mTorr
Fig. 3. Stem-Volmer plot of the intercepts from fig. 2, i.e. 1/rr + k, Pm versus Pcm2 for CZ(B’ ‘El, u‘=O, J’=8) yields an intercept corresponding to a radiative lifetime T, = 11.6 f 1.4 us and a slope corresponding to k,= (3.2f0.6) x lo-’ ps-’ mTorr-‘.
bars reported in these tables are the 30 deviations. The random errors of these measured values should be reflected in the least-squares tits to curves of the type shown in fig. 3. However, the systematic errors are difficult to evaluate, but all of the measurements were on different days in a random way and this should minimize these types of errors. The experimental lifetimes for the S = 8 and J’ = 14 levels of the C,( B’ ‘I;:, v’=O) state, as shown in table 3, are about the same, but both are longer than those predicted by theoretical calculations. On the other hand, the experimental lifetime of the Cz (B’ ‘XL, v’ = 1) state is in excellent agreement with the theoretical calculations. However, Bruna and Wight have mentioned in their paper [ 111 that their estimate of the electronic dipole transition moment R.+, could be too high by 10%. If that is the case, their calculated radiative lifetimes would be about 20% too low, which is in closer agreement with our experimental values. The observed quenching rate constants of the Cz (B’ ‘Z: ) state by argon given in table 1 are of the order of lo-” cm3 molecule-’ s-l, which is extremely fast for any ordinary electronic-to-translational quenching reaction with a rare gas atom. The error for k5 at a particular C2Hz pressure represents the 30 error taken from the least-squares fit for a particular curve such as those given in fig. 2. All of the k5 should be the same at different CzHz pressure, so the mean value of k5 is reported along with the 3a
a=0.20f0.07
A2
v=O, J=14 5.0 10.0 20.0 40.0 80.0
3.5f0.6 4.1f0.6 4.2 + 2.4 3.5+ 1.2 4.0 f 0.6 k~=(3.9fl.O)xlO-*us-‘Tow’ =(1.2+0.3)x10-‘* cm3 molecule-’ s-i
reo.lgfo.05
AZ
YZl, J=8 5.0 10.0 20.0 40.0 80.0
3.4& 1.5 3.2f 1.2 2.8 + 0.6 3.4f0.6 2.6f0.6 kr=(3.1f1.1)x10-2ps-‘Torr-’ =(1.0f0.3)X10-‘* cm3 molecule-’ s-i 0=0.15+0 - .05 A2
*) The reported error bars are the 3u values for the rate constants, 5, and the quenching cross sections, u. deivation from the mean. This 317deviation is larger than the mean value of the 3a deviations of the individual k5 values. The large rate constants for quenching by argon can be explained by referring to the energy level diagram for C2 shown in fig. 4. The rotational levels of the C2(X ‘xl, v”= 9 and 10) states are close to those rotational levels with the same quantum number J of the C2(B’ ‘xl, u’=O and 1) states. Since both
213
Table 2 The rate constants, k.,, and the quenching cross sections, u, by C2H2 for different rotational levels of the C,( El’‘2: ) state ‘)
v=o,J=8
14 January 1994
CHEMICAL PHYSICS LETTERS
Volume 2 17. number 3
ml700
k.,=(3.2f0.6)x10-3ps-LmTorr-L =(l.0+0.2)x10-‘0cm’molecule-‘s-’
B'
1
kg4
x tcg+
I
a=l4?3A2 v=O,J=l4
kq=(3.9f0.6)x10-3ps-’ mTorr-’ =(l.2~0.2)x10-‘0cm3molecule-‘s-’
v=lO
a=17+3A* v=l,J=8
lob3 ns-’ mTorr-’ = (l.4~0.2)x10-‘0cm3molecule-‘s-’
kd=(4.4f0.6)x
a=19?3A2 ‘) The reported error bars are the 3a values for the rate constants, k4, and the quenching cross sections, 0. Table 3 The radiative lifetimes of CZ(B’ ‘Z,+, v,J) states ‘) Calculated
1111(KS)
, / / s
Experimental (us)
v=9
v=o, J=8
~0,
J=l4
v=l, J=8
11.6kl.4
10.42 1.9
I3.3+ 1.9
V=O
r(v=O)=8.0 r(v= 1) = 7.7 r(v=2)=7.4 r(v=3)=7.2 r(v=4)=6.9 l)
The errors are the 3a errors from the weighted least-squares tits.
