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GEOPHYSICAL RESEARCH LETTERS, VOL. 36, L03816, doi:10.1029/2008GL036170, 2009
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Temperature dependence of OH diffusion in air and He
Yong Liu,1 Andrey V. Ivanov,1 and Mario J. Molina1
Received 29 September 2008; accepted 6 January 2009; published 10 February 2009.
[1] Although accurate knowledge of OH diffusion under
atmospheric conditions is important, only one experimental
study has been carried out at room temperature. Here, we
report laboratory measurements of the OH diffusion
coefficient in He and in a mixture of He and air over the
range 218 – 318 K, using a temperature-controlled flow
tube coupled to a low-pressure chemical ionization mass
spectrometer. The results, which show a strong, almost square
dependence of the diffusion coefficient on temperature
in He and air, are consistent with predictions obtained
from our theoretical calculations for diffusion of its polar
diffusive analogue, H2O, using the 6 – 12 Lennard-Jones
potential model with the collision parameters of water. This
supports our hypothesis that the diffusion of OH can be
accurately represented in the atmosphere by water, its polar
diffusive analogue. Citation: Liu, Y., A. V. Ivanov, and M. J.
ficient for predicting the heterogeneous loss of gas-phase
species on atmospheric particles and cloud droplets and
also for analyzing laboratory data, to our knowledge no
information is available in the literature about the temperature dependence of the radical diffusion in the gas phase.
A limited number of experimental studies exist, mostly in
He [Gershenzon et al., 1986; Bertram et al., 2001; Ivanov
et al., 2007], with one measurement in air [Ivanov et al.,
2007] carried out previously in our laboratory at room
temperature.
[4] The objective of the present study is to determine
experimentally the temperature dependence of OH diffusion
in He and air in order to provide information that can be
used to test theoretical calculations and to help in atmospheric modeling of the heterogeneous chemistry of OH
radicals.
Molina (2009), Temperature dependence of OH diffusion in
air and He, Geophys. Res. Lett., 36, L03816, doi:10.1029/
2008GL036170.
2. Experiment
1. Introduction
[2] The OH radical is a key oxidant in the atmosphere
[Finlayson-Pitts and Pitts, 2000; Seinfeld and Pandis,
2003] — one that determines the heterogeneous chemistry
of the troposphere, initiating the heterogeneous oxidation
of organic particulate matter [Bertram et al., 2001; Molina
et al., 2004; Hearn and Smith, 2006; McNeill et al., 2007;
Vlasenko et al., 2008], being responsible for halogen
heterogeneous activation of the marine and polar troposphere
[Oum et al., 1998; Knipping et al., 2000; Knipping and
Dabdub, 2002], and being involved in cloud chemistry
[Chameides and Stelson, 1992; Hanson et al., 1992]. These
heterogeneous interactions of OH with atmospheric particles and cloud droplets are characterized by a strong
coupling of its heterogeneous reactions with diffusion
delivery to the surface [Schwartz, 1986; Frank-Kamenetsky,
1955].
[3] Under atmospheric conditions, high pressure and
below room temperature, this coupling often results in the
diffusion limitation, that is, diffusion being the ratedetermining step of an entire process of heterogeneous
interactions because of high OH uptake by aerosol materials [Bertram et al., 2001; Gershenzon et al., 1986]. To
what extent the heterogeneous reactions of OH are limited
in the atmosphere due to its relatively slow diffusion is
important for atmospheric models in which OH uptake is
involved. Despite the importance of the OH diffusion coef1
Department of Chemistry and Biochemistry, University of California,
San Diego, La Jolla, California, USA.
Copyright 2009 by the American Geophysical Union.
