Low temperature relaxation of OH in the X2U and a2Σ states in an argon free-jet

Article abstract of DOI:10.1063/1.478763

Low temperature (translational temperatures below 10 K) relaxation of OH in the X ²Π and A ²Σ states has been studied in an argon free jet. We determine upper limits on υ = 1 relaxation in the X ²Π manifold from laser induced fluorescence (LIF). We measure absolute relaxation rate coefficients for υ = 2(N), υ = 1(N), and υ = 0(N) levels in the A ²Σ state manifold. In addition, from comparison of the dispersed LIF we obtain state-to-state rate coefficients for υ = 1, N=0 and N = 1 going to υ′ = 0,N′ levels in the A ²Σ manifold. Bimolecular rate coefficients are reported which are all much greater than similar measurements at room temperature. Rates for vibrational relaxation at these low temperatures are 5.7(±0.7) × 10^-1 cm³/s for υ(2-1) relaxation, 3.2 (± 1) × 10^-10 cm³/s for υ(1-0) relaxation, and we report rotational relaxation rates for N = 1 and 2 of υ = 0, 1 and 2 excited states, all near the collision limited values.

Full text of DOI:10.1063/1.478763

Low temperature relaxation of OH in the X 2 Π and A 2 Σ states in an argon free-jet
Michael M. Ahern and Mark A. Smith
Citation: The Journal of Chemical Physics 110, 8555 (1999); doi: 10.1063/1.478763
View online: http://dx.doi.org/10.1063/1.478763
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 110, NUMBER 17
1 MAY 1999
2
2
Low temperature relaxation of OH in the X ⌸ and A ⌺ states
in an argon free-jet
Michael M. Ahern and Mark A. Smith
Department of Chemistry, University of Arizona, Tucson, Arizona 85721
͑
Received 23 June 1998; accepted 12 January 1999͒
2
2
Low temperature ͑translational temperatures below 10 K͒ relaxation of OH in the X ⌸ and A ⌺
states has been studied in an argon free jet. We determine upper limits on vϭ1 relaxation in the
2
X ⌸ manifold from laser induced fluorescence ͑LIF͒. We measure absolute relaxation rate
2
coefficients for vϭ2(N), vϭ1(N), and vϭ0(N) levels in the A ⌺ state manifold. In addition,
from comparison of the dispersed LIF we obtain state-to-state rate coefficients for vϭ1, Nϭ0 and
2
Nϭ1 going to vЈϭ0,NЈ levels in the A ⌺ manifold. Bimolecular rate coefficients are reported
which are all much greater than similar measurements at room temperature. Rates for vibrational
Ϫ10
3
relaxation at these low temperatures are 5.7(Ϯ0.7)ϫ10
cm /s for v(2Ϫ1) relaxation, 3.2
cm /s for v(1Ϫ0) relaxation, and we report rotational relaxation rates for Nϭ1 and
of vϭ0, 1 and 2 excited states, all near the collision limited values. © 1999 American Institute
Ϫ10
3
(
Ϯ1)ϫ10
2
of Physics. ͓S0021-9606͑99͒00214-7͔
2
2
I. INTRODUCTION
OH͑A ⌺,v ,N ͒ϩAr→OH͑A ⌺,v ,N ͒ϩAr,
͑1͒
i
i
f
f
where v and N refer to the quantum numbers for vibration
and pure rotational angular momentum, while the subscripts
i and f refer to initial and final states, respectively. In addi-
The OH radical is a key intermediate in a wide variety of
chemical, atmospheric and astrophysical systems. The in-
elastic and chemical behavior of OH is important in such
diverse environments as high temperature flames and low
temperature planetary atmospheres. As a result, the tempera-
ture dependence of its inelastic and chemical behavior over
wide ranges is of both applied and fundamental importance.
We have recently reported some aspects of the chemical be-
havior of OH into the low temperature realm.1–3 The OH
radical has a large dipole moment, vibrational frequency and
rotational constant similar to HCl and HF but as an open-
shelled system, has very different chemical properties than
those molecules. The inelastic collisional properties of
ground state closed shell hydrides have been very well
tion, we are able to report upper bounds to the very slow
2
vibrational relaxation rates observed for the OH ⌸ state
3/2
and some qualitative observations regarding efficient relax-
ation of rotation and fine structure label ͑total angular mo-
2
mentum͒ in the OH ⌸ manifold.
J
II. EXPERIMENT
The free jet flow reactor used in this study has been
extensively described in earlier reports.16 To generate the
OH/Ar flow, we employed a pulsed free jet consisting of
99.7% argon and 0.3% water. The water was triple deionized
while the argon was UHP grade, both used without further
purification. The mixture was prepared actively by combin-
4
documented. Open shell systems prove to be a greater chal-
lenge and thus the data is more limited. Owing to this reason,
the fundamental nature of the OH radical and its natural im-
portance, the low temperature rate behavior of the open shell
OH system is particularly important to understand.
