Effect of collisions on one-color polarization spectroscopy of OH A2Σ+-X2Π

Article abstract of DOI:10.1063/1.1615515

The phenomenological rate constants for the collisional suppression of PS signals of OH (A-X) are presented. The pump power, OH number density, and collider pressure dependences of the PS signal was investigated. Such experiments were the first stage in a program to develop polarization spectroscopy as a probe of the dynamics of inelastic collisions. The rate of loss of signal as a function of increasing collider pressure was unexpectedly extremely rapid, a process attributed to predominately velocity changing collisions.

Full text of DOI:10.1063/1.1615515

Effect of collisions on one-color polarization spectroscopy of OH A 2 Σ + –X 2 Π
Hilary J. Crichton, Matthew L. Costen, and Kenneth G. McKendrick
Citation: The Journal of Chemical Physics 119, 9461 (2003); doi: 10.1063/1.1615515
View online: http://dx.doi.org/10.1063/1.1615515
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 119, NUMBER 18
8 NOVEMBER 2003
Effect of collisions on one-color polarization spectroscopy
2
¿
2
of OH A ⌺ –X ⌸
Hilary J. Crichton, Matthew L. Costen,a) and Kenneth G. McKendrick
School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS,
United Kingdom
͑
Received 7 July 2003; accepted 12 August 2003͒
The effect of collisions on the magnitude of polarization spectroscopy ͑PS͒ signals from the OH
2
ϩ
2
radical on the A ⌺ –X ⌸ ͑0,0͒ band has been studied. OH was produced by the 266-nm
photolysis of H O and detected by one-color degenerate PS, using Ϸ5-ns pulses from a Nd:YAG
2
2
pumped dye laser. Spectra with both circular and linear pump polarizations are reported, together
with signal dependence on OH number density and pump pulse fluence. The relative line intensities
in the spectra and measured square dependence on OH number density are consistent with a
description of PS as a variant of four-wave mixing spectroscopy. The pump pulse fluence
dependence is fitted well by literature saturation curves. The collisional dependence of the PS signal
was investigated by adding increasing pressures of He, Ar, or N collider gases for fixed overlapping
2
pump and probe pulses. The principal finding is the very rapid loss of the PS signal with increasing
collider pressure. The resulting phenomenological rate constants are in the range 5–9
Ϫ9
3 Ϫ1
ϫ10 cm s . We discuss these rate constants with reference to the literature rotational energy
transfer and dephasing rate constants. We propose that the very large observed values may be
explained by the effect of elastic velocity changing collisions. © 2003 American Institute of
Physics. ͓DOI: 10.1063/1.1615515͔
I. INTRODUCTION
tum polarization. Angular momentum polarization in elec-
tronic energy transfer has not received the same level of
attention. Among the very few studies that have been re-
A. General background
6
It is a very-well-established fact that molecules may be
collisionally removed from electronically excited states. To-
tal rate constants for this ‘‘quenching’’ have been measured
on numerous occasions. However, the fate of the quenched
molecules has been little studied. Dagdigian recently re-
viewed the current state of the field for the simplest molecu-
lar systems: diatomic molecules.1 Rotational- or vibra-
tional-state product distributions have been measured for
only a limited range of molecular species, with state-to-state
relative rate constants being the most detailed level of infor-
mation obtained. A quantitative theoretical understanding of
these processes is still lacking, and simple models of energy
disposal have been shown to have generally poor predictive
ported, Jackson et al. measured polarization retention in in-
elastic electronic energy transfer in the SiF radical. These
experiments were performed using dispersed fluorescence to
detect the collisionally transferred population. The method
involved resolving the polarization of the emitted fluores-
cence with a photoelastic modulator and polarizer combina-
tion. These experiments proved extremely challenging within
the practical signal-to-noise limits provided by dispersed
fluorescence.
We have recently extended our studies of electronic en-
ergy transfer to the A and B states of the CH radical with a
range of colliders.7 This has been shown to be a rapid pro-
cess with a variety of partners, and vibrationally resolved
branching ratios have been established. The rotational distri-
bution of the transferred CH has been resolved using one of
the more efficient partners: CO2 ͑Ref. 9͒. However, the
signal-to-noise limits of dispersed fluorescence again prevent
the practical extension of this work to polarization studies of
the CH system.
