- Email: [email protected]
Radiative lifetime and collisional quenching of NO2 flourescence and nature of the air afterglow
Volume 2. number S
RADIATIVE
LIFETIME
FLUORESCENCE
Department
December 1968
CHEiMICAL PHYSICS LETTERS
of Chemistry.
AND AND
COLLISIONAL
NATURE
OF
QUENCHING THE
L. F. KEYSER and F. KAUFMAN University of Pittsburgh. Pittsburgh.
AIR
OF
NO2
AFTERGLOW
Pennsylvania
15213, USA
Pennsytt-ania
15213.
and Department
of Physics,
Uniwrsity
E. C. ZIPF of Pittsburgh.
Pittsburgh,
USA
Received 24 October 1968
Continued interest in the detailed mechanism of the 0 + NO chemiluminescence has stimulated work pn the fluorescence of NO2 between 4000 and 8000 A. Myers, Silver and Kaufman [l] recently reported a large decrease in the Stern-Volmer quenching constant with increasing energy separation between exciting and fluorescent radiation, which suggests (but does not prove) stepwise vibrational deactivation of the electronically excited state, very probably NO2(2B1) [2,3]. Three sets of measurements have now been made to clarify the fluorescence: A. Stern-Volmer experiments with steady, monochromatic illumination at 4047, 4358, 5461, and 5’780 A and measurement of fluorescence using interfereace filters at ten wavelengths from 4700 to 7850 A; B. Direct measurements of the lifetime of NO2 fluorescent emission by the phase shift method using modulated excitation at 4358, 5461, and 5780 A; C. A search for an excited state of NO2 whose lifetime would correspond to the integrated absorption coefficient of NO2 [4] and which was postulated in the 0 + NO chemiluminescence [5], even though Douglas [S] has shown that apparent discrepancies between measured radiative lifetimes and those calculated from the integrated absorption coefficient can be explained satisfactorily for a single excited state. A block diagram of the apparatus is shown in fig. 1. Fluorescence intensities were measured by a Keithley picoammeter and pen recorder for experiments with steady illumination: and by pulse
:‘Jxs.ra
_
FILTER FLEIECEXE i
i
Fig. 1. Block diagram of apparatus.
counting, time-to-amplitude conversion, multichannel analysis of the fluorescent signal wave form, and integration for 10 minutes (4 to 12 x x 106 cycles) for experiments with modulated illumination. Tine modulator consisted of two closely spaced quartz discs, each with 512 equidistant, radial metal strips vapor-deposited over a Length of 19 mm. One disc was stationary while. the other was rotated at a constant speed up to 2300 RPM. The collimated light beam from a high pressure mercury arc traversed this modulator and was then focused on the 0.5 mm wide entrance slit of the smaLL a meter grating monochromator. The spectrat half width of the incident light was 60 h and that of the ten interference {ilters for the fl%orescent light from 4700 to 7850 A was 50 to 100 A. The fluorescence photomuLtiplier tube (EMR-641) was cooled to - 77oC, and 523
Volume 2. number 6
CHEMICAL PHYSICS LETTERS
had a background counting rate of 2 see-l. The principal results of these three sets of measurements are as follows: A. Stern-Volmer plots, *02 jlF versus PNi& for a given excitation frequency, v~, are linear if the fh3OreSCenCe fri?quenCy, vF, is Close t0 v& but show increasing curvature at low &nz as bvZ VE- “F increases. At high PNoz (‘: 30 m Torr) they are Linear, but the effective quenching constant, a (high pressure slope divided by IGW pressure intercept) decrease? sharply with increasing Av. For XE = 4358 A, for example, n = = 247, 129, 74, 64, or 5p Torr-1 for XF = 4700, 5460, 6350, ‘7000, 7850 A. Because of increasing experimental scatter, accurate values of the Iimiting low pressure (C 1 mTorr) quenching constant, a~, could not be measured; but there is a decrease in the observed Low pressure (G 10 m’i’orr) slope for increasing AU. The continuous and gradual change of a with Au and the ‘curvature of the Stern-VoImer pLots at low pressure suggest the stepwise vibrational de-excitation (w) of a single NO5 electronic state, concurrent with its electronic, 02~1, and radiative (lz~ = l/r~) de-excitation. Calculations using such a cascade model under steady-state conditions show that
+JG2 - IF
B(l fQ#&
[I +aE(1 +Q)+02
= (El +a~(1 +Q)pN02pz
pz
- (~EQPNo~)~)
.
