NO x cycle and the tropospheric ozone isotope anomaly : an experimental investigation

The oxygen isotope composition of nitrogen oxides (NOx) in the atmosphere is a useful tool for understanding the oxidation of NOx into nitric acid / nitrate in the atmosphere. A set of experiments was conducted to examine change in isotopic composition of NO x due to NOx–O2– O3 photochemical cycling. At low NOx / O2 mixing ratios, NOx became progressively and nearly equally enriched in 17O and18O over time until it reached a steady state with 117O values of 39.3±1.9 ‰ andδ18O values of 84.2±4 ‰, relative to the isotopic composition of the initial O 2 gas. As the mixing ratios were increased, the isotopic enrichments were suppressed by isotopic exchange between O atoms, O 2, and NOx. A kinetic model was developed to simulate the observed data and it showed that the isotope effects occurring during O3 formation play a dominant role in controlling NOx isotopes and, in addition, secondary kinetic isotope effects or isotope exchange reactions are also important during NOx cycling. The data and model were consistent with previous studies which showed that the NO + O 3 reactions occur mainly via the transfer of the terminal atoms of O 3. The model predicts that under tropospheric concentrations of NOx and O3, the timescale of NOx–O3 isotopic equilibrium ranges from hours (for ppbv NO x / O2 mixing ratios) to days (for pptv mixing ratios) and yields steady state 117O and δ18O values of 45 ‰ and 117 ‰ respectively (relative to Vienna Standard Mean Ocean Water (VSMOW)) in both cases. Under atmospheric conditions when O 3 has high concentrations, the equilibrium between NO x and O3 should occur rapidly (h) but this equilibrium cannot be reached during polar winters and/or nights if the NO x conversion to HNO3 is faster. The experimentally derived rate coefficients can be used to model the major NO x–O3 isotopologue reactions at various pressures and in isotope modeling of tropospheric nitrate.


Introduction
The NO x cycle is the key driver of tropospheric chemistry (Monks et al., 2009;Seinfeld and Pandis, 1998) and the stable isotope composition of NO x is a useful tool for deciphering oxidation mechanisms during photochemical cycling (Michalski et al., 2003;Morin et al., 2008;Savarino et al., 2008).Oxygen isotope analysis is particularly useful for understanding oxidation chemistry because the original oxygen isotopic signatures of NO x inherited from diverse sources should be quickly erased due to rapid cycling of oxygen in the NO x system.There are, however, no oxygen isotope measurements of in situ NO x because it is highly reactive, has low mixing ratios (in the range of pptv to ppbv), and is prone to react with water when concentrated by collection devices.Variations in oxygen isotope abundances are usually quantified using δ (in ‰, or parts per thousand) where δ x O (‰) = (R sam / R ref −1) • 1000, where R sam and R ref denote the x O/ 16 O ratio (x = 17 or 18) in the sample and reference, respectively.The 17 O value is the measure of the 17 O excess found in a compound over what is expected based on its δ 18 O value assuming the rule of mass dependence during isotope partitioning, where 17 O = 1000• ln(1+δ 17 O / 1000)−0.516• 1000 • ln(1+δ 18 O/1000) (Miller, 2002).Atmospheric nitrate, which is the main end product of NO x oxidation chemistry, has characteristic oxygen isotopic variations, with elevated δ 18 O (Elliott et al., 2009;Hastings et al., 2003) and 17 O values (Michalski et al., 2003;Morin et al., 2008;Savarino Published by Copernicus Publications on behalf of the European Geosciences Union.et al., 2008), believed to be caused by isotope effects during NO x cycling in atmosphere known as the Leighton cycle (Finlayson-Pitts and Pitts, Jr., 2000;Leighton, 1961).