,8
2
ability.
In the more developed field of study of reactive colli-
sions, the vector properties ͑for example, rotational angular
momentum polarization͒ of the process have been shown to
be a sensitive probe of the forces between the molecules.3
For inelastic collisions such properties have also been mea-
sured, but to a much more limited extent. They have given
new insights into the nature of the collisional interactions,
notably in the very detailed recent work on NO/Ar rotational
energy transfer ͑RET͒ collisions by Cline and co-workers.4
These studies measured state-to-state differential cross sec-
tions and scattering angle-resolved product angular momen-
CH, typical of many other systems, does not happen to
provide any suitable higher-lying electronic states through
which to perform an alternative optical–optical double-
resonance experiment—for example, by laser-induced fluo-
,5
rescence ͑LIF͒—as has been reported for some other limited
classes of molecules.1
0,11
We have therefore been trying to
develop a method of measuring the influence of collisions on
the angular momentum polarization of electronically excited
species.
a͒Author to whom correspondence should be addressed. Electronic mail:
M.L.Costen@hw.ac.uk
0021-9606/2003/119(18)/9461/8/$20.00
9461
© 2003 American Institute of Physics
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1

9462
J. Chem. Phys., Vol. 119, No. 18, 8 November 2003
Crichton, Costen, and McKendrick
cm3 sϪ1 for H O. This included an assumed contribution of
The spectroscopic technique we are using is polarization
spectroscopy ͑PS͒. Wieman and H a¨ nsch first developed po-
2
Ϫ10
3 Ϫ1
4
.5ϫ10
cm s
to account for the unmeasured
larization spectroscopy as a variant of saturation spec-
⌳-doublet changing collisions. These rate constants were for
1
2
troscopy. In the simplest implementation of PS the output
of a single tunable laser is split into two beams. The first of
these, the pump beam, is either circularly or linearly polar-
ized. The second, the probe beam, is linearly polarized be-
fore passing through the sample ͑at a 45° angle to the pump
beam polarization if that is also linearly polarized͒, after
which it encounters a blocking crossed polarizer. The pump
and probe beams are overlapped in the sample, in either a
copropagating or counterpropagating geometry. When the
pump beam is resonant with a transition in the sample it can
be considered to produce a polarization-dependent satura-
tion. The probe beam ‘‘sees’’ the sample as birefringent, and
consequently the polarization of the transmitted probe beam
becomes slightly elliptical, with a change in principal axis.
The resulting component of the probe beam normal to the
initial polarization then leaks through the crossed analyzing
polarizer and may be detected, typically by a photomultiplier
tube.
the lowest five or so rotational levels and were essentially
invariant with NЉ.
A more sophisticated experiment has been performed by
24,25
2
Hickson et al.
OH X ⌸ was produced by photolysis of
HNO at 266 nm. A single ⌳-doublet selected rotational
3
level was prepared in the OH vЉϭ1 vibrational level, using
a pulsed tunable infrared laser. The evolution of the resulting
population in the prepared state and its transfer into other
rotational levels was then monitored by LIF on the A–X
band. The ⌳-doublet changing collision rates were found to
depend strongly on the identity of the collider. The transfer
rate constant for Jϭ3.5 with HNO was found to be 2.4
3
Ϫ9
3
Ϫ1
Ϫ10
ϫ10 cm s , while that for Ar was only 0.5ϫ10
cm s . Total removal rate constants excluding ⌳-doublet
3
Ϫ1
Ϫ10
3 Ϫ1
transfer ranged from 1.0ϫ10
cm s
for Ar to 5.0
Ϫ10
3 Ϫ1
ϫ10
cm s for HNO3 .
These two studies quote rotational energy transfer rate
2
In recent years PS has undergone something of a revival
and has been widely applied in combustion diagnostics as a
constants for OH X ⌸ that agree well with older literature
and show that the process is very rapid with H O and HNO .
2
3
1
3,14
15
16
26
tool to detect radical species, notably OH,
NH, C2 ,
Measurements by Andersen et al. indicate that H O is also
2 2
1
7
and NO. These applications are all of degenerate PS, in
which a single laser is used to generate both pump and probe
beams. Infrared–ultraviolet double-resonance polarization
very efficient, with total rate constants of the order of
Ϫ10
3 Ϫ1
1
–10ϫ10
Both electronic quenching of the A ⌺ state and RET
within it have been studied on numerous occasions. Jorg
cm s
.
