Interactive comment on “ Sulfur isotope fractionation during oxidation of sulfur dioxide : gas-phase oxidation by OH radicals and aqueous oxidation by H 2 O 2 , O 3 and iron catalysis ” by E

We thank the reviewer, Becky Alexander, for agreeing to review the manuscript and will incorporate all the suggestions for improvement. In fact, her very helpful suggestions as reviewer of the manuscript Sinha et al. (2009) have prompted us to undertake this research and perform laboratory experiments prior to any further measurements on ambient particle (Alexander 2009). We will address each comment pointwise below.


Introduction
Sulfate and sulfur dioxide play an important role in environmental chemistry and climate through their effect on aerosols.The majority of anthropogenic sulfur is released directly as SO 2 , and a significant fraction of biogenic and natural sulfur (e.g.OCS, DMS) is also either directly released as SO 2 or oxidised to SO 2 in the atmosphere (Berresheim et al., 2002;Seinfeld and Pandis, 1998).Around 50 % of global atmospheric sulfur dioxide is then oxidised to sulfate, while the rest is lost through dry and wet deposition (Chin et al., 1996).The oxidation pathway -heterogeneous or homogeneous -is an important factor because it determines the effect that sulfate will have on the environment.
Homogeneous oxidation in the gas phase by OH radicals follows several steps (Tanaka et al., 1994): Published by Copernicus Publications on behalf of the European Geosciences Union.

E. Harris et al.: Sulfur isotope fractionation during oxidation of sulfur dioxide
The product is sulfuric acid, which can stick to the surface of existing particles or nucleate to form new particles in the atmosphere (Benson et al., 2008;Kulmala et al., 2004).These new particles have a direct radiative effect and may also grow to act as cloud condensation nuclei (CCN).Heterogeneous oxidation acts upon S(IV) in solution or on particle surfaces.The major oxidants are H 2 O 2 , O 3 and O 2 , the latter being catalysed by Fe 3+ and other transition metal ions in a radical chain reaction pathway (Herrmann et al., 2000).The dissolution of SO 2 before oxidation follows several steps (Eriksen, 1972a): SO 2 (aq) + H 2 O ↔ HSO − 3 + H + (5) Equation ( 6) has a pK a of 1.77 and Eq. ( 7) has a pK a of 7.19 (Moore et al., 2005).Oxidation by H 2 O 2 is not significantly dependent on pH within normal atmospheric pH ranges (pH = 2-7), while oxidation by transition metal catalysis and O 3 becomes faster as pH increases (Seinfeld and Pandis, 1998).Heterogeneous oxidation produces sulfate on the surface of particles or in droplets, changing their CCN activity and lifetime through growth and increased hygroscopicity (Bower and Choularton, 1993;Mertes et al., 2005).Thus, a comprehensive knowledge of the oxidation and removal of SO 2 and sulfate is key to understanding and modelling aerosol and cloud formation and processes and their effects on past and future climate.Aerosol direct and indirect effects continue to contribute the largest uncertainty to estimates of anthropogenic global mean radiative forcing (IPCC, 2007).Global emissions of anthropogenic sulfur in Europe and North America have decreased significantly in the past few decades, however as Asian sulfur emissions are increasing due to energy demand and coal use, and are not expected to decrease until at least 2020 (IPCC, 2007), anthropogenic emissions are likely to remain the major global source of non-sea salt sulfate (Chin et al., 1996;Seinfeld and Pandis, 1998).Understanding the sulfur cycle is therefore necessary to reduce the uncertainty in aerosol forcing estimates.
This study presents measurements of stable sulfur isotope fractionation during gas-phase oxidation by the OH radical and oxidation in the aqueous phase with H 2 O 2 , O 3 and iron catalysis as terminating reactions.These reactions are considered to be the most important sulfur dioxide oxidation pathways on a global scale.We demonstrate that stable sulfur isotope ratios can be used to investigate partitioning between atmospheric sulfur oxidation pathways and are particularly useful to estimate the importance of radical chain reactions for the atmospheric sulfur cycle.Differentiating between gas-phase oxidation by the OH radical and oxidation in the aqueous phase by H 2 O 2 or O 3 will only be possible if stable sulphur isotope analysis is combined with studying the mass independent oxygen isotopic fractionation.

Sulfur isotopes in the environment
The isotopic composition of sulfur in the environment reflects its sources, transport and chemistry, so measurements of stable sulfur isotopes can be effectively used to constrain the sulfur cycle.Sulfur has four naturally-occurring stable isotopes: 32 S, 33 S, 34 S and 36 S. The isotopic composition of a sulfur sample is represented by its delta value, which is the permil deviation of the ratio of a heavy isotope to the most abundant isotope ( 32 S) in the sample compared to a standard ratio: where n is the number of atoms, x S is one of the heavy isotopes, 33 S, 34 S or 36 S, and V-CDT is the international sulfur isotope standard, Vienna Canyon Diablo Troilite, which has isotopic ratios of 34 S/ 32 S = 0.044163 and 33 S/ 32 S = 0.007877 (Ding et al., 2001).Chemical reactions, for example the oxidation of SO 2 to sulfate, cause fractionation of isotope ratios between reactants and products as long as the reaction does not go to completion.The fractionation may be due to equilibrium or kinetic discrimination, and is represented by the fractionation factor α.For an irreversible reaction, fractionation is kinetic and α is the ratio of the rate constants: α = k x /k 32 .When the reactant is present as an infinite reservoir and not affected by the reaction, α 34 can be calculated from the isotopic compositions of products and reactants: where R = 34 S 32 S .Thus, α>1 indicates that the heavy isotopes react faster than the light isotopes.The permil differences between reactants and products with regards to α and reaction extent in a closed system are described by the Rayleigh laws (Mariotti et al., 1981;Krouse and Grinenko, 1991), which are discussed in Sects.3.2.3 and 4.1.1.Thus, isotopic fractionation can not only distinguish between reactions: For known irreversible reactions in a closed system, the isotopic fractionation can provide quantitative information about how far the reaction has gone to completion.
The isotopic composition of many major sources of atmospheric sulfur have been measured (e.g., Rees et al., 1978;Krouse et al., 1991;Nielsen et al., 1991;Sanusi et al., 2006).The isotopic composition of anthropogenic sources is highly variable on a global scale, though individual sources are often well constrained.The isotopic composition of industrial emissions is also affected by process technology such  as the flue gas desulfurization unit of an industrial plant (Derda et al., 2007).However, for field studies measuring the isotopic composition of both ambient SO 2 and sulfate, the major limitation to interpreting atmospheric isotope measurements is the lack of laboratory studies of the isotopic fractionation factors involved in the most common atmospheric reactions of sulfur (Tanaka et al., 1994;Novak et al., 2001;Tichomirowa et al., 2007).For heterogeneous oxidation, equilibrium fractionation of 34 S/ 32 S during the uptake of SO 2 into solution and the subsequent acid-base equilibria has been measured in several studies.The results range between α het = 1.010 and 1.017 at 25 • C (Egiazarov et al., 1971;Eriksen, 1972a).So far, the isotopic effect of the terminating oxidation of S(IV) to S(VI) has not been investigated.
The kinetic fractionation during homogeneous gas-phase oxidation of SO 2 by OH radicals has been estimated to be α hom = 0.991 by ab initio calculations (Tanaka et al., 1994) or to be α hom = 1.14 by RRKM theory (Leung et al., 2001).The discrepancy between these two estimates is larger than the measured variation in atmospheric sulfur samples (Norman et al., 2006).Several atmospheric studies have also tried to infer the fractionation during this reaction.Seasonality in data, with lower δ 34 S values measured for sulfate in summer, could show that the gas-phase fractionation factor is less than the heterogeneous fractionation factor and probably less than 1 (Saltzman et al., 1983;Sinha et al., 2008a).However, seasonality may also be explained by changing sources or the temperature-dependence of fractionation factors (Caron et al., 1986;Novak et al., 2001;Ohizumi et al., 1997).The study of 17 O of sulfate trapped in ice cores showed that the ratio of gas-phase to aqueous-phase oxidation was higher and the δ 34 S was lower during the last glacial maximum than the preceeding and subsequent interglacials (Alexander et al., 2002(Alexander et al., , 2003)).The authors suggest isotopic fractionation progressively affects the SO 2 reservoir during transport as the sulfate is removed quickly, thus the data would show that α hom >α het .However, this progressive depletion in the reservoir signature has not been explicitly modelled and compared with measurements, so the isotopic composition in the icecore could be directly representative of the oxidation and show that α hom <α het .Therefore, the goal of this study is to determine sulfur isotope fractionation factors for the main oxidation pathways of SO 2 to facilitate the use of sulfur isotopes in understanding the atmospheric sulfur cycle.