where oE = k&kR, Q = kv/kE, 3 is an experimentally determined constant, and n is the effective number of vibrational states, i.e. n = 1 + + & LJ/Av where AuV is the vibrational energy transferred p5-r average collision. At sufficiently high pressure (pN(& ‘> l.‘a~,Q), this expression becomes Linear and the effective quenching CORstant can be written as: a = [aE(l+
Qln]/[(l+
Q)“-
Q’“] .
In deriving the above expressions, we have made the simplifying assumptions that neither kE, $.r. nor kR vary with the vibrational Level of NO2, and that all excited state levels capable of radiating at VF contribute equally to the fluorescence. A calculation of tbe factor, -(l + Q)n/[(l c QJn -Qa], in the expression for a shows that Q must be greater than 5 to account for the large observed variation in a (by a factor of 4 to 5) with 0~. Stern-Volmer plots calculated from the expression for Pi’Z given above agree quaLitativeIy with the experZmenta1 curves but are relatively ir.sensitive to the choice of Q and Cyl. This makes it diffi‘524
December 1968
cult to estimate these quantities accurately; however, comparison of several representative experimental Stern-Volmer plots with calcuLated curves shows that the best fit occurs for AuV between 600 and 2300 cm-1 (AEV - 2.5 kcal mole-l), Q about 50, and yields an aE about 9 Torr-1. Similar values of Q and aEV are obtained if the contribution of different vibrational states to the fluorescence intensity is estimated from the 0 + NO emission spectrum [7]. B. The radiative lifetime, TR, was me?.&red for XE = 4358, 5461 and 5780 A, with AF close to, the excitation wavelength (4700, 5990, and 6350 A, respectively) in order to reduce the contribution of vibrationally quenched NOi to the fluorescence. In this case, w/‘tan& E 1/4obs
= [I + nE(l +Q)PNO2]/TR
where w is the angular modulation frequency, and Q, is the measured phase shift. The results are that 7~ = F5, 58, and 53 + 6 psec at 4358, 5461, and 5780 A, in reasonably good agreement with Neuberger and Duncan’s [4] 44 ,usecOmeasurement for excitation at 4000 to 4600 A and also showing the independence of TR on excitation energy. For Q - 50 and ‘R = 55 @set, kv and kE are about 25 and 0.5 x lo-11 cm3 molecule-l set-l for 4358 A excitation. C. The observed iifetime should be independent of the moduIation frequency if only one state contributes to the fluorescence intensity. Initial experiments in which the modulation frequency was varied from 8 to 20 kS-Izhave shown no indication of another, “faster* state of ‘R = 0.2 I.rsec, although calculation shows that the simultaneous presence of as little as 5% of “fast” radiation would have been easily observable. This approach will be further pursued, but our results combined with other evidence [S] weigh against the model which postulates two electronically excited states. It has also been proposed [8] that electronically excited NOa is in equilibrium with highly vibrationally excited levels of the ground state which couiti explain the radiative lifetime discrepancy by the much greater density of states for NO2 than for NO;. However, the required equilibrium constant of about 200 would make kE for NO2 200 times Larger than the estimated 0.5 x 10-11, i.e. about five times gas kinetic, and this interpretation appears to be unlikely. It is possible, however, that such an equilibrium exists, but that the equilibrium constant, K, is, say, 10 or 20, and that other explanations will bridge the remaining gap between the radiative lifetime and the integrated absorption coefficient. The equilibrium assumption decreases the true radiative lifetime
Volume
2. number
8
CEiEhllCAL
PHSSlCS