2
ϩ
spectroscopy of OH and CH has also very recently been
3
1
8
demonstrated. A number of experiments have been devoted
to studying the collisional evolution of the signal as a func-
tion of the delay time between pump and probe pulses. The
majority of these studies have been performed in atmo-
spheric pressure flames, using picosecond lasers and optical
27,28
2
ϩ
et al.
have measured RET rate constants for OH A ⌺
(
vЈϭ0) with a variety of combustion-related collision part-
ners and rare gases. These experiments were performed by
dispersed fluorescence measurements after pumping of
2
ϩ
single rotational levels in the A ⌺ state. With H O as a
1
9,20
2
delay lines.
Only a single study has been performed in a
collision partner, individual state-to-state rate constants of up
controlled temperature and pressure environment containing
a single collider species, without variation of the pump–
Ϫ10
3 Ϫ1
to 4ϫ10
cm s were measured, with a total removal
Ϫ10
3 Ϫ1
2
1
rate constant of approximately 9ϫ10
individual rate constants up to 1ϫ10
removal rate constant of approximately 5ϫ10
cm s . N2 gave
probe delay time. In related work, Wilson and McCaffery
have used continuous-wave lasers in a double-resonance PS
experiment to measure line shapes and hence infer details of
Ϫ10
3 Ϫ1
cm s and a total
Ϫ10
3 Ϫ1
cm s
,
2
2
while total removal rate constants for Ar and He were 2.5
the differential scattering cross sections.
Ϫ10
Ϫ11
3 Ϫ1
ϫ10
and 7.5ϫ10
cm s , respectively.
The majority of the collision partners discussed here
show A ⌺ state electronic quenching rates which are much
B. OH collisional energy transfer
2
ϩ
We have chosen the OH radical as a test case for our
initial development of our experiments as it is simple to pro-
duce and probe. Collisions of this radical have been the sub-
ject of numerous previous experimental studies in both the
slower than the RET rates. N has typical rotational-level-
2
Ϫ11
dependent quenching rate constants of k ϭ2ϫ10
cm s , while He and Ar have quenching rates that are
Q
3
Ϫ1
negligible.2
9,30
H2O, on the other hand, has a very large
2
2
ϩ
ground X ⌸ and excited A ⌺ states, primarily because of
Ϫ10
3 Ϫ1
quenching rate constant k Ϸ7ϫ10
cm s , effectively
Q
its importance in combustion and the atmosphere. There
3
1,32
2
independent of rotational level.
have been several recent studies of the ground X ⌸ state.
Kliner and Farrow23 measured the evolution of the nascent
In this paper, we present phenomenological rate con-
stants for the collisional suppression of PS signals of OH
A–X). PS was performed in a degenerate ͑pump and probe
rotational-state distribution produced by the 266-nm photoly-
sis of H O using picosecond LIF. The rotational-state dis-
(
2
2
beams from the same laser͒ copropagating configuration. We
investigate the pump power, OH number density, and col-
lider pressure dependences of the PS signal. Pump power
and number density dependences are discussed in light of
previously published theory. The principal new result, the
effect of collisions on the PS signal, is discussed in the con-
text of other literature OH collisional rate constants.
tributions at different photolysis–probe delays were recorded
and a variety of collisional models were used to simulate
them. Several different colliders were used—H O, Ar, N ,
2
2
and O —and the data were well fitted by an exponential gap
2
law model. Most relevant for the current work were the re-
ported total depopulation rate constants. These span the
range from 2ϫ10Ϫ10 cm s for Ar through to 8.9ϫ10
3
Ϫ1
Ϫ10
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J. Chem. Phys., Vol. 119, No. 18, 8 November 2003
One-color polarization spectroscopy of OH
9463
that the probe beam just passed its edge. This ensured that
the overlap length was as long as possible. Both beams over-
lapped the photolysis beam ͑counterpropagating to the pump
and probe beams͒ in the center of the cell. At the exit of the
cell the pump beam was picked off by another mirror and
passed to an energy monitor ͑Molectron͒. The probe beam
passed through an iris and then a second, identical high-
quality polarizer, mounted in a precision rotation stage ͑Ber-
nard Halle/Newport͒. This polarizer was crossed with respect
to the first. The signal beam that emerged from this analyzing
polarizer was passed by a number of mirrors around the op-
tical table a distance of approximately 2.5 m to a spatial filter
and then through a 308-nm centered interference filter to a
photomultiplier tube ͑PMT͒, which was carefully shielded
from the ambient light.