electronic states have the same symmetry, they must mix with each other. Actually, the mixing between the B’ ‘Cl state and the ground electronic state, X ‘Cl, of C2 was previously discussed as part of the results of several ab initio calculations [4,7,11]. These studies have found that mixing among the first three ‘I;: states of Ca, i.e. the X, B’, and E states, is quite significant in the range of 2.0
214
,
(8)
Fig. 4. Diagram of rotational energy levels of C,( B’ ‘Z: ) and C2(X’Zl) between 16000and 18000cm-‘.
C2(B1C:, v’,J’)+Ar -C2(B1A~)+Ar+A&,
(9)
C,(B’ ‘Z;8’, v’, J’) +Ar -+C2(X ‘xl)
+Ar+AE,,
.
(10)
The efficiency of either one of the above processes depends upon the selection rules for the collision process and the energy gap for the reaction. The most efficient reaction should be reaction ( 10). The AE values for the rotational levels of the B’ ‘C: state that are mixed with the X ‘C: state are 119, 140, and 200 cm-’ for the [(B”Z:, v’=O, J’=8) and (X’Z:, v’=9, 5’=8)], [(B”Z,+, v’=O, S=14) and (X1Z:,v’=9,S=14)],and [(B”&++v’=l,S=8) and (X ‘ZB+, v’= 10, J’= 8) 1, respectively. In the adiabatic approximation, the efficiency of E-T transfer should be proportional to the factor exp( -Al&/H’). On the basis of this model, the predicted values for the relative ratio of k5( z/=0, J’=8):k,(v’=O, J’=14):ks(zY=1, S=8) are 1.5 : 1.3 : 1.O, while the measured values for this ratio
Volume 2 17, number 3
CHEMICAL PHYSICS LETTERS
are 1.3 : 1.2 : 1.O. This is excellent for such a simple model. In addition, the fast quenching rate by Ar may also be related to the collisional-induced mixing. Further experiments on the pressure dependence of line-shifts and perturbations in the spectra of B”Ep’ and X ‘El states are needed to investigate this mechanism. The rate constants for the reaction of the C*(B”Zg+, J’=8) ofthe v’=O and v’=l levels with CzH2 are about the same and are about gas kinetic. This suggests that vibrational excitation does not enhance the rate constant for this reaction. The reaction probably has no barrier since the reaction rate constant is so large. It is likely that the reaction proceeds by chemical quenching, such as C2(B”Cg+, v’,J’)+CzH2+C4Hf
(11)
rather than by physical quenching.
4. Conclusions Experimental measurements of the radiative lifetimes of several individual rotational levels of the B’ ‘Z,’ state of C, in both v’=O and v’= 1 vibrational levels have been made. The measured radiative lifetimes are in reasonable agreement with the theoretical values on the basis of ab initio calculations. The quenching rate constants for u’=O and v’= 1 levels of the Cz (B’ 5: ) state by argon are faster than one would expect for an E-T quenching. This can be explained in terms of quenching to nearby levels of the X ‘x2 state with the proper symmetry and angular momentum. A simplified model based upon the energy gap law gives excellent agreement with the relative magnitude of the measured rate constants. The reaction rate constant for reaction of C,( B’ ‘xl ) with &Hz is of the order of gas kinetic
14 January 1994
rate constants and it is likely the result of a chemical reaction. Vibrational and rotational excitations of the Cz (B’ ‘Cc ) radicals do not appear to enhance the reaction.
Acknowledgement The authors gratefully acknowledge the financial support of the National Science Foundation under grant CHE-900892.