of the excited state by the factor K + 1, since 5he observed radiative decay includes the continuous replenishment of excited state from vibrationally excited (non-radiating) ground state. It is the clear implication of these studies that the model of a singLe effective NO; state of known radiative Lifetime, and with efficient stepwise vibrational relaxation, represents the smallest set of assumptions necessary to explain all fluorescence phenomena. This same model may now be applied to describe the 0 + NO chemiluminescence where one may assume that the initial collision comp!ex of 0 and NO is formed in the 2B1 state: that it may re-dissociate, radiate, be electronically quenched, or step-wise vibrationally relaxed to other energy levels of NOi which have similar options except that they can no Longer redissociate. Making all of the above assumptions about kR, kv, and kE, and reaLizing that re-dissociation will be orders of magnitude faster than all other routes for the unstabilized collision complex, we may write for the effective secondorder rate constant, I,, for chemiluminescent recombination
‘0 = kRKo l + (kv
WMI +kE)[M]
+{ (kv
+kR +
kv2P42
+RE)[M] + kR}2
+ ---
1
where K, is the equilibrium constant for forming the collision complex. This expression neglects the spectral change for different radiating levels. At pressures above about 0.1 Torr, where &v i= &)[M] > kR, it reduces to
This formulation predicts: (a) a fall-off of 1, with decreasing pressure [Y-l?], but a levelling-off to a lower second-order rate constant at Iow pressure which represents the radiation from the unstabilized collision complex (For Q - 50 and rz - 10. the low pressure limit of IO would be approximately & its high pressure .limit. ); (b) A spectral shift with decreasing pressure favoring lower wavelength emission [12], because the collision complex has lost none of its energy and can radiate farther towards the low X limit; (c) A small spec-
LETTERS
December
1966
tral dependence on M at higher pressures 1131, because with increasing complexity of M the amount of vibrational energy transferred per average collision will be larger and n therefore smaLLer. Eificient M molecules therefore should produce relatively more radiation at the “blue” end of the emission, because they have a lower R and relatively more radiation comes from the unstabifized complex; (d) More efficient M molecules should produce less light [9] for the same reason as given in (c). All of these effects have been observed experimentally, with the possible exception of the low pressure levelling-off of IO which is under further study in this laboratory.
This work was supported by the Department of the Air Force under Contract No. AF 19(628)-5056, and by the Advanced Research Projects Agency under ARPA Order No. 826.
REFERENCES [l]
G. H. Myers. D. JI. Silver and F. Kaufman. J. Chem. Phys. 41 (1966) 718. [2] L_Burnelle. A.&I.&In)- and R.A.Gangi. J. Chem. Phys.. in press. [3] L.Burnelle, P.Beaudouin and L.J_Scttaad. J. Phys. Chem. 71 (1967) 22-&O. [a] D.Neuberger and h.B.F.Cuncan. J. Chem. Phys. 22 (1954) 1693. [5] H. P.Broida. H. E. Schiff and T.M. Sugden. Trans. Faraday Sot. 57 (1961) 259. [6] A. E. Douglas. J. Chem. Phys. 4s (1966) 1007. [i] A.Fontijn. C.B.&Ieyer and H.I.Schiff. J. Chem. Phys. 40 (196-l) 64. [S] D. B. Hartley and B.-q. Thrush. Discussions Faraday Sot. 37 (1964) 220. [S] F. Kaufman and J. R. Kelso, Symposium on Chemiluminescence. Durham. h*orth Carolina. 1965. 1101 N. Jonathan and R. Petty. Trans. Faraday Sot. 64 (1968) 1210. [Ill A.RfcKenzie and B.A.Thrush. Chem. PRys. Letters 1 (1968) 681. [I21 E.Freedman and J.R.Keiso, Bulf. Am. Phys. Sot. 11 (1966) 453. [13] E. Freedman rtld J. R. Kelso. 133rd Meeting Am Chem. Sot. April 1967. Section R. Abstract 29.