0094-8276/09/2008GL036170$05.00
[5] Experimental studies were carried out under flow
conditions using the same experimental setup that we utilized
in our early diffusion and uptake measurements [Bertram
et al., 2001; Molina et al., 2004; Ivanov et al., 2007]. For
temperature-dependent diffusion measurements, we have
modified the cylindrical flow reactor to control the gas
temperature by adding a thermostated inner jacket and an
evacuated (104 Torr) outer jacket to achieve a smooth
temperature profile in the flow tube. The desired temperature
in the flow reactor was set by circulation of heat transfer fluid
(Paratherm CR or water) through the inner jacket with the
help of a low-temperature circulator, the ULT 95 (Neslab;
Thermo Fisher Scientific; Newington, NH, USA). The temperature in the flow tube was measured by a chromel-alumel
thermocouple. The modified flow tube was coupled to a lowpressure chemical ionization mass spectrometer (CIMS) for
OH detection. OH was produced with the H + O2 source (H +
O2 + M followed by H + HO2 to give 2 OH) at a concentration
level of 109 molecule cm3 and was detected in the
chemical ionization zone with SF
6 as the parent ion. The
CIMS detection limit to OH (a signal-to-noise ratio of 1 with
a 5 s integration time) was 106 molecule cm3 at 3 Torr.
Typical flow conditions were the following: the flow velocity
of 8 to 17 m s1 and pressure of 1.5 to 5 Torr at 218 to 318 K.
The diffusion measurements were performed using the following surfaces: paraffin wax, pyrene, and aluminum oxide.
As these surfaces are reactive towards OH, they proved to
be convenient for measuring the diffusion coefficient of
OH [Bertram et al., 2001; Ivanov et al., 2007]. The surface
preparation has been described in detail in our early publications [Bertram et al., 2001; Molina et al., 2004; Ivanov
et al., 2007].
[6] The gases employed were He (BOC, 99.999%), synthetic air (BOC, grade 0.2), H2 (Matheson, 99.5%), and O2
(Matheson, 99.5%). The surface materials used were Al2O3
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LIU ET AL.: OH DIFFUSION IN AIR AND HE
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Figure 1. The pressure dependence of 1/kobs in (left) He and in (right) He-air at various temperatures.
(Aldrich, 99.9%), paraffin wax (melting range 346 to 353 K,
Aldrich), and pyrene (Aldrich, 98%).
3. Results and Discussion
[7] We determined the OH diffusion coefficient based on
the rule of additivity of kinetic resistances [Zasypkin et al.,
1997]: in a cylindrical flow reactor, the first-order rate
constant of OH heterogeneous loss, kobs(T), as observed in
our experiments is related to the uptake coefficient, g(T), and
the gaseous diffusion coefficient, D(T), as follows:
1
1
1
¼
þ
kobs ðTÞ kkin ðTÞ kdif ðTÞ
2g ðTÞ
2g ðTÞ
wðTÞ
2r
ð1Þ
1
Dð TÞ
r2 ,
where kkin(T) =
and kdif(T) = Kdif which
are the kinetic and diffusion limits of the observed firstorder rate constant of heterogeneous loss, respectively; T is
the temperature; w(T) is the mean thermal velocity; r is the
radius of the cylindrical flow reactor; and Kdif = 3.66 (for a
cylindrical flow tube), which is the dimensionless geometric
parameter [Zasypkin et al., 1997]. This approximation is valid
for the uptake coefficient independent of time, as observed in
this study. According to equation (1), the pressure dependence of 1/kobs should be linear with the slope inversely
proportional to the diffusion coefficient.