The Leighton reactions refer to the closed photochemical cycling of NO-O 2 -O 3 -NO 2 in the atmosphere.It is initiated when NO 2 is photolyzed by UV-visible light in the blue region of the spectrum (< 400 nm) yielding a ground state oxygen atom O( 3 P).The main fate of the oxygen atom is to combine with O 2 to form O 3 , which then oxidizes NO back to NO 2 (Finlayson-Pitts and Pitts Jr., 2000;Leighton, 1961): Ozone (O 3 ) produced during photolysis (and discharge) in laboratory experiments (Reaction R2 and R3) has high 17 O values, typically ranging from 30 to 50 ‰ (known as mass independent fractionation or MIF) (Thiemens and Heidenreich III, 1983;Thiemens and Jackson, 1987;Thiemens and Jackson, 1990) and elevated δ 18 O values (80-120 ‰) relative to the parent oxygen reservoir (Janssen et al., 2003;Mauersberger, 1981;Morton et al., 1990).This pattern of isotopic enrichment in O 3 results from symmetry restrictions during isotopologue formation (Gao and Marcus, 2001;Hathorn and Marcus, 1999).Isotopically homogenous O 3 ( 16 O 3 ) has C 2v symmetry, but when one of the terminal atoms (but not the central atom) is isotopically substituted the symmetry is reduced to C s .The vibrationally excited C s -type O 3 intermediates have a longer lifetime due to increase in the number of allowed vibrational couplings, which facilitates intramolecular and intermolecular energy redistribution.This extended lifetime gives the asymmetric O 3 species a higher probability of being quenched (Reaction R3) by a third body (M) relative to the symmetric species (like 16   Ivanov and Babikov (2013) regarding the molecular origin of the symmetry effect suggest that the lifetime of the metastable * O 3 states differ "due to differences of the tunneling rates in/out of the reaction channels for symmetric and asymmetric isotopomers due to distortion of vibrational wave functions by isotopic substitution".The consequence of the symmetry effect is that all of the 17 O enrichment and a significant portion of the δ 18 O enrichment are located in the terminal atoms of the O 3 molecule.This pattern has been observed by Tuzson and Janssen (2006) by spectroscopy, albeit with large errors.Hence, by isotope mass balance, the 17 O values of the terminal atoms should be 3/2 times higher than the 17 O value of the bulk O 3 (Michalski and Bhattacharya, 2009).This enrichment is believed to be transferred to various NO x species and to nitrate during oxidation by ozone.
Based on experimental studies of the pressure and temperature dependence of the δ 18 O and 17 O values of ozone (Morton et al., 1990;Thiemens and Jackson, 1990), tropospheric O 3 should have a relatively narrow range of 17 O (32 ± 2 ‰) and δ 18 O (90 ± 10 ‰) values.Indeed, some measurements of the δ 18 O and 17 O value of O 3 in the troposphere (Johnston and Thiemens, 1997;Krankowsky et al., 1995) are similar to laboratory measurements, but most (more than 90 %) are below the expected values (Johnston and Thiemens, 1997;Krankowsky et al., 1995;Vicars et al., 2012).It is unclear whether the disagreement between experimental and observed O 3 δ / values are due to problems in O 3 collection or analytical bias, unknown chemical or exchange reactions in the troposphere, or caused by a different enrichment mechanism when ozone is produced by atoms generated in NO 2 photolysis (in atmosphere) rather than in O 2 photolysis or discharge (in laboratory).
Regardless, the intimate coupling between NO x and O 3 in the Leighton cycle is believed to be the driver of the high δ 18 O and 17 O values observed in atmospheric nitrate (Michalski et al., 2003;Morin et al., 2008;Savarino et al., 2008).High δ 18 O and 17 O values can be generated in NO x and NO y compounds when O 3 transfers one of its oxygen atoms (R4) to the NO y products (Savarino et al., 2008).It has been hypothesized that NO-O 2 -O 3 -NO 2 photochemical cycling in atmosphere results in NO x becoming enriched in the heavy oxygen isotopes through interactions with O 3 during intermediate oxidation steps (Michalski et al., 2003;Morin et al., 2008).Indeed, an initial NO x -O 3 isotopic equilibrium is the a priori assumption used in current models that predict atmospheric nitrate 17 O values (Michalski et al., 2003;Morin et al., 2008;Alexander et al., 2009).However, these equilibrium 17 O (or δ 18 O) values are based on assumptions about the isotopic composition of O 3 in the troposphere and isotope transfer mechanisms during NO x oxidation.Such assumptions could easily be wrong given the large number of possible reactions that can take place between the isotopologues of O 2 , O 3 , NO and NO 2 during the Leighton cycle, including photolysis, oxidation and isotope exchange.It was proposed that nitrate's isotopic compositions can be used as a way of inferring changes in oxidation chemistry in the modern atmosphere (Michalski et al., 2003;Morin et al., 2008) and that ice core nitrate may be a proxy for oxidation chemistry in ancient atmosphere (Alexander et al., 2004;Kunasek et al., 2008).If these approaches are to be implemented, we need a better understanding of the interacting role of the various isotopologues involved in the reactions of the Leighton cycle (Finlayson-Pitts and Pitts Jr., 2000;Leighton, 1961).
Therefore, a quantitative laboratory study that investigates isotope effects arising during the Leighton reactions is required.Here we address this issue for the first time by conducting a series of controlled photolysis experiments and assessing the isotopic enrichment in NO x as a function of reaction time and the partial pressures of O 2 and NO 2 .

