Photoacoustic
spectroscopy is a sensitive in situ technique for measuring the absorption
coefficient for gas and aerosol samples. Photoacoustic spectrometer (PAS)
instruments require accurate calibration by comparing the measured
photoacoustic response with a known level of absorption for a calibrant.
Ozone is a common calibrant of PAS instruments, yet recent work by Bluvshtein
et al. (2017) has cast uncertainty on the validity of ozone as a calibrant at
a wavelength of 405 nm. Moreover,
Fischer and Smith (2018) demonstrate
that a low O2 mass fraction in the bath gas can bias the measured PAS
calibration coefficient to lower values for wavelengths in the range
532–780 nm. In this contribution, we present PAS sensitivity measurements
at wavelengths of 405, 514 and 658 nm using ozone-based calibrations with
variation in the relative concentrations of O2 and N2 bath
gases. We find excellent agreement with the results of Fischer and Smith at
the 658 nm wavelength. However, the PAS sensitivity decreases significantly
as the bath gas composition tends to pure oxygen for wavelengths of 405 and
514 nm, which cannot be rationalised using arguments presented in previous
studies. To address this, we develop a model to describe the variation in PAS
sensitivity with both wavelength and bath gas composition that considers
Chappuis band photodynamics and recognises that the photoexcitation of
O3 leads rapidly to the photodissociation products O(3P)
and O2(X, v>0). We show that the rates of two
processes are required to model the PAS sensitivity correctly. The first
process involves the formation of vibrationally excited
O3(X̃) through the reaction of the nascent
O(3P) with bath gas O2. The second process involves the
quenching of vibrational energy from the nascent O2(X,
v>0) to translational modes of the bath gas. Both of these
processes proceed at different rates in collisions with N2 or
O2 bath gas species. Importantly, we show that the PAS sensitivity is
optimised for our PAS instruments when the ozone-based calibration is
performed in a bath gas with a similar composition to ambient air and
conclude that our methods for measuring aerosol absorption using an
ozone-calibrated PAS are accurate and without detectable bias. We emphasise
that the dependence of PAS sensitivity on bath gas composition is
wavelength-dependent, and we recommend strongly that researchers characterise
the optimal bath gas composition for their particular instrument.
Introduction
The shortage of measurements of aerosol optical properties for light
absorbing aerosol precludes their accurate representation in climate models
(Stier et al., 2007). In particular, the light absorption for a particular
class of aerosol referred to as brown carbon is poorly known, giving
large uncertainties in the impact of brown carbon on climate (Feng et al.,
2013; Lin et al., 2014). Moreover, light absorption by brown carbon depends
strongly on wavelength, with larger absorption at short (∼400 nm)
compared to longer (∼700 nm) visible wavelengths. Therefore, the
development of improved instruments for accurate aerosol absorption
coefficient (αabs) measurements over the visible spectrum –
particularly at short visible wavelengths relevant to brown carbon studies –
is crucial to reduce the uncertainties in absorbing aerosol optical
properties. Photoacoustic spectroscopy is a sensitive technique for measuring
αabs in situ for analytes that include gaseous or
aerosol samples (Miklós et al., 2001; Moosmüller et al., 2009). Our
research focusses on developing PAS instruments to provide accurate and
sensitive measurements of aerosol absorption coefficients in both laboratory
and field studies (Davies et al., 2018; Lack et al., 2012).
To characterise aerosol in the natural environment, field-deployable
instruments need to be both robust and compact. For example, we often
operate our instrument aboard the UK research aircraft (FAAM BAe-146) which
imposes constraints on the instrument weight and dimensions. Traditional
filter-based techniques for aerosol absorption measurement use a
photo-detector to record the light transmission through a filter substrate
on which ambient aerosol is impacted. These instruments are lightweight and
robust and can operate over long periods (∼ days) unattended
(Cappa et al., 2008; Sedlacek and Lee (2007); Virkkula et al., 2005). However, there
are known biases in the retrieved aerosol absorption coefficient. For
example, Lack
et al. (2008) report biases in the range 50 %–80 %, with larger biases
associated with aerosol samples containing a large organic fraction relative
to black carbon, although we have demonstrated recently that advanced
correction schemes can remove the bias dependence on organic mass fraction
with modest biases in derived absorption coefficients of up to 17 %
(Davies et al., 2019). Biases
are also attributed to processes that include the modification of the filter
substrate by liquid aerosol components, changes in the aerosol structure and
size upon impaction (e.g. from the redistribution of organic components and
the aggregation of particles) and multiple scattering interactions.
Filter-based absorption measurements are limited by their inability to study
aerosol in situ.
The PAS uses a laser beam to heat (by photoexcitation) the analyte aerosol in situ, and
the heated sample cools by collisional relaxation with the bath gas. The
bath gas consequently undergoes adiabatic thermal expansion and generates an
acoustic pressure wave for detection by a sensitive microphone. The
microphone response is directly proportional to αabs and
therefore provides an in situ measure of aerosol absorption. The relationship
between this microphone response and the absorption coefficient is
determined by calibrating the PAS with a calibrant of known or independently
measured absorption, with the quality of this calibration determining the
accuracy of PAS absorption measurements.
Researchers have used a variety of analytes to calibrate their PAS systems,
including gas or aerosol calibrants
(Bluvshtein et al., 2017; Davies et al., 2018; Fischer and Smith, 2018; Lack et al., 2006,
2012). For aerosol absorption measurement applications, an aerosol calibrant
may be desired
(Bluvshtein et al., 2017; Haisch, 2012). However, there can be large uncertainties in
aerosol-based calibrations that rely on a known refractive index for the
aerosol and accurate measurements of the size distribution and number
concentration of the aerosol passed to the PAS. In particular, typical
biases in number concentration are often quoted to be as large as 10 %
(Miles et al., 2011). Moreover, aerosol-based
calibrations require additional equipment such as a differential mobility
analyser that are not deployed conveniently in the field. Therefore, many
researchers use a gas species to calibrate their PAS. Such calibrations
typically pass the gaseous sample through the PAS to record the microphone
signal S before measurement of the gas extinction coefficient (αext) by cavity ring-down spectroscopy (CRDS) using an in-line
spectrometer. CRDS measures αextdirectly (without calibration) from
the change in attenuation rate for transmitted light through a multi-pass
optical cavity, and, in the case of a gas species for which scattering can be
assumed negligible, αext is equivalent to αabs.
Therefore, the CRDS-measured αabs is related to S via the PAS
calibration coefficient (often referred to as the sensitivity) by
C=Sαabs.
Both NO2 and ozone are popular analytes for calibration of PAS
instruments (Bluvshtein et al., 2017; Davies et al. , 2018; Fischer and Smith, 2018; Lack et al., 2006, 2012).
The O3 absorption cross section varies by only 2
orders of magnitude over the wavelength range of our spectrometers (405–658 nm),
while the NO2 cross section varies by 3 orders of
magnitude. The large NO2 absorption cross section range causes
saturation in the 405 nm spectrometers for concentrations that are optimal
for the 658 nm spectrometers, preventing the fast (∼1 h)
and simultaneous calibration of all our photoacoustic spectrometers from a
single source of calibration gas. Importantly, NO2 photodissociates at
optical wavelengths < 430 nm, with NO2 lost irreversibly from
the sample to form stable nascent NO and O2 products
(Tian et al., 2013). This photodissociation
pathway limits NO2 as a calibration standard for photoacoustic
spectrometers at short visible wavelengths. Therefore, we use ozone to
calibrate our PAS instruments.