Apparatus
The reaction system used to investigate the oxidation of SO 2 is shown in Fig. 1.The reactors were made of glass and their internal surfaces were coated with FEP 121a (Dupont) to minimise wall loss of H 2 SO 4 .PFA tubing and connectors were used for gas transfer between experimental components.Pressure was monitored with a capacitance manometer.The reactor had a thermostatted jacket connected to a circulating cooler (Julabo Labortechnik GmbH, Model F81-HL) to regulate temperature.The actual gasphase reaction temperature was calibrated to the set temperature of the Julabo instrument with a PT-100 resistance

E. Harris et al.: Sulfur isotope fractionation during oxidation of sulfur dioxide
sensor fitted into the glass reactor.The flows of all gases to the reactor were controlled using mass flow controllers referenced to standard conditions of temperature and pressure for N 2 (T s = 273.15K, P s = 1013.25 mBar) (MKS Instruments Deutschland GmbH, uncertainty = 0.5 % of reading plus 0.2 % of full scale), and flows and leaks were checked regularly with a Gilibrator (Sensidyne, uncertainty < 1 % of reading).SO 2 gas (Westfalen AG, Linde AG, both 102 ppm±2 % in synthetic air) was diluted with synthetic air (Westfalen AG, 20.5 % O 2 in N 2 ) to the desired concentration before it entered the reactor.The outflow from the reactor passed through the H 2 SO 4 glass and SO 2 bubbler collectors, described in detail in Sect.3.4.The length of tubing from the reactor to the H 2 SO 4 collectors was <7 cm, which would lead to a maximum of ∼22 % loss of H 2 SO 4 according to the wall loss calculations from Zasypkin et al. (1997) (Eq. 15).This will be higher than the actual wall loss as the estimate is for glass and not PFA.The sulfuric acid will at this stage be nucleated (see Section 3.4.1),thus the isotopic effect will be negligible as the relative mass difference due to an isotopic substitution in a particle will be 1 %.Most experiments were run for 7-8 h to generate sufficient product for isotopic analysis.The exact conditions of each experiment are detailed in the relevant section.Following each experiment, the collection systems were emptied immediately.The solution from the SO 2 bubblers, containing hydrogen peroxide and sulfate, was poured into a clean beaker and the bubblers were rinsed with MilliQ water several times into the beaker.The H 2 SO 4 trap was rinsed at least five times with MilliQ water to remove all the adsorbed H 2 SO 4 , and the solution was collected in a beaker.An excess of BaCl 2 was added to each solution to precipitate S(VI) as BaSO 4 , as well as sufficient HCl to lower the pH to approximately 3 for optimal precipitation (Rees and Holt, 1991).After at least 12 h to ensure complete precipitation, the solutions were filtered through Nuclepore track-etch polycarbonate membrane filters (Whatman Ltd.) with 0.2 µm pores, which had been coated with a 10 nm thick gold layer using a sputter coater (Bal-tec GmbH, Model SCD-050) prior to sample collection.Several rinses with MilliQ water removed any remaining BaCl 2 from the BaSO 4 precipitate and the filters were dried at room temperature.Samples with a large amount of material, where sulfate grains were clumped in groups, were gold-coated to prevent charging during SEM and NanoSIMS analysis.

Aqueous oxidation by the radical chain reaction mechanism
Aqueous oxidation by a radical chain reaction initiated by Fe 3+ (Herrmann et al., 2000) was measured by bubbling SO 2 through a solution containing 0.1 M Fe(Cl) 2 and 0.1 M Fe(Cl) 3 .The product sulfate was collected from two bub-blers in series.The quantity and isotopic composition of the sulfate in the second bubbler was equal to that in the first bubbler, showing the SO 2 was not significantly depleted.

Aqueous oxidation by H 2 O 2 in bulk aqueous phase
SO 2 gas was collected by bubbling through a solution of 6 % H 2 O 2 in an ice bath, thus the fractionation during collection of SO 2 is a direct measure of the fractionation during oxidation of SO 2 by H 2 O 2 in solution at 0 • C under nonequilibrium conditions.This reaction was run eight times under a variety of conditions to fully characterise collection of SO 2 as described later in Section 3.4.2,and these experiments gave a robust value for the fractionation of sulfur isotopes during oxidation of SO 2 by H 2 O 2 .