Experimental procedure
A cylindrical photolysis chamber attached to a vacuum extraction system (Fig. 1) was used for the experiments.The Pyrex chamber was 122 cm in length and 15 cm in diameter with a total volume of ∼20 L. One end of the chamber was fitted with a 6 cm diameter quartz window.A light source was placed ∼10 cm from the quartz window and oriented so that the beam passed along the axial direction of the chamber.The other end of the chamber was connected to a vacuum line capable of holding a vacuum of 10 −6 torr.Three vacuum components were located between the vacuum pumps and the chamber: a spiral trap for collecting condensable gases, a discharge chamber, and a molecular sieve trap for collecting and separating N 2 and O 2 .The temperature of the chamber was maintained at 298 K by dripping water along the length of the chamber using a recirculation pump.
The light source used to induce NO 2 photolysis was a 150 watt xenon solar simulator (PTI Photon Technology International, Ushio bulb model UXL 151H) that had a maximum output of 3500 lumens at full efficiency.It emits brightly in the visible region and simulates sunlight (6,000K emission spectrum), but its emission in the 300-400 nm range, the main NO 2 dissociation window, is only ∼10 % of the total spectral flux (∼10 18 photons cm −2 s −1 ).There was small unwanted tailing flux (less than 1 % of the total) at wavelengths shorter than 300 nm (O 3 dissociation window) which were further reduced via absorption by the quartz window.Light attenuation caused by lamp distance, geometry, and absorption by the quartz window was estimated at 5-10 %.Using the spectral characteristics of the Xe lamp, and the lamp lumen output, the photon flux for three spectral windows (250-300, 300-350, 350-400 nm) were calculated to be 0.46, 0.79, and 1.2 × 10 16 photons cm −2 s −1 , respectively.Based on the NO 2 dissociation cross sections in these windows (0.9, 2.2, and 5.5 × 10 −18 cm 2 ) and unit quantum yields at these wavelengths (Sander et al., 2006), a NO 2 j coefficient of 0.0086 s −1 was calculated.However, this value is considered an upper limit because it assumes that the lamp was operating at full wattage and no light leakage occurs from the collimator, both of which were unlikely.
The NO 2 gas used in the photolysis was produced in the laboratory by reacting 200 torr of NO (99 % pure) with an excess (600 torr) of O 2 (99.99 % pure) for several hours.At these high mixing ratios of NO the reaction goes to greater than 99 % completion in less than one minute.The product NO 2 was then purified using cryogenic separation and stored in a 2 L Pyrex bulb wrapped in aluminum foil to prevent exposure to light.For each experiment an appropriate amount of NO 2 was transferred to a U-trap (20 mL volume) using liquid nitrogen.After pumping away non-condensable gases, the trap was warmed to room temperature and pure NO 2 was allowed to expand into the reaction chamber.The 1000 : 1 chamber to trap volume ratio (20 L: 20 mL) ensured that most of the NO 2 entered the chamber.Ultra high purity O 2 (99.999 %) was then introduced to the chamber through the same U-trap (to flush out small amount of remaining NO 2 ) until the desired pressure was reached (50 to 750 torr).Next, the xenon lamp was switched on and the lamp was aligned and focused such that its light entered the reaction chamber through the quartz window.
Three sets of photolysis experiments were carried out.The first set (Set 1) examined the isotope effect that occurred when the time of illumination was varied at a fixed NO 2 / O 2 ratio of 24 × 10 −6 .In the second set (Set 2), the NO 2 / O 2 mixing ratio was varied from 3.6 × 10 −5 to 4.3 × 10 −4 by altering the amount of NO 2 used while keeping the O 2 pressure (500 torr) constant and also keeping illumination time constant (∼60 min).The final set (Set 3) examined the isotope effect by changing O 2 pressure for a fixed amount of NO 2 (20 × 10 −6 mole).In each case, after the specified time, the light was switched off and the vessel was kept in the dark for about 60 min to allow reaction of the residual O 3 with NO.It is assumed that at the conclusion of the photolysis reactions there is a mixture of NO x and O 2 .We also assume that higher oxides of nitrogen are not produced significantly and can be neglected.For example, it is known that gas phase N 2 O 3 is formed when NO and NO 2 react, but it rapidly decomposes back to NO and NO 2 at room temperature, inducing isotopic exchange (Sharma et al., 1970;Freyer et al., 1993).Therefore, we consider no significant net production of N 2 O 3 during photolysis.