Lack et al. (2006) calibrated their 532 nm
PAS with ozone and demonstrated a precision in the calibration coefficient
of 0.09 %. Moreover, subsequent measurements of αabs for
nigrosin aerosol were in excellent agreement with expected values calculated
from the known aerosol refractive index, controlled particle size and
measured number concentration. However,
Bluvshtein et al. (2017) repeated the experiments
of Lack et al. (2006) using a PAS wavelength of 405 nm and found an
unaccounted-for factor of 2 discrepancy between ozone-based and aerosol-based
calibrations. This result challenged the validity of ozone as a calibrant for
photoacoustic spectrometers at short wavelengths, i.e. the wavelength range
that is often of most interest to studies of brown carbon. We repeated the
experiments of Bluvshtein et al. (2017) using our photoacoustic
spectrometers that operate at wavelengths of 405, 514 and 658 nm and instead
observed excellent agreement between ozone and aerosol calibrations across
all wavelengths, including the short 405 nm wavelength (Davies et al.,
2018).
Most recently, Fischer and Smith (2018) recognised that one key difference
between the ozone calibrations performed by ourselves and by Bluvshtein et
al. (2017) was the composition of the bath gas. Bluvshtein et al. (2017)
diluted an ozonised oxygen flow with N2 to give an overall bath gas
composition of 90 % N2 and 10 % O2, while we (Davies
et al., 2018) injected an ozonised oxygen flow into ambient air to give an
overall bath gas composition of 76 % N2 and 24 % O2
(ignoring <1 % concentrations of argon, CO2 and trace
gases). Fischer and Smith (2018) measured the PAS calibration coefficient as
a function of the O2:N2 ratio for PAS wavelengths of 532, 662 and
780 nm. They showed that the PAS calibration coefficient depends on the
O2 mole fraction, with a factor of 2 increase in the PAS calibration
coefficient as the bath gas O2 mole fraction increased from 0.0 to
1.0, reaching an asymptotic maximum value that agreed with calibration
coefficients measured using NO2 gas or an aerosol calibrant. We
highlight three important aspects of the work of Fischer and Smith. First,
the asymptotic value in the calibration coefficient is attained at an
O2 mole fraction of ∼0.2 within measurement uncertainty, i.e.
at the O2 mole fraction that is relevant to our previous work (Davies
et al., 2018). Second, the PAS sensitivity is reduced to only ∼20 %
of the asymptotic value at the O2 mole fraction of 0.1 that pertains
to
Bluvshtein et al. (2017). Therefore, the impact
of bath gas does not reconcile our past measurements with those of
Bluvshtein et al. (2017), if the observed variations in PAS sensitivity with bath gas
composition at wavelengths >532 nm also apply at 405 nm. Third,
the authors account for the asymptotic behaviour by using a model that
treats the relaxation of photoexcited ozone and the relative rates at which
this excited state is quenched by either O2 or N2 bath gas
species. Their model ascribed the drop in PAS sensitivity (i.e. the
calibration coefficient) at low O2 mole fractions to poorer quenching
of photoexcited O3 by N2. The authors concluded that ozone
calibrations should be performed in a bath gas of pure O2.
One drawback of the Fischer and Smith (2018) study is that the PAS sensitivity measurements were not performed for
the 405 nm wavelength for which Bluvshtein et al. (2017) reported significant discrepancies between ozone and aerosol
calibrations. This omission prevents a direct assessment of the contribution
of bath gas to biases in the ozone calibrations performed in the
Bluvshtein et al. (2017) study. A second drawback
is that, in developing a model to describe their measured PAS data, they
attribute the generation of a photoacoustic signal to the direct relaxation
of O3* (the superscript * implying that O3 is in an
electronically excited state). However, as we discuss further in this
contribution, O3 photoexcitation within the Chappuis band (spanning an
approximate wavelength range of 400–700 nm) gives photodissociation to
O(3P) and O2(X) within <1 ps (picosecond) irrespective of bath
gas. The nascent photofragments subsequently undergo further collisional
reactions and relaxation. As we argue here, these collisional processes must
be taken into account when interpreting the PAS response.
Here, we present measurements of the dependence of PAS sensitivity on the
bath gas O2:N2 ratio at three wavelengths of 405, 514 and
658 nm that span the Chappuis band. Importantly, our measurements include
the 405 nm wavelength at which our previous work and that of Bluvshtein et
al. (2017) were performed (Bluvshtein et al., 2017; Davies et al., 2018). At
short visible wavelengths, we report very different variations in the PAS
sensitivity with bath gas O2 mass fraction than those reported by
Fischer and Smith (2018), although our measurements agree at the longer
658 nm wavelength. To describe our results and reconcile them with those of
Fischer and Smith, we present a complete description of Chappuis band
photodynamics, accounting for the photodissociation of ozone, and develop a
PAS sensitivity model treating the relative rates of collisional reactions
and energy quenching of the nascent photofragments in the presence of both
O2 and N2 bath gas species. In the following section, we
describe briefly our instrument and our method for performing ozone-based
calibrations for different bath gas compositions. Section 3 presents
measurements of the variation in PAS sensitivity with bath gas composition,
develops a model to describe the measured variations in PAS sensitivity, and
justifies the determined relaxation rates of the nascent photofragments from
Chappuis band photolysis in the context of previously published studies.
Experimental methods and data processing
We have described our CRDS and PAS instrument in detail in a previous
publication, and only a brief overview of our spectrometers is provided here,
with the reader directed to Davies et al. (2018)
for further details. The following sub-sections describe the methods used to
generate ozone, control the bath gas composition, measure the sample
extinction using CRDS and measure the sample absorption using the PAS.
Ozone generation
Figure 1a shows how we generated an ozone-laden
oxygen flow that was then split to provide ozone to three flow lines that
included PAS instruments operating at wavelengths 405, 514 or 658 nm. A mass
flow controller (MFC) passed 0.15 standard litres per minute (SLPM) of high-purity (99.999 %) O2 from a gas cylinder supply through an ozone
generator that used a cold corona discharge. We varied the frequency of this
discharge to control the ozone concentration in the output O3–O2
flow. For our calibrations, we chose 10 values of discharge frequency in
the range 3–800 Hz, with higher frequencies providing larger ozone
concentrations. The frequency of the ozone generator was controlled directly
by a LabVIEW software interface. A manifold then split the ozone-laden
sample into five lines, although only three of these ozone lines were used for
direct injection of ozone into the bath gas that then passed to 405, 514 and
658 nm spectroscopy channels (with channels referring to spectrometers operating at
different wavelengths; see Fig. 1c). The output
from the remaining two ozone lines was sent to an exhaust. Each ozone line
had an approximate flow rate of 0.03 SLPM, although these rates were not
exactly equal for all lines, and we discuss this further in Sect. 2.5. The
ozone flows were passed through 0.125 in. Teflon tubing that minimised
contamination.
Schematic diagrams of the experimental arrangements for
(a) the generation of ozone, (b) the control of the
composition of the bath gas, and
(c) performance of CRDS
and PAS measurements of extinction and absorption, respectively, at different
optical wavelengths. MFC denotes a mass flow controller.