Aqueous oxidation by H 2 O 2 and O 3 in droplets
Oxidation by H 2 O 2 and O 3 in the atmosphere occurs primarily in droplets and not in the bulk phase, thus it is necessary to investigate whether droplet-specific effects such as surface tension, the difference in saturation vapour pressure over a curved surface compared to a bulk solution, and changes in droplet pH as the reaction proceeds, affect the isotopic fractionation.
Reactor 2 (Fig. 1) did not produce detectable OH (see Sect. 3.3.1 for details of OH quantification) at the reaction point where the humid, UV-irradiated air was mixed with the SO 2 flow.A small amount of OH was generated at the lamp tip in this reactor, however the residence time of humidifed air at the lamp was short and all OH generated was lost before reaching the reaction point.H 2 O 2 was produced following H 2 O photolysis to OH, and as the lifetime of H 2 O 2 is longer than that of the OH radical, ∼5 ppbv (mol mol −1 gas at atmospheric pressure; ppbv will only be used to discuss gas phase concentrations in this paper) of H 2 O 2 is present at the reaction point.O 3 resulted from O 2 photolysis and was present at concentrations of >10 ppmv at the reaction point.
The reaction was therefore run in Reactor 2 at close to 100 % relative humidity to investigate aqueous oxidation by H 2 O 2 and O 3 in droplets rather than a bulk solution in the absence of OH.The experiments were run at room temperature.Humid air was generated by bubbling synthetic air through water and was added both through the photolysis tube and through a second entry into the reactor normally used to monitor pressure.Neither flow passed through a trap to break up or remove large droplets and the humidity was negligibly reduced by the addition of 10 sccm dry SO 2 gas to make a total flow of 600 sccm, so the reactor was operated at 98 % relative humidity in the presence of droplets.Although oxidation by ozone would initially dominate, the pH in the system would very quickly decrease as sulfate was generated so the bulk of the reaction would be due to H 2 O 2 (Seinfeld and Pandis, 1998).A very large amount of product (>1 mg) was generated, which significantly altered the isotopic composition of the SO 2 gas.The fractionation factor α must therefore be found from the Rayleigh equations for residual reactants and products (Mariotti et al., 1981;Nriagu et al., 1991): where f is the fraction of reactant (SO 2 ) remaining after the reaction time (residence time = 26 seconds) and R 0 , R R and R P are the isotope ratios 34 S/ 32 S for the initial gas, the residual reactant and the product respectively.The reaction extent can be found from the isotopic mass balance: where δ 34 S i is the initial composition of SO 2 and δ 34 S SO 2 and δ 34 S H 2 SO 4 are the isotopic compositions of residual SO 2 and product H 2 SO 4 when a fraction f of the initial SO 2 remains.Around 65 % of SO 2 was oxidised under high humidity conditions.
To isolate the effect of O 3 on the product isotopic composition, the reaction was run with a glass attachment that passed dry synthetic air over the Hg lamp to generate 1000 ppm ozone.As the photolysed air was dry the H 2 O 2 concentration will be negligible.Humidified air at 40 % relative humidity was added to the reactor and was not exposed to UV light.The product sulfate and the residual SO 2 were collected and there was no significant change in the SO 2 isotopic composition.

Gas-phase oxidation
OH radicals were generated from the photolysis of water vapour, and allowed to react with SO 2 in the reactor shown in Fig. 1.The SO 2 concentration was much higher than the OH concentration so the isotopic composition of SO 2 was not significantly affected by the reaction.The sulfuric acid gas product was collected, as described previously in Sect.
3.1, to determine the value of the fractionation factor for the reaction of SO 2 and OH.

OH generation
OH was generated from the photolysis of water vapour at around 30 % relative humidity.100 sccm of humidified nitrogen was passed over a low-pressure mercury vapour lamp (Jelight Company Inc., USA), which produces light at 184.9 nm resulting in the generation of OH radicals (Cantrell et al., 1997): The OH concentration was determined by chemical titration with pyrrole (Sinha et al., 2008b(Sinha et al., , 2009)), which entered the reactor through the SO 2 inlet and thus saw the same OH flux as SO 2 .Two similar reactors were used to measure the OH + SO 2 reaction and the influence of potential interfering reactions (Fig. 1).Reactor 1 produced 11 ppbv of OH.Reactor 2 did not produce detectable OH at the reaction point and was used to measure interferences.A small amount of OH would have been generated at the lamp tip, however the residence time of humidifed water at the lamp was short and all OH generated was lost before entering the reactor.
The OH concentration is dependent on the water vapour concentration (Young et al., 2008).In these experiments the relative humidity is kept constant by passing the humid air stream through glass wool held at the reaction temperature, in order to remove excess humidity and large droplets so that aqueous oxidation is minimised, thus the water vapour concentration will change exponentially with temperature according to the vapour pressure of water.The quantity of sulfate produced at the four different reaction temperatures was measured as described in Sect.3.5.2and found to follow the expected exponential relationship as shown in Fig. 2b.

H 2 SO 4 collection
Sulfate is removed from the gas stream by passing through two 40-cm long glass vessels with a rough inside wall, which will increase turbulence and internal surface area (Fig. 1).Two forms of sulfate product need to be collected in the experiments: 1. Aqueous droplet oxidation will results in water droplets containing sulfate.These will be lost to the glass walls by gravitational settling and by electrostatic attraction, which leads to collisions with the walls (Lai, 2006).This is a bulk process and is assumed not to introduce a significant isotopic effect, and will be very efficient given the length and roughness of the collectors.
2. Sulfuric acid gas will initially be produced in the gasphase oxidation experiments but will nucleate to form particles of 1.5-2 nm diameter as the concentration of H 2 SO 4 is >0.01-0.1 of the saturation vapour pressure (33 ppbv for 99 % H 2 SO 4 ) (Kulmala et al., 2004(Kulmala et al., , 2007)).
The loss of H 2 SO 4 (g) to the walls of glass vessels is described by: where [H 2 SO 4 ] 0 and [H 2 SO 4 ] t are the gas phase concentrations of H 2 SO 4 at time = 0 and time = t, k is the diffusion-limited first order reaction coefficient: k = 3.65 D r 2 , D is the diffusion coefficient and r is the radius of the reactor (Zasypkin et al., 1997;Young et al., 2008).D = 0.095 cm 2 s −1 in dry air at atmospheric pressure and decreases to 0.075 cm 2 s −1 at high humidity (Hanson and Eisele, 2000).These equations apply only to well-established laminar flow conditions in a cylindrical reactor and can provide a lower limit to wall loss in this system.Nanoparticles in the size range of 2 nm will follow Brownian motion, like the sulfuric acid gas molecules, thus the wall loss calculation can be extended to estimate the loss of these ultrafine particles.The diffusion coefficient for 2 nm particles is ∼0.035 cm 2 s −1 (extrapolated from Rudyak et al. (2009)), so the predicted wall loss will be >97 % in the two condensers.The actual wall loss will be considerably higher than predicted as turbulence and electrostatic attraction in the system will increase the frequency of collisions with the walls.At this efficiency, there should be no significant difference between the initial and the product isotopic composition.
No isotopic standard of gaseous H 2 SO 4 was available, so the fractionation during collection was measured by analysing the product from two collectors arranged in series.A flow of N 2 6.0 (Westfalen AG) was passed through a 1 M solution of H 2 SO 4 and the resulting mixture flowed through the two 40 cm-long glass collection vessels.This experiment will involve collection primarily of sulfuric acid droplets and not gas, however the results are relevant to the collection in the experiments since the gas-phase experiments will primarily result in freshly-nucleated particles while the aqueous droplet phase experiments will result in sulfate in droplets.
Following the experiment, the collectors were rinsed and sulfate was precipitated by adding BaCl 2 and analysed as described in Sect.3.5.The average measured differences between the δ 34 S and δ 33 S of the two collectors are −1.1±2.6 ‰ and −0.3±1.5 ‰ respectively, showing that there is no systematic fractionation introduced beyond the precision of the measurement (Table 1).A small or insignificant difference between the two collectors can only be achieved with a low collection efficiency or a fractionation factor close to 1, otherwise the δ 34 S and δ 33 S of the H 2 SO 4 entering the second collector would be altered by the first collector.A high efficiency was theoretically predicted, and supported by the fact that very little product was seen on the second filter during analysis.Therefore, the fractionation introduced by this collection method is insignificant and the δ 33 S and δ 34 S of H 2 SO 4 in later experiments does not need to be corrected for an isotopic change during collection.
It is important to consider possible breakthrough of H 2 SO 4 gas to the SO 2 gas collection system.Although H 2 SO 4 is efficiently removed, when the H 2 SO 4 concentration was more than three times as high as the SO 2 concentration, breakthrough of H 2 SO 4 could be detected in the isotopic composition of SO 2 .The sensitivity of the isotopic composition of the SO 2 to breakthrough also depends on the difference in δ 34 S between SO 2 and H 2 SO 4 .To completely avoid effects from breakthrough of H 2 SO 4 the reaction yield was kept below two thirds of the total SO 2 .