[8] Figure 1 (left) illustrates a typical pressure dependence
of the observed first-order loss rate constant of OH in He
at different temperatures. As seen in Figure 1 (left), 1/kobs
is linearly dependent on pressure with the slope inversely
proportional to DOH-He = 636 ± 32 Torr cm2 s1 at 298 K,
which is, within error, consistent with our previous measurements at room temperature [Bertram et al., 2001; Gershenzon
et al., 1986; Ivanov et al., 2007]. The measured temperature
dependence of the OH diffusion coefficient in He can be
represented as follows:
DOHHe ðTÞ ¼ DOHHe ð298 KÞ
1:850:05
T
T ¼ 218-298 K:
298 K
at lower temperatures, prevents performing accurate measurements. For this reason, we replaced the Al2O3 surface with more reactive surfaces, such as paraffin wax
(or pyrene with lower vapor pressure to reduce the contribution from the gas-phase chemistry at 318 K) and measured the diffusion coefficients of OH in a mixture of He
and air with the molar ratio of 0.7: 0.3. Figure 1 (right)
shows pressure dependence of the observed first-order loss
rate constant of OH in the He-air mixture at various
temperatures. These data were further used to determine
the diffusion coefficient of OH in air, using the measured
diffusion coefficient of OH in He and Blanc’s empirical
law [Blanc, 1908]:
ð2Þ
[9] It should be noted that for significantly slower
diffusion of OH in air in comparison with He, especially
DOHair ðTÞ
¼
1
1
cHe
; cHe ¼ 0:7:
1 cHe DOHHeair ðTÞ DOHHe ðTÞ
ð3Þ
[10] The measured temperature dependence of the diffusion coefficient of OH in air can be represented as follows:
DOHair ðTÞ ¼ DOHair ð300 KÞ
2:030:12
T
T ¼ 243-318 K
300 K
ð4Þ
where DOH-air(300 K) = 198 ± 20 cm2 Torr s1, which is
the diffusion coefficient of OH in air at 300 K and which
is, within error, consistent with our previous meaurement
[Ivanov et al., 2007].
[11] In our previous diffusion study at room temperature
[Ivanov et al., 2007], we showed that OH diffusion can be
accurately represented by diffusion of H2O, its polar diffusive analogue. To verify this conclusion at temperatures
different from room temperature, we compared the temperature dependence of the OH diffusion coefficient measured
experimentally with that of H2O calculated using the 6 – 12
Lennard-Jones potential model [Hirschfelder et al., 1954;
Sherwood, 1958]. The calculation method and the individual and binary collision parameters of H2O, He, N2, and O2
used in that calculation have been described in detail elsewhere [Ivanov et al., 2007].
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LIU ET AL.: OH DIFFUSION IN AIR AND HE
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Table 1. Individual Binary Collision Parameters
Species
˚
s, A
e/k, K
Ref
H2 O
He
N2
O2
2.641
2.551
3.798
3.467
809.1
10.22
71.4
106.0
22
21
22
22
[12] In brief, within the 6 –12 Lennard-Jones potential
model, the ordinary diffusion coefficient is determined as
follows [Hirschfelder et al., 1954; Sherwood, 1958]:
DðTÞ ¼
0:002628T1:5
D
E ; atm cm2 s1
ð2mÞ0:5 s2 Wð1;1Þ* ðqÞ
ð5Þ
Figure 2. Comparison of DOH (points) and DH2O (lines).
where T is temperature, m is the reduced mass of the colliding
species, hW(1,1)* (q)i is the collision integral normalized to
its rigid sphere value, q = kBT/e is the reduced temperature,
and kB is Boltzmann’s constant. Collision diameter (s) and
potential well depth (e) are parameters for the 6 –12 LennardJones potential and are characteristic of the colliding
molecules. Table 1 shows these parameters taken from the
literature [Mason and Monchick, 1962; Massman, 1998].
Parameters used for calculations of binary diffusion coefficients can be approximated with the parameters of individual
species within the Lennard-Jones potential model according
to the combination rules [Marrero and Mason, 1972]:
sij ¼
0:5
si þ sj
and eij ¼ ei ej
2
Atmosphere, 1976 [United States Committee on Extension
to the Standard Atmosphere, 1976]. As seen in Figure 3,
DOH-air increases by a factor of 2.6 as altitude increases
from 0 to 11 km. While temperature decreases linearly with
altitude, the calculated dependence of DOH-air shows that the
diffusion limitation in the troposphere becomes smaller at
higher altitudes, indicating that the dependence on pressure
is stronger than that on temperature.