FIG. 1. Schematic of the experimental apparatus used for one color polar-
ization spectroscopy. WPϭwaveplate, DFRϭdouble Fresnel rhomb, BC
ϭBerek’s compensator, SFϭspatial filter, PMTϭphotomultiplier tube, and
MϭMolectron energy meter.
A second PMT collected LIF from the central portion of
the cell. No collection optics was used. In fact, it was nec-
essary to attenuate the fluorescence using neutral density fil-
ters to avoid saturation of the PMT. Signals from both PMTs
and the energy monitor were passed to boxcar averagers
II. EXPERIMENT
The experimental apparatus is shown in Fig. 1. Experi-
ments were conducted in a glass flow cell ͑50 cm long, 5 cm
diameter͒, evacuated by a rotary pump. The cell had win-
dows ͑UV, synthetic fused silica͒ at each end and one on the
͑SRS͒ and thence to a computer on a shot-to-shot basis. The
computer also controlled the wavelength scanning of the dye
laser via purpose-written Labview software.
A significant limitation in the application of PS in sealed
environments arises from stress-induced birefringence in the
windows of the cell. The birefringence causes the polariza-
tion of the probe beam to become elliptical, resulting in a
constant background signal passing through the analyzing
polarizer, independent of whether the probe beam is resonant
with a transition in the sample. In these experiments, it was
found that applying a compensating stress to the cell was
capable of nulling any stress-induced birefringence to ac-
ceptable levels. The birefringence of the windows was mini-
mized before each experiment, and checked at regular inter-
vals.
side for LIF detection. Hydrogen peroxide ͑50% wt /H O)
2
was introduced by bubbling the selected quenching gas
through the solution and the pressure regulated by a needle
valve; additional quencher was added downstream when re-
quired through a secondary needle valve. All of the piping
and valves after the bubbler were made of Teflon to reduce
dissociation of the hydrogen peroxide. The hydrogen perox-
ide was photodissociated using the fourth-harmonic output of
a Nd:YAG laser ͑Continuum Surelite II-10͒ at 266 nm, pro-
2
ducing OH X ⌸ radicals. A Nd:YAG pumped dye laser
͑Continuum Surelite II-10, Sirah Cobrastretch, nominal pulse
length 5 ns, R640 dye͒ provided tunable narrow-band radia-
tion in the 308-nm range, resonant with the OH A–X(0,0)
band. A delay of 8 ␮s, controlled by an electronic delay
generator ͑SRS DG535͒, was introduced between the firing
of the two laser systems to allow relaxation of the nascent
OH to thermal Boltzmann rotational and translational distri-
butions.
III. THEORY
Polarization spectroscopy is a specialized form of four-
wave mixing ͑FWM͒.33 Like FWM, in the perturbative low-
power limit the signal depends on the square of the pump
beam fluence and linearly on the probe beam. Similarly, the
signal depends on the square of the number density of the
probed species and quartically on the line strength of the
transition used.34 Beyond the perturbative treatment, there
A central portion of the dye laser output, Ϸ2 mm in
diameter, was selected by an iris and used in the subsequent
experiments. All beam steering was carried out using broad-
band dielectric mirrors ͑Balzers͒. The beam was split into
two parts using a tunable waveplate and a calcite polarizer.
The weaker of these beams ͑the probe beam͒ was passed
to a high quality polarizer ͑Bernard–Halle, extinction ratio
have been a number of papers treating the strong-field limit
using numerical simulations.3
5,36
Crucial to this study, the
signal also depends on the collisional processes of both the
ground and excited states linked by the probed transition.
Collisions that involve pure dephasing as well as population
Ϫ6
Ͻ1ϫ10 ) mounted in a precision rotation stage ͑Newport͒.