References [ 1] M. Martin, J. Photochem. Photobiol. A 66 ( 1992) 263. [ 2 ] R.S. Urdahl, Y. Bao and W.M. Jackson, Chem. Phys. Letters 152 (1988) 485.
[ 31 D.M. Cooper and R.W. Nicholls, J. Quant. Spectry. Radiative Transfer 15 (1975) 139. [4] CF. Chabalowski, S.D. Peyerimhoff and R.J. Buenker, Chem. Phys. 81 (1983) 57. [ 5] W. Bauer, K.H. Becker, M. Bielefeld and R. Meuser, Chem. Phys. Letters 123 (1986) 33. [6] W. Bauer, K_H. Becker, C. Hubrich, R. Meuser and J. Wildt, Astrophys. J. 296 (1985) 758. [7] E.F. Van Dishoeck, Chem. Phys. 77 (1983) 277. [ 8 ] S.V. O’Neil, P. Rosmus and H.-J. Werner, J. Chem. Phys. 87 (1987) 2847. [9] W.H. Smith, Astrophys. J. 156 (1969) 791. [lo] L. Curtis, B. Engman and P. Erman, Physica Scripta 13 (1976) 270. [ll]P.J.BnmaandJ.S. Wright,Chem.Phys. 157 (1991) 111. [ 121 M. Douay, R. Nietmann and P.F. Bemath, J. Mol. Spectry. 131 (1988) 261. [ 131 Y. Bao, R.S. Urdahl and W.M. Jackson, J. Chem. Phys. 94 (1991) 808. [ 141 F. Mohammad, Y. Bao, R.S. Urdahl, M. Zahedi and W.M. Jackson, Dissociation Dynamics in the Photolysis of CrH, and C,H at 193.3 nm, Festschrift volume for H.C. McBay (MIT Press, Cambridge), to be published. [ 151 S.E. Bialkowski, D.S. King and J.C. Stephenson, J. Chem. Phys. 72 (1980) 1156.
215
Volume 2 17, number 3
LIF measurements Mengxiong
14 January 1994
of radiative lifetimes of the C2 (B’ ‘Xi ) state
Gong, Yihan Bao, Randall S. Urdahl and William M. Jackson
Department of Chemistry, University of California, Davis, CA 95616, USA
Received 30 September 1993; in final form 8 November 1993
The 193 nm photolysis of acetylene has been used as a source of &(B ‘Z: ) radicals, which are subsequently detected by laserinduced fluorescence technique. The pressure-dependent collisional lifetimes of this radical are experimentally determined by delaying the probe laser with respect to the photolysis laser, thus allowing extraction of the pseudo-first-order rate constants. Stem-Volmer plots of these rate constants versus pressure yield the natural radiative lifetimes of the state. Three different rotational levels of the C2(B’ ‘8: ) state were studied. The natural radiative lifetimes were 11.6 f 1.4 us and 10.4 k 1.9 us for the D’=0, J’= 8 and J’= 14 levels, respectively, and 8.3 f 1.9 us for the II’= 1, J’= 8 level. These values are in reasonable agreement with the recent theoretical calculations. In addition, the second-order rate constants for the excited state quenching by Ar have also been calculated from the data.
