Are primary quantum yields of NO2 photolysis at λ ≤ 398 nm smaller than unity?

Article abstract of DOI:10.1524/zpch.2000.214.5.573

Primary quantum yields φ of NO₂ photolysis at wavelengths λ ≤ 398 nm and at bath gas pressures below 1 bar are analyzed. Stern-Volmer plots for collisional photolysis quenching, from experiments at pressures between 10 and 1000 bar, do not indicate a substantial reduction of the quantum yield below unity for pressures below 1 bar. The consequences of the recently discovered fluctuations of specific rate constants k(E) for NO₂ dissociation on collisional photolysis quenching are analyzed. These effects can lead to a small reduction of φ at pressures below 1 bar which, however, is also smaller than the reduction reported in some experiments. Reanalysis of these experiments shows instead that, apart from experimental artifacts, the influence of the secondary reactions O + NO₂ (+ M) → NO₃ (+ M), NO₃ + NO → 2 NO₂, and O + NO₂ → O₂ + NO was underestimated. As a consequence, all experimental evidence so far is in favour of a low pressure primary quantum yield which is unity over the complete wavelength range 300-398 nm. This leads to a revised recommendation of quantum yields φ for the range 300-430 nm at 298 K and 248 K. A revision of the limiting low pressure rate constant at 298 K of the reaction O + NO₂ + N₂ → NO₃ + N₂ of (1.6±0.2) × 10^-31 [N₂] cm³ molecule^-1 s^-1 is also recommended (to be employed together with F_c = 0.6 and a limiting high pressure value of 2.2 × 10^-11 cm³ molecule^-1 s^-1). by Oldenbourg Wissenschaftsverlag, Muenchen.

Full text of DOI:10.1524/zpch.2000.214.5.573

Zeitschrift für Physikalische Chemie, 214, 5, 573Ϫ581 (2000)
by Oldenbourg Wissenschaftsverlag, München
Are Primary Quantum Yields of NO2 Photolysis
at λ ≤ 398 nm Smaller than Unity?
By Jürgen Troe
Institut für Physikalische Chemie, Universität Göttingen, Tammannstraße 6,
D-37077 Göttingen, Germany
Dedicated to Prof. Dr. Dr. h. c. mult. H. Gg. Wagner
on the occasion of his 70th birthday
(Received February 4, 2000; accepted February 8, 2000)
Photolysis / Atmospheric Chemistry / Elementary Gas Phase Reactions
Primary quantum yields Φ of NO2 photolysis at wavelengths λ Յ 398 nm and at bath
gas pressures below 1 bar are analyzed. Stern-Volmer plots for collisional photolysis
quenching, from experiments at pressures between 10 and 1000 bar, do not indicate a
substantial reduction of the quantum yield below unity for pressures below 1 bar. The
consequences of the recently discovered fluctuations of specific rate constants k(E) for
NO2 dissociation on collisional photolysis quenching are analyzed. These effects can lead
to a small reduction of Φ at pressures below 1 bar which, however, is also smaller than
the reduction reported in some experiments. Reanalysis of these experiments shows
instead that, apart from experimental artifacts, the influence of the secondary reactions
O ϩ NO2 (ϩ M) → NO3 (ϩ M), NO3 ϩ NO → 2 NO2, and O ϩ NO2 → O2 ϩ NO was
underestimated. As a consequence, all experimental evidence so far is in favour of a low
pressure primary quantum yield which is unity over the complete wavelength range 300Ϫ
398 nm. This leads to a revised recommendation of quantum yields Φ for the range 300Ϫ
430 nm at 298 K and 248 K. A revision of the limiting low pressure rate constant at
Ϫ31
298 K of the reaction O ϩ NO2 ϩ N2 → NO3 ϩ N2 of (1.6Ϯ0.2)ϫ10
limiting high pressure value of 2.2ϫ10Ϫ11 cm3 moleculeϪ1 sϪ1).
[N2] cm3
Ϫ1 Ϫ1
s
molecule
is also recommended (to be employed together with Fc ϭ 0.6 and a
1. Introduction
Because of its crucial role in driving tropospheric photochemistry the pho-
tolysis
NO2 ϩ hν → O ϩ NO
(1)
has been studied over many decades. Absorption cross sections and quan-
tum yields have been measured with increasing detail and precision (for a
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summary of references and results, see [1]). In spite of these efforts the
reasons for a number of discrepancies have not completely been identified.