The probe beam passed directly through the cell without en-
countering any additional optics other than the cell windows.
The more intense beam ͑henceforth the pump beam͒ was
passed through a double Fresnel rhomb and calcite polarizer
combination, which acted as a variable attenuator. The pump
beam was passed through a Berek’s compensator ͑New Fo-
cus͒ to produce light that could be selected as either circu-
larly polarized or linearly polarized at a 45° angle to the
polarization of probe beam. The pump beam was then over-
lapped with the probe by positioning a final turning mirror so
transfer out of, or between, the m sublevels of the two reso-
J
nant states are significant. This results in a dependence on
both pure rotational population transfer and orientation or
alignment loss.
The detailed contributions of these different processes
will be addressed fully in future reports. In this paper, we
restrict ourselves to degenerate one-color experiments and
assume a single phenomenological collisional decay rate
containing contributions from both the ground and excited
states.
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9464
J. Chem. Phys., Vol. 119, No. 18, 8 November 2003
Crichton, Costen, and McKendrick
pump light at 45° to the probe polarization, ͑b͒ PS with cir-
cularly polarized pump light, and finally ͑c͒ LIF simulation
͑
LIFBASE͒.37 The PS spectra were taken under slightly satu-
rating pump laser conditions. Very clear differences are ap-
parent between all three pairs of spectra. It is immediately
obvious that neither PS spectrum resembles the LIF spec-
trum with respect to line intensities. The linearly polarized
pump PS spectrum predominately features Q-branch lines,
while in the circularly polarized pump spectrum P- and
R-branch lines are most intense. These observations are, as
expected, consistent with previous descriptions of PS.1
Orientation is not an efficient process with circularly polar-
ized light via Q-branch transitions and becomes increasingly
difficult with increasing rotational quantum number. This ex-
plains the strong preference for P and R branches in Fig.
3,15,17
2
͑b͒. Alignment with linearly polarized light is stronger via
Q-branch transitions than P/R. Additionally, analogous with
degenerate four wave mixing ͑DFWM͒, we expect the PS
signal to depend on the line strength of the transition to the
fourth power, which will strongly favor the Q branch over P
or R, as seen in Fig. 2͑a͒. In both PS spectra, the signal
intensity drops off much more rapidly with increasing rota-
tion than in the LIF spectrum. This is also consistent with a
DFWM description, from which we expect the signal to de-
pend on the square of the number density of the probed spe-
cies, as quantified in the next section.
B. Number density dependence of signals
The number density dependence of the PS signal was
determined by varying the OH concentration via the photoly-
sis fluence. As an example, the probe laser wavelength was
centered on the P (1) line and the signal-to-noise optimized
1
at maximum photolysis fluence, as measured immediately
before the cell using an energy meter ͑Scientech͒. Data were
acquired in the form of averages of 100 laser shots. The
fluence was then reduced by altering the photolysis laser
flashlamp voltage and the measurement repeated. The mea-
surements were made over the full range of available flu-
ences. The polarization spectroscopy data were corrected for
minor variations in probe laser system fluence ͑see next sec-
tion͒. The results are shown in Fig. 3, and the PS signal
clearly follows a nonlinear dependence on the OH number
density. This shows good agreement with the expected
2
͓
OH͔ -dependent curve also shown in Fig. 3.
C. Effect of pump laser fluence
2
ϩ
2
FIG. 2. Part of the OH A ⌺ –X ⌸ ͑0,0͒ band with partial assignment. ͑a͒
Polarization spectroscopy with 45° linearly polarized pump light of rotation-
ally thermalized OH. ͑b͒ Polarization spectroscopy with circularly polarized
pump light of rotationally thermalized OH. ͑c͒ LIFBASE simulation of LIF
spectrum produced by a 300-K Boltzmann distribution. Spectra recorded
with 2 Torr of Ar buffer and 8-␮s photolysis/PS delay under slightly satu-
rating pump fluence conditions.
The pump beam fluence was varied by adjusting the tun-
able waveplate prior to the second calcite polarizer; this al-
lows independent control of the pump and probe fluences.