The NO x was collected by pumping the NO 2 -O 2 mixture slowly (∼2 hours) though a spiral trap immersed in liquid nitrogen.At this low temperature NO 2 and NO combines to form N 2 O 3 as a stable solid (vapor pressure ∼10 −14 torr at 77K).After warming the trap the purified NO x was transferred to a small trap and converted to N 2 and O 2 by electric discharge produced by a Tesla coil (Savarino et al., 2008;Michalski et al., 2002;Bes et al. 1970).The discharge chamber was a double wall Pyrex cylinder with a grounding screen surrounding the outer wall and a 5M NaCl solution in the center volume.The tesla coil was immersed in the salt solution, which acts as a homogenous electrode creating potential between the solution and the grounding screen.Discharge occurs in the low pressure NO x contained between the double walls and converts NO x into N 2 and O 2 .The discharge was executed three times, resulting in N 2 -O 2 yields of > 97 %.The non-condensable gases were collected after each discharge on a 5A molecular sieve at 77 K.The final O 2 fraction was chromatographically separated from the N 2 fraction using a 5A molecular sieve column cooled to 173 • K using ethanol slush (Thiemens, 1984).The O 2 isotope ratios were determined using a Thermo Delta-V isotope ratio mass spectrometer in dual inlet mode.This method was used in the original calibration of the nitrate standard USGS35 (Michalski et al., 2002) that was subsequently confirmed, within the analytical uncertainty, using thermal reduction (Bohlke et al., 2003) indicating accuracy ∼precision (0.3 ‰) for this method.The δ 18 O and δ 17 O values of the tank O 2 were −10.84 ‰ and −5.69 ‰ (relative to VSMOW) respectively and the δ-values of the NO 2 were −2.26 ‰ and −1.25 ‰ as determined by the discharge method.

Systematic and random errors in the discharge method
The above-described measurement procedure of oxygen isotope ratios of product NO 2 involves four important steps: discharge of NO 2 to produce O 2 and N 2 , chromatographic separation of O 2 from N 2 using an MS column, collection of O 2 using MS pellets, and its mass spectrometric analysis.We did a few control experiments to assess the uncertainties associated with these steps.Firstly, it is seen that the discharge yield is always less than 100 % which could be due to recombination of N 2 and O 2 along with their various charged and ionic species to form back some amount of NO x .However, the discharge recycles the O 2 quickly and the final O 2 isotope ratios are expected to be close to the true value.Ozone formation could in principle be a serious issue but its amount is small.We estimate (based on a model discussed later) that only about 0.05 µmole of ozone can be produced from 50 µmole of oxygen (the amount expected from 50 µmole of initial NO 2 ).We also tested the purity of the O 2 fraction after its separation from N 2 by MS.For the small column used here at room temperature there was always a small amount of nitrogen (estimated to be less than 5 % of the total gas) in the O 2 fraction.This introduces a small positive change in the δ-value of O 2 depending on the relative amount of N 2 .Collection of oxygen was done by ∼ 5 pieces of 5A MS pellets kept at LN 2 until O 2 was completely adsorbed (as indicated by line pressure).The gas was released by keeping the tube at room temperature for at least 30 min.Based on control experiments using tank O 2 , we noted that this particular step increases the δ 18 O value by 0.1 to 0.2 ‰.To test the overall effect we analyzed three aliquots of tank NO 2 by this method and found the uncertainty to be 0.6 (δ 18 O) and 0.4 (δ 17 O) ‰.
Assuming additional uncertainty due to collection of NO x we estimate 1σ errors of 1.2 and 0.6 ‰ in the determination of δ 18 O and δ 17 O of NO x in our experiment.

Set 1 experiment
Experiments in this set were designed to determine the time required for the NO x cycle to achieve isotopic steady state under the applied photochemical conditions (Fig. 1).Photochemical steady state in the NO x -O 3 cycling (Reactions R1-R3) is well known under tropospheric conditions (Finlayson-Pitts and Pitts, 2000;Leighton, 1961) by: where j 1 is the photon flux and k 4 is the rate constant of Reaction (R4).For initial [NO 2 ] 0 with [O 3 ] 0 = [NO] 0 = 0 solving for the evolution of O 3 (which is always equal to NO in the steady state) we obtain (Seinfeld and Pandis, 1998): This steady state is shifted when NO x is present in high mixing ratios (> 1ppmv) because the O sink reactions given by: become important (Crutzen and Lelieveld, 2001) and reduce the O 3 production rate so that Reaction (R6) no longer holds true.
