Compilation and evaluation of gas-phase diffusion coefficients of reactive trace gases in the atmosphere : Volume 1 . Inorganic compounds

Diffusion of gas molecules to the surface is the first step for all gas-surface reactions. Gas 10 phase diffusion can influence and sometimes even limit the overall rates of these reactions; however, there is no database of the gas phase diffusion coefficients of atmospheric reactive trace gases. Here we compile and evaluate, for the first time, the diffusivities (pressure-independent diffusion coefficients) of atmospheric inorganic reactive trace gases reported in the literature. The measured diffusivities are then 15 compared with estimated values using a semi-empirical method developed by Fuller et al. (1966). The diffusivities estimated using Fuller’s method are typically found to be in good agreement with the measured values within ±30%, and therefore Fuller’s method can be used to estimate the diffusivities of trace gases for which experimental data are not available. The two experimental methods used in the atmospheric chemistry community 20 to measure the gas phase diffusion coefficients are also discussed. A different version of this compilation/evaluation, which will be updated when new data become available, is uploaded online (https://sites.google.com/site/mingjintang/home/diffusion).


Introduction
Airborne particles, including aerosol particles, cloud, fog, rain droplets and ice crystals, are ubiquitous in the atmosphere.The interactions of atmospheric trace gases with these particles, i.e. heterogeneous reactions, play important roles in many aspects of atmospheric chemistry (Abbatt et al., 2012;Kolb et al., 2010;Ravishankara, 1997).For example, the heterogeneous reaction of ClONO 2 with polar stratospheric clouds (PSCs) is a key step to re-activate chlorine in the stratosphere and thus plays a critical role in stratospheric ozone depletion (Molina, 1996;Solomon, 1999).In the troposphere, the reactions of trace gases with mineral dust (Dentener et al., 1996;Usher et al., 2003), sea salt (Finlayson-Pitts, 2003;Rossi, 2003), soot (Monge et al., 2010), organic aerosols (Stemmler et al., 2006), ice particles (Abbatt, 2003;Huthwelker et al., 2006) and liquid cloud droplets (Lelieveld and Crutzen, 1990) can significantly impact the budgets of NO x , O 3 and OH radicals.These reactions can also change the compositions of aerosol particles, e.g.mineral dust (Laskin et al., 2005;Sullivan et al., 2007), sea salt (Gard et al., 1998;Rossi, 2003) and organic aerosols (George and Abbatt, 2010), thus modifying their cloud formation ability (Cziczo et al., 2009;Reitz et al., 2011;Sullivan et al., 2009b).The removal, production and/or transformation of gaseous pollutants due to the interactions with indoor surfaces may play an important role in indoor air quality and human health (Nazerroff and Cass, 1989).
Heterogeneous interactions of trace gases with particles in the atmosphere (and with all surfaces) are very complex and usually consist of several steps (Davidovits et al., 2011;Pöschl et al., 2007): (1) gas molecules diffuse towards the surface; (2) gas molecules collide with the surface, and some are then accommodated on the surface; (3) molecules adsorbed on the surface can desorb from the surface, undergo reactions on the surface or diffuse into the bulk, and get dissolved and/or react with other species in the bulk; (4) gaseous Published by Copernicus Publications on behalf of the European Geosciences Union.
products formed in the heterogeneous reactions can diffuse towards the surface, desorb from the surface, and finally diffuse into the gas phase.The overall kinetics of a heterogeneous reaction can be described by the uptake coefficient, γ , which is the net probability that a molecule X undergoing collision with a surface is actually taken up by the surface.The uptake coefficient links the processes at the interface and beyond with an apparent first-order loss of X in the gas phase (Ammann et al., 2013;Crowley et al., 2010): where [X] g is the concentration of X in the gas phase (molecule cm −3 ), k I is the apparent first-order loss rate of X, c(X) is the average molecular speed (cm s −1 ) of X and [SS] is the concentration of the surface area available for the heterogeneous uptake (cm 2 cm −3 ).
The uptake of a trace gas onto the surface can cause depletion of the trace gas close to the surface, leading to an effective uptake coefficient, γ eff , which is smaller than the true uptake coefficient, γ .The relation between γ eff and γ , under appropriate steady-state assumptions, can be described by the following equation (Davidovits et al., 1995(Davidovits et al., , 2011)): where diff describes the gas phase diffusion limitation.Formulas to calculate diff have been derived in previous studies (Davidovits et al., 1995;Pöschl, 2011).diff depends on the geometry of the surface (e.g.surface of a spherical particle, or inner wall of a cylindrical flow tube), the size of the surface (e.g.diameter of the particle or the flow tube) and the diffusion coefficient of the trace gas in the bath gas (Crowley et al., 2010).
For the uptake onto mono-disperse spherical particles, several methods can be used to calculate diff (Pöschl et al., 2007) -for example, the Fuchs-Sutugin equation: where Kn is the Knudsen number, given by where D(X) is the diffusion coefficient of X (cm 2 s −1 ), d p is the diameter of the particle (cm) and c(X) is average molecular speed of X (cm s −1 ).For fast uptake processes (i.e.large uptake coefficients) and big particles, gas phase diffusion of X can limit the overall rate of the uptake of X onto the surface.A method used to calculate diff for poly-dispersed aerosol particles has also been developed (Tang et al., 2012(Tang et al., , 2014)).As shown in Eqs. ( 3) and ( 4), the diffusion coefficient determines to which extent the effective uptake coefficient is impacted by gas phase diffusion.An accurate knowledge of the diffusion coefficient is thus important to apply the uptake coefficient to atmospheric particles and to derive the true uptake coefficient from the experimentally measured uptake coefficient in laboratory studies.Aerosol flow tubes (Hallquist et al., 2000;Tang et al., 2012;Thornton et al., 2003;Vlasenko et al., 2009), droplet train flow reactors (Deiber et al., 2004;Worsnop et al., 1989) and aerosol chambers (Mogili et al., 2006;Wahner et al., 1998) are widely used to investigate the heterogeneous interaction of airborne particles or droplets with trace gases.The effect of diffusion in the gas phase on the uptake of a trace gas onto spherical particles at 760 Torr (N 2 ) and at 296 K is illustrated in Fig. 1a.N 2 O 5 , with a diffusion coefficient of 0.085 cm 2 s −1 at 760 Torr and at 296 K (Wagner et al., 2008) and an average molecular speed of 24 096 cm s −1 , is used as the representative trace gas for the calculations.For spherical particles with diameters of < 200 nm, when the true uptake coefficient is < 0.1, the influence of gas phase diffusion, defined as (γ − γ eff )/γ , is smaller than 5 %.When the true uptake coefficient is < 0.001, the influence of gas phase diffusion is < 7 % for particles with diameters of < 20 µm.Increasing the particle diameter and the uptake coefficient will increase the effect of gas phase diffusion, and gas phase diffusion becomes important with (γ − γ eff )/γ larger than 20 % for fast uptake (γ > 0.04) onto larger particles (d p > 2 µm), as shown in Fig. 1a.