Control of the bath gas composition
A schematic for the control of the bath gas composition is shown in
Fig. 1b. The flow rate at point “4” in
Fig. 1b is determined by the total flow rate
regulated by the MFCs in Fig. 1c, the flow rate
of the ozonised flow and the flow rate of purge gas used to prevent
deposition of contaminants on the CRDS mirrors (see Sect. 2.3). An aluminium
mixing vessel with a 1.1 L volume was used to mix ambient air with a
controlled flow of either O2 or N2 from a high-purity (99.999 %)
gas cylinder. A MFC was used to set the mass flow of either O2 or
N2 into the mixing volume, with any make up flow consisting of ambient
air (∼21 % O2, 78 % N2, 1 % argon and trace
amounts of other gases) with an in-line HEPA filter used to remove aerosol.
The mass flow rate of ambient air into the mixing volume was monitored with
a mass flow meter, with the magnitude determined by the total flow rate at
position “4” and the controlled mass flow of O2 or N2 into the
mixing volume. By changing the mass flow rate of the high-purity gas
species, we varied the oxygen mass fraction of the bath gas over the range
0.0–1.0. The mixed gas was then passed through a Nafion dryer that dried
the gas to a relative humidity <4 % before passing to a
NOx/O3 scrubber to remove contributions to gas phase absorption
from trace bath gas species. Finally, the bath gas passed through a further
HEPA filter. We confirmed that the bath gas was devoid of particles by using
a condensation particle counter.
Figure 1c shows that the bath gas was split into
three flow lines corresponding to the 405, 514 and 658 nm spectroscopy
channels. Each ozonised flow was mixed with bath gas 1 cm prior to a
spectrometer sample inlet. The total sample flow rates through the three
spectroscopy flow lines were controlled by MFCs set to 1.0 L min-1.
This flow rate corresponded to mass flow rates of 0.97 SLPM at the 950 hPa
pressure measured for all the experiments performed in this work.
Figure 1c shows that we operated CRDS cells at wavelengths of 405 and 658 nm
and PAS cells at wavelengths of 405, 514 and 658 nm. For each channel, the
sample (bath gas with added ozonised flow and CRDS purge gas) passed through
both a CRDS and PAS channel that operated at the same wavelength. We chose to
pass the sample through the CRDS channel first because its 0.8 s residence
time was lower than for the PAS cell (∼12 s). The low residence time
in the CRDS channels minimised ozone loss to surfaces between successive
spectrometer measurements. Moreover, we maintained short
(<15 cm) lengths of 0.25 in. conductive tubing between the CRDS
and PAS. No corresponding CRDS channel operating at the same wavelength was
available for the 514 nm PAS, and the sample passed through the 514 nm PAS
only. We now describe the operation of our cavity ring-down and photoacoustic
spectrometers.
Cavity ring-down spectrometers
We used two cavity ring-down
spectrometers with identical configurations, albeit using different laser
sources and cavity mirrors optimised for two different wavelengths. The
output from a continuous-wave diode laser was injected into a high finesse
optical cavity that consisted of two highly reflective mirrors
(reflectivities of >99.999 %) separated by a distance of
40 cm. The laser diode current was modulated with a 50:50 duty cycle square
wave signal to pulse the laser power between 0 and ∼300 mW at a
frequency of 2000 Hz. The spectral widths of the lasers (∼100 GHz)
were much larger than the free spectral range of the CRDS optical cavity
(∼375 MHz). Therefore, the laser coupled passively into the optical
cavity and overlapped numerous longitudinal modes. For each pulse injected
into the optical cavity, a fraction of light leaking from the rear mirror was
detected with a photomultiplier tube, the voltage from which was recorded by
a 2.5 mega-samples per second (MS s-1) data acquisition (DAQ) card. The
time trace in this voltage is referred to as the ring-down trace. In the case
that the linewidth of the sample extinction is larger than the linewidth of
light circulating in the optical cavity, a criterion met for the cases of
ozone in the Chappuis band and for aerosol, Zalicki and Zare (1995)
demonstrated that the time dependence in the cavity output intensity obeys a
single exponential decay, with the characteristic 1/e folding time for this
decay referred to as the ring-down time (τRD). Therefore, by
fitting the ring-down trace to a single exponential, τRD was
determined. We used the linear regression of the sum method described by
Everest and Atkinson (2008) for the fast and accurate retrieval of
τRD in real time. The cavity mirrors were mounted on kinematic
mirror mounts (Newport), and the alignment of each mirror was optimised to
maximise both τRD and the maximum intensity (voltage) in the
ring-down trace, thereby maximising the sensitivity of each CRDS channel.
Sample inlet and outlet ports were located at opposite ends of the cavity
and 3 cm away from the CRDS mirrors. To prevent contaminants depositing on
the highly reflective mirror surfaces, a 0.0125 SLPM purge gas flow was
passed over the mirror surfaces. Zero air was used as the purge gas for
calibrations corresponding to a bath gas O2 mole fraction of 0.23 (i.e.
ambient conditions) only and represents the purge gas used in measurements
(including calibrations) under normal operation of the instrument in the
field or laboratory. Otherwise, high-purity N2 or O2 purge flows
were used.
From knowledge of the ring-down time in the presence (τRD) and
absence (τRD,0) of the sample, the extinction coefficient αext is calculated using
αext=RLc1τRD-1τRD,0,
in which c is the speed of light, and RL is the ratio of the cavity mirror
separation (40 cm) to the length over which the sample occupies the cavity.
We take this latter length to be the distance between the sample inlet and
outlet ports (34 cm), and RL is taken as 1.1765 for both CRDS channels.
We applied a small correction to αext to account for the small
dilution of the sample by the purge gas flows. Typical values of τRD,0 are 24±0.004 and 34±0.04µs for the 405 nm
and 658 nm CRDS channels, with the quoted uncertainties corresponding to 1 standard deviation over 60 s.
For the calibrations in this work, the ozone extinction at the 514 nm PAS
wavelength (αext,514) was calculated from the 658 nm
CRDS-measured extinction (αext,658) from knowledge of the
variation in ozone cross section with wavelength using
αext,514=αext,658⋅σO3,514σO3,658,
in which σO3,514 and σO3,658 are the O3
absorption cross sections at 514 and 658 nm, respectively. We used the
recommended absorption cross sections for O3 provided by the NASA Jet
Propulsion Laboratory (Burkholder et al.,
2015). We also applied a further correction to αext,514 to
account for the difference in ozone concentrations between the 514 nm PAS
and the 658 nm CRDS due to the parallel flow configurations for these two
spectrometers. This correction is described in Sect. 2.5. We can also
calculate αext,514 from the 405 nm CRDS measurements using the
same approach above. However, Sect. 3.1 shows that there is significant
uncertainty in the αext,514 arising from uncertainty in the
405 nm laser wavelength. Therefore, this work only presents αext,514 data calculated from 658 nm CRDS measurements.