As mentioned, the experiments in Set 1 tested the time scale for achieving NO x -O 3 isotopic steady state.When there was 20 ppmv NO 2 in the chamber, the observed NO x -O 3 isotopic steady state was achieved on the order of 30 minutes (Fig. 2).The isotopic steady state was attained more slowly than the time required for the chemical steady state (∼5-6 minutes).This is mainly due to isotope mass balance dynamics, which require multiple Leighton cycles to occur before isotope equilibrium is reached, and possibly because of small mixing scale length.When the initial NO 2 amount was higher (for example, ∼240 ppmv) the photolytic supply of O-atom was higher and isotope exchange between O and NO x was faster than the time required to achieve NO x -O 3 steady state and overall isotopic equilibrium was expected to be achieved in less time (based on the chemical simulation model described later).Based on these considerations, we decided to carry out photolysis experiments for the duration of one hour to ensure that NO x -O 3 isotopic steady state is always achieved.

Set 2 and Set 3 experiments
The second set of experiments (Set 2) was designed to determine the change in the NO x isotopic composition as a function of different initial NO 2 mixing ratios at constant pressure.This was achieved by varying NO 2 amount from 19.5 × 10 −6 to 236.0 × 10 −6 moles (i.e.µmole) while keeping the O 2 at a pressure of 500 torr corresponding to 0.55 moles (Table 1 and Fig. 3).In contrast, the last set of experiments (Set 3) was performed by keeping the initial NO 2 amount fixed at ∼20 µmole and changing the O 2 pressure from 50 to 750 torr (Table 2).The results are plotted in terms of NO x 17 O and δ 18 O values as a function of O 2 pressure (Fig. 4).

Discussion and model predictions
Both the data sets show that the steady state δ 18 O and 17 O values are a strong function of the NO 2 / O 2 mixing ratio (Fig. 5).As the NO 2 mixing ratio decreased, the 17 O and δ 18 O values of NO x increased until they were nearly constant when NO 2 mixing ratio reached about 20 ppmv (Tables 1  and 2).requirement for isotope analysis by dual-inlet method.For example, we could not investigate typical troposphere ratios (∼ 10 ppbv) which would have resulted in only about 10 −9 mole of NO 2 in the system.A qualitative analysis of the reaction kinetics showed that the key to understanding the two data sets (Set 2 and Set 3) is the exchange reactions between oxygen atoms and NO x or O 2 (for simplicity we write: O = 16 O, P = 17 O and Q = 18 O) : Analogous exchanges occur with the 17 O (P) isotopic species.All three exchange rate constants are of similar magnitude (Anderson et al., 1985;Jaffe and Klein, 1966;Sharma et al., 1970) but the NO x exchange rate constants are slightly higher than the rate for O-O 2 exchange, albeit with considerable uncertainties (Jaffe and Klein, 1966).Since the overall rate of exchange is proportional to concentration, isotopic exchange between NO x and O 2 (the bath gas) via R8-R10 is expected to be a strong function of mixing ratio.
We hypothesize that the high isotope enrichments, reflected in both the δ 18 O and the 17 O values, occur when O 3 oxidation of NO is faster than NO x -O-O 2 isotopic exchange.Isotopic enrichments associated with the formation of O 3 have been extensively studied (Mauersberger et al., 1999;Guenther et al., 1999;Mauersberger et al., 2003;Thiemens, 1999).At temperature and pressure range of the present experiments, the recombination process should generate O 3 with δ 18 O values between 90-130 ‰ and 17 O values between 30-45 ‰ (Mauersberger et al., 2003).Our hypothesis suggests that that during oxidation of NO, the oxygen isotopic enrichments in O 3 are transferred to the product NO 2 .However, the enrichment in the product NO 2 gets diluted or even erased when NO x and O atom exchange is fast via Reactions (R7a), (R7b), (R9), and (R10).This is because O 2 dominates the oxygen reservoir by about four orders of magnitude compared to O 3 or O-atoms and any O atoms produced by NO 2 photolysis quickly equilibrate with the O 2 via Reaction (R8).The equilibrated oxygen atom loses the heavy isotopic signal that arises from the Reactions (R2) and (R3).Therefore, there is a competition between the NO x -O atom exchange and the oxidation by O 3 .This hypothesis was tested using the chemical kinetic simulations discussed below.