In addition, especially when the heterogeneous reactions of interest are slow, coated or wetted wall flow tubes are used in laboratory studies, in which the solid or liquid substrates form a film on the inner wall of the flow tube to interact with the trace gas under investigation (Abbatt and Molina, 1992;Adams et al., 2005;Hanson et al., 1992;Pouvesle et al., 2010).For the uptake onto the inner wall of a cylindrical tube, diff is given by (Hanson et al., 1992;Wagner et al., 2008) where d t is the inner diameter of the flow tube (cm).The quantitative effect of gas phase diffusion on the uptake of a trace gas onto the inner wall of a cylindrical flow tube (inner diameter: 2.0 cm) at 296 K is shown in Fig. 1b as a function of pressure (N 2 ).N 2 O 5 is again used as the representative trace gas.When the true uptake coefficient is < 1 × 10 −5 , the effect of gas phase diffusion is relatively small (< 25 %) even at high pressure (close to 1 atm).Increase in the true uptake coefficient enhances the effect of gas phase diffusion.Therefore, in many studies coated-wall flow tubes are operated at low pressures of He, to increase the gas phase diffusion rate and thus suppress the effect of gas phase diffusion on the overall effective uptake rate.When the true uptake coefficient is close to 0.1, as shown in Fig. 1b, the uptake onto the wall is entirely controlled by gas phase diffusion (γ eff / γ is ∼ 0.1) and therefore the upper limit for accurate uptake measurement using this method is around 0.1.Another type of coated wall flow tube in which the solid substance under Influence of gas phase diffusion on the effective uptake coefficients (defined as γ eff / γ , the ratio of the effective uptake to the true uptake coefficient) as a function of the true uptake coefficient.N 2 O 5 , with a diffusion coefficient of 0.085 cm 2 s −1 at 760 Torr and 296 K and an average molecular speed of 24 096 cm s −1 , is used as the representative trace gas for the calculations.(a) Uptake onto spheric particles with different diameters at 760 Torr and 296 K; (b) uptake onto the wall of a cylindrical flow tube (inner diameter: 2.0 cm) at 296 K and at different pressures.
investigation is coated on the outer wall of the injector instead of the inner wall of the flow reactor has also be used (Bedjanian et al., 2005;Gershenzon et al., 1995), and details on how to derive γ from γ eff are provided by Gershenzon et al. (1995).
The interaction of trace gases with surfaces, and therefore gas phase diffusion coefficients, are not only important in the investigation of atmospheric heterogeneous reactions, but are also important to describe the efficiency of diffusion denuders which are widely used to collect trace gases or to separate trace gases from aerosol particles.For example, denuder tubes in which inner walls are coated with adsorbents are widely used to capture trace gases such as HNO 3 (Braman et al., 1982;Durham et al., 1987;Eatough et al., 1985), HONO (Ferm and Sjodin, 1985) and NH 3 (Braman et al., 1982) for online/offline analysis, and to separate aerosol particles from gases (e.g. to separate NH 3 from particulate NH + 4 ).Aerosol particles which remain in the flow exiting the denuders can then be collected for further online/offline analysis, and artifacts due to interferences of trace gases (for example, particulate nitrate versus gaseous HNO 3 , and ammonium versus NH 3 ) can be minimised (Ferm, 1986).Denuders are also widely used in laboratory studies to remove reactive trace gases to terminate heterogeneous reactions (Sullivan et al., 2009a), or selectively remove reactive trace gases whose detection can interfere with others (Ammann et al., 1998).In addition, catalytic tubes are used to convert trace gases to products which can then be more easily detected.For example, the widely used chemiluminescence method to measure NO 2 is based on conversion of NO 2 to NO in a catalytic conversion tube coated with metal films such as nickel or gold (Fahey et al., 1985).The removal and/or conversion of trace gases in a denuder or catalytic tubes requires the diffusion of trace gases towards and collision with the inner wall, and therefore the knowledge of diffusion coefficients is helpful for the optimisation of the design of denuder and catalytic conversion tubes (Murphy and Fahey, 1987).
The importance of further research on atmospheric heterogeneous reactions has been underscored (Abbatt et al., 2014;Kolb et al., 2010), the necessity of adopting consistent terminology, formalism and parameters in the heterogeneous reaction studies has been highlighted (Kolb et al., 2010;Pöschl et al., 2007), and comprehensive models have been developed to take into account all the steps involved in heterogeneous reactions (Pöschl et al., 2007;Shiraiwa et al., 2010).Two independent international panels, the IUPAC Subcommittee for Gas Kinetic Data Evaluation (Ammann et al., 2013;Crowley et al., 2010) and the NASA/JPL Panel for Data Evaluation (Sander et al., 2011) have been evaluating and recommending the experimental kinetic data for atmospheric heterogeneous reactions.However, gas phase diffusion coefficients of atmospheric reactive trace gases have only been occasionally measured during the investigation of heterogeneous reactions and development of denuder methods.To the best of our knowledge, these data have not been compiled previously.When unavailable, these values have to be estimated, and even sometimes were arbitrarily chosen, leading to additional errors.Therefore, a compilation and/or evaluation of measured diffusion coefficients is clearly required.We note that there are several databases on the binary gas phase diffusion coefficients (Berezhnoi and Semenov, 1997;Gordon, 1977;Marrero and Mason, 1972); however, the existing databases focus on stable gases which are of limited relevance for atmospheric chemistry.
Here we compile and evaluate the diffusion coefficients of atmospheric inorganic reactive trace gases reported in the literature, with the hope that this work will enhance the dissemination of the reported diffusion coefficients and stimulate further experimental measurements.We also compare the measured values to those estimated using Fuller's method, in order to evaluate the performance of this method.Fuller's method is a semi-empirical method to directly estimate the gas phase diffusivities (Fuller et al., 1966(Fuller et al., , 1969)).
The diffusivities of organic species are beyond the scope of this paper (the only included organic molecule is CH 3 SO 3 H).The uptake of organics, particularly oxygenated organics, onto aerosol particles and cloud droplets can also be important in the atmosphere.We have started to compile and evaluate the diffusion coefficients of organic species of atmospheric interest, and plan to publish another review in the near future.Marrero and Mason (1972) compiled the diffusivities of some alcohols, ketones, aldehyde and carbonic acids, though many of them may not be of direct atmospheric interest.