There are several measurements of the quantum yields at wavelengths
λ smaller than the photolysis threshold λ0 ϭ 397.9534 (Ϯ0.0008) nm [2]
which gave low pressure primary quantum yields below unity. So far no
explanation of this observation has been presented. Photolysis quenching
experiments at high bath gas pressures (up to 1000 bar) [3Ϫ5] and direct
time-resolved photolysis experiments [6Ϫ8] (or the analysis of absorption
line widths [9]) all led to specific rate constants k(E) for NO2 dissociation
Ϫ1
in the range 1010Ϫ1013 s . From these results one would conclude that low
pressure primary quantum yields should be equal to unity over the full range
300Ϫ398 nm. Values smaller than unity would indicate that nonreactive
states of NO2 exist above the dissociation energy. It is the aim of the present
article to critically review the experimental evidence for quantum yields
below unity and to estimate possible magnitudes of quantum yield re-
ductions.
Primary quantum yields at λ Ͼ λ0 fall off over several tens of nm. This
effect in part is explained by the combined use of the photon energy and
thermal rovibrational energy of the NO2 molecules prior to excitation for
breaking the OϪNO bond [10]. In addition, collisional activation from ini-
tially nondissociative to dissociative states, during the anomalously long
radiative lifetime of NO2 [11], after excitation at λ Ͼ 398 nm can also lead
to photodissociation [5, 12]. A semiquantitative master equation treatment
of this mechanism has been presented in [5] and [12]. Recent progress in
the calculation of the potential energy surface and of the specific rate con-
stants k(E,J) for dissociation [13, 14] allows for a more quantitative model-
ing of this effect [15]: the centrifugal barriers E0(J) of the dissociation,
which restrict the use of rotational energy for bond breaking, are better
characterized; also collisional energy transfer now is better understood. Never-
theless, the uncertainties of quantum yield measurements at λ Ͻ 398 nm
have also consequences for the experimental results at λ Ͼ 398 nm. It is aim
of the present article to elucidate the origin of experimental uncertainties
in order to arrive at a better quantum yield recommendation over the full
wavelength range 300Ϫ430 nm.
2. Experimental low pressure quantum yields
at λ ≤ 398 nm
An excellent summary of earlier quantum yield measurements, identifying
some artifacts in earlier work, has been presented together with extensive
new data in [12, 16]. Table 1 shows the new results for Φ, obtained at NO2
pressures in the range 0.2 to 0.4 Torr and in the presence or absence of the
buffer gas N2. Although there is a trend of Φ to decrease when λ increases
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Are Primary Quantum Yields of NO2 Photolysis .. .
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Table 1. Experimental primary quantum yields for NO2 photolysis at 298 K.
Wavelength
Quantum yield
(λ/nm)
from [16]a
from [12]b
334.1
364.9
378.6
383.8
394.0
396.8
404.3
0.99Ϯ0.05
1.01Ϯ0.07
0.98Ϯ0.04
0.97Ϯ0.06
0.95Ϯ0.07
0.89Ϯ0.05
0.36Ϯ0.04
0.93Ϯ0.10 (388Ϫ398 nm)
0.41
a
b
At NO2 pressures between 0.2 and 0.36 Torr; at N2 buffer gas pressures of
150 Torr.
towards λ0, Φ is below unity outside of the specified uncertainty only at
λ ϭ 396.8 nm and at λ Ͼ λ0. The most extensive earlier data from [17],
obtained at low NO2 pressures (between 0.5 and 4.5 Torr) and in the absence
of a buffer gas, give Φ below unity also only at λ Ն 390 nm. However, the
most recent and probably most careful measurements [12] between 388 and
398 nm led to Φ ϭ 0.93Ϯ0.10 at 298 K and Φ ϭ 0.90 at 248 K. In this
case, buffer gas pressures of 150 Torr and 300 Torr of N2 were employed.
No wavelength dependence of Φ over the range 388Ϫ398 nm was noticed.
The conclusion of these most recent experiments is, thus, that there exists
a quantum yield reduction below unity at λ Ͻ 398 nm although this is
not outside the experimental uncertainty. In the following we question this
conclusion.