SO 2 collection
Sulfur dioxide is traditionally collected on filters impregnated with alkaline solutions such as Na 2 CO 3 (Novak et al., 2001;Huygen, 1963).A variety of solutions were tested with varying amounts of Na 2 CO 3 , BaCl 2 , triethanolamine, glycerol and H 2 O 2 , and the average fractionation factor was measured as α 34 = 1.007±0.003for all methods tested.The recovery of SO 2 was found to vary from less than 5 % to more than 40 % depending on the length of time that SO 2 was collected and the amount taken up relative to the alkalinity capacity of the filter, rather than on the solution composition.The fractionation in the final product could then vary from at least 4.5 to 10.6 ‰, with even larger variations introduced for longer experiments or very high filter loads.This method of collection is not suitable for our laboratory experiments due to the low relative humidity and high concentrations of SO 2 in our samples combined with the need for a constant, correctable isotopic fractionation.
Alternatively, SO 2 can be collected by passing the gas stream through bubblers containing hydrogen peroxide, which oxidises the S(IV) in the solution to sulfate (US-EPA, 2010).This method was tested by passing SO 2 of known isotopic composition (δ 34 S = 1.25±0.3‰) through two bubblers in series containing a solution of 6 % hydrogen peroxide, held at 0 °C in an ice bath to increase SO 2 solubility (Fig. 1).Following the experiment a BaSO 4 precipitate was prepared by adding BaCl 2 , and the precipitate was collected on a gold-coated Nuclepore filter.This experiment was repeated eight times, seven of which were analysed with the NanoSIMS as described in Sect.3.5.3.One sample was analysed by traditional dual-inlet isotope ratio mass spectrometry at the Massachusetts Institute of Technology according to the methods described in Ono et al. (2006).The reaction conditions are shown in Table 2.

Scanning electron microscopy
A LEO 1530 field emission scanning electron microscope (SEM) with an Oxford Instruments ultra-thin-window energy-dispersive x-ray detector (EDX) was used to locate and characterise particles before NanoSIMS analysis.The samples were directly analysed in the SEM after collection on gold-coated filters without any further treatment.The SEM was operated with an accelerating voltage of between 10 and 20 keV, a 60 µm aperture and a working distance of 9.6 mm."High current mode" was used to increase the EDX signal and improve elemental sensitivity.All samples were viewed with the SEM to investigate the coverage, size and shape of sulfate grains.A transfer of the coordinate system between the NanoSIMS and the SEM is possible using several well-defined origin points, which allows the same grain or area to be found and analysed in both instruments.An example of a barium sulfate grain with its EDX spectrum is shown in Fig. 3.

Quantification with the SEM
The EDX spectrum can be used to roughly quantify compounds and particles on the filters, and thus estimate the extent of reactions.An automatic analysis of the filter is taken, with EDX analysis points distributed at regular intervals in each image.As long as the diameter of the largest particle is smaller than the distance between EDX points, the probability of the point falling on a particular particle is proportional to the area covered by that type of particle (Winterholler, 2007).Moreover, if an element is just in one form, for example sulfur is only present as BaSO 4 , the number of points with a sulfur signal will be proportional to the area covered by BaSO 4 .The volume and hence mass of BaSO 4 can be found by considering the average height of the BaSO 4 grains, as long as it is evenly distributed and not clumped in large heaps.The sample height was estimated to be 0.2 µm based on the movement in the Z-direction of the microscope needed to focus on the filter and on the top of a representative number of BaSO 4 grains.The largest source of uncertainty for quantification of the collected BaSO 4 is that grains can flake off the filter during handling of the samples.
The presence of a "signal" for an element in this quantification method requires differentiating between background noise and actual signal.Quantifying sulfur compounds on gold filters is challenging, because the gold peak overlaps strongly with the sulfur peak, as shown in Fig. 3.The contribution of the gold peak to the sulfur peak approximately follows a Gaussian distribution, as gold is present in all sampled EDX points.An example is shown in Fig. 4. The sulfur signal is superimposed on the Gaussian distribution of the gold signal, as the X-ray emission depth and spot size means the gold signal will always be present even when the sampling point falls on a barium sulfate grain (Goldstein et al., 1981).Thus, the presence of a significant sulfur signal was defined as falling above the 99.9 % confidence limit for the gold Gaussian distribution (x > µ + 3.09σ ).The contribution of S in BaSO 4 to the signal in the sulfur channel shows a peak, however the number of sulfur points is too low to calculate the Gaussian distribution for these samples.To account for the tail of the Gaussian curve of Au that is above the 3.09σ limit, which could be a large part of the signal at low sulfate concentrations, the integrated background (bcg)  above the 3.09σ limit was subtracted, and the number of points with a significant sulfur signal was defined as: The Gaussian curve does not always fit cleanly to the data.For samples where the area coverage is significantly less than 25 %, a second estimate of the 3σ limit can be approximated by Q u + 1.726(Q u -Q l ), where Q u and Q l are the upper and lower quartiles of the raw signal for the element of interest.This has previously been used to define the background of an SEM-EDX signal for a similar quantification method (Winterholler, 2007;Stoyan, 1998).EDX points with the signal for both barium and sulfur above the background are then 1.0118 0.0040 1.0048 0.0019 radical chain 0.9894 0.0043 0.9928 0.0022 used to quantify BaSO 4 .The quantity of sulfate measured for a sample with the two methods has an average uncertainty of 40 % and shows no systematic offset.The sulfate production in each experiment is an average of at least two duplicate samples both measured with the two methods.The limit of detection for quantification is the amount of sulfate when only one point shows a significant signal, and thus it depends on the total number of points taken.For most samples 10 000 EDX points were measured, giving a detection limit of 0.2 nmol of sulfate, or 0.18 ppbv at the typical flow rate of 600 sccm.