Gas phase diffusivity
The theory describing diffusion in binary gas mixtures at low to moderate pressure can be derived by solving the Boltzmann equation, and the diffusion coefficient can be expressed as (Reid et al., 1987) where D(A, B, P ) is the diffusion coefficient (cm 2 s −1 ) of gas A in gas B at a pressure of P (bar), T is the temperature (K), M(A, B) is equal to twice of the reduced mass of molecule A and molecule B, σ is the characteristic length (10 −1 nm), and D is the dimensionless diffusion collision integral.To derive Eq. ( 6), it is also assumed that the gases investigated obey the ideal-gas law and gas A is only present in trace amount compared to B.
To estimate diffusion coefficients using Eq. ( 6), the values of σ and D need to be calculated/estimated.Ghosal (1993) used the Lennard-Jones method to estimate the diffusion coefficients of a variety of atmospheric trace gases, and Ivanov et al. (2007) found that the diffusion coefficients of OH, HO 2 , and O 3 estimated by the Lennard-Jones method agree well with their experimentally measured values.However, to calculate σ and D , the Lennard-Jones method requires molecular parameters which are not readily available.
Several empirical/semi-empirical methods are available to directly estimate diffusion coefficient, e.g. the method proposed by Fuller et al. (1966Fuller et al. ( , 1969)).Reid et al. (1987) compared the estimated diffusion coefficients of a large range of molecules using different methods, including the Lennard-Jones method and Fuller's method, with measured values, and found that Fuller's method in general yields the smallest errors.Therefore, in this work Fuller's method is used.