3. Collisional quenching of photolysis
One may ask whether buffer gas pressures of 150 Torr of N2, such as applied
in the experiments of [12], could have resulted in collisional quenching of
the primary photolysis. The high pressure measurements of [3Ϫ5] led to
linear Stern-Volmer representations of the primary quantum yields of the
form
Φ([N2] → 0)/Φ([N2]) ϭ 1 ϩ a(λ)[N2]
(2)
with a(λ) ϭ 35, 45, 80, 110, and 210 cm3 mol for the wavelengths λ ϭ
385.5, 392, 394, 399, and 402 nm, respectively. At a buffer gas pressure of
150 Torr this corresponds to a quantum yield at 399 nm of Φ ϭ 0.999. This
type of quenching, hence, cannot be the reason for a noticeable quantum
yield reduction at λ Ͻ λ0.
Ϫ1
While Eq. (2) seems to rule out collisional quenching as a cause for
marked primary quantum yield reductions at pressures below 1 bar, a new
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phenomenon has appeared on the scene which requires consideration. Quan-
tum wavepacket calculations of NO2 photodissociation [18] have indicated
strong fluctuations of the specific rate constants k(E,J ϭ 0). This is in agree-
ment with experimentally observed linewidth fluctuations [9, 19] and also
nonexponential decays of narrow-band excited NO2 [18]. One has to investi-
gate whether there is substantial collisional quenching of the most long-
lived from the broad lifetime distribution of dissociative NO2.
The distributions of fluctuating specific rate constants k(E) were rep-
resented by a Porter-Thomas distribution of the form [20]
N/2Ϫ1
N
Nk
exp(ϪNk/2͗k͘)
Γ(N/2)
P(k) ϭ
(3)
ͩ ͪ
2͗k͘ 2͗k͘
where ͗k͘ denotes the average of k(E,J ϭ 0) and k is the fluctuating specific
rate constant. Fitting the experimental nonexponential decay of dissociating
NO2 molecules in [18] was achieved with parameters N ϭ 1.5Ϯ0.5 of the
distribution. The Stern-Volmer constants a(λ) in Eq. (2) can be influenced
by the rate constant distribution. As long as the Stern-Volmer plots are
linear, the a(λ) are related to ͗k͘ through
a(λ) Ϸ γcZLJ/k(E,J ϭ 0) ϭ γcZLJ/͗k͘
(4)
where γc is a ͗k͘-dependent effective collision efficiency [21], ZLJ is the
Lennard-Jones collision frequency, and the energy E is related to the exci-
tation wavelength λ. To a first approximation, we connect a fluctuation of
specific rate constants with fluctuations of Stern-Volmer constants about the
average a(λ) such that
a/a(λ) ϭ k(E,J ϭ 0)/k ϭ ͗k͘/k.
(5)
On this level one may then estimate Φ from
ϱ
Φ([N2])
P(x)dx
Ϸ
.
(6)
͐
Φ([N2] → 0)
0
1 ϩ a(λ)[N2]/x
A more rigorous master equation treatment with Monte Carlo sampling
from the distribution (3) appears premature at this stage. For several values
of the parameter N of the distribution, Table 2 compares quantum yields
from Eq. (2) with values from Eq. (6); the product a(λ) [N2] from the linear
Stern-Volmer plot (2) in this representation is used as wavelength-specific
reduced concentration measure. One realizes that there is indeed an en-
hancement of the quantum yield reduction by collisional quenching. How-
ever, the effect is too small to account for quantum yield reductions to 0.93
Ϫ1
at buffer gas pressures of 150 Torr. E.g. with a(398 nm) Ϸ 100 cm3 mol
and N Ϸ 1.0, Φ decreases from unity to about 0.99 at 150 Torr of N2. The
effect quickly becomes even less important at decreasing wavelengths. We
conclude that lifetime fluctuations can have an influence on collisional
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Are Primary Quantum Yields of NO2 Photolysis .. .
577
Table 2. Influence of lifetime fluctuations (Porter-Thomas distribution with parameters N
in Eq. (3)) on quantum yields Φ (Φb from Eq. (6)) at different values of a(λ) [N2] in the
Stern-Volmer plots (Φa from Eq. (2)).