The PS signal and pump fluence after the cell were averaged
over 50 shots: then, the pump fluence was altered and the
process repeated. The pump fluence was varied over the de-
sired range several times during a single experiment to en-
sure against other possible systematic experimental varia-
tions. A number of different transitions were studied, with
both linear and circular pump polarizations. All of the spec-
tra show similar functional forms, with clear evidence of
saturation at the higher fluences.
IV. RESULTS
A. Spectra
2
ϩ
2
Figure 2 shows three spectra of the OH A ⌺ –X ⌸
0,0͒ transition for comparison: ͑a͒ PS with linearly polarized
͑
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J. Chem. Phys., Vol. 119, No. 18, 8 November 2003
One-color polarization spectroscopy of OH
9465
dependence at low fluence is shown in the inset diagram. It is
observed that the signal follows a squared dependence at the
lowest pump fluence. All further experiments were per-
formed in this low-power regime.
D. Effect of varying collider pressure
The primary aim of this wider program of experiments is
to study inelastic collisional processes using polarization
spectroscopy. This first stage is aimed at establishing the
evolution of the PS signals with increasing collision number.
Varying the time between the pump and probe pulses at con-
stant pressure would clearly be a straightforward way of
achieving this. However, in the current one-color degenerate
experiment this can only be realized by introducing an opti-
cal delay line, and while this has been used in several pico-
second PS studies, the path lengths required are clearly not
practical in this nanosecond experiment.
The alternative approach of varying the collider pressure
at fixed pump–probe delay was thus applied. The laser
wavelength was centered on the selected transition with the
pump and probe beams essentially coincident in time
through having traversed beam paths of equal length. The PS
signal was then acquired for 100 shots, along with the shot-
to-shot pulse energy of the pump beam and LIF signal. The
pressure of the selected collider gas was then altered and the
procedure repeated. The LIF signal was acquired to allow
normalization of the PS signal to the number density of OH
produced by photolysis. Several difficulties presented them-
selves. The concentration of H2O2 required to produce suf-
ficient signal-to-noise was high enough that significant
FIG. 3. Polarization spectroscopy signal as a function of OH number den-
sity. Open circles are experimental data; the solid line is a ͓OH͔ simulation.
2
Walewski et al. recently published a paper on the effect
of pump fluence on polarization spectroscopy signals.38 They
listed several functional forms for the expected dependence,
drawing on simple descriptions of the saturation dependence
of DFWM experiments, including
2
Ipump
I ϭA
,
͑1͒
PS
ͩ
PS
ͪ
IpumpϩIsat
2
ϩ
quenching of the OH A ⌺ fluorescence was observed. This
where IPS is the measured signal, I
intensity, A is an arbitrary scaling factor, and Isat is a satura-
tion intensity.
is the pump laser
pump
PS
is a side effect of the relatively modest photodissociation
Ϫ20
2
cross section of H O at 266 nm ͓5ϫ10
cm ͑Ref. 39͔͒.
The addition of extra collider gas was found to alter the flow
rate of H O , which could not be controlled using a mass
2
2
An example of the fit of Eq. ͑1͒ to the data for linear
polarization on the P (1) line is shown in Fig. 4. It can be
2
2
1
flow controller due to the rapid dissociation of the H O on
seen that the functional form fits the data well. The signal
2
2
stainless steel surfaces. Both the OH concentration and
2
ϩ
quenching of the OH A ⌺ fluorescence were affected by
the selected pressure of the collider gas. The integrated OH
LIF signal over a fixed time gate was thus not a simple direct
measure of the OH concentration.
Therefore, the LIF decay trace was acquired using a
digital storage oscilloscope ͑LeCroy 3900͒ at each pressure
point. The resulting exponential lifetime from a fit to this
decay trace was used together with the known collision free
2
ϩ
fluorescence lifetime of OH A ⌺ to correct the LIF signal
for the effects of quenching. The hypothetical magnitude of
the LIF signal without quenching was established at each
pressure. The square of this value was then used to normalize
the measured PS signal with respect to OH concentration.
The PS signal was also normalized with respect to the dye
laser fluence. This should be a squared dependence on the
pump power and linearly on the probe fluence or cubic in the
total. However, the LIF signal is itself linear in the laser
fluence, and dividing by the square of the LIF signal has
already introduced a partial normalization for variations in
laser fluence. The PS signal was accordingly divided linearly
by the laser fluence, resulting in the correct overall normal-
ization.