Fuller's method
Measured gas phase diffusion coefficients, D(A, B, P ), usually reported in cm 2 s −1 , depend on the pressure under which the diffusion coefficients were measured.Pressureindependent diffusion coefficients (torr cm 2 s −1 ), D(A, B), sometimes called diffusivities, are reported by dividing D(A, B, P ) by the pressure.In this work for clarity and consistency, the pressure-independent diffusion coefficient, D(A, B), is referred to as diffusivity, and all the reported diffusion coefficients are converted to diffusivities.
The diffusivity of gas A in gas B, estimated using Fuller's method, can be described by (Fuller et al., 1966(Fuller et al., , 1969) where D(A, B) is the diffusivity of A in B (Torr cm 2 s −1 ) at the temperature of T (K), and m(A, B) (g mol −1 ) is given by where m A and m B are the molecular weights (g mol  1, can be calculated by summing the diffusion volumes of all the atoms it contains: where n i is the number of the atom with a diffusion volume of V i contained by the molecule.The diffusion volumes of a few atoms of atmospheric interest are listed in Table 1.Readers are referred to Table 11-1 of Reid et al. (1987) for the diffusion volumes of other molecules and atoms not included in Table 1 of this paper.
The atomic diffusion volumes are determined by regression analysis of experimental data on gas phase diffusion coefficients of a large range of molecules.Calculation of molecular diffusion volumes from atomic diffusion volumes may lead to different errors for different molecules.The diffusion volume of SO 2 would be 35.12 if derived from atomic diffusion volumes according to Eq. ( 9), and it is 41.8 (as listed in Table 1) which is directly calculated from extensive experimental data set of gas phase diffusivities of SO 2 .As shown in Tables 2-5, we find that, compared to the experimental values, the diffusivities estimated using Fuller's method are typically 20-50 % larger for atmospheric trace gases that we include in this work.We suggest that this mainly results from underestimation of molecular diffusion volumes derived from atomic diffusion volumes.
The diffusion of a trace gas, A, in the binary mixture of B1 (e.g.N 2 ) and B2 (e.g.H 2 O), can be calculated as (Reid et al., 1987;Fickert et al., 1999) 1 where x(B1) and x(B2) are the molar fractions of B1 and B2 in the mixture, D(A,B1,B2), D(A,B1) and D(A,B2) are the diffusivities of A in the binary mixture (of B1 and B2), B1, and B2, respectively.

Measurements of diffusion coefficients
Gas phase diffusion coefficients have been measured since the late 19th century, and many experimental methods have been developed (Marrero and Mason, 1972); however, most (if not all) of these methods can only by applied to relatively stable gases and thus are not suitable for determining the diffusivities of atmospheric reactive trace gases.To our knowledge only two methods, i.e. flow tubes and denuders, have been used to measure the diffusivities of trace gases by the atmospheric chemistry community.Both methods use the same principle: a flow containing the trace gas is delivered through a tube (usually cylindrical) which is coated on its inner wall with a very reactive substance and thus serves as a perfect sink for trace gas molecules colliding with the wall.Therefore, the overall loss rate of the trace gas is entirely controlled by its diffusion in the gas phase towards the wall and not influenced by the reactivity of the surface.The two methods are briefly discussed below.

Flow tubes
If the inner wall of a cylindrical flow tube is very reactive towards the trace gas, the loss rate of the trace gas onto the wall can then be used to determine the gas phase diffusion coefficient.Under laminar flow conditions, D(A, B, P ) can be related to the measured wall loss rate, k w , by where r t is the radius of the flow tube (Zasypkin et al., 1997).This equation is only valid for conditions under which the Peclet number, Pe, is larger than 20 (Zasypkin et al., 1997).
Pe is given by where v is the linear flow velocity in the flow tube.It is necessary to measure D(A, B, P ) at different pressure to derive the diffusivity, D(A, B).If the wall serves as a perfect sink for the trace gas, D(A, B) measured at different pressure should show good agreement (Fickert et al., 1999;Liu et al., 2009).

Denuders
A laminar flow containing stable mixing ratios of the trace gas passes through the denuder which consists of several sections with the same length.The trace gas is collected on the inner wall of each section and converted to a stable adsorbate, which is then quantified offline to determine the collection efficiency, E (Ferm and Sjodin, 1985): where c i and c i+1 are the amount of adsorbate being collected on the ith and (i+ 1)th sections, respectively.For a cylindrical tube whose inner wall acts as a perfect sink for the trace gas, E can be related to the diffusion coefficient, D(A, B, P ) by where L is the length of each section of the denuder (cm), and F is the volume flow rate of the flow passing through the denuder (cm 3 s −1 ) (Ferm and Sjodin, 1985).
It is important for both methods to ensure that the wall remains as a perfect sink for the trace gas during the experiment so that the overall loss of the trace gas is controlled by www.atmos-chem-phys.net/14/9233/2014/Atmos.Chem.Phys., 14, 9233-9247, 2014 gas phase diffusion.In a flow tube experiment, this can be checked be measuring the diffusion coefficients at different pressures over a broad range (Fickert et al., 1999;Ivanov et al., 2007).A denuder is normally operated at constant pressure (close to atmospheric pressure) and therefore it is often not verified whether the inner wall of the denuder is a perfect sink.Fast-response online detectors are often available to measure the decay of trace gases in a flow tube, enabling relatively quick determination of the diffusivities.The denuder method usually requires a substantial period to collect enough samples which will then be post-processed and analysed, making it quite laborious.Therefore, the flow tube method appears to be a better method for the determination of diffusivities in the gas phase.We recommend that such measurements should be performed over a broad range of pressure, in order to ensure that the inner wall serves as a perfect sink.