N
a(λ) [N2]
Φa
Φb
1.5
0.0001
0.001
0.01
0.9999
0.9990
0.9901
0.9091
0.9993
0.9936
0.9506
0.7710
0.1
1.0
0.0001
0.001
0.01
0.9999
0.9990
0.9901
0.9091
0.9990
0.9905
0.9311
0.7278
0.1
0.5
0.0001
0.001
0.01
0.9999
0.9990
0.9901
0.9091
0.9985
0.9857
0.9025
0.6720
0.1
quenching of photolysis but that the effect is too small to account for Φ-
values near 0.93 at buffer gas pressures near 150 Torr.
4. Reanalysis of secondary reactions
It is well known that secondary reactions of the photolysis (1) can influence
the total quantum yields Φtot measured in photolysis experiments. In search
of other possible reasons for quantum yield reductions, it appeared neces-
sary to reinspect the influence of these reactions. At low buffer gas pres-
sures, the reaction
O ϩ NO2 → O2 ϩ NO
(7)
dominates the sequence of possible secondary reacations and leads to Φtot ϭ
2 Φ where Φ, as before, denotes the primary quantum yield. With increasing
pressures the sequence
O ϩ NO2 ϩ M → NO3 ϩ M
NO ϩ NO3 → 2 NO2
(8)
(9)
reduces Φtot. Further reactions, forming O3 and N2O5, with increasing pres-
sure also enter Φtot [5]. However, for buffer gas pressures below 1 bar, only
reactions (1), (7)Ϫ(9) matter, at quasistationary state leading to
Φ
1
k8([M])
2 k7
ϭ
ϩ
(10)
Φtot
2
where k8([M]) denotes the pseudo-second order rate constant of reaction
(8). Measurements of the pressure dependence of Φtot through Eq. (10) have
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provided an access to k8([M]) as long as k7 was measured independently.
The data bases in use [1, 22] recommend values of k8([M]) which were
obtained in this way. There is only one direct measurement of k8([M]) for
300 and 400 K at pressures above 1.5 bar from our laboratory [23], see
below. Unfortunately, changes in k7 have not consistently been translated
into changes of k8([M]). Furthermore, transfers of the ratio k8([M])/2 k7
from one [M] to another require careful account of the falloff properties of
the pressure-dependent rate coefficient k8([M]). This is the issue of the fol-
lowing discussion. We argue that insufficient account of the term k8([M])/
2 k7 is responsible for the apparent quantum yield reduction below unity in
the experiments from [12]. The influence of secondary reactions, of course,
has been considered in the original evaluation of these experiments: using
the data base from [22], a quantum yield reduction of 3% at 298 K and
150 Torr, and of 12% at 248 and 300 Torr was accounted for. In the follow-
ing we show that these corrections were too small.
For 1 bar of N2 and 298 K, the ratio k8([M])/k7 has been measured to be
0.33Ϯ0.08 [24], 0.27Ϯ0.03 [25], or 0.22Ϯ0.01 [26]. The experiments of
[25] were extended up to pressures of 1000 bar, giving k8,ϱ/k7 ϭ 2.3Ϯ0.3.
Extrapolating down to 150 Torr of N2 cannot simply be done by assuming
that the low pressure limit is realized at 1 bar of N2. Instead a full falloff
curve has to be constructed in such a way that the experimental ratios of
k8/k7 are reproduced at all pressures. We do this by the usual procedure [27]
in expressing k8 by
2
Ϫ1
k8,0
1 ϩ log
k8
1
ͫ ͩ ͪͬ
k8,ϱ
Ϸ
Fc
(11)
ͩ ͪ
k8,0
1 ϩ k8,0/k8,ϱ
where we assume Fc to be close to 0.6. In addition, we assume that k7 is
pressure independent. A more detailed theoretical prediction of Fc is un-
derway [23] but the used value of Fc near 0.6 [28] well reproduces the
experimental falloff curves from [23, 25]. This analysis leads to k8
(150 Torr)/k8,0 ϭ 0.86 and k8(1 bar)/k8,0 ϭ 0.70 such that k8(150 Torr)/k7 ϭ
(k8(1 bar)/k7)ϫ(0.86/0.70)ϫ(150/760). This gives a choice of k8(150 Torr)/
k7 ratios of 0.24ϫ0.33, 0.24ϫ0.27, and 0.24ϫ0.22, depending on which
of the a priori equivalent studies from [24Ϫ26] is preferred. The corre-
sponding quantum yield reductions relative to the P→0 values are 7.9%,
6.5%, or 5.3%. Subtracting the 3% correction already accounted for in [12],
instead of Φ ϭ 0.93 Ϯ0.1 leads to Φ ϭ 0.98, 0.96, or 0.95. Allowing
for another (1Ϫ2%) increase as a consequence of the lifetime fluctuations
discussed in section 3, makes the measured quantum yield indistinguishable
from unity.