1. Introduction The natural radiative lifetime for many of the electronic states of CZ has been either theoretically calculated and/or experimentally measured [ 11. For the b ?Zg state (T,=6434.27 cm-‘), which is the upper state of the Ballik-Ramsay bands, the experimental lifetime, 7, of 17.2 p (v=O) is in good agreement with theory [ 2,3]. By contrast, two experimental measurements of 7(v) for Cz(A ill,) yielded values of 18.5 us for v= 0 and 11.4 us for v= 3 in one study and 13.4 us for v= 0 and 12.0 us for v= 3, which are in reasonable agreement with each other [ 4,5]. These values are typically 30%-50% larger than those predicted by theory [ 6,7]. Numerous experimental studies of the familiar visible transitions in the Swan system (d ‘$+a ‘II,) give lifetimes of x 100 ns for both the v= 0 and v= 1 levels of the d “l-l, state (T,=20022.5 cm-‘) [2,8], but there have been no theoretical calculations to compare with these experimental values. In the case of the most common ultraviolet transitions, radiative lifetime measurements of the upper levels of the C ilIp and D ‘Z: states of the Deslandres-d’Azambuja and Mulliken systems yield values of 7(C ‘II,, v=O) = 65 ns [ I] andr(D1C,+,v=0)=15.6ns [9], 18.1 ns [lO],but 210
only the latter values are in modest agreement with theory [2]. Theoretical lifetime calculations have recently been performed on the infrared transitions of two newly detected electronic states of CZ, namely the B ‘4 (T,=12082 cm-‘) and B”Xl (T,=15409 cm-‘), for which no experimental lifetime data currently exists [ 11,12 1. In addition to the intrinsic value of this information, knowledge of the CZ(B’ ‘X: ) radiative lifetime would be useful in determining the contribution of cascade processes to the measured lifetime oftheA’II,state [ll]. In the present experiments, the radiative lifetimes of the B’ ‘Ep’, v= 0 and 1 states of CZ have been determined by photolyzing CzH2 with a focused ArF excimer laser and using a tunable dye laser for LIF detection of individual rotational levels of these states. The lifetimes are measured by delaying the probe laser with respect to the photolysis laser, which yields pseudo-first-order rate constants. StemVolmer plots of these rate constants yield the lifetime of this state, as well as the rate constants for electronic quenching by Ar. The lifetimes of three different rotational levels were studied, namely the J= 8 and J= 14 levels of the v= 0 vibrational level, and the 5~8 level of the v= 1 vibrational level.
0009-2614/94/$ 07.00 0 1994 Elsevier Science B.V. All rights reserved. SSDI OOOOS-2614(93)E1374-P
Volume 2 17, number
3
CHEMICAL
PHYSICS
2. Experimental
The experimental conditions were similar to those described earlier [ 8 1, so that only the few changes that were made will be described. The output from an ArF excimer laser (Lambda Physik EMG 101 MSC) was apertured and focused with a 38 cm UV fused-silica lens into the 130 liter stainless steel vacuum chamber used for the static cell experiments. Typically, laser energies of =4 mJ/pulse were focused to a 0.3 mmX 1.5 mm rectangular spot, yielding fluences of zz 1 J/cm’. Excitation of the C2( B’ El > radical was performed with a XeCl extimer-pumped tunable dye laser (Lambda Physik EMG 101 +MSC/FL2002) operated with BMQ in dioxane, where the wavelength was tuned into a given rotational line of the D ‘Ef tB’ ‘Ez, Au=0 transition. The Mulliken band emission was collected with a Dynasil-1100 lens, isolated with a 25 nm fwhm interference filter (Corion) centered at 239 nm and focused onto the cathode of an EM1 9789QB photomultiplier tube (PMT). The output from the PMT was integrated by an Evans 4130 gate integrator and then fed into a Laser Interface LI-1000 series data acquisition system for signal averaging and analysis. The data acquisition system can be used to scan the delay time between the photolysis and probe lasers without affecting the delay time of the gate after the probe laser. At each pressure, care was taken to ensure that the PMT was not saturated. The acetylene (Matheson, 99.6% purity) was purified using a dry ice/acetone slush trap. The purity of Ar (Spectra Gases) was 99.999W.
3. Results and discussion Recently we have shown that the C2(B’ ‘Ez ) radicals are produced in the photolysis of C2H2 via the following reaction scheme [ 13,14 ] : W-b +ha,m+H+GH, CZH+~h93nm
+H+C2(B”C,+,
(1)
v,J) .