ing argon and H O saturated argon flows from two indepen-
2
dent flow controllers ͑Tylan model FC-280͒. The free jet
nozzle was a Series 9 General Valve with a 0.4 mm diameter
orifice, d, and was pulsed at 10 Hz ͑duty cycle of 125͒ with
a backing pressure of 600–1200 Torr into a vacuum chamber
There have been numerous studies of OH relaxation at
room temperature5
–14
but only a few using argon as the
buffer gas. Argon, as with most rare gas atoms, is an ineffi-
cient relaxant at ambient temperatures. We have observed
argon to be an effective rovibronic relaxant at the extremely
low temperatures in free jets.15 As a result, we chose to ex-
plore the relaxation efficiency of Ar with the polar OH sys-
tem to determine the generality of inverse temperature de-
pendence of inelastic rate processes in the extremes of low
temperature. In the OH system, such behavior has been pre-
dicted by Copeland et al.6
Ϫ4
with a pressure kept less than 10 Torr. After the water/
argon mixture has left the nozzle, it continues to expand
through an electrically grounded plate (thicknessϭ0.3 mm)
with a 1 mm hole at a downstream position of z/dϭ4, where
z is the axial distance from the actual nozzle exit plane of
diameter d. Another plate with a 4 mm hole which was float-
ing at Ϫ600 V was positioned at z/dϭ8. Self-induced break-
down produced a transient discharge across the 2 plates gen-
erating the OH radicals. This arrangement leads to at least an
open 40° aperture for the expanding gas emerging from the
nozzle. Due to the nonspherical expansion of free jets in the
initial few nozzle diameters, this effective aperture is most
likely even larger. Since we sample only the angular aperture
Most of this study involves the measurement of energy
2
transfer process occurring within the A ⌺ state of the OH
molecule. We have measured the low temperature (Ttrans
)
below 10 K rate coefficients for specific OH rovibronic
states,
0021-9606/99/110(17)/8555/9/$15.00
8555
© 1999 American Institute of Physics
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1

8556
J. Chem. Phys., Vol. 110, No. 17, 1 May 1999
M. Ahern and M. Smith
2
Ϯ5%) population of OH X ⌸3 (vϭ1) population in the
/2
far field of the jet. This allows the ability to prepare and
2
measure relaxation from the vϭ2 level of the A ⌺ state,
pumped here via the A–X(2–1) transition, previously only
accessible through the ͑2–0͒ band, which has a much less
favorable transition probability.18 It is important to point out,
as can be seen from the spectrum in Fig. 1, that in the far
flow field (zϾ2 cm or z/dϾ50, with z/dϭ8 being the posi-
tion of the final discharge plate͒ the rotational state distribu-
tions of OH in either the vϭ0 or 1 level correspond to popu-
lations near 98% residing in the lowest rotational level, N
ϭ1. It is also interesting to note that observed population in
2
Ϫ1
2
the OH ⌸1 , which lies 139 cm above the OH ⌸
/2
3/2
FIG. 1. Far field, terminally cooled laser induced fluorescence excitation
spectrum of the OH A–X ͑0–0͒ transition. The nozzle conditions were 900
Torr Ar. 0.3% water using a 0.4 mm diam nozzle. Excitation and fluores-
cence collection occurred at z/dϭ20.
(vϭ0) level was populated at less than 1% of the ground
state. By the point in which we could probe by LIF, beyond
0
.8 cm, the vast majority of the nascent population in this
higher fine structure state generated from the dissociation
process appears to have been fully relaxed. Thus we have a
kinetic situation where 98% of all the OH X state population
corresponding to less than a central 17° of the flow, we feel
that the discharge plates do not present a flow perturbation of
significance to this study. This supposition is supported by
the fact that the ratio of the mean free path to the aperture
diameter ͑an effective Knudsen number in this case͒ at the
position of each of the apertures is approximately 0.01. This
effectively indicates a continuum flow regime near the aper-
tures, where the aperture presence would not be expected to
seriously effect the central flow streamlines at radial dis-
tances below 50% of the aperture diameters. In addition it
indicates that the radicals generated in the plasma contained
between the plates undergo many collisions in the subse-
quent expansion. This final argument is strongly supported
by the extremely relaxed rotational and electronic state dis-
tributions of the OH radical, which is apparent in Fig. 1. Due
to the much lower vibrational relaxation rates in the OH
2
resides in a single ⌸3 Nϭ1 lowest rotational level and we
/2
can specifically excite vϭ0 or vϭ1 levels for selective
population transfer and kinetic analysis.
The relaxation rate coefficients are calculated by deter-
mining relative populations in different v,N states through
detection of OH fluorescence of directly pumped A states as
well as states not directly pumped but populated through
collisional transfer. The first type of states will be termed
‘
‘
‘initial states’’ and the second kind of state will be termed
‘transfer states.’’ These transfer states have undergone ei-
ther rotational or vibrational relaxation. The conversion of
relative fluorescence intensities from either of these types of
states to relative state populations is accomplished through
the use of published line strength factors.1
9,20
Comparison of
transfer state populations to initial state populations as a
function of laser probe position from the nozzle is used to
determine rates of relaxation for OH in the A state ͑see Ap-
pendix͒. Thus, as one probes farther down the jet axis, the
number of collisions occurring during the average fluores-
2
X ⌺ state, to be discussed later, population in the OH X(v
ϭ1) state is near 15%. However, it should be noted that the
rotational/electronic distribution for OH(vϭ0) and (vϭ1)
are identical.
2
cent lifetime decreases as 1/z . Since the fluorescence life-
The OH was laser excited using a Nd:YAG pumped dye
2
time is much less than the transit time of the jet across 1 mm,
the sample can be considered spatially fixed during this fluo-
rescence clock time. In this way the fluorescence lifetime
serves as the reaction clock for a sample at a known density
and temperature. Comparisons of total fluorescence intensity
as a function of distance are used to determine rates for
laser to pump the vϭ0, 1, and 2 levels of the A ⌺ state ͓for
example, the Q ϩQ (1) line wavelengths of 307.935 ͑0–
1
21
0͒, 281.997 ͑1–0͒, and 288.314 ͑2–1͒ nm, respectively͔.
Fluorescence was measured perpendicular to the laser beam
with an RCA 1P28 photomultiplier with a 0.5 m Czerny–
Turner monochromator preceding it. The signal was fed to
either a boxcar integrator ͑Stanford Research model 250͒ or
a photon counter ͑Stanford Research model 460͒ depending
on signal intensity. The two devices were calibrated for rela-
tive sensitivities using medium level signals. The outputs of
the photon counter and the boxcar integrator were sent to a
PC and signal averaged for 10–200 laser shots. A beam po-
larization scrambler was used before the monochromator to
ensure that detection sensitivity enhancements due to polar-
ization of different rotational branches were not present. The
monochromator/photodetection system was calibrated for
wavelength and response as a function of wavelength with a
NIST-traceable mercury pen lamp ͑Oriel model 6035͒.17
Since the OH is made from discharge in a mixture of
water and argon, it is found to produce a reasonable (15
2
2
transfer processes in the OH X ⌸ and A ⌺ states.
III. RESULTS
Conversion from signal intensity to relative state popu-
lations is needed to measure the relaxation rate coefficients.