FIG. 4. Polarization spectroscopy signal as a function of pump laser fluence.
Open circles are experimental data; the solid line is a fit of equation 1 to the
data. Inset diagram shows an expanded view of the low-fluence region.
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9466
J. Chem. Phys., Vol. 119, No. 18, 8 November 2003
Crichton, Costen, and McKendrick
rate constants derived are not purely the result of collisions
with the added collider gas, owing to the varying precursor
partial pressure. However, the precursor partial pressure de-
creased as the collider pressure was increased, and we be-
lieve that the derived rate constants are hence primarily de-
termined by the collider gas.
We have subsequently repeated a limited number of
these measurements under different experimental conditions.
These experiments were performed in a steel high-vacuum
chamber, with OH radicals produced by the 193-nm photoly-
sis of HNO . The much larger cross section for HNO pho-
3
3
Ϫ17
Ϫ2
todissociation at this wavelength ͓1.1ϫ10
cm
͑Ref.
4
0͔͒ resulted in excellent signal to noise with a partial pres-
sure of only 10 mTorr of HNO precursor. The different
3
chamber and pumping and gas handling systems enabled the
partial pressure of the precursor to be kept much more stable
as the collider gas pressure was increased. The low HNO3
partial pressure also resulted in no significant quenching of
the OH LIF. As a result, the LIF signal was a much more
direct measurement of the OH concentration, and a consid-
erably less severe normalization of the PS signal was re-
quired compared to the results reported above. The pump and
probe pulses were provided by separate lasers, the probe
pulse by the same Nd:YAG/dye-laser combination as the
one-color experiments and the pump pulse by a separate
Nd:YAG/dye-laser system ͑Lumonics Hyperdye͒. The pump
and probe pulses with synchronized temporally using a digi-
tal delay generator ͑SRS DG535͒. All other conditions were
identical to the previous experiments. These later measure-
ments also found extremely rapid phenomenological decay
rates, confirming the results of the earlier measurements.
This independent verification reinforces our confidence in
the reported rate constants.
FIG. 5. Polarization spectroscopy signal as a function of Ar collider pres-
sure, for the P (1) transition with circularly polarized pump light. Open
1
circles are experimental data: the solid line is a first-order exponential fit to
the data.
The total pressure of precursor and collider was varied
over a range of Ϸ0.5 to Ϸ5 Torr. At the lowest total pres-
sures the observed LIF lifetime indicated that the H O pre-
2
2
cursor partial pressure was Ϸ80 mTorr, falling to Ͻ10 mTorr
at the highest total pressures. The colliders used were He, Ar,
and N . Additionally, O , CO , and H were also tried, but
2
2
2
2
produced such rapid quenching of the LIF that normalization
to the varying OH concentration became unreliable. For each
of the collider gases used, both circular and linear polariza-
tions of the pump laser were applied. For the linearly polar-
V. DISCUSSION
ized pump experiments the measured transitions were P (1),
1
The measured signals have the anticipated dependence
on laser pulse fluence and OH concentration from analogy
with DFWM theory, with a squared dependence on the pump
laser power and on OH number density. The strong variation
of PS signal with transition branch seen in the spectra is
consistent with a fourth-power line strength dependence. The
squared number density dependence and low room-
temperature Boltzmann rotational populations, arising from
the large rotational constant of OH, restrict us to only low N
Q (2), and Q (3) and for the circularly polarized pump the
1
1
P (1) and P (3). First-order exponential decays were non-
1
1
linear least-squares fitted to the resulting curves of PS signal
versus total pressure (collider ϩH O /H O). An example
2
2
2
decay trace and fit are shown in Fig. 5. The resulting decay
constants were converted to second-order rate constants by
assuming a time scale of 5 ns, consistent with the
manufacturer-quoted full width at half maximum ͑FWHM͒
pulse width of the Continuum/Sirah laser system. The rate
constants derived for the three gases with both pump polar-
izations using the above transitions are listed in Table I. The
͑
Ͻ4͒ with a practical signal-to-noise ratio in these experi-
ments.