Plots of oxygen isotope enrichments in dual isotope ratio space support the hypothesis that NO x cycling effectively equilibrates NO x with O 3 (Fig. 6).The NO x δ 17 O and δ 18 O data in both experiments align nearly along a line of slope 1 reflecting the progressive transfer of O 3 isotopic ratios to NO x .This slope value is similar to the one found experimentally for O 3 isotope ratios by earlier workers (Mauersberger et al 2005) as shown in Fig. 6.The observed NO 2 isotopic equilibrium values, when the NO x -O exchange was minimized (i.e., at ∼20 ppmv and O 2 pressure of 750 torr), yielded a mean 17 O value of 39.3 ± 1.9 ‰ and δ 18 O value of 84.2 ± 4 ‰.The corresponding values expected for bulk O 3 enrichment at 750 torr (based on the model discussed later) are 30.6 and 90.4 ‰.Unfortunately, in the present experiment the O 3 could not be measured directly for its isotopic composition due to its low amount (∼0.2 to 20 × 10 −9 mole) and that it was mixed in large quantity of  (Peiro-Garcia and Nebot-Gil, 2002;Redpath et al., 1978;Savarino et al., 2008).Therefore, ignoring any mass independent or mass dependent isotope effects in the NO x cycling other than isotopic transfer from O 3 to NO x it is expected that at standard temperature and pressure the steady state NO 2 17 O values would be 1.5 × 30.6‰ ∼ 45.9‰, higher (by ∼ 6 ‰) than our observed value of ∼ 39.3 ‰.Part of this discrepancy can be explained by the NO x -O exchange still occurring at 20 ppmv NO x / O 2 mixing ratio.The second possibility is that a fraction of the NO and O 3 reactions are occurring through abstraction of the central oxygen atom in O 3 (Redpath et al., 1978;Vandenende et al., 1982;Vandenende and Stolte, 1984).In this case the 1.5 factor used to scale the bulk O 3 isotope ratios would be too high.Savarino et al. (2008) performed a single step oxidation experiment of NO by O 3 to derive a conversion formula (= 1.18 • 17 O(O 3 )+6.6),which would give NO 2 17 O value (42.7 ‰) only slightly higher than our observed value.
It is unlikely that any normal or anomalous isotope effects were caused by photolysis or self shielding in the chamber.Firstly, in the experiments with the highest 17 O values (700 torr, 20 µmol) the NO 2 number density (6 × 10 15 molecule/cm 3 ), cross section (6 × 10 −19 cm 2 ) and chamber length 122 cm would result in only 3 % attenuation of the incoming light (Beer-Lambert law).In contrast, the exiting light would decrease by 32 % in the experiment with the lowest observed isotope anomaly, the opposite of what would be expected if self shielding were present.Secondly, the light source warms its end of the chamber, relative to the opposing end, which would induce rapid convective mixing within the chamber.This would move any shielded NO 2 located at the far end of the chamber to the front where it would be re-photolyzed.Based on the experimental J coefficient (0.0086 s −1 ) the lifetime for NO 2 photolysis is less than 2 minutes, so each NO 2 molecule undergoes ∼120 photolysis reactions in different parts of the chamber and would unlikely be affected by any potential self shielding that requires gases to be isolated in space and time.A related issue is possible isotope fractionation associated with photolysis.Zero point energy differences during photolysis of NO 2 isotopologues have been demonstrated experimentally (Michalski et al., 2004) but these were detected only under jet cooled conditions where population of ground state rotational levels was minimized.At the temperature of our experiments (298K) the NO 2 absorption spectrum is convoluted and has chaotic state mixing near the dissociation limit (Delon et al., 2000), which would likely limit any zero point energy effect during photolysis.Based on this consideration, no isotope effect was imposed on the photolysis reactions in the kinetic modeling of the data.

Chemical kinetic modeling
In order to quantitatively interpret the observed NO x isotope values and evaluate the recombination rate constants of the various O 3 isotopomers and isotopologues, a chemical kinetic model was used.The model called Kintecus (Ianni, 2003) simulated isotope effects that occur during the photochemical cycling of NO x by tracking interactions among the major isotopologues present in the chamber.The initial isotopologue reactant concentrations, the forward and backward reactions between various isotopologues, and their rate constants are supplied as inputs.The rate equations are solved numerically and the products are accumulated dynamically as the system evolves up to a pre-specified period (60 min in the present case).The model calculates the number of molecules of each reactant at small intervals (∼0.1 sec to 1 µsec) and finally displays the results at chosen time intervals.

Reactants, their initialization and delta definition
The model was initialized with the following 17 species: O, P, Q, OO, OP, OQ, ONO, PNO, QNO, NO, NP, NQ, OOO, OQO, OOQ, OPO, and OOP.Note that we neglect to differentiate between 15 N and 14 N since the N-isotopes are not of our concern in these experiments.We also did not include minor species like PP or QQ or QQQ etc. since their influence on the isotope system is small due to their low natural abundances.This neglect causes a minor problem of isotope balance since, in reality, all possible reactions involving all possible isotopologues occur in the reaction chamber and they affect the final abundances of the species.Obviously, the heavy isotopes distributed among the neglected species are not accounted for in the calculation of final delta values.However, this approximation results in model predictions that differ only slightly (less than 0.1 ‰) from the values if the minor isotopologues were included.For example, when we estimate isotope ratio Q/O in oxygen from molecular species ratio [OQ]/{2[OO]+[OP]+[OQ]}disregarding contribution from QQ isotopologue the true ratio Q/O would be underestimated by only about 2.4 ppt.