The transition probability or Einstein coefficient for emis-
vЈNЈ
vЉNЉ
sion, A
in a given (vЈNЈ–vЉNЉ) band, may be written
vЈNЈ 3
64␲4
͑␯
͒
vЈNЈ
vЉNЉ
vЈNЈ
vЉNЉ
A
ϭ
p
S
,
͑2͒
hc3
vЉNЉ NЈNЉ
3
2NЈϩ2
vЈNЈ
vЉNЉ
where p
is the probability for the transition between the
is the rotational line-
two vibration-rotation levels, S
N N
Ј Љ
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J. Chem. Phys., Vol. 110, No. 17, 1 May 1999
M. Ahern and M. Smith
8557
vЈNЈ
strength, and ␯
is the average frequency of the transition.
vЉNЉ
The quantum number N ͑labeled K by Dieke and
Crosswhite ͒ is defined as total angular momentum minus
spin and is always an integer, thus NϭJϪ 2 for OH. This
2
1
1
notation is strictly only applicable in Hund’s Case B cou-
2
2
pling but is used for both the X ⌸ ͑case A͒ and A ⌺ ͑case
B͒ states of OH, consistant with notation used by Dieke and
Crosswhite and almost all subsequent OH relaxation studies.
3
The intensity of a band, or power radiated from 1 cm of the
gas containing n molecules in the vЈ ͑upper͒ vibrational
vЈ
level, is
vЈNЈ
vЉNЉ
vЈNЈ vЈNЈ
I
ϭn
hv
A
͑3͒
vЈNЈ vЉNЉ vЉNЉ
and has units of erg cmϪ3 sϪ1. In this study, selected A fac-
tors were measured and compared to the detailed study and
literature survey of Crosley and Lengel.20
FIG. 2. Time dependence of the total fluorescence decay curves for the OH
X–A(v) transitions. The fluorescence lifetime of the OH A ⌺ (vϭ2) state
is significantly reduced relative to the low N, vϭ1 or 0 levels owing to
2
In the absence of self-absorption, the ratio of different
fluorescence transition intensities from transitions with the
same upper vibrational level should be a constant. In our
study, pumping Nϭ1 and collecting all fluorescence, we
predissociation induced by mixing with the near lying crossing of the dis-
4
sociative OH ⌺ state ͑Ref. 16͒.
2
1
2
2
measured the A /A ratio via the following relationship
2
1
2
2
2
A
A
I ␯
1
2
1
not resolvable. For example, R 1 and R 1 are unresolved
1
21
ϭ
,
͑4͒
2
I ␯
under our conditions. The peaks were assigned and labeled
2
21
with the notation of Dieke and Crosswhite. ͑A very good
where n
from the above equation drops out if the upper
N v
23
Ј Ј
vibrational level is the same for both transitions. We found
program by Luque and Crosley tabulates line positions, A
1
1
1
0
2
1
2
2
and B factors and makes spectral simulations.͒ When the
R 1(0–0)ϩR 1(0–0) line is pumped, ͑under high power
the A /A and A /A ratios and compared them to literature
1
21
values. The ratios, within experimental error are equivalent
to previous measurements.20 For calculating rate coefficients
conditions, both lines are pumped within the resolution of
the laser͒, there are many lines that can be seen when dis-
persing the emission without relaxation, namely the R11
ϩR 1, R 1, Q 2ϩQ 2, Q 2ϩQ 2, P 3, P 3ϩP 3, and
we use the rotational transition probabilities of Chidsey and
Crosley and vibrational Einstein A factors of Crosley and
Lengel without any corrections.
1
9
2
0
21
2
1
21
2
12
1
12
2
O 4 lines. The convention used is such that lines with only
12
A. Rotational relaxation
one subscript have the upper and lower fine state number
equal. For example, R 1 means that the lower and upper fine
The rotational relaxation rate coefficients for the OH
A ⌺ vϭ0, 1, and 2 states were measured. There was spe-
2
2
structure state is the one labeled 2 and the 1 indicates the
value of N. Sometimes these two fine states are referred to as
F and F . For a label with 2 subscripts, the first one is the
cific interest in the question of whether the predissociative
nature of the vϭ2 state would affect the rate of relaxation.
The vϭ2 state has a much shorter lifetime than the vϭ1
state due to predissociation and lifetime comparisons are
shown in Fig. 2. Our lifetime measurements are in agreement
with those of Brzozowski et al.,22 showing that there was not
1
2
level in the upper state, the A state, and the second is the
lower state, the X state. The upper case number remains N
for the lower, X state.
2
Initially, some rotational level, N, of the A ⌺ state is
2
significant electronic quenching of OH in the A ⌺ state by
populated by the laser. At close distances from the nozzle,
the higher density leads to greater relaxation before fluores-
cence, yielding newly populated relaxed states, which lead to
new lines in the emission spectrum. The P211 and P12
ϩP 2 lines shown in Fig. 3͑a͒ are larger than the P 3
any of the species in the free jet meaning that during the
fluorescence lifetime the OH remains in a single collision
dominated regime.
The rotational relaxation is as follows:
21
1
ϩP 3 line which originates from the initially prepared state
21
OH͑v,N͒ϩAr→OH͑v,NϪ1 or NϪ2͒ϩAr.
The OH in state (v,N) collides with an argon atom and
relaxes to a lower rotational level within the same vibrational
level. The fluorescence from both the OH (v,N), and the OH
v,N-1 or NϪ2͒ in the A state can be detected with the
monochromator.
The X–A pump energy and wavelength are kept con-
͑5͒
at zϭ0.4 cm. When zϭ1.2 cm, as in Fig. 3͑b͒, the number of
collisions is reduced due to the decreased number density
and so the populations of molecules that underwent relax-
ation are decreased with respect to the directly populated
states.
Multiple scans, similar to Fig. 3, are made at varying
distances from the nozzle. Derivation of a rotational rate co-
efficient for such a data set is outlined in the Appendix. A
rate coefficient is determined from the integrated rate rela-
tionship
(
stant, leading to constant preparation of an initially selected
2
OH A ⌺(v,N) state, while the monochromator is scanned.