(2)
Transitions between the B’ ‘El state and the ground X ‘EC state of C2 are forbidden, thus any C2 radical produced in the B’ ‘Ez state will radiatively decay to the A ‘IIu state or be quenched. The radiative decay
LETTERS
14 January
1994
process creates infrared fluorescence, which is more difficult to measure than ultraviolet or visible radiation. Therefore, the probe laser was used to excite the D ‘Cz (v’, J’)+-B’ ‘E,‘( v”, Y’) transition at z 356 nm. The actual lifetime of the B’ ‘2: state was measured by determining the intensity of the emission from the D ‘E: (v’, J’) state as the probe laser was delayed with respect to the photolysis laser. Signal loss due to mass transport effects has to be taken into account, since the time evolution of the LIF signal depends not only on the radiative decay and quenching process, but also on the diffusion of excited radicals out of the probe laser volume, Bialkowski et al. [ 151 have derived the mass transport equations appropriate for a cylindrically symmetric, collinear or perpendicular pump-probe experiment. Their equations were used to estimate the minimum pressure of Ar (2 Torr) that needs to be added to insure that the loss of signal due to diffusion is less than 10% of what the signal would be without diffusion. The rotational relaxation within the same electronic and vibrational state could affect the measured quenching and radiative lifetimes. In our laboratory, we have measured the nascent rotational distributions of this fragment in the 193 nm photolysis of acetylene. Our results indicate that the nascent rotational distributions of the C2(B’ ‘Ep’ ) fragment can be approximately respected by the Boltzmann-like distributions with a rotational temperature of 670 K for the v=O level and 500 K for the v= 1 level [ 141. Using Ar as the buffer gas not only reduced the diffusion, but also quenched the rotational excitation in the nascent C2(B’ ‘El ) before any experimental data were collected. The range of Ar pressures used in the experiments is about 2 to 40 Torr, and the minimum delay time between the photolysis laser and probe laser is 0.5 ps. With the minimum Ar pressure we used, at the time for collecting the first data point (0.5 ~LSdelay time), there were already about 10 collisions between C2(B’ ‘Ez ) and Ar, which is sufficient to quench the rotational excitation in the nascent C2(B’ ‘Eg’ ) radicals formed in the photolysis of acetylene. Since the FranckCondon factors for the D ‘E,’ +-B’ ‘Ez transition are not available yet, we are unable to calculate the relative vibrational populations of the nascent C2( B’ ‘Cl ) radicals. Since the vibrational relaxation 211
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takes much longer than the rotational relaxation, the measured lifetimes and rate constants could be affected by the vibrational excitation which may exist in the nascent C2(B’ ‘Ez ) radical. However, if quenching of the excited vibrational levels was a problem, the measured rate constant for Ar quenching for the v”= 1 level should be larger than that for the v” = 0 level. In fact, as we shall see later, they are about the same. The reactions controlling the intensity of LIF signal can be summarized as follows: &(B”Z,+,
v’,.Z’)-C~(A
‘I&, ~“,J”)+hy,
(3)
&(B’%B+, v’,J’)+C,H,+products,
(4)
Cz (B’ ‘Xz , Y’, S ) + Ar+ quenching ,
(5)
where k3 is the radiative decay rate constant which is equal to the reciprocal of the radiative lifetime r3, k4 is the total rate constant for the reaction and quenching of the C,(B’ ‘El ) state with CzH2, and k5 is the quenching rate constant by Ar. The time dependence of the fluorescence intensity, Zf, is given by Zr=ZOexp( -t/r)
,
Delay
Time/ps
Fig. 1. D ‘C,’ -+X ‘xi emission as a function of the delay time between the ArF photolysis laser and the D ‘Z: tB’ ‘Xl excitation laser. The experimental conditions were Pcm2= 40 mTorr and P&Z 2.5 Torr, and the measured lifetime T= 3.46 ps.
(6)
where 1/~=l/~3+k4PC2Hz+kSPAr.