Photoacoustic spectrometers
The output from a continuous-wave diode laser was directed into an astigmatic
multi-pass optical cavity that provided multiple reflections (∼50) of
the laser beam through a photoacoustic cell (PAS cell). The intensity of the
laser beam was periodically modulated with a frequency that matched the
resonance frequency of the PAS cell (see below). A photodiode behind the rear
cavity mirror monitored the rms laser
power, Wrms. The geometry of the cell has been described
previously by Lack et al. (2012) and consisted of two cylindrical resonators
(an upper and lower resonator) that were coupled through acoustic buffer
volumes. We used Brewster-angled windows to minimise the detection of laser
interactions with the PAS cell windows and improve sensitivity. The laser
beam was multi-passed through the lower resonator of the PAS cell. Sample
inlet and outlet ports were located in opposite acoustic buffer volumes, and
the sample flow was drawn through the PAS cell. Ozone passing through the
laser beam was photoexcited, and the bath gas was heated through collisional
energy transfer from the ozone photoproducts to translational degrees of
freedom of the bath gas. The heat in the bath gas generated a pressure
(acoustic) wave through adiabatic expansion. These pressure waves were
coupled into a standing wave pressure eigenmode of the PAS cell, with the
amplitude of the excited eigenmode detected by sensitive microphones located
in each resonator. The voltage from each microphone was passed through a
differential amplifier and the amplified output sent to a DAQ card that
recorded the microphone waveform with a time resolution of 8 MS s-1
over a 1 s interval.
A speaker was located close to the microphone in the lower resonator and
was driven by a voltage waveform that, in the frequency domain, was a top
hat distribution over the frequency range 1250–1650 Hz. At multiple
intervals during the calibration routine using ozone, the speaker was used
to excite the standing wave eigenmode of the PAS cell. The 1 s microphone
time trace was recorded and processed through a fast Fourier transform that
gave an acoustic spectrum with a Lorentzian distribution (see Fig. 2 of
Lack et al., 2012). By fitting this
measured distribution to a Lorentzian function, the cell resonance frequency
fres and quality factor Q were measured. Importantly, this measured
fres was used to set the modulation frequency of the laser to ensure
this frequency matched the PAS cell resonance frequency at all times.
To measure the PAS response from ozone absorption during calibrations, 1 s
waveforms were recorded, and the amplitude of the frequency component
corresponding to fres was measured. This amplitude is referred to
as the raw photoacoustic signal Sraw. As described in previous
publications (Davies et al., 2018; Lack et al., 2012), Sraw
requires fres, Q and
Wrms to be corrected for, and it can be shown from first principles
(Miklós et al., 2001) that this correction
should be performed according to
Scorr=Sraw⋅fresWrmsQ,
in which Scorr is the corrected PAS signal. In our measurements,
Wrms is measured from the voltage response of an uncalibrated photodiode
detector. Therefore, the units of Wrms and Scorr are arbitrary. An
additional correction is required to account for a background contribution
to Scorr from laser interactions with the PAS cell windows. We denote
this background contribution Scorrbg. Scorrbg is constant
over a calibration and typically represents <10 % of the
photoacoustic signal during calibrations with ozone. Each ozone calibration
performed for this work lasted ∼1 h during which the ozone
concentration was increased sequentially. Before and after this
∼1 h period when the PAS cells were devoid of any
absorbing sample, the mean Scorrbg was characterised over 60 s
periods. These two mean background values were identical within measurement
precision, and a linear interpolation between these values was used to
describe Scorrbg over the calibration period. The PAS signal of
interest is then given by
Sfinal=Scorr-Scorrbg.
For the 405 and 658 nm PAS channels that were in a serial flow
configuration with a CRDS channel (see Fig. 1c), an additional
but small correction was applied to Sfinal to
account for dilution by the CRDS purge flows.
Correction of αext,514 for differences in
ozone concentrations
Section 2.3 stated that a correction to the calculated
αext,514 was applied to account for unequal ozone
concentrations between the 514 nm PAS and 658 nm CRDS channels. We used our
measurements of fres for the 514 and 658 nm PAS channels to
calculate the relative difference in O3 between flow lines. We
demonstrated in
Davies et al. (2018) that the resonance frequency
shift Δfres upon the introduction of the ozonised flow could be
used to correct αext,514 according to
αext,514corr=αext,514⋅Δfres,514Δfres,658.
Calibration procedure and the calculation of PAS sensitivity
We measured the PAS calibration coefficient for multiple values of bath gas
O2 mass fraction. Each calibration involved measuring
Sfinal and corrected extinction coefficients for 10 ozone
concentrations (10 values of coronal discharge frequency), and the
calibration procedure was controlled by automated LabVIEW software. For a
given coronal discharge frequency, we waited 120 s for the new ozone
concentration to stabilise across all channels. The fres and Q
for the PAS channels were measured at the end of this wait period. Then,
Sraw and αext were measured at 1 Hz and
averaged over a 60 s period before the coronal discharge frequency was
increased to a higher level. The Sraw and αext
for each ozone concentration were corrected using the procedures described in
Sect. 2.3–2.5, giving the values Sfinal and
αextcorr. PAS sensitivity was calculated from a
linear regression of the variation in the mean Sfinal with mean
αextcorr for all 10 ozone concentrations
constrained through the intercept Sfinal=0, consistent with the
definition of PAS sensitivity in Eq. (1).
For each PAS channel, example calibration measurements of PAS
response variation with CRDS-measured extinction for an analyte of ozone gas.
Each plot shows typical calibration data for ozone gas in bath gases composed
of a mixture of N2 and O2, with O2 mole fractions of 0.04
(near-pure N2), 0.23 (ambient air composition) and 1.0 (pure O2).
All data points include error bars corresponding to 1 standard deviation in
the measured PAS response or extinction, although these error bars are not
visible on the plot scales because of the low variance in the measurements.
Dashed lines represent straight line fits to the measured data, with the fit
constrained such that the intercept is zero.
Results and discussionMeasured variations in PAS sensitivity with bath gas composition
For each PAS channel, Fig. 2 shows example calibration plots for the
variation in PAS response (Sfinal) with the CRDS-measured
extinction (αextcorr) for bath gas compositions
with oxygen mass fractions (xO2) of xO2=0.04
(near-pure N2), 0.23 (ambient air with added ozonised O2
flow) and 1.0 (pure O2). The plot for the 514 nm PAS channel does
not show data for the xO2=1.0 calibration. This is because the
derived 514 nm extinction relies on correcting the 658 nm extinction,
measured by CRDS in a parallel flow configuration, for differing ozone
concentrations caused by unequal splitting of the ozonised flow by the gas
manifold (Fig. 1a). As described in Sect. 2, a correction factor for this
uneven ozone splitting is determined by the ratio of PAS resonance frequency
shifts in the 514 and 658 nm channels, Δfres,514/Δfres,658, upon the addition of the ozonised flow. In the case of
a bath gas of xO2=1.0, the resonance frequency shift in all
PAS cells upon the addition of the ozonised flow is zero, thus precluding the
calculation of Δfres,514/Δfres,658 and
the 514 nm extinction.
In Fig. 2, each data point corresponds to the mean values for measurements of
Sfinal and αextcorr over a 60 s
period at a given corona discharge lamp frequency, with 1 standard
deviation error bars shown; these uncertainties are barely visible on Fig. 2
due to their low value. Typical 1σ uncertainties in the extinction
and absorption measurements are 0.74 % and 0.17 % for
αext-405 and αext-658 respectively and
2.43 %, 0.36 % and 0.32 % for Sfinal,405,
Sfinal,514 and Sfinal,658 respectively. The 1σ uncertainty in αext-514 is related to that in
αext-658, although there is additional uncertainty in the
514 nm extinction measurement arising from the correction factors for
Δfres,514/Δfres,658 and differences in
ozone cross section at the 514 and 658 nm laser wavelengths. Typically, the
standard error in Δfres,514/Δfres,658
is 1.67 %. Meanwhile, the uncertainty in O3 cross section ratio
σO3-514/σO3-658 for a 1 nm wavelength
uncertainty in the 658 nm laser wavelength is 1.8 %. Therefore, the
uncertainty in the measured αext-514 is 2.5 %. For
comparison, the uncertainty in the ratio σO3-514/σO3-405 for a 1 nm uncertainty in the 405 nm laser
wavelength is 7.5 % and would correspond to a 7.7 % uncertainty in
the measured αext-514. Hence, due to the sensitivity of the
O3 cross section ratios to uncertainties in the laser wavelength, we
opt to use the 658 nm laser in calibrating our 514 nm PAS channel. For
completeness, we find that the calculated αext-514 from
extinction measurements at the 405 and 658 nm wavelengths is well
correlated (with a linear Pearson correlation coefficient of 0.93), and the
average αext-514 is 14 % larger when calculated from 405
compared to 658 nm measurements.