The upper state fine structure emission in our experiment is
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8558
J. Chem. Phys., Vol. 110, No. 17, 1 May 1999
M. Ahern and M. Smith
FIG. 3. Example of the axial position dependence of rotational relaxation within the OH A 2⌺ (vϭ0) rotational manifold during the initial state radiative
2
2
lifetime. The initial state corresponds to OH A ⌺ (vϭ0, Nϭ2͒. When excitation occurs close to the nozzle, as in ͑a͒ at 0.4 cm, emission from OH A ⌺
vϭ0, Nϭ0, 1, and 2͒ is observed due to pure rotation collisional relaxation in the reasonably dense free jet. At farther axial distances in the jet, as in ͑b͒ at
.2 cm, the emission begins to show less relaxation and the emission predominates from the initially prepared state.
(
1
2
2
A ⌺ ͑ ϭ0, Nϭ2͒ state in Fig. 4. The total and state-to-state
v
Iref
k z
kЈ
Q
fi
ϭ
ϩ
.
͑6͒
rotational relaxation rate coefficients are listed in Table I.
From the intercepts of the integrated rate plots ͑Fig. 4͒, we
2
IN
kNϪNЈM0z0 kNϪNЈ
Ј
Here INЈ is the relative number density of the state to which
population has been transferred while Iref is the total relative
number density for molecules initially excited to the OH
can obtain values of k , the pure electronic quenching rate
Q
coefficient. This quenching rate is found to be very slow.
The observed values of kQ are always less than 20% of all
other collisional processes being measured.
As can be seen, all rotational transfer rate coefficients
are quite large at the very low temperatures present in the
2
A ⌺(v,N) state. INЈ is obtained from the integrated fluores-
cence intensity of all OH lines originating from the OH
2
A ⌺(v,NЈ) transfer state, while I derives from the sum of
ref
the intensity of all lines corrected for rotational line strength
factors. The value, k , corresponds to the fluorescence rate
fi
from the initially pumped state, determining the clock by
which relaxation must compete against. The quantity,
2
2
(
M z /z ), where M is the stagnation density of the relax-
0 0
0
ant gas and z is a distance scale related to the nozzle orifice
0
diameter, represents the local density of the relaxant M at
axial position z in the flow.16 Since the quantities, k , M ,
fi
0
and z are all well known, the slope from a plot of I /INЈ vs
0
ref
2
z
provides a direct measure of the absolute state-to-state
rotational transfer rate coefficient, kNϪNЈ . In the case where
2
more than one relaxation channel is present, as in OH A ⌺
(
vϭ0, Nϭ2͒, the total relaxed population is used and the
total relaxation rate is obtained. Using the relative product
fluorescence line intensities extrapolated to the limit of no
relaxation ͑i.e., to single collision conditions͒ provides the
nascent branching ratios for product states allowing the total
rate to be deconvoluted into the state specific rates. An ex-
ample of such a plot of Iref /INЈ is shown for the total OH
FIG. 4. A fit of fluorescence intensity to the integrated rate law, Eq. ͑6͒ for
2
the pumping of the OH A ⌺ (vϭ0, Nϭ2͒ state. The slope of the line
Ϫ10
3 Ϫ1
yields a total rotational relaxation rate coefficient of 1.80ϫ10
cm s for
the 10 K collisional conditions within the free jet. From the relative rota-
tional line strengths observed in the dispersed spectrum, the state-to-state or
detailed rotational relaxation rate coefficients reported in Table I are ob-
tained.
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1

J. Chem. Phys., Vol. 110, No. 17, 1 May 1999
M. Ahern and M. Smith
8559
2
TABLE I. Relaxation rate coefficients for OH A ⌺ in collisions with Ar ͑in
The determination of vibrational relaxation rate coeffi-
cients for the A ⌺ state are similar to the method employed
Ϫ11
3 Ϫ1
units of 10
cm s ͒.
2
for rotational relaxation. One difference in the data analysis
Rotational relaxation from:
Tϭ300 K
TϽ10 K ͑this work͒
involves the need to measure the relative populations of the
vϭ2, Nϭ2
vϭ2, Nϭ1
vϭ1, Nϭ2
vϭ1, Nϭ1
vϭ0, Nϭ2
20Ϯ4
13Ϯ4.5
11Ϯ2
2
vЉϭ0 and vЉϭ1 levels in the X ⌸3 state. This was ac-
/2
complished before rates could be calculated. To measure
relative populations, the P 1(0–0) and P 1(1–1) bands
6.7Ϯ1
1
1
ktotϭ18Ϯ2
k2–1ϭ12Ϯ1
k2–0ϭ6.0Ϯ1
6.6Ϯ1
were excited at varying laser intensities with the monochro-
mator set to a resolution of 8 nm in order to collect all emis-
sion of an individual vibrational transition. The P 1(0–0)
1
vϭ0, Nϭ1
excitation was followed by collection of all rotational
Vibrational relaxation from:
branches of ͑0–0͒ emission. Similarly, when the P 1(1–1)
1
band was excited, all rotational branches of ͑1–1͒ emission
were collected.
vϭ2
vϭ1
5.7Ϯ2.6
3.2Ϯ0.8
0.41Ϯ0.03a
Data were taken at a wide variety of laser powers owing
to difficulty of obtaining OH spectra under either completely
saturated or completely unsaturated conditions. At low pow-
ers the relationship between signal intensity and number of
aL. R. Williams and D. R. Crosley, J. Chem. Phys. 104, 6507 (1996).
free jet. It is interesting to note that the rotational relaxation
rates in the free jet, for both ⌬Nϭ1 and 2 are significantly
greater than those values observed for higher N levels at 300
23
molecules in a particular state is given by
vЉNЉ
Ј Ј
vЈNЈ
Љ Љϫ͑1ϪeϪ͑t/␶͒͒, ͑8͒
3
1
I
N ϰn N ϫB
vЉ Љ vЉ Љ
ϫ␶ϫ
͚
A
v N
v N
K by Jorg et al.
where I
is the fluorescence intensity of the emission col-
vЉNЉ
B. Vibrational relaxation
lected when exciting molecules from the vЉNЉ ground state,
n
is the number density of molecules in the vЉNЉ ground
The vibrational relaxation rates we report are for the
following process:
vЉNЉ
vЉNЉ
state, B
is the Einstein B-coefficient for absorption from
vЈNЈ
vЉNЉ
2
2
the vЉNЉ level. Here ͚A
represents the sum of all Ein-
OH A ⌺͑v,N͒ϩAr→OH A ⌺͑vϪ1,NЈ͒ϩAr.