Results
The recommended diffusivities in air are summarised in Table 2. Since the diffusivity of a trace gas in air is approximately the same as its diffusivity in N 2 / O 2 , no adjustment was made if measurements were performed in N 2 / O 2 instead of air.The diffusivities of some important reactive trace gases in air (or in N 2 / O 2 ), e.g.HO 2 , O 3 , HOCl and ClONO 2 , have not been experimentally determined, and therefore no recommendation can be made.However, these species are listed in Table 2 to highlight the urgency to measure their diffusivities.A different version of this compilation/evaluation, which largely follows the format of online reports prepared by the IUPAC Task Group on Atmospheric Chemical Kinetic Data Evaluation (http://iupac.pole-ether.fr/), is uploaded online (https://sites.google.com/site/mingjintang/home/diffusion) and will be updated when new data are available.
For trace gases whose diffusivities were measured under the same (or similar) conditions by more than one study, the preferred diffusivity is the average of the measured values and the given uncertainty is the corresponding standard deviation, after excluding studies whose results appear significantly different.However, except for a few trace gases (e.g.HNO 3 and NH 3 ), the diffusivities of most trace gases have only been reported by one study.If there is only one experimental value available, the experimental value is temporarily preferred, and the given uncertainty reflects the difference between the measured and estimated diffusivities, e.g. if the estimated diffusivity is 30 % larger than the measured value, an uncertainty of ±30 % is given to the preferred value.
Preferred diffusivities in air (or N 2 / O 2 ) at 296 K are recommended.If the measurement was not carried out at 296 K, the original diffusivity was adjusted to 296 K, assuming that the temperature dependence can be described by Fuller's method: where T is the temperature (K) at which the measurement was performed, and D(296) and D(T ) are the diffusivities at the temperature of 296 K and T , respectively.If the difference between T and 296 K is ≤ 10 K, the difference in the diffusivities is not larger than 6 % which is negligible compared to the uncertainties of reported diffusivities, and thus no adjustment due to temperature difference was performed.
In the following sections, we compile and discuss experimental gas phase diffusivities reported in the literature, and compare them to estimated values using Fuller's method.Diffusivities for individual molecules are then recommended if possible.

HNO 3 and NH 3
The diffusivities of HNO 3 were all measured by using denuders at 296-298 K.As shown in Table 3, all the reported values agree well with each other except a much smaller value reported by De Andrade et al. (1992).The preferred diffusivity of HNO 3 in air at 296 K, (87 ± 7) Torr cm 2 s −1 , is the average value of all the measurements except De Andrade et al. (1992).On average the estimated diffusivity using Fuller's method is ∼ 30 % larger than the measured values.
As shown in Table 3, the diffusivity of NH 3 in N 2 (or air/O 2 ) was measured over a wide temperature range (293-523 K) prior to 1960, and the reported values at 296-298 K agree very well with more recent measurements in N 2 using flow tubes (Hanson and Kosciuch, 2003) and denuders (Braman et al., 1982;Spiller et al., 1989).The preferred diffusivity of NH 3 in N 2 (or air/O 2 ) at 296 K, (176 ± 10) Torr cm 2 s −1 , is the average of those reported by all the studies at this temperature.The estimated diffusivities using Fuller's method agree very well with the measured ones.

NO, NO 2 , NO 3 , N 2 O 5 and HONO
The diffusivities of NO and N 2 O 5 in N 2 were only determined once, to the best of our knowledge.The results are listed in Table 4.The estimated diffusivities using Fuller's method are 2 % higher than the measured values for NO, and 45 % for N 2 O 5 .Since their diffusivities were only reported once and the measured values agree reasonably well with estimates using Fuller's method, the reported values are preferred.Uncertainties of ±10 % and ±50 % are given to the preferred diffusivities of NO and N 2 O 5 , reflecting the difference between the measurement and the estimation.More measurements are needed to reduce the relatively large uncertainty of the diffusivity of N 2 O 5 , considering the importance of its uptake onto airborne particles in both the troposphere and the stratosphere.The diffusivity of NO 2 in N 2 was measured once by Chambers and Sherwood (1937).A high partial pressure of NO 2 was used in the experiment and therefore the presence of N 2 O 4 in the system was significant.The diffusivity of NO 2 was experimentally determined by assuming that the diffusivity of NO 2 is a factor of 1.43 of that of N 2 O 4 .The measurements were carried out at two different temperatures, and the estimated diffusivities using Fuller's method are 35 % larger than the measured values, as shown in Table 4.The preferred diffusivity of NO 2 in N 2 at 296 K, (106 ± 37) Torr cm 2 s −1 , is based on the value reported at 283 K by Chambers and Sherwood (1937), extrapolated to 296 K.The given uncertainty (±35 %) reflects the difference between the measurement and the estimation at 283 K.
The diffusivities of NO 3 radicals in N 2 , O 2 , He and H 2 O were determined using a flow tube (Rudich et al., 1996).The measured diffusivity in N 2 , as expected, agrees very well with that in O 2 .The estimated diffusivities using Fuller's method are 50 % larger than the measured values for NO 3 radicals.The preferred diffusivity of NO 3 radicals in N 2 at 296 K, (92 ± 46) Torr cm 2 s −1 , is based on the measurement of Rudich et al. (1996) at 273 K and extrapolated to 296 K using Eq. ( 16).The large uncertainty we give to the preferred value reflects the relatively significant difference between the measurement and the estimation using Fuller's method, and highlights that further measurements are desired.
The diffusivity of HONO in He was measured to be (433 ± 38) Torr cm 2 s −1 at 294 K (Hirokawa et al., 2008) and (490 ± 50) Torr cm 2 s −1 at 300 K (El Zein and Bedjanian, 2012) using flow tubes, as listed in Table 4.The two studies are in good agreement, and differences between the measured and estimated diffusivities are < 20 %.The diffusivity of HONO in air at 298 K reported by Benner et al. (1988) is significantly smaller than that reported at 296 K by Ferm and Sjodin (Ferm and Sjodin, 1985), though denuders were used in both studies.The preferred diffusivity of HONO in air at 296 K, (96 ± 26) Torr cm 2 s −1 , is the average of those reported by the two studies (Benner et al., 1988;Ferm and Sjodin, 1985).Since the difference between the two studies is statistically significant, further studies, preferably using a flow tube, are needed to reduce the uncertainty of the diffusivity of HONO in air (or N 2 , O 2 ).