525
RADIATIVE
LIFETIME
FLUORESCENCE
Department
December 1968
CHEiMICAL PHYSICS LETTERS
of Chemistry.
AND AND
COLLISIONAL
NATURE
OF
QUENCHING THE
L. F. KEYSER and F. KAUFMAN University of Pittsburgh. Pittsburgh.
AIR
OF
NO2
AFTERGLOW
Pennsylvania
15213, USA
Pennsytt-ania
15213.
and Department
of Physics,
Uniwrsity
E. C. ZIPF of Pittsburgh.
Pittsburgh,
USA
Received 24 October 1968
Continued interest in the detailed mechanism of the 0 + NO chemiluminescence has stimulated work pn the fluorescence of NO2 between 4000 and 8000 A. Myers, Silver and Kaufman [l] recently reported a large decrease in the Stern-Volmer quenching constant with increasing energy separation between exciting and fluorescent radiation, which suggests (but does not prove) stepwise vibrational deactivation of the electronically excited state, very probably NO2(2B1) [2,3]. Three sets of measurements have now been made to clarify the fluorescence: A. Stern-Volmer experiments with steady, monochromatic illumination at 4047, 4358, 5461, and 5’780 A and measurement of fluorescence using interfereace filters at ten wavelengths from 4700 to 7850 A; B. Direct measurements of the lifetime of NO2 fluorescent emission by the phase shift method using modulated excitation at 4358, 5461, and 5780 A; C. A search for an excited state of NO2 whose lifetime would correspond to the integrated absorption coefficient of NO2 [4] and which was postulated in the 0 + NO chemiluminescence [5], even though Douglas [S] has shown that apparent discrepancies between measured radiative lifetimes and those calculated from the integrated absorption coefficient can be explained satisfactorily for a single excited state. A block diagram of the apparatus is shown in fig. 1. Fluorescence intensities were measured by a Keithley picoammeter and pen recorder for experiments with steady illumination: and by pulse
:‘Jxs.ra
_
FILTER FLEIECEXE i
i
Fig. 1. Block diagram of apparatus.
counting, time-to-amplitude conversion, multichannel analysis of the fluorescent signal wave form, and integration for 10 minutes (4 to 12 x x 106 cycles) for experiments with modulated illumination. Tine modulator consisted of two closely spaced quartz discs, each with 512 equidistant, radial metal strips vapor-deposited over a Length of 19 mm. One disc was stationary while. the other was rotated at a constant speed up to 2300 RPM. The collimated light beam from a high pressure mercury arc traversed this modulator and was then focused on the 0.5 mm wide entrance slit of the smaLL a meter grating monochromator. The spectrat half width of the incident light was 60 h and that of the ten interference {ilters for the fl%orescent light from 4700 to 7850 A was 50 to 100 A. The fluorescence photomuLtiplier tube (EMR-641) was cooled to - 77oC, and 523
Volume 2. number 6
CHEMICAL PHYSICS LETTERS
had a background counting rate of 2 see-l. The principal results of these three sets of measurements are as follows: A. Stern-Volmer plots, *02 jlF versus PNi& for a given excitation frequency, v~, are linear if the fh3OreSCenCe fri?quenCy, vF, is Close t0 v& but show increasing curvature at low &nz as bvZ VE- “F increases. At high PNoz (‘: 30 m Torr) they are Linear, but the effective quenching constant, a (high pressure slope divided by IGW pressure intercept) decrease? sharply with increasing Av. For XE = 4358 A, for example, n = = 247, 129, 74, 64, or 5p Torr-1 for XF = 4700, 5460, 6350, ‘7000, 7850 A. Because of increasing experimental scatter, accurate values of the Iimiting low pressure (C 1 mTorr) quenching constant, a~, could not be measured; but there is a decrease in the observed Low pressure (G 10 m’i’orr) slope for increasing AU. The continuous and gradual change of a with Au and the ‘curvature of the Stern-VoImer pLots at low pressure suggest the stepwise vibrational de-excitation (w) of a single NO5 electronic state, concurrent with its electronic, 02~1, and radiative (lz~ = l/r~) de-excitation. Calculations using such a cascade model under steady-state conditions show that
+JG2 - IF
B(l fQ#&
[I +aE(1 +Q)+02
= (El +a~(1 +Q)pN02pz
pz
- (~EQPNo~)~)
.