(7)
the maximum value of Zfat t = 0, PCzH2and PA, are the partial pressures of CzHz and Ar, respectively, l/r is the reciprocal of the total decay rate constant, which is obtained from the slope of the In of the LIF signal versus the delay time between the photolysis laser and the probe laser. A typical decay curve of the LIF signal is shown in fig. 1. The observed lifetime, r, was then measured as a function of PA, at a,given constant PCZHl.The results, which are plotted in fig. 2, are in accord with eq. (7) and yield straight lines whose intercepts are l/ and whose slopes are k5, the quenching ~3+k4&m, rate constants for Ar. The intercepts of the lines increase with increasing PCzH2,whereas the slopes of the lines are reasonably constant. This means that the experimental results have not been influenced by diffusion. The intercepts obtained from fig. 2 are then converted to the Stem-Volmer plot shown in fig. 3. The intercept of this line is l/r3 and the slope is k4. FiIO is
212
o.oi::::;::.:;:: 0
5
10
zi:’ 15
,::::,::,..::::,t 20
25
30
35
P(Ar) / ToriFig. 2. The observed lifetime of C2(B’ ‘Z:, u‘=O, J’=8) versus
Pk at constantpressuresof &Hz ( (0 ) P,-w= 5.2 mTorr; (0 ) Pc2H2 = 10mTorr; ( A ) Pczm= 20 mTorq (W ) Pczm= 40 mTorr, (0) Pcm2= 80 mTorr) . The solid straight lines are least-square tits to the measured points. The slope of the line is k5 and the intercept gives 1/q + k4 Pcm .
nally, a least-squares fit was used to determine the radiative lifetime, r3, and the quenching rate constants for acetylene, k4. The procedure described above was used for the R8 and R14 lines of the (0,O) band, and the RS line of the ( 1, 1) band. The experimental values of k5, k,, and r3 obtained for the J’S 8, 14 levels of the v’=O vibrational level and the J’= 8 level of the v’= 1 vibrational level are summarized in tables 1, 2, and 3. The theoretical lifetimes of the C2(B’ ‘Zl ) state are also listed in table 3 for comparison. All the error
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CHEMICAL PHYSICS LETTERS
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Table 1 The rate constants, 5, at different C2Hz pressures and the quenching cross sections, u, by Ar for different rotational levels of the C,(B’ ‘El ) state ‘) CzHz (mTorr)
k5x 10’
5.2 10.0 20.0 40.0 80.0
4.3* 1.2 4.5f0.6 3.9f 1.2 4.5f0.6 3.4f 1.2
(us-’ Torr-‘)
v=o, J=8
P
I
I
00 0
*o
20
30
40
50
60
70
80
90
100
ks=(4.1+1.4)x10-2ps-‘Torr-’ =(1.3+0.4)x10-‘* cm3 molecule-’ s-i
P(C,H,)/ mTorr
Fig. 3. Stem-Volmer plot of the intercepts from fig. 2, i.e. 1/rr + k, Pm versus Pcm2 for CZ(B’ ‘El, u‘=O, J’=8) yields an intercept corresponding to a radiative lifetime T, = 11.6 f 1.4 us and a slope corresponding to k,= (3.2f0.6) x lo-’ ps-’ mTorr-‘.