SO 2 , SO 3 , H 2 SO 4 , and CH 3 SO 3 H
The diffusivity of SO 2 in air was measured at 263 K (Mason and Monchick, 1962), 293 K (Andrew, 1995), and 298 K (Fish and Durham, 1971).The reported values in these three studies agree well with the estimates using Fuller's method, as shown in Table 5.The preferred diffusivity of SO 2 in air at 296 K, (94 ± 13) Torr cm 2 s −1 , is the average of the values measured by Andrew (1955) and Fish and Durham (1971) at room temperature.
The diffusivity of SO 3 in N 2 was measured at 295 K by Lovejoy and Hanson (1996) and at 300 K by Jayne et al. (1998), both using flow tubes.The measured diffusivities agree well with each other, and are also in good agreement with the estimated values.The preferred diffusivity of SO 3 in air at 296 K, (91 ± 6) Torr cm 2 s −1 , is the average of those reported by Lovejoy and Hanson (1996) and Jayne et al. (1998).
The diffusivities of H 2 SO 4 in N 2 were reported to be (85 ± 15) Torr cm 2 s −1 at 295 K (Lovejoy and Hanson, 1996), (71 ± 5) Torr cm 2 s −1 at 298 K (Hanson and Eisele, 2000), and (67 ± 1) Torr cm 2 s −1 at 303 K (Pöschl et al., 1998).All three studies used flow tubes.As shown in Table 5, the diffusivity reported by Lovejoy and Hanson (1996) is in excellent agreement with the estimated value, while the values reported by Pöschl et al. (1998) and Hanson and Eisele (2000) agree with the estimated ones reasonably well (within ∼ 30 %).The preferred diffusivity of H 2 SO 4 in N 2 at 296 K, (74 ± 10) Torr cm 2 s −1 , is the average of the three studies.No adjustment due to the temperature difference is done because difference in the diffusivities between 296 K and the temperatures at which the measurements were carried out is very small.
The diffusivity of CH 3 SO 3 H in N 2 at 296 K was determined to be 60 Torr cm 2 s −1 (Hanson, 2005).The uncertainty was not clearly stated in the original study, and the mea-sured value is 30 % lower than that estimated using Fuller's method.The preferred diffusivity of CH 3 SO 3 H in N 2 , is recommended to be (60 ± 18) Torr cm 2 s −1 , and the uncertainty associated with the preferred value reflects the difference between the measured diffusivity and the estimated one.

O 3 , OH, HO 2 , and H 2 O 2
The diffusivity of O 3 was only measured by one flow tube study, to be (410 ± 25) Torr cm 2 s −1 at 295 K in He (Ivanov et al., 2007), and the estimated value by Fuller's method is 27 % higher, as shown in Table 5. Unfortunately no measurement of the diffusivity of O 3 in air (or N 2 / O 2 ) has been performed and therefore no recommendation can be made, despite the central importance of O 3 in the troposphere and stratosphere.
The diffusivities of OH radicals were measured at 218-298 K in He and at 243-318 K in air (Liu et al., 2009).The results are in good agreement with the diffusivities in He (Bertram et al., 2001;Ivanov et al., 2007) and air (Ivanov et al., 2009) at room temperature reported by the same group, as shown in Table 5.The preferred diffusivity of OH radicals in air at 296 K, (179 ± 20) Torr cm 2 s −1 , is the average of values reported by Ivanov et al. (2007) and Liu et al. (2009).The diffusivity of HO 2 radicals in He was measured using flow tubes at 296 K (Ivanov et al., 2007;Lovejoy and Hanson, 1996), and the results reported by these two studies are in good agreement, as shown in Table 5.The diffusivity of HO 2 radicals in He, estimated using Fuller's method, is 40 % larger than the measured values.The diffusivity of HO 2 radicals in air (or N 2 / O 2 ) has not been measured and thus no recommendation can be made.The uptake of HO 2 radicals onto aerosol particles in the troposphere is suggested to be very fast and may have a significant impact on the oxidation capacity of the troposphere (Mao et al., 2013).Therefore an accurate determination of the diffusivity of HO 2 in air (or N 2 / O 2 ) is clearly of importance.
Only one study measured the diffusivity of H 2 O 2 (in air), and a value of (143 ± 3) Torr cm 2 s −1 at 333 K was reported (McMurtrie and Keyes, 1948).The estimated diffusivity using Fuller's method, is 27% larger than the measured value.The preferred diffusivity of H 2 O 2 in air is (143 ± 43) Torr cm 2 s −1 at 333 K and (116 ± 35) Torr cm 2 s −1 at 296 K.An uncertainty of ±30 % is given for the preferred values, taking into account the difference between the measured and estimated values.