NanoSIMS
The sulfur isotopic composition was determined with the Cameca NanoSIMS 50 ion probe at the Max Planck Institute for Chemistry in Mainz (Hoppe, 2006;Groener and Hoppe, 2006).The NanoSIMS 50 has a high lateral resolution (<100 nm) and high sensitivity and can simultaneously measure up to five different masses through a multicollection system, allowing high precision analysis of the small sample quantities ( 1 mg) required for this study.The use of this instrument to analyse sulfur isotope ratios is described in detail elsewhere (Winterholler et al., 2006(Winterholler et al., , 2008)), and only a brief description will be given here.
BaSO 4 is analysed directly without further processing after it is collected on gold-coated filters as described in Sect.3.1.A ∼1 pA Cs + beam is focussed onto a ∼100 nm sized spot and rastered in a 2 µm×2 µm grid over the grain of interest.The ejected secondary ions are carried into the mass spectrometer and multicollection system.Each measurement consists of 200-400 cycles of 4.096 s duration preceded by varying lengths of presputtering until the gold coating is removed and the count rate is stable.Presputtering is carried out on an area of at least 10 µm×10 µm to avoid crater effects in the analysed area.Secondary ions of 16 O − , 32 S − , 33 S − , 34 S − and 36 S − were simultaneously detected in five electron multipliers at high mass resolution (M/ M >3900 for 33 S).The detector dead time is 44 ns and the count rates were corrected accordingly.The energy slit was set at a bandpass of 20 eV and the transmission was set at 15-20 % with the fifth entrance slit (10×100 µm) and the fourth aperture slit (80×80 µm) in order to reduce the effect of quasisimultaneous arrival (QSA; Slodzian et al. (2001)).
Mass-dependent and mass-independent instrumental mass fractionation (IMF) can occur at several stages of the SIMS analysis, so the IMF correction factor in each measurement session is determined with the commercially available BaSO 4 isotope standards IAEA-SO5 and IAEA-SO6.Correction for the quasi-simultaneous arrival (QSA) effect was carried out as described by Slodzian et al. (2004), however a factor of 0.75 rather than 0.69 was used as this minimised the dependence on count rate best for these samples.
The number of counts is assumed to follow a Poisson distribution, so the counting statistical error is √ n, i.e. the relative error is 1/ √ n (Bevington and Robinson, 1992).Some spot-to-spot variation is also seen between individual measurements on a filter, most likely due to topographic effects or nanoscale inhomogeneity.Thus, at least five grains on each sample filter were measured, and a weighted average was calculated using 1/σ 2 for the weighting function, where σ is the counting statistical error of individual measurements.To calculate the overall measurement uncertainty the error of the weighted mean is multiplied by χ 2 for χ 2 >1 in order to account for the larger uncertainty introduced by the spotto-spot variability.The counting statistical error was typically 1-2 ‰ and the overall error for each sample 2-5 ‰.

Aqueous oxidation
The fractionation factors during aqueous oxidation by H 2 O 2 , O 3 and radical chain reaction initiated by Fe are shown in Fig. 5 and Table 3.All oxidants other than O 3 produce massdependent fractionation, and the deviation from the mass- dependent fractionation line seen for O 3 is almost certainly a measurement artefact as only two samples were measured. 33S measurements with the NanoSIMS are more uncertain than 34 S measurements.They can be systematically inaccurate on a individual filter due to factors such as a change in the interference from 32 SH between the sample and the standard; thus they are only reliable if a larger number of samples are measured.The radical chain reaction, which has a fractionation factor of α 34 = 0.9894±0.0043at 19 • C, is the only measured aqueous reaction to favour the light isotope.This agrees relatively well with measurements by Saltzman et al. (1983), where a fractionation factor of 0.996 for oxidation of HSO − 3 by dissolved O 2 was indicated by laboratory experiments.

Isotopic fractionation during SO 2 collection
SO 2 was collected by bubbling through a solution of H 2 O 2 , which oxidises the S(IV) to sulfate.The collection is not complete, and as >1 % of SO 2 is oxidised it can no longer be considered an unchanged reservoir.Thus the isotopic composition of the product depends on the value of the kinetic fractionation factor α (= k 34 /k 32 ) and the fraction of reactant remaining, as described by the Rayleigh fractionation laws (Mariotti et al., 1981;Nriagu et al., 1991).Equation ( 12) from Sect.3.2.3 can be used directly for the first bubbler, and adapted to represent the second bubblers in series: where α 2 is the value of α 34 calculated from the second bubbler, f is the fraction of reactant (SO 2 ) remaining and R 0 ,

E. Harris et al.: Sulfur isotope fractionation during oxidation of sulfur dioxide
and R P 2 are the isotope ratios 34 S/ 32 S for the initial gas and the product of the second bubbler respectively.R * 0 is the initial isotopic composition entering the second bubbler, that is, the residual SO 2 remaining after the first bubbler: The collection efficiency (1 − f ) must be known to find α from these equations.Grains can flake off the filter during handling when a large amount of product is present (i.e. a layer rather than individual grains), leading to greater losses from the filter from the first bubbler as it has more product.Thus quantification by SEM-EDX as described in Sect.3.5.2does not give an accurate value for f .Gravimetric determination of f is not possible due to the interference from coprecipitated BaCl 2 and the very small quantities of sulfate on the second filter.The fraction of SO 2 remaining was therefore determined as the value that would give an equal α for the first and second collectors, found for each experiment by iteration with Eqs. ( 12) and ( 17).The weighted average of the individual values shows that 39 % of SO 2 is collected per bubbler.The total collection efficiency of two bubblers in series is 63±11 %.A higher concentration of H 2 O 2 may be expected to improve collection efficiency, however this was not possible as it resulted in destruction of the gold-coating on the filters during filtering to collect BaSO 4 .
Equations ( 12) and ( 17) were then used to find α for each bubbler measurement.The reaction conditions and results are shown in Table 2 and Fig. 6.The weighted average α 34 is 1.0160±0.0013at 0 • C, which results in a product δ 34 S change of +9.2±0.7 ‰ following the two bubblers.This is consistent with expectations for aqueous oxidation by H 2 O 2 (Eriksen, 1972a;Egiazarov et al., 1971) and is robust over a large range of flows and SO 2 concentrations.The gas temperature does not affect the measured fractionation since the collector is held at 0 • C and the quantity of gas passed through the sampling system is not sufficient to change the temperature within the collection system.
Measurements of δ 33 S by NanoSIMS are more uncertain than δ 34 S due to counting statistics.The measured α 33 is 1.007±0.002,which is not significantly different from the value expected for mass-dependent fractionation (MDF: α 33 /α 34 = 0.515, t-test, P = 0.05).The mass-dependent nature of the fractionation is confirmed by the high precision fluorination measurement of Sample 8, which showed 33 S = 0.05 ‰.The change in δ 34 S SO 2 and δ 33 S SO 2 due to reactions of interest in all other experiments can be isolated by considering the measured fractionation due to collection and the initial isotopic composition.