It should be mentioned at this point that the given falloff analysis based
on Eq. (11) with Fc ϭ 0.6 also leads to a revised value of k8,0. For the three
Ϫ12
measurements of [24Ϫ26] and a preferred value at 298 K of k7 ϭ 9.7ϫ10
Ϫ1 Ϫ1
Ϫ31
cm3 molecule
s
[1] one derives k8,0 ϭ (1.85, 1.51, or 1.37)ϫ10
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Table 3. Recommended primary quantum yields for NO2 photolysis at buffer gas pres-
sures → 0 (measurements from [12], rescaled by forcing Φ (λϽ398 nm) to unity, see
text).
Wavelength
Quantum yield Φ
(λ/nm)
at 298 K
at 248 K
300Ϫ398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
1.00
0.95
0.88
0.75
0.62
0.53
0.44
0.37
0.30
0.26
0.22
0.18
0.15
0.13
0.11
0.09
0.08
0.06
1.00
0.94
0.86
0.69
0.56
0.44
0.34
0.28
0.22
0.18
0.14
0.12
0.10
0.08
0.07
0.06
0.04
0.03
Ϫ1 Ϫ1
s
Ϫ32
[N2] cm3 molecule
instead of the recommended value of 9.0ϫ10
Ϫ1 Ϫ1
[N2] cm3 molecule
s
from [1]. Averaging of these three values gives
k8,0 ϭ (1.6ϫ10Ϫ31 Ϯ0.2) [N2] cm3 molecule s . We note that this value
is nicely consistent with the direct measurements from [23]. The low value
from [1] is due to the preference of the data of [26], a choice of Fc ϭ 0.8
instead of 0.6 as used here, and some internal inconsistency.
Ϫ1 Ϫ1
The effects discussed in sections 3 and 4 do not apply to the low pres-
sure experiments from [16], for which a quantum yield reduction below
unity at λϽλ0 is outside the stated error limits only for the single wave-
length of 396.8 nm where Φ ϭ 0.89Ϯ0.05 was found.
The discussed corrections from section 4 are wavelength independent.
We, therefore, recommend to correct all quantum yield data from [12] up-
ward by a factor of 1/0.93 at 298 K and 1/0.90 at 248 K. Table 3 gives the
resulting new recommendation of low pressure quantum yields. The effects
of quantum yield reductions by secondary reactions, in laboratory studies
of NO2 photolysis at 298 K, should be calculated with k7 ϭ 9.7ϫ10Ϫ12 cm3
Ϫ1 Ϫ1
Ϫ31
Ϫ1 Ϫ1
molecule s , k8,0 ϭ (1.58Ϯ0.2)ϫ10 [N2] cm3 molecule s , k8,ϱ
ϭ
2.2ϫ10Ϫ11 cm3 molecule
s
and Fc ϭ 0.6.
Ϫ1 Ϫ1
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5. Conclusions
In summarizing the preceding discussion we conclude that there is no exper-
imental evidence for values below unity of the primary quantum yield of
NO2 photolysis at λϽ398 nm and at low gas pressures. This conclusion
leads to a slight upward revision of recommended primary quantum yields
for NO2 photolysis in the wavelength range 300Ϫ430 nm.
Acknowledgements
Financial support of our work by the Deutsche Forschungsgemeinschaft
(SFB 357 “Molekulare Mechanismen unimolekularer Prozesse”) as well as
helpful discussions with B. Abel and K. Luther are gratefully acknowledged.
The author thanks Professor Heinz Georg Wagner for his continuing interest
and support.
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