HOX and HX
The diffusivity of HOBr was measured to be (237 ± 1) Torr cm 2 s −1 at 255 K (Adams et al., 2002) and (319 ± 48) Torr cm 2 s −1 at 274 K (Fickert et al., 1999) in He, and (84 ± 7) Torr cm 2 s −1 in N 2 at 274 K (Fickert et al., 1999), using flow tubes.As shown in Table 6, the estimated diffusivity using Fuller's method is ∼ 10 % larger than the measured value for HOBr in N 2 .The preferred diffusivity of HOBr in N 2 at 274 K, (84 ± 9) Torr cm 2 s −1 , is based on the measurement of Fickert et al. (1999), and the uncertainty of the preferred value reflects the difference (∼ 10 %) between the measurement and the estimation.To the best of our knowledge, the diffusivity of HOCl has not been reported.
The diffusivity of HOI in He was measured to be (191 ± 38) Torr cm 2 s −1 at 243 K and (225 ± 12) Torr cm 2 s −1 at 253 K (Holmes et al., 2001), and the estimated values using Fuller's method are ∼ 30 % larger.No measurement of the diffusivity in air / N 2 / O 2 has been reported.The diffusivities of HOBr and HOI in gaseous H 2 O were also measured (Adams et al., 2002;Holmes et al., 2001), and the estimated values using Fuller's method are 110 % and 194 % larger than the measured diffusivities in H 2 O, as shown in Table 6.In contrast, the estimated diffusivities of HOBr in He and N 2 and of HOI in He are in reasonably good agreement with the measured values.This may indicate that intermolecular interaction may occur between HOBr/HOI and H 2 O molecules, thus slowing down the diffusion.
The diffusivities of HCl in N 2 were measured in the temperature range of 324-523 K (Mian et al., 1969), and the difference between the measured and estimated values are < 20 %, as shown in Table 6.If the diffusivity measured at 324 K is adjusted to that at 296 K using Eq. ( 16), it gives a value of 113 Torr cm 2 s −1 .This agrees well with the diffusivity (122 Torr cm 2 s −1 ) of HCl measured in air at 296 K using denuders (Matusca et al., 1984).The preferred diffusivity of  HCl in N 2 at 296 K, (118 ± 7) Torr cm 2 s −1 , is the average of the values reported by Matusca et al. (1984) at 296 K and Mian et al. (1969) after being extrapolated to 296 K.Only one study reported the diffusivity of HBr, which was measured in N 2 from 336 to 525 K (Mian et al., 1969).As shown in Table 6, the differences between the measured and estimated diffusivities are usually < 20 %.The preferred diffusivity of HBr in N 2 , (95 ± 29) Torr cm 2 s −1 , is an extrapolation of the measured value at 336 K by Mian et al. (1969) to 296 K using Eq. ( 16), and the uncertainty reflects the difference between the measured and estimated diffusivities of HBr in N 2 at 336 K.

Nitrogen-containing halogen species
The diffusivities of ClNO 2 in N 2 and He were measured at 275 K in a flow tube study (Fickert et al., 1998), and the agreement with estimated values is within 20 %.The preferred diffusivities of ClNO 2 in N 2 are recommended to be (75 ± 15) Torr cm 2 s −1 at 275 K and (85 ± 17) Torr cm 2 s −1 at 296 K, based on the measurement of Fickert et al. (1998).The assigned uncertainty reflects the difference between the measured and estimated diffusivity at 275 K.The diffusivi-ties of ClONO 2 or BrONO 2 have not been reported, despite their importance in the stratosphere and possibly also in the troposphere.

X 2 and XY
The diffusivity of Cl 2 in air was reported to be (94 ± 2) Torr cm 2 s −1 at 293 K (Andrew, 1955).Though the measurement is in excellent agreement with the estimation, an uncertainty of ±10 % is given to the preferred value at 296 K, i.e. (94 ± 10) Torr cm 2 s −1 .The diffusivities of Br 2 in air was measured to be (69 ± 3) Torr cm 2 s −1 at 293 K (Andrew, 1955), (80 ± 3) Torr cm 2 s −1 at 301 K (Brockett, 1966), and (81 ± 1) Torr cm 2 s −1 at 298 K (Lugg, 1968).As shown in Table 6, all three measurements are in good agreement with the estimation.The preferred diffusivity of Br 2 in air at 296 K, (75 ± 6) Torr cm 2 s −1 , is the average of the values reported by Andrew (1955), Brockett (1966) and Lugg (1968).The reported diffusivities of I 2 in air at 298 K and in N 2 at 273 K (Trautz and Muller, 1935) agree reasonably well with the estimated values (within ±20 %).The preferred diffusivity of I 2 in air at 298 K, (64 ± 13) Torr cm 2 s −1 , is based on the value reported by Trautz and Muller (1935).The diffusivities of ICl in He measured using a flow tube at 278 and 293 K (Braban et al., 2007) show good agreement with the estimated values.The discrepancy between measured and estimated diffusivities for ICl in H 2 O is significantly larger than that in He.Similar discrepancies were also observed for HOBr and HIO in H 2 O, as discussed in Sect.3.5.1,and this may suggest that in general Fuller's method works better for diffusivities in N 2 , O 2 , air and He than that in gaseous H 2 O.The diffusivity of BrCl or ICl in air / N 2 / O 2 has not been reported.