͑7͒
vЈNЈ
stein A coefficients for spontaneous emission from the vЈNЈ
upper state, ␶ is the lifetime of the vЈNЈ excited state, and t
is the time following which the fluorescence was collected
after the laser excitation. In our case, we collected emission
from the LIF for times much longer than the lifetime of the
state so the last term in the above equation goes to unity.
At high powers the relationship between initial state
number density and emission intensity simplifies to
We report vibrational relaxation from the vϭ2 to vϭ1 state
and the vϭ1 to vϭ0 state. Relaxation of vϭ2 to vϭ0
could not be detected within our signal to noise. Less than
5% of the vϭ2 population relaxing undergoes a ⌬vϭϪ2
transition. Comparison of product branching into particular
NЈ levels allows, in principle, conversion of the total vibra-
tional relaxation rate coefficient ͑summed over all NЈ͒ to be
converted to v,N to vЈ,NЈ state-to-state coefficients. Unfor-
tunately these product branching ratios required to generally
accomplish this could not be easily obtained under single
collision conditions. As a result we must settle for partially
relaxed product distributions. These are reported in Fig. 6
while the total rates, not affected by this are given in Table I.
vЈNЈ
vЉNЈ
͚
A
I
ϰn
ϫ
.
͑9͒
vЉNЉ
vЉNЉ
␶
We compared our relative populations of ground state
vЈϭ0 and vϭ1 in the limits of low and high laser power
using the above relationships. We determined an
We have also been able to determine upper limits to the very
2
slow total relaxation rate of the OH X ⌸ (vϭ1) state also
2
2
3/2
OH X ⌸3 (vϭ0)/OH X ⌸ (vϭ1) population ratio of
/2 3/2
shown in Table I.
7
.0Ϯ0.3 independent of the power limit and constant under
The first vibrational relaxation rate that will be discussed
all of the conditions employed in this study. This quantity
can now be used to derive an expression relating dispersed
LIF emission intensities from the pumping of either OH
X ⌸(v) state to vibrational relaxation rate coefficients. A
full derivation of this relationship is provided in the Appen-
2
is the relaxation of vϭ1 in the X ⌸ state. This was mea-
sured via the methods previously described by this labora-
tory for the determination of rate coefficients for reactions
within free jet flows.16 The method uses the loss of reactant
density as a function of flow distance to calculate a vibra-
2
dix and only the result is given here
tional relaxation rate coefficient. In our experiment we ob-
2
serve no relaxation of the vϭ1 X ⌸3 state and are able
Iref
trЈ ͑z,tϭ0͒ ͑k ϩk ͒
/2
v
pd
fi
Ј
z2
ϭ
ͩ
ϫ
ͪ
ͪ
only to calculate an upper bound for relaxation of the vϭ1
I
iv͑z,tϭ0͒
M z k
0 0 rel
vЈ
2
Ϫ13
3
X ⌸ state of kϽ5ϫ10
cm /s. Due to intrinsic limitations
owing to the low jet densities, this upper bound for a rate
coefficient is more generous than that of room temperature
k ϩk
trЈ ͑z,tϭ0͒
rel
Q
v
Ј
ϩ
ͩ
ϫ
.
͑10͒
krel
iv͑z,tϭ0͒
7
,8
experiments. As will be shown, however, it is at least three
orders of magnitude slower than vibrational relaxation in the
The ratio, trЈ (z,tϭ0)/i (z,tϭ0) is determined by consid-
eration of the relative Einstein B coefficients for the pumped
vЈ
v
2
A ⌺ state.
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8560
J. Chem. Phys., Vol. 110, No. 17, 1 May 1999
M. Ahern and M. Smith
transitions preparing trЈ and i and the original state popu-
vЈ
v
2
lations ͑if different͒ for the OH X ⌸(v) levels used. Since
the quantities, kpd , k , M , z , (trЈ (z,tϭ0)/i (z,tϭ0))
fi
0
0
v
v
Ј
are known, k can be determined from a plot of I /IvЈ vs
rel
ref
2
z . It is important to note that the determination of all of the
rate coefficients in this study is independent of which satu-
ration regime one is in when preparing the OH A state. That
is due to the fact that all analyses are independent of the
absolute population in the single initially prepared
2
A ⌺(v,N) level.
2
The vibrational relaxation rate coefficients for the A ⌺
vϭ2 and vϭ1 states are shown in Table I. Note that all
2
A ⌺ vibrational relaxation rates are of the order of magni-
tude of both the rotational rates and the total collision rates.
The vibrational rate coefficients appear to be independent of
the rotational level pumped in this study. Adding one quanta
of rotational energy did not affect the vibrational relaxation
rates for either state within our error limits.
C. Rotational partitioning in vibrational relaxation
By employing the monochromator at its maximum oper-
able resolution, the vibrationally relaxed emission can be re-
solved into its rotational components. One example of this
dispersed emission is shown in Fig. 5. For v(1–0) relax-
ation of the A state, the rotational distribution was measured
from the intensities of the vϭ0 emission in the limit of early
relaxation time. The large lines at longer wavelength are due
to the ͑1–1͒ band of the A–X transition, including the effects
of Nϭ1 to NЈϭ0 relaxation within the vϭ1 manifold. The
smaller lines at shorter wavelength are due to the vibrational
relaxation of the vϭ1A state producing A(0–0) emission
from a wide range of final NЈ levels in the vϭ0 manifold.
The intensity of the ͑0–0͒ lines are enhanced by a greater
FIG. 5. Dispersed fluorescence spectrum of the OH X–A transition follow-
ing excitation of the Q 1 ͑1–0͒ line at a position of zϭ1.0 cm in an Ar free
1
jet of stagnation pressure 900 Torr and dϭ0.4 cm. ͑a͒ Low amplification
spectrum highlighting rotational relaxation from Nϭ1 to NЈϭ0 within the
2
OH A ⌺ (vϭ1) manifold. ͑b͒ Expanded scale of the same spectrum high-
2
0
1
20
lighting emission from OH A ⌺ (vϭ0, NЈϭ0–12͒ induced by vibrational
Einstein A coefficient, A /A ϭ1.7.