Figure 2 demonstrates the excellent linearity in
calibrations for all channels and bath gas compositions over the extinction
range covered. Each calibration is fit to a straight line via a least squares
fit routine, with the intercept constrained to pass through zero. The slope
of this linear fit is equal to the PAS sensitivity C (see Eq. 1). For all calibrations performed for this
publication, the mean standard errors in C arising from the aforementioned
least-squares fit routine are 0.31 %, 0.33 % and 0.40 % for the 405,
514 and 658 nm PAS channels respectively.
Figure 2 also demonstrates that there are
significant variations in C with bath gas composition at all PAS wavelengths
for the limited range of calibrations at different xO2 values
presented. Meanwhile, Fig. 3a shows all our
measurements of PAS sensitivity with variation in xO2 for 16
separate calibrations at 14 different bath gas compositions. Our
658 nm measurements demonstrate similar behaviour to that reported by
Fischer and Smith (2018), approaching
a plateau as xO2 tends to 1. However, the PAS sensitivities for
wavelengths of 405 and 514 nm demonstrate a very different dependence on
O2 mass fraction. In both of these channels, the PAS sensitivity is a
maximum at O2 mass fractions close to 0.2 (i.e. at mass fraction values
similar to that of ambient air) and is lower at other O2 mass
fractions.
(a) The measured PAS sensitivity C with variation in the
bath gas O2 mass fraction (points) and best fit descriptions of the
data for the model described by Eqs. (8), (11) and (12). The measured data
include vertical error bars that represent 1 standard deviation in the
measured sensitivity, although these error bars are not visible on the
vertical scale shown. Horizontal error bars represent the uncertainty in
O2 mass fraction arising from the standard errors in the mass flow
controller flow rates that control concentrations of O2 and N2 in
the bath gas. (b) The best fit model description from (a) and the
contributions from the two components of the model that correspond to
quenching of O(3P) and O2(X3Σg-, v>0).
To explain the measured variation in PAS sensitivity with bath gas
composition and excitation frequency, we consider the potential energy
surfaces for ground and photoexcited states of O3. Grebenshchikov et
al. (2007) provide an excellent review of O3 photodissociation over
various bands that include the Chappuis band (wavelengths in the range of
∼400–700 nm). The authors calculate the potential energy surfaces for
O3, including potential energy cuts along the O2–O
dissociation coordinate, and describe the Chappuis band photodynamics
concisely. The Chappuis band arises from excitation to two adiabatic
1A′′ states. The lower state correlates asymptotically to the formation
of O(3P)+O2(X3Σg-) and is a
repulsive surface, while the upper state is bound with a dissociation energy
(corresponding to the formation of O(1D)+O2(a1Δg)) that cannot be overcome from Chappuis band
excitation at room temperature. To support this latter point, the experiments
of Levene et al. (1987) find no evidence for the formation of
O2(a1Δg) state following Chappuis band photoexcitation.
A symmetry-allowed conical intersection connecting the two 1A′′ states
is located close to the Franck–Condon point and the equilibrium bond length
of the upper 1A′′ state. After photoexcitation in the Chappuis band, the
electronically excited O3* population is distributed equally
between the two electronic states as the two adiabatic transition dipole
moments are similar in the Franck–Condon region. While O3* in
the lower repulsive state dissociates within a few tens of femtoseconds to
form O(3P)+O2(X3Σg-),
O3* population in the upper 1A′′ state may undergo two
vibrations at most before crossing the 1A′′ conical intersection and
dissociating via the lower repulsive state to O(3P)+O2(X3Σg-) (Flöthmann et al., 1997).
Nevertheless, the lifetime of the population in this upper state is less than
a few picoseconds, demonstrated by the diffuse structures in the absorption
cross section for O3 within the Chappuis band. Importantly, the ∼10-12 s timescale for photodissociation is much faster than the
modulation period of our PAS laser intensity (τmod is in the
range 600–780 µs, corresponding to modulation frequencies of
1280–1640 Hz)
and can be considered an instantaneous process. Ultimately,
Chappuis band excitation leads to the prompt photodissociation of
O3(1A′′) and to the formation of O(3P) and
O2(X3Σg-), in which the nascent O2
photofragment is vibrationally excited (v>0) (Flöthmann
et al., 1998):
O3+hv(λ=400–700 nm)→O(3P)+O2(X3Σg-,v>0).
For PAS measurements of absorption by O3, we need to consider the
subsequent fate of O(3P) and O2(X3Σg-,v>0) and, importantly, the rate at which energy is
quenched into translational modes of bath gas M=N2 and
O2 for the generation of a PAS signal.
First, we note that the nascent O2(X3Σg-,v>0), although formed in the ground electronic state, is
vibrationally excited (Flöthmann et al., 1998). For our PAS measurements,
we need to consider the rates of quenching of energy from
O2(X3Σg-, v>0) to
translational modes of both bath gas species M=N2, O2
through the quenching reaction:
O2(X3Σg-,v)+M(v′)→O2(X3Σg-,v-1)+M(v′).
Second, the nascent O(3P) rapidly combines with bath gas O2
(collision frequency on the order of 1012 s-1) to form
ground-state O3(X̃) via Reactions (R3) and
(R5):
R3O(3P)+O2(X3Σg-)⟶k1O3‡(X̃)R4O3‡(X̃)⟶k2O(3P)+O2(X3Σg-)R5O3‡(X̃)+M⟶k3O3(X̃,v>0),
in which M (N2 or O2) is a third body that removes energy
from the initial metastable O3‡(X̃);
because the nascent O(3P) has significant kinetic energy following
photodissociation, the initial O3‡(X̃)
has energy above the energy threshold correlating to O(3P)+O2(X3Σg-). We emphasise that the resulting
O3 is now in the ground electronic state but is vibrationally excited
(v>0). The collisional stabilisation of O3‡(X̃) (Reaction R5) competes with the re-dissociation of
O3‡(X̃) to O(3P)+O2(X3Σg-) (Reaction R4), with this latter process
expected to be fast compared to the stabilisation pathway. The contribution
to the PAS signal from O3(X̃, v>0)
will depend on (i) the rate at which stabilised
O3(X̃, v>0) (through collision
with M=N2, O2) is formed and (ii) the rate of energy
quenching from vibrationally excited O3(X̃,
v>0) into translational modes of M=N2,
O2. For this latter process, Ménard-Bourcin et al. (1991) and
Zeninari et al. (2000) measured vibration-to-translation (V–T) energy
transfer rates for both N2 and O2 bath species, with similar
rates of ∼7.6×105 s-1 atm-1 that correspond to a
characteristic timescale for quenching of ∼1.4µs at the
950 hPa pressure measured during our experiments. This timescale is
sufficiently fast compared to our PAS modulation period that it can be
considered instantaneous. We note that Ménard-Bourcin et al. (1991) and
Zeninari et al. (2000) studied the V–T relaxation of ozone in a
vibrationally excited state containing a single quantum of energy
corresponding to a symmetric stretch (v1=1103 cm-1),
bend (v2=701 cm-1) or asymmetric stretch (v3=1042 cm-1);
i.e. O3 was in the (v1, v2, v3) state of
(1, 0, 0), (0, 1, 0) or (0, 0, 1) prior to V–T relaxation. However,
Siebert et al. (2002) show that O3 exists in vibrational states as
high as (7, 0, 0) for energies below the O3 photodissociation
threshold (approximately 1 eV =8065 cm-1).