Temperature dependence of diffusivities
Only a few studies measured the diffusivities of atmospheric reactive trace gases at several temperatures.The diffusivities of NH 3 , HCl and HBr in N 2 were measured from ∼ 300 to > 500 K.As shown in Tables 3 and 6, over the broad temperature ranges investigated, the measured diffusivities agree well with the estimated values using Fuller's method.However, the temperature ranges (300-500 K) in which the diffusivities of NH 3 , HCl and HBr were determined are of little atmospheric relevance.
Using a flow tube, Liu et al. (2009) measured the diffusivities of OH radicals in air over the range of 243-318 K.The diffusivities reported by Liu et al. (2009) and those estimated using Fuller's method are plotted in Fig. 2 as a function of temperature.The ratios of the estimated diffusivity to the measured one (red curve, right y axis) are also shown in Fig. 2, suggesting that Fuller's method can predict the diffusivities of OH radicals over a broad temperature range within ±30 %.The diffusivities of most of atmospheric reactive trace gases have not been measured at different temperatures, although the temperature dependence may be reasonably well estimated using Fuller's method.

Conclusions
The critical role of heterogeneous reactions in atmospheric chemistry has been widely accepted, and the necessity of adopting consistent terminology and having high quality of kinetic data have also been well recognised (Ammann et al., 2013;Crowley et al., 2010;Kolb et al., 2010;Pöschl et al., 2007;Sander et al., 2011).The diffusion of gas molecules towards the surface is the first step in a heterogeneous reaction, and it can influence and sometimes even control the overall rate of the uptake of a trace gas onto the surface.However, to the best of our knowledge, there is no database of the gas phase diffusion coefficients of atmospheric reactive trace gases.
In this work we have compiled and evaluated the available experimental data for the diffusivities of atmospheric inorganic reactive trace gases.The measured diffusivities are also compared with those estimated using Fuller's semi-empirical method.It is found that Fuller's method can typically estimate the diffusivities to within ±30 %.Therefore, in cases where the diffusivity of a trace gas has not been measured, Fuller's method can be used to estimate the diffusion coefficient.
The preferred diffusivities together with estimated uncertainties are tabulated to provide a quick and simple overview of the data currently available.This compilation/evaluation is also uploaded online (https://sites.google.com/site/mingjintang/home/diffusion), enabling further updates when new data become available.It should be noted that further measurements may change the uncertainties and/or the currently preferred values.Another aim of this work is to help identify and highlight areas of uncertainty or lack of data, therefore stimulating further measurements.We have started to compile and evaluate the diffusion coefficients of organic species, which will be published in another review in the near future.
Figure1.Influence of gas phase diffusion on the effective uptake coefficients (defined as γ eff / γ , the ratio of the effective uptake to the true uptake coefficient) as a function of the true uptake coefficient.N 2 O 5 , with a diffusion coefficient of 0.085 cm 2 s −1 at 760 Torr and 296 K and an average molecular speed of 24 096 cm s −1 , is used as the representative trace gas for the calculations.(a) Uptake onto spheric particles with different diameters at 760 Torr and 296 K; (b) uptake onto the wall of a cylindrical flow tube (inner diameter: 2.0 cm) at 296 K and at different pressures.

Figure 2 .
Figure 2. Temperature dependence of the diffusivity of OH radicals in air: comparison of measured diffusivity (Liu et al., 2009, black solid curve, left y axis) with estimated values (black dashed curve, left y axis).The ratios of estimated diffusivities to the measured ones (red curve, right x axis) are also plotted as a function of temperature.
−1 ) of A and B, and V A and V B are the dimensionless diffusion volumes of A and B, respectively.Pressure is given in Torr instead of SI units (e.g.Pa) in this work, because Torr is widely used as the pressure unit in flow tube studies and many diffusivities are reported in Torr cm 2 s −1 .The dimensionless diffusion volumes of a few simple molecules, including N 2 , O 2 , He, H 2 O, NH 3 , SO 2 , Cl 2 , and Br 2 , are listed in Table1, and the diffusion volume of air is 19.7.The diffusion volume of a molecule, if not listed in Table

Table 2 .
Summary of preferred diffusivities of atmospheric reactive trace gases in air at 296 K. Several trace gases without recommended diffusivities are also listed to highlight the necessity of further measurements.
n.m.: no measurements available

Table 3 .
Summary of measured diffusivities of HNO 3 and NH 3 , and comparison with the estimated values.

Table 5 .
Summary of measured diffusivities of SO 2 , SO 3 , H 2 SO 4 , O 3 , OH, HO 2 and H 2 O 2 , and comparison with the estimated values.

Table 6 .
Summary of measured diffusivities of halogen species, and comparison with the estimated values.