0
1
2
relaxation caused by OH A ⌺ (vϭ1, Nϭ1͒–Ar collisions.
The distribution of population with NЈ quanta of rota-
tional energy is shown in Figs. 6͑a͒ and 6͑b͒ for relaxation of
2
2
OH A ⌺ (vϭ1, Nϭ1͒ and OH A ⌺ (vϭ1, Nϭ0͒, respec-
tively. The conditions of the relaxation are such that on the
average, only 10% undergo a collision. The error on the
populations in Fig. 6 is approximately 20% with an absolute
error of 1.5% for the Nϭ12 and 13 levels. The distributions
in Fig. 6 were produced iteratively using the Lifbase soft-
ware of Luque and Crosley.23
ergy being lost in the reactant. The NЈϭ8,9,10 levels seem
to be the most favored products. The vЈϭ0, NЈϭ12 level of
2
Ϫ1
the A ⌺ state at 35 038 cm is the closest exothermically
Ϫ1
accessible state to the vϭ1, Nϭ0 state at 35 429 cm . The
observed population of 2% in vϭ0, Nϭ13 in the vϭ1, N
ϭ0 relaxation is consistent, within the errors, of a mean
translational temperature below 10 K. The vϭ1, Nϭ2 state
Relaxation spectra taken at different distances from the
nozzle showed no population differences, which was a check
that the OH molecules were truly in the low collision limit. If
there had been many relaxing collisions per molecule, one
would expect spectra taken at higher density ͑closer to the
nozzle͒, to have colder distributions. It is interesting to note
that the rotational distribution of products having undergone
Ϫ1
at 35 461 cm is high enough that the relaxation to vЈϭ0,
Ϫ1
NЈϭ13 at 35 459 cm is exothermic. The energies of the
2
4
states were taken from the work of Coxon.
2
The relaxation of the A ⌺ (vϭ1, Nϭ1͒ originates from
both of the fine states populated by the excitation laser. Their
intensity distribution determined by dispersed fluorescence
2
2
2
one quanta of vibrational relaxation in the A ⌺ state is nei-
shows no propensity to go to the ⌸3 vs the ⌸ state. A
/2 1/2
2
ther a Boltzmann distribution nor the cold distribution pro-
duced by a free jet. In addition, the two graphs look very
similar showing that the one extra quanta of rotation makes
little difference in the partitioning of the vibrational relax-
ation. The population appears to be strongly distributed
among states from Nϭ1 to 10, tapering off when the rota-
tional energy of the product approaches the vibrational en-
more interesting case is when the excited state is the A ⌺
(vϭ1, Nϭ0͒ state which has only one fine state level, the
F . The vibrational relaxation of this level still shows no
1
propensity to go to one or the other lower fine state (F vs
1
F ͒ showing that the electronic states are completely and
2
randomly scrambled during a vibrationally inelastic colli-
sion.
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J. Chem. Phys., Vol. 110, No. 17, 1 May 1999
M. Ahern and M. Smith
8561
relaxation of the very strong collisions of Xeϩ 2P1/2 with a
variety of rare gases, including Ar, showed no evidence of
relaxation in the 1 K limit.26 Also in contrast with NO, elec-
2
tronic quenching remains slow for OH A ⌺ in the near zero
Kelvin limit, as observed in this study.
2
Vibrational relaxation of OH X ⌸3 (vϭ1) by Ar was
/2
found to remain extremely slow at the free jet temperatures.
This is consistent with the known poor efficiency of Ar as a
vibrational relaxant at higher temperatures, but is in contrast
ϩ
15
to studies of NO (vϭ1) relaxation by Ar near 1 K. In this
ϩ
latter study, Ar was found to relax NO (vϭ1) with near
single collision efficiency. It would appear that the weaker
long-range attraction of the dipole-atom interaction potential
2
in OH X ⌸–Ar collisions as compared to the strong ion-
ϩ
induced dipole NO –Ar interactions must play a role here.
Long-lived complex formation has been used to explain the
strong inverse temperature dependence of many relaxation
2
7,28
processes in the low temperature limit.
In the case of OH
2
X ⌸ (vϭ1), it would appear that the complex lifetimes
remain sufficiently short that vibrational predissociation of
the complex remains poorly competitive with simple adia-
batic back-dissociation along the incoming potential surface.
The case of low temperature OH A ⌺ rotation/vibration
relaxation appears quite different from that in the OH X ⌸
FIG. 6. The rotational dependence of vibrational relaxation showing nascent
2
distribution of population in the vϭ0 level of A state after excitation into
2
2
the vϭ1 level of the OH A ⌺ state. ͑a͒ Distribution when exciting the N
2
ϭ1, vϭ1 level. ͑b͒ Distribution when exciting the Nϭ0, vϭ1 level.
manifold. In OH A ⌺ (v,N) levels, vibrational relaxation by
Ar appears to be strongly competitive with rotation, both
occurring near the collision limit. The collision rate coeffi-
cient can be well approximated using a capture model for
complex formation. Employing a two term long range inter-
action potential including both dipole-induced dipole and
simple dispersion terms, one can derive a simple expression
for the capture rate
A comparison of rotational partitioning at room tempera-
ture can be made using the study of Lengel and Crosley.11
The authors were not able to measure relaxation of OH with
argon but were able to use hydrogen and nitrogen as buffer
gases. Their high-resolution spectra of OH having undergone
vibrational relaxation to multiple N states looks qualitatively
similar to ours for Ar ͑Fig. 5͒. They fit their rotational par-
titioning to a Boltzmann relationship, which gave a rotational
temperature of 670 K for hydrogen and 900 K for nitrogen.