Therefore, the relaxation of ozone in our studies that
is formed in vibrational states close to the O–O2 bond
dissociation threshold will occur on a timescale longer than the
1.4 µs estimated above. However, we do not anticipate that the
timescale for the removal of ∼7 quanta of energy will be sufficiently
larger than the 1.4 µs timescale for single quantum relaxation as
to impact on the PAS signal, and we assume the relaxation of O3(X,
v>0) occurs much faster than the PAS laser modulation
period. Thus, while we can assume that the quenching rate of vibrationally
excited O3(X̃, v>0)
is essentially instantaneous on our PAS timescale, the rates
of formation of O3(X̃, v>0) from Reactions (R3)–(R5)
for bath gases M=N2, O2 are not well
studied. We expect the process of O3(X̃,
v>0) formation to impact on the measured PAS sensitivity if
the associated formation rate is slow. Indeed, this recombination process is
likely to proceed at a slower rate than that for the quenching of the
stabilised O3(X̃, v>0); the
collisional stabilisation of O3‡(X̃) to form
O3(X̃, v>0) (Reaction R5) competes with
re-dissociation of O3‡(X̃) to
O(3P)+O2 (Reaction R4). This latter process likely proceeds
on a timescale of tens of picoseconds at most.
We now develop a model to describe our PAS sensitivity. We will show that
processes with associated timescales that are slow compared to the PAS laser
modulation period degrade the PAS sensitivity. Therefore, while the processes in
Reaction (R1) for the production of O(3P)+O2(X3Σg-, v>0) and for the energy quenching of the
stabilised O3(X̃, v>0) can be
considered instantaneous, the rates of V–T relaxation of
O2(X3Σg-, v>0) and the rate
at which stabilised O3(X̃, v>0) is
formed could be slow.
A PAS sensitivity model that considers energy transfer rates from both
O(3P) and O2(X3Σg-, v>0)
Using the model of Kosterev et al. (2006), the photoacoustic signal C is
described by Arnott et al. (2003) and Moosmüller et
al. (2009)
C=C01+2πfresτ2,
in which fres is the frequency of the laser modulation that is set to
the resonant frequency of the PAS cell, τ is the relaxation time of
the excited state and C0 is the PAS sensitivity in the limit τ≪2πfres-1; i.e. quenching is fast compared to the
modulation period of the laser intensity. In the current case of PAS
measurements of O3, a contribution to the total PAS signal is made from
quenching of energy from both O(3P) and O2(X3Σg-, v>0), and we write
Ctotal=CO1+2πfresτO2+CO2*1+2πfresτO2*2.
Here, O2* represents ground-state O2 in a vibrationally
excited state. As described above, the rate of quenching of energy from
O(3P) is limited by the recombination of O(3P) with
O2, with stabilisation by a further bath gas species of either
O2 or N2. From Eqs. (R3)–(R5), we can write rate equations
for the production of the intermediate O3‡(X̃) and, under the steady-state approximation, we find
that the rate of O3(X, v>0) production is given by
dO3(X,v>0)dt=k1k3O(3P)[O2][M]k2+k3[M],
in which the rate constants k1–k3 are those for Reactions (R3)–(R5),
respectively. As discussed above, we expect the rate of collisional
stabilisation of O3‡(X̃) (proceeding with
a rate constant k3) to be slow compared to that for the re-dissociation
pathway (proceeding with a rate constant k2). In the limit k2≫k3[M], Eq. (9) simplifies such that the production rate of O3(X,
v>0) depends on [O][O2][M], and the rate at which
O(3P) is lost is described by
-d[O(3P)]dt=kO-O2-N2[O(3P)][O2][N2]10+kO-O2-O2[O(3P)][O2]2,
in which kO-O2-N2 and kO-O2-O2 are rate
coefficients related to the formation rate for O3‡(X̃) (k1), the re-dissociation of
O3‡(X̃) (k2) and the
quenching rate of O3‡(X̃) to
O3(X, v>0) by M (k3), for M=N2 or
O2 bath gas species respectively. Thus, the time dependence in the
loss of O(3P), and the formation of
O3(X̃, v>0), follows an
exponential form with a time constant:
τO=kO-O2-N2O2N2+kO-O2-O2O22-1.
Similarly, we write the characteristic relaxation time of
O2(X3Σg-, v>0) by
τO2*=kO2*-N2N2+kO2*-O2O2-1,
in which kO2*-N2 and kO2*-O2 are
quenching rate constants in bath gas N2 or O2, respectively.
We fit the model of Eq. (8) to our measured PAS data, using expressions for
τO and τO2* provided in Eqs. (11) and (12),
respectively. For this fitting, the values of kO-O2-N2,
kO-O2-O2, kO2*-N2 and
kO2*-O2 are constrained such that their values are
invariant with wavelength. Although nascent products may be produced in
different vibrational states for different photolysis energies, we find the
aforementioned constraint on rate constants is necessary to reduce the
uncertainties in fit parameters and give meaningful insight into the
wavelength dependence of the PAS sensitivity to O3 absorption. Also,
we have reported previously (Davies et al., 2018) the excellent agreement
between measured aerosol absorption (using an ozone calibration in a bath gas
of ambient air) and predicted values, with a maximum discrepancy of 9 %.
Therefore, we expect the relaxation time constants τO and
τO2* to be near-instantaneous relative to the PAS
modulation frequency at ambient-air bath gas composition and
Ctotal=CO+CO2*. Thus, in fitting the above
model, we constrained the sum CO+CO2* such that the
maximum allowed value is 20 % larger than the measured maximum in
Ctotal. The resonant frequency fres in
Eq. (8)
varies with the bath gas O2 mass fraction and is taken as the mean
measured cell resonance frequency during a calibration for a given bath gas
composition. Figure 4 shows these measured variations in fres
with O2 mass fraction for each PAS channel, with fres
decreasing by ∼7 % as xO2 increases from
xO2=0 to xO2=1. In contrast, the fres
values vary by <2 Hz (<0.14 %) over a single
calibration as the O3 concentration is increased over the calibration
period.
The variation in the mean measured PAS cell resonance frequency with
O2 mass fraction for each PAS channel used in this study.