Temperature-dependence of fractionation during oxidation by H 2 O 2 and O 3
Several previous studies have considered the fractionation during aqueous SO 2 oxidation and the combined results are presented in Fig. 7.The weighted linear fit to all points shown in Fig. 7 (except those for SO 2 (g) ↔ SO 2 (aq)) shows that: where T is the temperature in degrees celsius.There is no significant difference between the α 34 at 19 • C measured for H 2 O 2 /O 3 (α 34 = 1.0118 ± 0.0040) and O 3 (α 34 = 1.0174 ± 0.0028) in droplets and the bulk H 2 O 2 measurements (α 34 = 1.0151 ± 0.0013).This shows that droplet-specific effects do not affect isotopic fractionation, and thus the results of bulk phase experiments are relevant to atmospheric reactions, which will primarily occur in droplets.The droplet measurements have a larger uncertainty, which is due to small variations in reaction conditions, particularly relative humidity.The previous studies do not consider oxidation to S(VI) (see Eqs. ( 4)-( 8)), and comparison of the measured fractionation can show which stages of the reaction are most important for isotopic fractionation.Chmielewski et al. (2002) and Eriksen (1972b) consider only the equilibrium SO 2 (g)↔SO 2 (aq) and measure a much lower fractionation factor (α = 1.00256 at 10 • C).This shows that physical phase transfer is responsible for only a small part of isotopic fractionation, and protonation and acid-base equilibria in solution cause the majority of fractionation for the SO 2 (g)-S(IV) (aq) system.
The results of Egiazarov et al. (1971) and Eriksen (1972a,b,c,d) compare well with the results of the present study, although these earlier studies both consider only the equilibrium to S(IV) in solution while this study includes oxidation to S(VI).This shows that the terminating oxidation reaction has a negligible effect on isotopic fractionation,  Egiazarov, 1971Eriksen, 1972Chmielewski, 2002 SO 2 (g) SO 2 (aq): Eriksen, 1972 SO 2 (g) sulfate (aq) (this study): SO 2 (g) S(IV) (aq): explaining why H 2 O 2 and O 3 produce the same fractionation factors despite very different mechanisms (Savarino et al., 2000).Eriksen (1972a) considers the equilibrium between 1 M NaHSO 3 at low pH as acid is constantly added to the system, thus the concentration of SO 2− 3 will be negligible.The experiments of Egiazarov et al. (1971) consider the equilibration of 3 M NaHSO 3 at pH≈4, so unlike Eriksen (1972a) these results will include some equilibration to SO 2− 3 as well as significant production of S 2 O 2− 5 .The fractionation factor measured by Egiazarov et al. (1971) (α = 1.0173±0.0003at 25 • C) is slightly higher than the fractionation factor measured by Eriksen (1972a) (α = 1.01033±0.00041at 25 • C), suggesting that equilibration towards higher-pH forms of S(IV) introduces a further enrichment of 34 S. The rate of S(IV) oxidation by O 3 increases by several orders of magnitude as the pH increases above 5.5 (Botha et al., 1994), and the fractionation factor measured for O 3 in this study (α = 1.0174±0.0028) is slightly higher than that measured for H 2 O 2 oxidation (α = 1.0151±0.0013),supporting the hypothesis that equilibration to higher pH increases fractionation, while the terminating oxidation to O 3 may have little effect on isotopic fractionation.Results investigating the isotopic effect of flue gas desulfurization provide another value of the fractionation factor at high pH for comparison: Derda et al. (2007) measured α 34 of 1.0026 for aqueous oxidation in a wet lime solution producing gypsum (the fractionation factor has been adjusted to have the same definition as the present study).This would provide a first estimate for the isotope fractionation during oxidation in an alkaline solution, but meaningful comparison with the results obtained in the present study is difficult, since an industrial scale process is not comparable to the carefully controlled environment of a laboratory reactor, and the process temperature has not been reported by Derda et al. (2007).The difference between measured fractionation during oxidation by O 3 and H 2 O 2 in this study is not significant considering the experimental error and a more detailed study of the pH-dependence of this sys-tem would be needed to fully resolve isotopic effects for each step in the pathway from SO 2 (g) → sulfate.