where oE = k&kR, Q = kv/kE, 3 is an experimentally determined constant, and n is the effective number of vibrational states, i.e. n = 1 + + & LJ/Av where AuV is the vibrational energy transferred p5-r average collision. At sufficiently high pressure (pN(& ‘> l.‘a~,Q), this expression becomes Linear and the effective quenching CORstant can be written as: a = [aE(l+
Qln]/[(l+
Q)“-
Q’“] .
In deriving the above expressions, we have made the simplifying assumptions that neither kE, $.r. nor kR vary with the vibrational Level of NO2, and that all excited state levels capable of radiating at VF contribute equally to the fluorescence. A calculation of tbe factor, -(l + Q)n/[(l c QJn -Qa], in the expression for a shows that Q must be greater than 5 to account for the large observed variation in a (by a factor of 4 to 5) with 0~. Stern-Volmer plots calculated from the expression for Pi’Z given above agree quaLitativeIy with the experZmenta1 curves but are relatively ir.sensitive to the choice of Q and Cyl. This makes it diffi‘524
December 1968
cult to estimate these quantities accurately; however, comparison of several representative experimental Stern-Volmer plots with calcuLated curves shows that the best fit occurs for AuV between 600 and 2300 cm-1 (AEV - 2.5 kcal mole-l), Q about 50, and yields an aE about 9 Torr-1. Similar values of Q and aEV are obtained if the contribution of different vibrational states to the fluorescence intensity is estimated from the 0 + NO emission spectrum [7]. B. The radiative lifetime, TR, was me?.&red for XE = 4358, 5461 and 5780 A, with AF close to, the excitation wavelength (4700, 5990, and 6350 A, respectively) in order to reduce the contribution of vibrationally quenched NOi to the fluorescence. In this case, w/‘tan& E 1/4obs
= [I + nE(l +Q)PNO2]/TR
where w is the angular modulation frequency, and Q, is the measured phase shift. The results are that 7~ = F5, 58, and 53 + 6 psec at 4358, 5461, and 5780 A, in reasonably good agreement with Neuberger and Duncan’s [4] 44 ,usecOmeasurement for excitation at 4000 to 4600 A and also showing the independence of TR on excitation energy. For Q - 50 and ‘R = 55 @set, kv and kE are about 25 and 0.5 x lo-11 cm3 molecule-l set-l for 4358 A excitation. C. The observed iifetime should be independent of the moduIation frequency if only one state contributes to the fluorescence intensity. Initial experiments in which the modulation frequency was varied from 8 to 20 kS-Izhave shown no indication of another, “faster* state of ‘R = 0.2 I.rsec, although calculation shows that the simultaneous presence of as little as 5% of “fast” radiation would have been easily observable. This approach will be further pursued, but our results combined with other evidence [S] weigh against the model which postulates two electronically excited states. It has also been proposed [8] that electronically excited NOa is in equilibrium with highly vibrationally excited levels of the ground state which couiti explain the radiative lifetime discrepancy by the much greater density of states for NO2 than for NO;. However, the required equilibrium constant of about 200 would make kE for NO2 200 times Larger than the estimated 0.5 x 10-11, i.e. about five times gas kinetic, and this interpretation appears to be unlikely. It is possible, however, that such an equilibrium exists, but that the equilibrium constant, K, is, say, 10 or 20, and that other explanations will bridge the remaining gap between the radiative lifetime and the integrated absorption coefficient. The equilibrium assumption decreases the true radiative lifetime
Volume
2. number
8
CEiEhllCAL
PHSSlCS