The 10 fit parameters that include kO-O2-N2,
kO-O2-O2, kO2*-N2 and
kO2*-O2, in addition to six coefficients corresponding
to CO and CO2* for each of our three PAS
wavelengths are fit to the measured data by minimising the sum of
least squares between measured
and modelled values of PAS sensitivity. Figure 3 shows these best-fit model
descriptions for each wavelength, while Table 1 summarises the best-fit
parameters. We fitted our model to measured data in the mass fraction domain,
and, therefore, the rate coefficients have units of s-1. The model
developed here describes the measured data very well, with the PAS signal
suppressed at high O2 mass fractions associated with a slow rate of
quenching of O2(X3Σg-, v>0)
energy into translational degrees of freedom of O2 bath gas
molecules. The model agreement with the 514 nm PAS measurements is worse
than that for the 405 and 658 nm channels, and considerations of the larger
errors associated with the 514 nm PAS measurements (as described in
Sect. 3.1) cannot fully reconcile these differences. Instead, this poorer
agreement is likely to be a consequence of the requirement to constrain the
four rate coefficients to be invariant with wavelength; as we discuss below,
different vibrational states of O2(X, v>0) are
accessed as the photolysis wavelength is reduced below ∼550 nm that
will affect relaxation rate constants. The calculated ratios
kO-O2-O2/kO-O2-N2 and
kO2*-O2/kO2*-N2 are also given in Table
1. Over all PAS wavelengths, the best fit of our model suggests that bath
O2 is more effective at stabilising the formation of
O3(X̃, v>0) by a factor of ∼11 compared to bath N2. However, there is significant uncertainty in
the fit values of kO-O2-N2 and kO-O2-O2, with
a factor of 2 increase in either rate constant having little impact on the
modelled PAS sensitivity. Reducing the uncertainty in this fit parameter
requires more measurements of the PAS sensitivity at low O2 mass
fractions (<0.2) and reductions in the uncertainty in the
O2 mass fraction measurement. Meanwhile, bath N2 is a factor
of 1.68 more effective at quenching vibrational energy from
O2(X3Σg-, v>0) into
translation modes compared to bath O2. We also examine the relative
contributions of the O(3P) and O2(X3Σg-, v>0) channels to the total PAS signal,
with CO2*/CO given in Table 1, while Fig. 3b shows
the contributions of both species to the total modelled PAS sensitivity.
Figure 3b shows that the signal contribution from quenching of energy from
O(3P) decreases to zero as the bath gas composition tends towards
that of pure N2. In this limit, the absence of O2 prevents
the formation of O3(X̃), and the characteristic
relaxation time in Eq. (11) tends to infinity. The
CO2*/CO ratio ranges from 1.3 to 4.1 as the
photolysis energy increases (wavelength decreases from 658 to 405 nm). This
suggests that the fraction of energy that goes into vibrational modes of the
nascent O2(X), compared to that partitioning to O(3P)
kinetic energy, increases with decreasing wavelength.
Summary of the best fit parameters for the PAS sensitivity model
described in the main text.
PAS wavelength in nm405514658CO11.38.42.9CO2*46.614.03.8kO-O2-N2/s-17.8×104kO-O2-O2/s-18.6×105kO2*-N2/s-11.3×104kO2*-O2/s-17.9×103CO2∗/CO4.11.71.3kO-O2-O2/kO-O2-N211.1 kO2*-O2/kO2*-N20.6 Understanding the best-fit rate
constants for O2(X3Σg-, v>0) and
O3‡(X̃)
We begin by considering the quenching of O2(X3Σg-, v>0) before considering that of
O3‡(X̃). First, we need to understand the
vibrational energy distribution for the nascent O2(X3Σg-, v>0); the relaxation rate of O2
will depend on its vibrational state. Flöthmann et al. (1998) calculated
the vibrational energy distribution of O2(X3Σg-) following the Chappuis band photodissociation. At a
photolysis wavelength of ∼620 nm, the authors predicted that the
vibrational energy distribution was Boltzmann-like, with the population of v=0 dominating the distribution and agreeing well with the experiments of
Levene et al. (1987). However, a shoulder in this distribution develops as
the wavelength decreases; at wavelengths in the range 450–500 nm, a
significant population of v=4–8 is predicted, and higher v is accessed
with decreasing wavelength. As the wavelength decreases further, we would
expect v>8 to be populated.
We now consider the rates of energy quenching from O2(X3Σg-, v>0) to bath gas molecules
and how these depend on v. Indeed, this quenching can occur through V–T and
vibration-to-vibration (V–V) energy transfer; while the bath gas translation
energy generates acoustic pressure waves relevant to a photoacoustic
measurement, V–V energy transfer could influence the vibrational state from
which V–T energy transfer occurs. Coletti and Billing (2002) reported
V–T and V–V rate constants for O2(X3Σg-, v>0) to O2 bath gas
for v in the range 1–29. Meanwhile, Billing (1994) reported the V–T
rate constants for O2(X3Σg-,
v) to N2 bath gas for v in the range 13–25, and Park and
Slanger (1994) measured the associated V–V rates. These studies provide data
for a temperature of 300 K, and the rate constants are plotted in Fig. 5. We
note that the total rate constants (the sum of the V–T and V–V rate
constants) for an O2 bath gas were validated by experimental
measurements of Park and Slanger (1994) and Hickson et al. (1998).
In a bath gas of pure O2 and for an initial nascent photoproduct
O2(X3Σg-, v) with v∼8
at wavelengths <500 nm, the V–V rate constant (∼6×10-14 cm3 s-1) is approximately 3 orders of magnitude
higher than the V–T transfer rate (∼2×10-17 cm3 s-1).
Therefore, V–V energy transfer dominates and rapidly quenches
O2(X3Σg-, v=m)
(with m>0) to m⋅O2(X3Σg-, v=1) via single quantum
transfer steps on a characteristic timescale of ∼0.4–0.6 µs.
Upon quenching all nascent O2(X3Σg-, v) to the v=1 level, V–T energy
transfer then becomes the only route to removing vibrational energy. For v=1, the V–T rate is ∼5×10-19 cm3 s-1 and
corresponds to a characteristic quenching timescale of ∼80 ms, i.e.
∼ 100 times slower than the PAS laser modulation period. Conversely, in a
pure N2 bath gas and for an initial nascent photoproduct
O2(X3Σg-, v) with v∼8, the V–V
rate is less than the V–T rate. For O2-to-N2V–V
energy transfer, the two quantum transition O2(X3Σg-, v) +N2(X, v′=0) →O2(X3Σg-, v-2) +N2(X, v′=1) is resonant at v=19 and gives rise to the maximum in the V–V rate
shown in Fig. 5 (Park and Slanger, 1994), but this rate decreases rapidly as
v departs from v=19. At v∼8, the V–V rate is ∼2×10-17 cm3 s-1, and the V–T rate is ∼8×10-17 cm3 s-1, with the
latter rate estimated from an exponential fit to V–T rates
available for v>13 extrapolated to lower v (see Fig. 5).
Assuming V–T energy transfer dominates at v∼8, energy is quenched into
N2 bath gas translational modes on a characteristic timescale of ∼500µs that is less (albeit only marginally) than the PAS modulation
period (600–780 µs). We emphasise that there are large
uncertainties in the V–T rates (Coletti and Billing, 2002 stated that
the accuracies are worse than 25 %) and in the exact vibrational states of
the initial O2(X3Σg-, v)
photoproducts. However, it is encouraging that we can reconcile our measured
decrease in PAS sensitivity as the bath O2 mass fraction increases with
calculated V–V and V–T rates. These rates predict a similar V–T quenching
timescale to the PAS laser modulation period in pure N2 but much
extended timescales (by a factor of ∼100) in pure O2. Moreover,
Billing (1994) noted that the calculated V–T rates for
O2(X3Σg-, v) are about a
factor of 2 larger for N2 bath gas compared to O2, that is
in good agreement with our measurements that suggest
kO2*-N2/kO2*-O2=1.68.