Quantification of interferences
Before calculating fractionation factors for SO 2 oxidation by OH radicals, a consideration of interferences from background sulfate is necessary.Possible interferences are sulfate impurities in reagents, direct photolysis of SO 2 , and reaction in the gaseous or aqueous phase with oxidants such as H 2 O 2 , HO 2 and O 3 , which are also generated during the photolysis of water (Atkinson et al., 2004).SO 2 photolysis can follow a number of pathways under UV light (Farquhar et al., 2001).The wavelength-dependent quantum yield of the different pathways is not well known and the fractionation occurring is not well-constrained (Farquhar et al., 2001;Lyons, 2009).The gas phase reactions of SO 2 with photochemical products other than OH are very slow (Atkinson et al., 2004), however oxidation on glass surfaces with adsorbed water could lead to sulfate production.
The trace sulfate content present in the MilliQ water used to rinse the product sulfate from the collectors was tested by adding BaCl 2 to 500 mL of MilliQ water.The BaSO 4 was then collected and quantified in the SEM.The effect of this blank (1.6±1 µg L −1 ) on the measured sulfate concentration was then converted to mol of blank per mole of sulfur produced during the experiment based on the volume of MilliQ used to wash the collectors and the quantity of sulfate produced in the individual experiment.The interference from sulfate impurities in MilliQ water contributed 6 % by mass of the total sulfate at −25 • C and less than 2.5 % of sulfate for all other temperatures.The equivalent in ppbv based on the average volume of MilliQ used to wash the collectors and the quantity of sulfate produced for an 8-h experiment considering flow rate, concentration temperature and pressure is shown in Fig. 2.
Oxidation by photochemical products other than OH, such as H 2 O 2 , HO 2 and O 3 , was tested with Reactor 2, which passed water vapour through UV light but did not produce detectable OH at the reaction point.A numerical simulation (Facsimile model, MCPA Software, Ltd.) of the chemical processes involved was run to investigate the species that would be present in the reactor following the photolysis of water, and may oxidise SO 2 .The species produced by Reactor 1 for the photolysis of water in synthetic air to generate 11 ppbv OH followed by immediate mixing with 1 ppm SO 2 are shown in Fig. 8.
Direct photolysis of SO 2 was measured by adding humidity 10 cm after the lamp, to ensure the water was not photolysed while allowing the reaction SO 3 + H 2 O → H 2 SO 4 to occur.This was done with both Reactors 1 and 2 so that direct photolysis of SO 2 and reaction with other lamp products, discussed in the previous paragraph, could be separated.The rate of pyrrole photolysis was measured to be the same for both reactors, so it can be assumed that the photolysis of SO 2 is also comparable between the two reactors.Direct photolysis was measured with both the standard Hg lamp, which produces 185 and 254 nm lines, and with an O 3 -free Hg lamp, which emits only the 254 nm line.The whole reaction system was also run with no lamps switched on to measure the quantity of sulfate oxidised by trace compounds in the water or glass walls.The quantification of these interferences is shown in Fig. 2. No sulfate was measured when SO 2 was run through the reaction system in the absence of humidity.
The quantity of sulfate produced under UV light does not significantly differ between Reactors 1 and 2, O 3 -free or normal Hg lamps, and whether humidity is passed over the lamp or not.Thus, all experiments with UV light were combined to find a background of 0.60±0.40ppbv sulfate in the absence of OH radicals at room temperature.The quantity of sulfate produced in the absence of UV light was 1.04±0.10ppbv, i.e., compatible with the former value within errors, and the δ 34 S values of the products in experiments with irradiation are not significantly different from the δ 34 S of the products in the absence of UV light (Fig. 9), thus the background sulfate is not due to irradiation.The quantity of sulfate collected in the absence of OH radicals was found to have an exponential relationship to temperature and thus was proportional to water vapour pressure.The measured temperature dependencies of sulfate quantity for no OH and OH experiments were adequately described by exponential curves and the fits were used to quantify the percentage contribution of the background to the total sulfate at each experimental temperature.The reaction of interest, SO 2 + OH, contributes between 77 and 85 % of the total collected sulfate, depending on the reaction temperature.As the average isotopic composition of the background (δ 34 S = 13.0±1.5 ‰) is consistent with that expected from aqueous oxidation (δ 34 S = 15.1±1.3‰), and the quantity of  background sulfate varies with the vapour pressure of water, it can be assumed the background sulfate reaction is aqueous oxidation due to an impurity in the water or an oxidation reaction in an H 2 O surface layer on the glass walls of the collector.As the fractionation for aqueous oxidation has a much lower uncertainty due to the large number of measurements and its temperature dependence is known, it can be used to correct for the background in the SO 2 + OH reaction.

Isotopic fractionation during the gas-phase oxidation of SO 2 by OH radicals
The oxidation of SO 2 by OH radicals in the gas phase was measured at four different temperatures in twelve individual experiments.The results are presented in Table 4 and Fig. 10.The correction for aqueous background oxidation as described in Sect.4.2.1 has only a small effect on the results as it accounts for less than 25 % of sulfate production.
The weighted fit to all points gives a temperature-dependent fractionation factor for 34 S of: The measured fractionation factor for 33 S is This is not significantly different from the fractionation of 33 S predicted from a mass-dependent relationship to 34 S.
Ab initio calculations using transition state theory for the reaction SO 2 + OH → HOSO 2 by Tanaka et al. (1994) estimated a fractionation factor for 34 S/ 32 S of 0.991, similar in magnitude but opposite in direction to the fractionation factor measured in this study.Leung et al. (2001) calculated the fractionation factor to be 1.14 based on RRKM theory.They found that although the positive difference in critical energies of the transition states would lead to a fractionation factor of <1, this is overcome by the denser vibrational manifolds of the 34 S transition state.However, the authors state that even considering the uncertainties in all parameters used they predict a fractionation factor > 1.07, almost 10 times larger in magnitude than the factor measured in this study.Even a fractionation factor of 1.07 rather than 1.14 is significantly larger than the variation observed in atmospheric samples (e.g.Norman et al. (2006); Novak et al. (2001)), so it is likely that RRKM theory can accurately predict only the direction and not the magnitude of this isotope effect.This is in agreement with recent results from Lin et al. (2011) andHattori et al. (2011), which found a similar overprediction of the sulfur isotopic fractionation during the photolysis of OCS by RRKM theory (Leung et al., 2002).

Comparison to previous studies
A number of studies have used field measurements to estimate the value of the fractionation factors for SO 2 oxidation.Atmospheric measurements of δ 34 S SO 4 and (δ 34 S SO 4 − δ 34 S SO 2 ) are often lower in summer than in winter (Mukai et al., 2001;Mayer et al., 1995;Saltzman et al., 1983).Oxidation by OH is expected to be highest in summer and this may therefore show that the fractionation factor for gas-phase oxidation is lower than that for aqueous oxidation, in agreement with the results of this study.Observations that sometimes δ 34 S SO 4 <δ 34 S SO 2 have previously been suggested to show that α OH <1, however the results of this study point to a dominance of transition-metal catalysed oxidation for these samples.Seasonality is not a direct measurement of oxidation and fractionation but reflects changing sources and oxidation pathways as well as lifetime and removal mechanisms such as dry and wet deposition.Hence, in order to estimate fractionation factors from seasonal data, seasonal changes in oxidant concentrations, local sources and climatic conditions would need to be considered very carefully.
The δ 34 S of stratospheric sulfate aerosol has been observed to first increase and then strongly decrease in the months following the eruption of Mt.Agung (Castleman et al., 1974), consistent with stratospheric oxidation favouring 34 S and progressively depleting the SO 2 reservoir.This was suggested to show that oxidation by OH favours the heavy isotope, as OH is normally the dominant stratospheric oxidant for SO 2 (Leung et al., 2001).However, strong 33 S signals found in ice core records of volcanic sulfate of the same event suggest photochemical oxidation is the dominant process producing these aerosols: The huge amount of SO 2 released during the eruption depletes the stratosphere of OH which means oxidation pathways, such as photolysis, which are normally not important in stratospheric SO 2 oxidation can begin to have a significant effect (Savarino et al., 2003a,b,c;Baroni et al., 2007Baroni et al., , 2008)).The contribution of OH and other oxidation pathways to oxidation of SO 2 following a stratospheric volcanic eruption are not well constrained, thus measurements from these eruptions are not reliable indicators of the magnitude and direction of α OH .
Interglacial-glacial changes in 17 O of ice core sulfate can provide information on the oxidation pathways of sulfur due to the large 17 O signal in O 3 and the smaller but significant 17 O signal in H 2 O 2 (Sofen et al., 2011;Alexander et al., 2002Alexander et al., , 2003;;Savarino et al., 2000).Transition metalcatalysed oxidation by O 2 and gas phase oxidation by OH both result in 17 O very close to 0 ‰ (Luz and Barkan, 2005;Sofen et al., 2011).The 17 O of ice core sulfate was larger in the surrounding interglacials than in the last glacial period, showing that oxidation by H 2 O 2 and O 3 was proportionally more important in the interglacial periods.The δ 34 S of sulfate was measured to be lower during glacial periods than surrounding interglacials (Alexander et al., 2003).It has been suggested that this shows a progressive depletion in 34 S during transport of SO 2 from lower latitude source regions, based on the α OH of > 1.07 from Leung et al. (2001).However, the results of this study suggest that the fractionation signature is directly transferred to ice-core sulfate, and increased oxidation by transition metal catalysis due to higher abundance of windblow dust could account for the lower values of δ 34 S measured in glacial periods.Considering the preindustrial partitioning between the sulfate production pathways from Sofen et al. (2011) and the fractionation factors  2011) and δ 34 S values of sources are from Rees et al. (1978), Krouse et al. (1991), Nielsen et al. (1991) and Sanusi et al. (2006).
measured in this study, the overall preindustrial change in δ 34 S between SO 2 and product sulfate would be +5.5‰.Alexander et al. (2003) saw a decrease in δ 34 S nss of ∼3‰ during glacial periods, which would mean a change in δ 34 S between SO 2 and product sulfate of +2.5‰ if sources were unchanged.Oxidation by transitional metal catalysis would need to increase from 8 % to 35 % of the total sulfate production to account for this change if the proportions of sulfate produced from the other oxidation pathways and the overall sulfur budget remained the same.A 10 % increase in transition-metal catalysed sulfate production was modelled for the pre-industrial to industrial periods by Sofen et al. (2011), thus a 27 % increase due to much higher dust loads in glacial times is not unreasonable.