bars reported in these tables are the 30 deviations. The random errors of these measured values should be reflected in the least-squares tits to curves of the type shown in fig. 3. However, the systematic errors are difficult to evaluate, but all of the measurements were on different days in a random way and this should minimize these types of errors. The experimental lifetimes for the S = 8 and J’ = 14 levels of the C,( B’ ‘I;:, v’=O) state, as shown in table 3, are about the same, but both are longer than those predicted by theoretical calculations. On the other hand, the experimental lifetime of the Cz (B’ ‘XL, v’ = 1) state is in excellent agreement with the theoretical calculations. However, Bruna and Wight have mentioned in their paper [ 111 that their estimate of the electronic dipole transition moment R.+, could be too high by 10%. If that is the case, their calculated radiative lifetimes would be about 20% too low, which is in closer agreement with our experimental values. The observed quenching rate constants of the Cz (B’ ‘Z: ) state by argon given in table 1 are of the order of lo-” cm3 molecule-’ s-l, which is extremely fast for any ordinary electronic-to-translational quenching reaction with a rare gas atom. The error for k5 at a particular C2Hz pressure represents the 30 error taken from the least-squares fit for a particular curve such as those given in fig. 2. All of the k5 should be the same at different CzHz pressure, so the mean value of k5 is reported along with the 3a
a=0.20f0.07
A2
v=O, J=14 5.0 10.0 20.0 40.0 80.0
3.5f0.6 4.1f0.6 4.2 + 2.4 3.5+ 1.2 4.0 f 0.6 k~=(3.9fl.O)xlO-*us-‘Tow’ =(1.2+0.3)x10-‘* cm3 molecule-’ s-i
reo.lgfo.05
AZ
YZl, J=8 5.0 10.0 20.0 40.0 80.0
3.4& 1.5 3.2f 1.2 2.8 + 0.6 3.4f0.6 2.6f0.6 kr=(3.1f1.1)x10-2ps-‘Torr-’ =(1.0f0.3)X10-‘* cm3 molecule-’ s-i 0=0.15+0 - .05 A2
*) The reported error bars are the 3u values for the rate constants, 5, and the quenching cross sections, u. deivation from the mean. This 317deviation is larger than the mean value of the 3a deviations of the individual k5 values. The large rate constants for quenching by argon can be explained by referring to the energy level diagram for C2 shown in fig. 4. The rotational levels of the C2(X ‘xl, v”= 9 and 10) states are close to those rotational levels with the same quantum number J of the C2(B’ ‘xl, u’=O and 1) states. Since both
213
Table 2 The rate constants, k.,, and the quenching cross sections, u, by C2H2 for different rotational levels of the C,( El’‘2: ) state ‘)
v=o,J=8
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CHEMICAL PHYSICS LETTERS
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ml700
k.,=(3.2f0.6)x10-3ps-LmTorr-L =(l.0+0.2)x10-‘0cm’molecule-‘s-’
B'
1
kg4
x tcg+
I
a=l4?3A2 v=O,J=l4
kq=(3.9f0.6)x10-3ps-’ mTorr-’ =(l.2~0.2)x10-‘0cm3molecule-‘s-’
v=lO
a=17+3A* v=l,J=8
lob3 ns-’ mTorr-’ = (l.4~0.2)x10-‘0cm3molecule-‘s-’
kd=(4.4f0.6)x
a=19?3A2 ‘) The reported error bars are the 3a values for the rate constants, k4, and the quenching cross sections, 0. Table 3 The radiative lifetimes of CZ(B’ ‘Z,+, v,J) states ‘) Calculated
1111(KS)
, / / s
Experimental (us)
v=9
v=o, J=8
~0,
J=l4
v=l, J=8
11.6kl.4
10.42 1.9
I3.3+ 1.9
V=O
r(v=O)=8.0 r(v= 1) = 7.7 r(v=2)=7.4 r(v=3)=7.2 r(v=4)=6.9 l)
The errors are the 3a errors from the weighted least-squares tits.
electronic states have the same symmetry, they must mix with each other. Actually, the mixing between the B’ ‘Cl state and the ground electronic state, X ‘Cl, of C2 was previously discussed as part of the results of several ab initio calculations [4,7,11]. These studies have found that mixing among the first three ‘I;: states of Ca, i.e. the X, B’, and E states, is quite significant in the range of 2.0
214
,
(8)
Fig. 4. Diagram of rotational energy levels of C,( B’ ‘Z: ) and C2(X’Zl) between 16000and 18000cm-‘.
C2(B1C:, v’,J’)+Ar -C2(B1A~)+Ar+A&,
(9)
C,(B’ ‘Z;8’, v’, J’) +Ar -+C2(X ‘xl)
+Ar+AE,,
.