The striking principal finding of these experiments is the
extremely rapid removal of the polarization spectroscopy
signal with increasing pressure. The rate constants quoted in
Table I assuming a 5-ns pulse length are of the order 5–8
TABLE I. Phenomenological rate constants of PS signal loss ͓k
Ϫ9
3
Ϫ1 Ϫ1
(
10 cm molecule
s
)] as a function of pump polarization, collider
gas, and transition probed. Errors quoted are 2␴ statistical uncertainties.
Ϫ9
3 Ϫ1
ϫ10 cm s . By analogy with DFWM, we should expect
the signal detected to depend on the square of the electric
field generated in the nonlinear process. The phenomenologi-
cal rate constants will hence be twice the rate constants for
the processes removing this signal electric field—for ex-
ample, RET or reorienting collisions. Even so, the implied
Linear pump
Circular pump
polarization collider
polarization collider
Transition
He
Ar
N2
He
Ar
N2
P (1)
5.4Ϯ1.2 8.8Ϯ0.8 6.2Ϯ1.0
8.0Ϯ1.6 8.0Ϯ0.4 7.6Ϯ0.8
8.0Ϯ0.6 8.2Ϯ1.2 6.7Ϯ0.6
1
P (3)
-
-
-
Ϫ9
3 Ϫ1
1
collisional rate constants of 2.5–4ϫ10 cm s are still
extraordinarily fast. As discussed in the Introduction, total
collisional removal rates for OH in the ground and excited
Q (2)
6.6Ϯ0.6 8.7Ϯ1.0 6.5Ϯ0.8
5.3Ϯ0.6 8.6Ϯ1.0 8.3Ϯ1.0
-
-
-
-
-
-
1
Q (3)
1
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J. Chem. Phys., Vol. 119, No. 18, 8 November 2003
One-color polarization spectroscopy of OH
9467
mated above would be produced by scattering through an
angle of only Ϸ3°. Such small-angle scattering around the
forward direction is known to typically have very large cross
sections.43 In the absence of further evidence, we propose
that such velocity changing collisions are the primary pro-
cess responsible for the loss of the signal in these experi-
ments.
In conclusion, these experiments have been the first
stage in a program to develop polarization spectroscopy as a
probe of the dynamics of inelastic collisions. We have man-
aged to produce high signal-to-noise PS signals in a sealed
environment at low pressure, overcoming the problems of
scattering pump light and birefringence introduced by the
cell windows. The signals behave in the expected fashion
with varying pump power or sample number density. The
rate of loss of signal as a function of increasing collider
pressure is unexpectedly extremely rapid, a process we at-
tribute to predominately velocity changing collisions.
states with Ar, N , or He as collision partners are at most of
2
Ϫ10
3 Ϫ1
the order of 5ϫ10
cm s . We thus need to consider
what other processes could be removing the signal in such a
rapid fashion.
We can clearly state that whatever process removes the
signal is collisional in nature. Polarization spectroscopy will
be sensitive to purely elastic dephasing collisions as well as
collisional removal or depolarization. The magnitude of
these dephasing rates can be estimated from a combination
of line broadening measurements, sensitive to both dephas-
ing and total removal rates, and the literature total removal
rates. The line broadening parameters for OH (A–X) with
Ar, He, and N2 are consistent with combined dephasing
Ϫ10
Ϫ10
and removal rate constants of 5ϫ10 , 2ϫ10 , and 8
ϫ10
Ϫ10
3
Ϫ1
41
cm s respectively. These are very similar to the
total collisional removal rate constants measured in other
experiments and discussed earlier. This suggests that dephas-
ing collisions are not a dominant influence on the observed
degradation of our PS signal.
Further collisional processes that could potentially de-
grade the signal are those that result in a velocity change.42
The physical principle is that molecules that have undergone
a velocity changing collision will emit spatially out of phase
with their counterparts that have not, and the resulting inter-
ference will be destructive and not generate a signal field.
The critical parameters are the wave vector for the signal
field generated in the nonlinear process, the velocity change
caused by collision, and the time scale between collisions
and photon interactions. The wavelength of the pump
and probe lasers is approximately 308 nm: from this, we find
that the wave vector in these experiments is of the order
ACKNOWLEDGMENTS
We thank the EPSRC for equipment funding. H.J.C.
thanks the EPSRC for a Ph.D. studentship. M.L.C. thanks the
Royal Society of Edinburgh for a BP research fellowship.
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