Conclusions
This study measured the fractionation factors for the most common pathways of SO 2 oxidation: gas phase oxidation by OH radicals, and aqueous phase oxidation by H 2 O 2 , O 3 , and a radical chain reaction initiated by Fe.The fractionation factors for these oxidation pathways are now well constrained compared to the previous estimates.A summary diagram of the main processes in the continental sulfur cycle and the fractionation factors involved is shown in Fig. 11.Isotopic measurements can now be used to constrain the dominant oxidation pathway in environmental samples by excluding pathways that do not agree with observed fractionation.A Cameca NanoSIMS 50 was used to measure the isotopic composition of the sulfate produced from the different reactions, which allowed these previously unknown fractionation factors to be measured despite the difficulties of obtaining enough product for traditional isotope measurement instruments.However, factors such as sample topography and charging mean that NanoSIMS results have a far greater uncertainty than traditional measurement techniques, and NanoSIMS measurement error contributes the major uncertainty in the results.NanoSIMS analysis allowed the reactor and collection system to be developed and the reaction to be thoroughly investigated for interfering reactions; the next step in laboratory studies of these fractionation factors would be to increase the sulfate production capacity of the system to allow traditional measurements with high precision, such as isotope ratio mass spectrometry (Ono et al., 2006).
The fractionation factors presented in this paper will allow stable sulfur isotopes to be used to understand the partitioning between these pathways in atmospheric samples, particularly if 17 O of sulfate is also measured allowing differentiation between oxidation by H 2 O 2 , O 3 and all other oxidants.The combined effect of uncertainty and variation in the isotopic composition of sources and fractionation during oxidation means field studies need to simultaneously measure both SO 2 and sulfate isotopic composition to gain insight into the sulfur cycle.Combining modelling with field studies of sulfur isotopes in the atmosphere can then use these fractionation factors to gain an increased understanding of the sulfur cycle and its effect on radiative forcing, aerosols and cloud condensation nuclei.Based on the unique fractionation factor of the reaction, sulfur isotope ratios will be particularly useful to constrain the importance of transition metal-catalysed sulfur dioxide oxidation in the atmosphere, which was the only reaction found to favour the light isotope in the current study.

Fig. 2 .
Fig. 2. Quantification of background in the reaction of SO 2 and OH.(a) Total sulfate collected at room temperature under various conditions (individual samples are shown as orange dots, error bars are 1σ standard deviation of individual samples): (1) Background from impurities in MilliQ water and BaCl 2 ; (2) Direct photolysis of SO 2 , 254 nm and 185 nm lines; (3) Direct photolysis, 254 nm line; (4) 254 nm and 185 nm lines, humidity passing over lamp; (5) 2-4 combined to show total production under UV light in the absence of OH; (6) no irradiation, no added oxidant; (7) 11 ppbv OH. (b)Temperature-dependence of sulfate production from OH reaction (black) and background from sulfate impurities in water (white) and background production (red), with the percentage contribution of the background to total collected shown in orange.

Fig. 4 .
Fig. 4.Frequency of signal height in the sulfur channel of an automatic EDX analysis of BaSO 4 on a gold-coated filter.The measured signal for the sulfur channel is shown in blue and the Gaussian fit to the contribution from the gold peak is shown in red.

Fig. 5 .
Fig. 5. Fractionation factors at 19 • C for the aqueous oxidation of SO 2 by radical chain reaction initiated by Fe, H 2 O 2 bulk solution (from temperature-dependent regression), and H 2 O 2 /O 3 and only O 3 in aerosol droplets.Error bars are the 1σ standard deviation and MDF is the mass-dependent fractionation line.

Fig. 6 .
Fig. 6.Fractionation introduced during collection of SO 2 in H 2 O 2 solution.The duel-inlet IR-MS sample was measured as described in Ono et al. (2006).The shown data of experiments 1-7 are the weighted averages of individual NanoSIMS measurements, while the horizontal dashed lines and the two data points at the right side show the weighted averages of all experiments.Error bars are the 1σ standard deviation.

Fig. 7 .
Fig. 7. Temperature dependence of fractionation during aqueous oxidation of SO 2 by H 2 O 2 and O 3 .Error bars are the 1σ standard deviation.

Fig. 8 .
Fig. 8. Facsimile model of potential oxidants and H 2 SO 4 produced as 11 ppbv OH is generated from the photolysis of water in 20 % oxygen and mixed with 1 ppm SO 2 at atmospheric pressure.

Fig. 9 .
Fig. 9. Isotopic composition of interferences in the reaction of SO 2 and OH.See Fig. 2 for explanation of legend numbers.Aq. ox.shows the isotopic composition of the products of aqueous oxidation by H 2 O 2 or O 3 .Error bars are the 1σ standard deviation.

Fig. 10 .
Fig. 10.Temperature dependent fractionation factors during the gas-phase oxidation of SO 2 by OH radicals.Pale points represent individual experiments while dark points with error bars are the average and 1σ error of the mean at each temperature.

Table 1 .
Fractionation of 34 S/ 32 S and 33 S/ 32 S between two collectors in series during collection of H 2 SO 4 .

Table 3 .
Fractionation factors at 19 • C for the aqueous oxidation of SO 2 by radical chain reaction initiated by Fe, H 2 O 2 bulk solution (from temperature-dependent regression), and H 2 O 2 /O 3 and only O 3 in aerosol droplets.

Table 4 .
Temperature dependent fractionation factors during the gas-phase oxidation of SO 2 by OH radicals.