Following the above constraint we need to define appropriately and consistently the isotope ratios of O 3 , NO 2 and NO in the model so that all δ-values are expressed in terms of enrichment relative to tank oxygen composition.We note that in experiments involving ozone formation and its analysis O 3 is usually first converted to O 2 and measured in IRMS.The distinction between isotopomers like OQO and OOQ is not maintained there.But in the model output these species are generated and have to be counted separately so that the model calculation of δ-values of ozone keeps track of the total number of O, P and Q isotopes.In this case, we use isotopic abundance or atom percent in O 2 and O 3 to calculate model δ-values of ozone: For At the beginning of a simulation only isotopologues of NO 2 and O 2 were present in the chamber.The initial amounts of species OO, OP and OQ as well as ONO, PNO and QNO (Table 3) were chosen such that the calculated δ-values (relative to VSMOW and according to the above definitions) of tank O 2 and starting NO 2 agree within 0.05 ‰ with the measured ones.A better agreement may be desirable but is not really necessary since all experimental and model δ-values (relative to the tank O 2 ) were obtained with less precision and accuracy.The δ-values (relative to VSMOW) were converted to absolute molecular abundances using the isotopic abundances of O, P and Q of VSMOW (Table 3) obtained from Coplen et al. (2002).The model output in terms of number of molecules of various isotopologue species (e.g., OOO, OQO or OOQ and ONO, ONP and ONQ) were converted to δ-values (or enrichment) relative to the tank O 2 .The O 3 enrichment values act as anchor points since the accuracy of the numerical results was ensured by comparing the model O 3 δ-values with experimental O 3 isotopic enrichment values (Fig. 6) available from pressure dependence studies of Morton et al., (1990) and Mauersberger et al. (2005).It is to be noted that for application to troposphere the derived enrichment values can be converted to δ-values relative to VSMOW by using the air O 2 isotope values (δ 18 O = 23.5 and δ 17 O = 12.2 ‰ relative to VSMOW).

Choice of kinetic rate constants
Once initialized, the Kintecus simulation after a given run produces isotopologues of all secondary reactants based on rate laws and constants (in units of cm 3 s −1 for bimolecular reactions and cm 6 s −1 for tri-molecular case) as listed in Table 4. Rate constants of NO oxidation by O-atom and O 3 were taken from the JPL listing (Sander et al., 2006) as was the rate for reaction O + ONO.The rates for all reactions involving isotopologues (either in dissociation or bi-molecular reactions) were adjusted for the reaction channel symmetry.For example, rate constant of the reaction PNO → P + NO was taken to be half of the ONO → O + NO rate constant.For reactions Q + ONO and P + ONO the collision frequency factors of 0.957 and 0.978 were used following the method of Pandey and Bhattacharya (2006).Rate constants that produced the minor oxygen isotopologues of nitrogen oxides (where no experimental data is available) were assumed to be the same as the major isotopic species (i.e., ignoring any kinetic isotope effect-KIE).
The NO x exchange reaction rate constants were taken from published works.The forward exchange rate (k f ) of Q isotope with ONO was based on Jaffe and Klein (1966).For backward exchange rate (k b ) we used the equilibrium constant (K eq ) tabulated by Richet et al. (1977) since at equilibrium (at any given temperature) K eq = k f / k b .Similar considerations were used for P + ONO exchange as discussed in Pandey and Bhattacharya (2006).In a similar way, exchange rates of O-atoms with NO were derived using Anderson et al. (1985) and Richet et al. (1977).Finally, the NO oxidation by O 2 was taken from Finlayson and Pitts (2000).For completeness, we included exchange of NQ with ONO and NP with ONO using the rate constants given by Sharma (1970) and assuming a mass dependent isotope exchange rate.