There is no de facto reason that the distribution of rotational
states should be a Boltzmann distribution, but if we fit ours
to such a relationship for comparison we obtain temperatures
near 1200 K for relaxation of vϭ1, Nϭ0 and Nϭ1, respec-
tively. It appears that we observe significantly greater rota-
tional excitation of our product distributions in this low tem-
perature OH–Ar relaxation. Also, our rotational distributions
⑀␣6 1/3 2kbT
1/6
kcaptureϭ6␲1/2⌫͑5/3͒ͩ ͪ ͩ
,
͑11͒
ͪ
2
␮
␮
where ␮ is the collision pair reduced mass, ⌫(x) is the
gamma function, and the effective Lennard-Jones param-
6
eters, ⑀␴ , can be represented by the expression
2
␮
␣Ar 3␣OH␣Ar IPOH͑A͒IPAr
D
6
⑀
␴ ϭ
ϩ
ͩ
ͪ
,
͑12͒
4
16
IPOH͑A͒ϩIPAr
where ␮ , ␣ , and IP represent dipole moment, polarizabil-
1
1
1
display greater deviations from a thermal relationship com-
29
pared with those of Lengel and Crosley.11
ity, and ionization potential of the ith component. Using a
calculated value ͑DFT͒ for the polarizability of the OH A
Ϫ31
3
state of 6.9ϫ10
m and experimental values for all other
IV. DISCUSSION AND CONCLUSIONS
2
quantities, we obtain an OH A ⌺–Ar collision capture rate
coefficient value between 6 and 9ϫ10
Ϫ11
3
We have measured rotation-vibration relaxation rate co-
efficients of OH in both the A and X states at the low trans-
lational temperatures within the core of an Ar free jet (Ttrans
below 10 K͒. From the observed rotational temperatures in
the OH X state, it appears that rotational relaxation in this
manifold is extremely fast, as would be expected from con-
sideration of rotational cooling in a wide variety of mol-
cm /s in the tem-
perature window between 1 and 10 K, respectively. This
range of values compare very favorably with the total relax-
2
ation rate coefficients observed in the jet for the OH A ⌺
state in either the vϭ0 or vϭ1 state.
It appears that energy transfer in the OH A ⌺ state by
Ar occurs for every collision. In the case of OH A ⌺ (v
2
2
2
5
ecules in free jets. In addition, the absence of any observ-
ϭ1, Nϭ1͒, pure rotational transfer proceeds roughly twice
2
2
able OH X ⌸
(vϭ0) indicates that this low energy
as fast as vibration, whereas in OH A ⌺ (vϭ2, Nϭ1͒ vi-
1
/2
excited state relaxes rapidly under the jet conditions. A simi-
lar result for the fine structure excited state of NO ͑Ref. 15͒
is well known. It is interesting to note that fine structure
brational energy transfer appears to display an efficiency
twice that of simple rotational relaxation. The pure rotational
relaxation processes studied appear to display only modest
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8562
J. Chem. Phys., Vol. 110, No. 17, 1 May 1999
M. Ahern and M. Smith
2
temperature dependence between 300 and 1 K. Since they
demonstrate weak inverse temperature dependence it does
suggest mild increase in relaxation through the increase in
lifetime of the OH–Ar complex as collision energy drops.
di
dt
z
0
ϭϪ
ͩ
͑k ϩk ͒M ͩ ͪ ϩk ϩk
ͪ
i,
͑A7͒
͑A8͒
rel
Q
0
pd
fi
z
2
2
dtr
dt
z
z
0
0
2
Ј
ϭk M0ͩ ͪ iϪ
ͩ
k
ϩk M ͩ ͪ ͪtr.
The OH A ⌺–Ar interaction potential at close range has
rel
ftr
Q
0
z
z
been well determined and is sufficiently shallow as to not
30
support vibrational quanta above 0 in the OH stretch. The
very strong inverse temperature dependence observed in vi-
brational relaxation is certainly consistent with a complex
vibrational predissociation mechanism.
The term M0 describes the Ar stagnation density and z0 is a
16
nozzle diameter scaling factor. These differential rate laws
ignore the normal transport terms appropriate to kinetics in
free jets since all of the rate processes studied in this paper
occur over times comparable to fluorescent lifetimes. In
these short times, jet transport is negligible and can be ig-
ACKNOWLEDGMENTS
2
nored. In other words, the initially prepared OH A ⌺ excited
state does not significantly move spatially during the kinetic
study. Integration of Eq. ͑A7͒ yields
Acknowledgment is made for the generous support of
this work by the National Science Foundation under Grant
No. CHE-9709656. We would also like to acknowledge use-
ful discussions with Dr. David Crosley, Dr. Jorge Luque, Dr.
Kristen Steffens, and Dr. Michael Heaven and we thank Dr.
Michael Barfield for calculating the polarizability of the OH
i͑z,t͒ϭi͑z,tϭ0͒
2
z
0
ϫexp
ͫ
Ϫ
ͩ
͑k ϩk ͒M ͩ ͪ ϩk ϩk
ͪ
t
ͬ
.
2
rel
Q
0
pd
fi
A ⌺ state.
z
͑
A9͒
APPENDIX
The integrated fluorescence of the initially prepared state at
some position, z, in the jet is given by
The processes of relevance to the determination of OH
A ⌺(v,N) relaxation rate coefficients are the following: The
relaxation event itself
2
ϱ
kfii͑z,tϭ0͒
Ii͑z͒ϭ
͵
kfii͑z,t͒dtϭ
.
2
k
rel
z
0
0
OH 2⌺͑v,N͒ϩAr→OH 2⌺͑vЈ,NЈ͒ϩAr
͑A1͒
͑krelϩkQ͒M0ͩ ͪ ϩkpdϩkfi
z
is in competition with several other processes, most impor-
tantly, fluorescence of the initial state
͑A10͒
Insertion of Eq. ͑A9͒ into ͑A8͒ followed by integration
k
fi
yields
OH 2⌺͑v,N͒→OH ⌸ ͑vЉ,NЉ͒
2
͑A2͒
͑A3͒
͑A4͒
J
2
z
0
electronic quenching
k M0ͩ ͪ i͑z,tϭ0͒
rel
z
k
Q
tr͑z,t͒ϭ
2
OH 2⌺͑v,N͒ϩAr→OH 2⌸͑vЈ,NЈ͒ϩAr,
and possible predissociation
z
0
kЈ Ϫ
ͩ
͑k ϩk ͒M ͩ ͪ ϩk ϩk
ͪ
fr
rel
Q
0
pd
fi
z
2
k
z
0
pd
OH 2⌺͑v,N͒→OϩH.
rel
Q
0
pd
fi
ϫ
ͩ
exp
ͫ
Ϫ
ͩ
͑k ϩk ͒M ͩ ͪ ϩk ϩk
ͪ
t
ͬ
z
The product of the relaxation in Eq. ͑A1͒ has two major
subsequent pathways open to it that are of significance,
mainly fluorescence
Ϫexp͓ϪkЈ t͔
ͪ
,
͑A11͒
fr
k
fr
where
kЈftrϭkftrϩM0
OH 2⌺͑vЈ,NЈ͒→OH ⌸ ͑vЉ,NЉ͒
2
͑A5͒
J
2
z
0
or subsequent quenching
kЈ .