Calculated quenching rates of O2(X3Σg-, v>0) for
V–T energy transfer to bath gas O2 (blue squares) or N2
(green circles), with variation in the vibrational quantum state. Also shown
are the corresponding variations in V–V quenching rates of
O2(X3Σg-,
v>0) in a bath gas of O2 (blue diamonds) and
N2 (green crosses). Data are taken from Billing (1994),
Coletti and Billing (2002) and Park and Slanger (1994).
We now focus briefly on the quenching rates of O3‡(X̃) by bath gas O2 and N2 and the
observation that the best-fit kO-O2-O2/kO-O2-N2
is ∼11. To the best of our knowledge, the quenching of the
O3‡(X̃) is ill studied and there are no
past measurements with which to compare our data. In studies of vibrational
quenching of hot O3 (below the dissociation threshold),
Ménard-Bourcin et al. (1991) and Zeninari et al. (2000) reported these
rates in O2 and N2 bath gases to be identical within
measurement uncertainties. As discussed above, our model is relatively
insensitive to kO-O2-N2. Indeed, with further measurements of
PAS sensitivity at lower O2 mass fractions and with reductions in the
uncertainties in O2 mass fraction determinations (e.g. controlling
the flow of the ozonised oxygen fraction into each channel directly with a
MFC), kO-O2-N2 should be retrieved to a higher accuracy, and
kO-O2-O2/kO-O2-N2 might be found to be closer
to unity.
Other possible routes to degrading the PAS sensitivity
We explored other possible mechanisms to account for the variation in PAS
sensitivity with bath gas composition. In particular, Greenblatt et
al. (1990) reported that the O2–O2 dimer has five sharp
absorption bands between 446 and 630 nm. However, none of these absorption
bands are predicted to contribute to extinction or absorption at our
spectroscopic wavelengths (see Fig. 1 of Greenblatt et al., 1990).
Moreover, the formation of the O2–O2 dimer increases strongly
with increasing O2 concentration, while our CRDS-measured extinction
does not demonstrate any increase as the bath gas O2 concentration
increases. This can be seen in Fig. 2, in which the maximum values in the
CRDS-measured extinction show no dependence on the bath gas O2 mass
fraction. However, other authors should consider the influence of
O2–O2 dimer absorption on their PAS measurements in the
visible range, particularly when the CRDS measurement of extinction is
performed at a different wavelength to that of the PAS measurement of
absorption. In particular, we note that dimer absorption at wavelengths of
477.3, 532.2, 577.2 and 630.0 nm corresponds to significant absorption
coefficients of 34.5, 5.5, 60.2 and 39.4 Mm-1 at atmospheric temperature
and pressure for a gas of pure O2. Indeed, Fischer and
Smith (2018) used a PAS channel operating at 532 nm that is close to a
dimer absorption feature at 532.2 nm, while the authors' CRDS measurements
were performed at λ=658 nm at which there is no dimer
absorption contribution. The recommendation of Fischer and Smith that
calibrations are performed in pure oxygen could be detrimental at some PAS
wavelengths due to effects associated with O2–O2 dimer
formation, and we have shown in this work that calibrations in pure oxygen
are detrimental at wavelengths below ∼600 nm associated with inefficient
V–T quenching of O2(X, v>0) by bath O2.
Summary
We have studied the impact of bath gas composition on the PAS calibration
coefficient determined using an ozone calibrant. We varied the ratio of
O2:N2 concentrations of the bath gas and measured the PAS
sensitivity for three photoacoustic spectrometers that operate at wavelengths
of 405, 514 and 658 nm. Our measured variation in PAS sensitivity with
O2 mass fraction at 658 nm is in excellent agreement with the
measurements presented by Fischer and Smith (2018). However, at the
shorter wavelengths of 405 and 514 nm (higher photolysis energies), we find
that the PAS sensitivity decreases as the O2 mass fraction is
increased above values of ∼0.3 (i.e. the approximate composition of
ambient air). We have developed a model to explain these measured variations
that fully accounts for the photodynamics of ozone in the Chappuis band. We
find that the reduced sensitivity in the limit of pure N2 corresponds
to the inefficient recombination of O(3P) with bath gas O2,
while the reduced sensitivity in the limit of pure O2 corresponds to
the inefficient quenching of energy from O2(X, v>0)
into translational degrees of freedom of bath O2 on the timescale of
the PAS laser modulation period.
Importantly, we have demonstrated that the PAS sensitivity is optimised
(i.e. biases are minimised) when the PAS calibration is performed in a bath
gas with a composition corresponding to that of ambient air. In combination
with the results of our previous publication demonstrating excellent
agreement between expected and PAS-measured (using ozone calibrations with
ambient bath gas compositions) aerosol absorption coefficient for a
laboratory aerosol standard (Davies et al., 2018),
we conclude that our methods for measuring aerosol absorption using an
ozone-calibrated PAS are accurate and without detectable bias.
Another important aspect to our work is that our calibrations were performed
at the PAS wavelength of 405 nm for which we have previously demonstrated
excellent agreement between an aerosol-based and ozone-based calibration
(Davies et al., 2018), while
Bluvshtein et al. (2017) find that the ozone
calibration differs from an aerosol calibration by a factor of 2. As
discussed above, the calibrations in our work are performed by injecting an
ozonised flow into ambient air, while those of Bluvshtein et al. (2017) are performed in
a bath gas composed of 10 % O2 and 90 % N2. Our measurements
predict only a 2 % difference in the PAS sensitivity at 405 nm for these
two bath gas compositions. Therefore, we support the conclusion of
Fischer and Smith (2018) that the low
bath O2 mass fraction does not explain the poor ozone calibration
results described by Bluvshtein et al. (2017).
We emphasise that the dependence of PAS sensitivity on bath gas composition
is wavelength-dependent within the Chappuis band, particularly for
wavelengths in the range 400–660 nm, and researchers should perform
measurements of their PAS sensitivity to ascertain the optimal bath gas
composition for their instrument. Furthermore, researchers must consider the
impact of O2 dimer absorption on their measurements, particularly when
the PAS and CRDS measurements of absorption are performed at different
wavelengths.
Finally, we note that some PAS instruments (including our own) are designed
to operate on aircraft platforms and measure aerosol absorption at high
altitude where the ambient pressure is reduced to values as low as 400 hPa.
One aspect not considered in the present work is the impact of pressure on
quenching rate coefficients and the impact this has on PAS sensitivity.
Therefore, future work will study the impact of pressure on the PAS
sensitivity variation with bath gas composition.
Data availability
For data related to this paper, please contact
Michael I. Cotterell (m.cotterell@exeter.ac.uk) or Justin M. Langridge
(justin.langridge@metoffice.gov.uk).
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
This work was funded by the Met Office. Michael I. Cotterell and Jim M. Haywood
thank the Natural Environment Research Council for support through
the CLARIFY-2017 grant (NE/L013797/1). Michael I. Cotterell also
acknowledges support from the Royal Society of Chemistry Analytical
Chemistry Trust Fund through a Tom West Fellowship. Further support was
provided by the Research Council on Norway via the projects AC/BC (240372)
and NetBC (244141). We thank Michael N. R. Ashfold (University of
Bristol) for useful discussions concerning the potential impacts of
O2–O2 dimer formation on the measurements presented in this work.
Review statement
This paper was edited by Mingjin Tang and reviewed by three anonymous referees.
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