of the excited state by the factor K + 1, since 5he observed radiative decay includes the continuous replenishment of excited state from vibrationally excited (non-radiating) ground state. It is the clear implication of these studies that the model of a singLe effective NO; state of known radiative Lifetime, and with efficient stepwise vibrational relaxation, represents the smallest set of assumptions necessary to explain all fluorescence phenomena. This same model may now be applied to describe the 0 + NO chemiluminescence where one may assume that the initial collision comp!ex of 0 and NO is formed in the 2B1 state: that it may re-dissociate, radiate, be electronically quenched, or step-wise vibrationally relaxed to other energy levels of NOi which have similar options except that they can no Longer redissociate. Making all of the above assumptions about kR, kv, and kE, and reaLizing that re-dissociation will be orders of magnitude faster than all other routes for the unstabilized collision complex, we may write for the effective secondorder rate constant, I,, for chemiluminescent recombination
‘0 = kRKo l + (kv
WMI +kE)[M]
+{ (kv
+kR +
kv2P42
+RE)[M] + kR}2
+ ---
1
where K, is the equilibrium constant for forming the collision complex. This expression neglects the spectral change for different radiating levels. At pressures above about 0.1 Torr, where &v i= &)[M] > kR, it reduces to
This formulation predicts: (a) a fall-off of 1, with decreasing pressure [Y-l?], but a levelling-off to a lower second-order rate constant at Iow pressure which represents the radiation from the unstabilized collision complex (For Q - 50 and rz - 10. the low pressure limit of IO would be approximately & its high pressure .limit. ); (b) A spectral shift with decreasing pressure favoring lower wavelength emission [12], because the collision complex has lost none of its energy and can radiate farther towards the low X limit; (c) A small spec-
LETTERS
December
1966
tral dependence on M at higher pressures 1131, because with increasing complexity of M the amount of vibrational energy transferred per average collision will be larger and n therefore smaLLer. Eificient M molecules therefore should produce relatively more radiation at the “blue” end of the emission, because they have a lower R and relatively more radiation comes from the unstabifized complex; (d) More efficient M molecules should produce less light [9] for the same reason as given in (c). All of these effects have been observed experimentally, with the possible exception of the low pressure levelling-off of IO which is under further study in this laboratory.
This work was supported by the Department of the Air Force under Contract No. AF 19(628)-5056, and by the Advanced Research Projects Agency under ARPA Order No. 826.
REFERENCES [l]
G. H. Myers. D. JI. Silver and F. Kaufman. J. Chem. Phys. 41 (1966) 718. [2] L_Burnelle. A.&I.&In)- and R.A.Gangi. J. Chem. Phys.. in press. [3] L.Burnelle, P.Beaudouin and L.J_Scttaad. J. Phys. Chem. 71 (1967) 22-&O. [a] D.Neuberger and h.B.F.Cuncan. J. Chem. Phys. 22 (1954) 1693. [5] H. P.Broida. H. E. Schiff and T.M. Sugden. Trans. Faraday Sot. 57 (1961) 259. [6] A. E. Douglas. J. Chem. Phys. 4s (1966) 1007. [i] A.Fontijn. C.B.&Ieyer and H.I.Schiff. J. Chem. Phys. 40 (196-l) 64. [S] D. B. Hartley and B.-q. Thrush. Discussions Faraday Sot. 37 (1964) 220. [S] F. Kaufman and J. R. Kelso, Symposium on Chemiluminescence. Durham. h*orth Carolina. 1965. 1101 N. Jonathan and R. Petty. Trans. Faraday Sot. 64 (1968) 1210. [Ill A.RfcKenzie and B.A.Thrush. Chem. PRys. Letters 1 (1968) 681. [I21 E.Freedman and J.R.Keiso, Bulf. Am. Phys. Sot. 11 (1966) 453. [13] E. Freedman rtld J. R. Kelso. 133rd Meeting Am Chem. Sot. April 1967. Section R. Abstract 29.
525