(10)
The efficiency of either one of the above processes depends upon the selection rules for the collision process and the energy gap for the reaction. The most efficient reaction should be reaction ( 10). The AE values for the rotational levels of the B’ ‘C: state that are mixed with the X ‘C: state are 119, 140, and 200 cm-’ for the [(B”Z:, v’=O, J’=8) and (X’Z:, v’=9, 5’=8)], [(B”Z,+, v’=O, S=14) and (X1Z:,v’=9,S=14)],and [(B”&++v’=l,S=8) and (X ‘ZB+, v’= 10, J’= 8) 1, respectively. In the adiabatic approximation, the efficiency of E-T transfer should be proportional to the factor exp( -Al&/H’). On the basis of this model, the predicted values for the relative ratio of k5( z/=0, J’=8):k,(v’=O, J’=14):ks(zY=1, S=8) are 1.5 : 1.3 : 1.O, while the measured values for this ratio
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CHEMICAL PHYSICS LETTERS
are 1.3 : 1.2 : 1.O. This is excellent for such a simple model. In addition, the fast quenching rate by Ar may also be related to the collisional-induced mixing. Further experiments on the pressure dependence of line-shifts and perturbations in the spectra of B”Ep’ and X ‘El states are needed to investigate this mechanism. The rate constants for the reaction of the C*(B”Zg+, J’=8) ofthe v’=O and v’=l levels with CzH2 are about the same and are about gas kinetic. This suggests that vibrational excitation does not enhance the rate constant for this reaction. The reaction probably has no barrier since the reaction rate constant is so large. It is likely that the reaction proceeds by chemical quenching, such as C2(B”Cg+, v’,J’)+CzH2+C4Hf
(11)
rather than by physical quenching.
4. Conclusions Experimental measurements of the radiative lifetimes of several individual rotational levels of the B’ ‘Z,’ state of C, in both v’=O and v’= 1 vibrational levels have been made. The measured radiative lifetimes are in reasonable agreement with the theoretical values on the basis of ab initio calculations. The quenching rate constants for u’=O and v’= 1 levels of the Cz (B’ 5: ) state by argon are faster than one would expect for an E-T quenching. This can be explained in terms of quenching to nearby levels of the X ‘x2 state with the proper symmetry and angular momentum. A simplified model based upon the energy gap law gives excellent agreement with the relative magnitude of the measured rate constants. The reaction rate constant for reaction of C,( B’ ‘xl ) with &Hz is of the order of gas kinetic
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rate constants and it is likely the result of a chemical reaction. Vibrational and rotational excitations of the Cz (B’ ‘Cc ) radicals do not appear to enhance the reaction.
Acknowledgement The authors gratefully acknowledge the financial support of the National Science Foundation under grant CHE-900892.
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[ 31 D.M. Cooper and R.W. Nicholls, J. Quant. Spectry. Radiative Transfer 15 (1975) 139. [4] CF. Chabalowski, S.D. Peyerimhoff and R.J. Buenker, Chem. Phys. 81 (1983) 57. [ 5] W. Bauer, K.H. Becker, M. Bielefeld and R. Meuser, Chem. Phys. Letters 123 (1986) 33. [6] W. Bauer, K_H. Becker, C. Hubrich, R. Meuser and J. Wildt, Astrophys. J. 296 (1985) 758. [7] E.F. Van Dishoeck, Chem. Phys. 77 (1983) 277. [ 8 ] S.V. O’Neil, P. Rosmus and H.-J. Werner, J. Chem. Phys. 87 (1987) 2847. [9] W.H. Smith, Astrophys. J. 156 (1969) 791. [lo] L. Curtis, B. Engman and P. Erman, Physica Scripta 13 (1976) 270. [ll]P.J.BnmaandJ.S. Wright,Chem.Phys. 157 (1991) 111. [ 121 M. Douay, R. Nietmann and P.F. Bemath, J. Mol. Spectry. 131 (1988) 261. [ 131 Y. Bao, R.S. Urdahl and W.M. Jackson, J. Chem. Phys. 94 (1991) 808. [ 141 F. Mohammad, Y. Bao, R.S. Urdahl, M. Zahedi and W.M. Jackson, Dissociation Dynamics in the Photolysis of CrH, and C,H at 193.3 nm, Festschrift volume for H.C. McBay (MIT Press, Cambridge), to be published. [ 151 S.E. Bialkowski, D.S. King and J.C. Stephenson, J. Chem. Phys. 72 (1980) 1156.
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