[15] Mass transport of OH to an aerosol particle or cloud
droplet can be described by equation (1), along with
[Schwartz, 1998]
kmt
kin ¼
ð6Þ
where the subscripts i. j, and ij refer, respectively, to the
individual and binary collision parameters. Table 2 shows the
binary collision parameters used in our calculation of the OH
diffusion coefficient in He, in the He-air mixture, and in air. In
addition, to estimate the binary diffusion coefficient in a
mixture of several gases, Blanc’s law [Blanc, 1908] was
also used.
[13] Figure 2 illustrates the comparison between the
measured OH diffusion coefficient and the calculated
H2O diffusion coefficients in He, in the He-air mixture,
and in air at 218 to 318 K. As seen in Figure 2, the corresponding pairs of the diffusion coefficients of OH and
H2O, within error, agreed, supporting our earlier conclusion that the diffusion of OH can be also accurately
represented by the polar analogue in the range of temperatures studied.
3aOH wOH
3DOHair
V
V and kmt
dif ¼
4r
r2
where r is the radius of an aerosol particle or cloud droplet,
aOH is the mass accommodation coefficient of OH, wOH is
the average thermal velocity of OH, and V is the particle/
droplet volume. The diffusion limitations become important
mt
if kmt
kin > kdif — i.e., if aOH > l/r, where l = 3DOH-air/wOH,
which is the mean free path of OH. Since aOH is the upper
limit of g OH, we can introduce the following parameter,
g*OH = l/r, in order to estimate diffusion-limited conditions
for OH uptake in the troposphere. Figure 4 shows the
dependence of g*OH on the particle/droplet radius for two
altitudes (in Figure 4, the solid line is for 0 km and the
dashed line is for 11 km). The diffusion limitations become
important if the OH uptake coefficient is greater than g*OH.
4. Atmospheric Implications
[14] Based on equation (4), we were able to estimate
DOH-air in the troposphere. Figure 3 illustrates the dependence of DOH-air on altitude, calculated using properties
(pressure and temperature) published in the U.S. Standard
Table 2. Calculated Binary Collision Parameters
Pairs
˚
s, A
e/k, K
H2O-He
H2O-N2
H2O-O2
2.596
3.220
3.054
90.93
240.35
293.82
ð7Þ
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Figure 3. DOH-air in the troposphere.
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LIU ET AL.: OH DIFFUSION IN AIR AND HE
Figure 4. Diffusion limitations in the troposphere.
For example, for large cirrus ice particles of 10 to 100 mm,
the measured OH uptake coefficient of 3102 [Cooper
and Abbatt, 1996] is greater than g*OH (the dashed line in
Figure 4), suggesting that the radical uptake will be diffusionally limited. For smaller organic particles of 0.01 to
0.2 mm, OH uptake is diffusionally limited at the ground
level, since the measured OH uptake coefficient of near
unity3 is greater than g*OH (the solid line in Figure 4). On
the other hand, the diffusion limitations become less important as the organic aerosol reaches higher (tropopause)
altitudes (the dashed line in Figure 4).
5. Conclusions
[16] We performed an experimental study of the temperature dependence of OH diffusion in He and air over the
temperature range from 218 to 318 K, using a temperaturecontrolled flow tube coupled to a CIMS. The obtained
results showed a strong, almost square dependence of OH
diffusion in He and air, which aligns with predictions based
on our calculations using the 6– 12 Lennard-Jones potential
model with the collision parameters of H2O, the OH diffusive polar analogue. This can be used to test theoretical
calculations and also for analyzing laboratory data.
[17] Based on the measured temperature dependence of
OH diffusion in air, we were able to calculate DOH-air under
tropospheric conditions. We have also estimated the potential contribution of the diffusion limitations to OH heterogeneous reactions in the troposphere using a new parameter,
g*OH, which is the ratio of the kinetic and diffusion limit
of the OH loss rate on aerosol surfaces. It is important for
predicting the heterogeneous loss of gas-phase species on
aerosol particles and cloud droplets in the atmosphere.
[18] Acknowledgments. The present work was supported partially by
NSF award (ATM 0630385).
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A. V. Ivanov, M. J. Molina, and Y. Liu, Department of Chemistry and
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