Q
͑A12͒
ͩ ͪ
z
kЈ
Q
OH 2⌺͑vЈ,NЈ͒ϩAr→OH͑vЉ,NЉ͒ϩAr,
where the product of Eq. ͑A6͒ could be either the A ⌺ or
͑A6͒
The integrated fluorescence intensity from the transfer state,
tr, is given by
2
2
2
z
X ⌸ state. When the result of process ͑A6͒ yields OH in the
A ⌺ state subsequent fluorescence is detected and attributed
to the relaxation event in Eq. ͑A1͒. In this way all product
population for process ͑A1͒ with the sole exception of elec-
tronic quenching is accounted for.
0
k M0ͩ ͪ i͑z,tϭ0͒
2
rel
kftr
z
I ϭ
tr
ϫ
.
͑A13͒
2
kЈ
z
0
ftr
ͩ
͑krelϩkQ͒M0ͩ ͪ ϩkpdϩkfi
ͪ
z
Taking into consideration the local conditions in the free
The ratio of the integrated intensities from the states, i and tr,
jet,16 we can write a differential rate law for both the initially
yields
2
prepared reactant, OH A ⌺(v,N) of Eq. ͑A1͒, labeled i, or
k z2
Ii
fi
kЈ k
Q
fi
for the transfer state, tr, which is the product OH
A ⌺(vЈ,NЈ) state of the relaxation Eq. ͑A1͒,
ϭ
ϩ
.
͑A14͒
2
0
2
Itr k M z
k k
rel fr
rel
0
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J. Chem. Phys., Vol. 110, No. 17, 1 May 1999
M. Ahern and M. Smith
8563
7
Equation ͑A14͒ is equivalent to Eq. 6 in the text for N
ϪNЈ pure rotational state transfer.
K. J. Rensberger, J. B. Jefferies, and D. R. Crosley, J. Chem. Phys. 90,
174 ͑1989͒.
2
8
9
0
I. W. M. Smith, J. Chem. Soc., Faraday Trans. 2 81, 1849 ͑1985͒.
R. K. Lengel and D. R. Crosley, J. Chem. Phys. 68, 5309 ͑1978͒.
R. K. Lengel and D. R. Crosley, J. Chem. Phys. 67, 2085 ͑1977͒.
R. K. Lengel and D. R. Crosley, Chem. Phys. Lett. 32, 261 ͑1975͒.
K. J. Rensberger, J. B. Jefferies, and D. R. Crosley, J. Chem. Phys. 90,
2174 ͑1989͒.
G. A. Raiche, J. B. Jefferies, K. J. Rensberger, and D. R. Crosley, J.
Chem. Phys. 92, 7258 ͑1990͒.
K. R. German, J. Chem. Phys. 64, 4065 ͑1976͒.
M. Hawley and M. A. Smith, J. Chem. Phys. 95, 8662 ͑1991͒.
M. A. Smith and M. Hawley, in Advanced Gas Phase Ion Chemistry,
edited by N. G. Adams and L. M. Babcock ͑JAI, Greenwich, CT, 1992͒,
Vol. 1, p. 167.
J. Reader, C. J. Sansonetti, and J. M. Bridges, Appl. Opt. 35, 78 ͑1996͒.
K. L. Steffens, J. Luque, J. B. Jefferies, and D. R. Crosley, J. Chem. Phys.
106, 6262 ͑1997͒.
For vibrational energy transfer, where the effects of v
dependent predissociation or electronic quenching could be-
come significant between the initial and transfer states, we
chose an alternative method to determine the rate coefficient,
krel . We still use Eq. ͑A13͒ to describe the fluorescence in-
tensity of the vibrationally relaxed level. However, for com-
parison, we reference this intensity to that obtained when the
same relaxed vЈ state, tr, is directly prepared by the laser.
This laser prepared vЈ population will be called trЈ. In this
case, the initially prepared state population in the lower ref-
erence vЈ state, trЈ(z,tϭ0), is related to the total fluores-
cence observed after preparation by
1
11
12
13
1
1
4
5
16
1
1
7
8
kfr
I ϭ trЈ͑z,tϭ0͒.
͑A15͒
19
ref
I. L. Chidsley and D. R. Crosley, J. Quant. Spectrosc. Radiat. Transf. 23,
kЈ
fr
187 ͑1980͒.
20
Taking the ratio of Eq. ͑A13͒ to Eq. ͑A15͒ yields
D. R. Crosley and R. K. Lengel, J. Quant. Spectrosc. Radiat. Transf. 15,
79 ͑1975͒.
5
2
Iref trЈ͑z,tϭ0͒ ͑k ϩk ͒z
21
pd
fi
G. H. Dieke and H. M. Crosswhite, J. Quant. Spectrosc. Radiat. Transf. 2,
7 ͑1962͒.
ϭ
ϫ
9
tftr
i͑z,tϭ0͒
M z k
0 0 rel
2
2
2
3
J. Brzozowski, P. Erman, and M. Lyyra, Phys. Scr. 17, 507 ͑1978͒.
J. Luque and D. R. Crosley, ‘‘LIFBASE Database and Spectral Simulation
Program ͑Version 1.1͒,’’ SRI International Report No. MP 96-001, 1996.
J. A. Coxon, Can. J. Phys. 58, 933 ͑1980͒.
͑
k ϩk ͒trЈ͑z,tϭ0͒
rel
Q
ϩ
ͩ
ͪ
,
͑A16͒
kreli͑z,tϭ0͒
24
25
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