A rate coefficient for NO 2 dissociation that reproduced the time dependent isotopic equilibration data (Fig. 2) was 0.004 s −1 and this was used as the coefficient for all NO 2 isotopologues but corrected for channel symmetry factors.This value is slightly less than the J coefficient estimated from the xenon lamp output for reasons explained before.We also tested the photolysis model's dependence on the NO 2 dissociation rate (j coefficient) and found little difference in the predicted NO x isotope values (± 0.5 ‰) when the j was increased by a factor of 1000 (4 s −1 ).The j coefficient, however, does change the timescale to reach isotopic steady state of NO x and the number 0.004 s −1 was selected to match the observed time to isotopic equilibrium in experiments of Set 1.This is analogous to estimating O 3 dissociation rate constant by measuring the product O 2 amount (Pandey and Bhattacharya, 2006) or NO 2 j coefficients using O 3 steady state concentrations (Sakamaki et al., 1980).These simulations confirm our expectation that the NO 2 j coefficient controls the timescale to NO x -O 3 equilibrium in the Leighton system.The model does not distinguish between the two N-isotopes and it also assumes that only terminal atoms take part in reaction or dissociation of tri-atomics.

Rates of ozone formation and dissociation
The rate constants of O 3 isotopologue formation were the crucial part of the reaction scheme because in these reactions the mass independent isotopic enrichment or MIF arises.
These formation rates at low pressure (∼50 torr) were mostly taken from Janssen et al. (2001).For the OOP case the relation between zero point energy changes and rate constant ratios (Janssen et al., 2001) was used (See discussion in Bhattacharya et al., 2008).We note that out of the nine rate constants only the rates of O + OQ → OOQ and O + OP → OOP are surprisingly large and these are the reactions that essentially determine the level of MIF in O 3 (Janssen et al., 1999).We shall assume that the observed pressure dependence of O 3 MIF is due only to the variation in these two rates.This hypothesis is based on the observation of Janssen et al. (1999) that O + OQ →OOQ is the channel which "almost exclusively is responsible for the observed enrichment in 50 O 3 ".With this simplification, the present model can be used to find the pressure dependence of these two rate coefficients relative to the rate of O + OO → OOO (denoted as r 18 and r 17 ) by fitting the modeled 17 O of NO 2 with the observed values.There is another important constraint in the selection of r 18 and r 17 , namely, the model δ-values of O 3 at various pressures should match those that occur by pressure variations (Morton et al., 1990;Mauersberger et al., 2005).We found that it is possible to obtain a consistent set of rate constants (given in terms of r 18 and r 17 values and shown in Table 5 and Fig. 7) corresponding to various pressures which satisfy both the O 3 MIF data and our observed NO x 17 O data.
The O 3 amount at any stage is quite small (O 3 / NO 2 ratio is about 3 × 10 −4 at 20 µmole of NO 2 at O 2 pressure of 50 torr) but for proper calculation of the isotope effect one has to account for O 3 dissociation.The rate constants of dissociation of various O 3 isotopologues were taken from Pandey and Bhattacharya ( 2006) and Chakraborty and Bhattacharya (2003) normalized to the rate for the main O 3 isotopologue 16 O 16 O 16 O; the latter was fixed by taking a NO 2 / O 3 cross section ratio of ∼4000 at the relevant wavelength range (< 400 nm) used in the experiment.Because the O 3 is a minor component in the system its dissociation rate does not affect significantly the final model outcome.This set of reactions, being mass dependent in nature, does not have a significant effect on the predicted 17 O value of NO x .

Accounting for isotopes of total NO x in the model
The output of the photolysis model showed that at the end of each exposure period the chamber contained a mixture of NO x and oxygen compounds (O, O 3 , O 2 ).We expect these gases would continue to react after the light source was turned off.In order to account for this, at the end of each 60 minute simulation the resultant isotopologue number densities for all species were used as inputs to a second run simulation that was identical to the first except all j coefficients were set to zero.This "dark" phase simulation was run for two hours to account for the one hour period after the light was turned off and the average residence time of NO x in the chamber during the collection step.The simulations show that O 3 and O istopologues quickly react (within several seconds) with NO to form NO 2 .During these two hours without photolysis, NO continues to react with O 2 with a rate primarily controlled by the O 2 number density (pressure).For example, at the end of the 500 torr O 2 light simulation, NO 2 accounts for 71 ± 1 % of NO x oxygen regardless of the initial NO 2 concentration, but it accounts for 89-99 % of NO x oxygen at the end of the dark simulation.In contrast, NO 2 makes up only 7 % of NO x oxygen in the 50 torr / 19 µmol light simulation and increases to only 39 % during the dark simulation.We note that the amount of NO converted into NO 2 during the dark phase, at a given O 2 pressure, goes as the square of the NO concentration i.e., dNO For example, in the 500 torr experiment using an initial NO 2 of 237 µmol, the NO accounted for 28 % of NO x oxygen at the end of the photolysis simulation but decreased to 1 % of NO x oxygen by the end of the dark phase.In contrast, in the 19 µmol (500 torr) experiment, NO (26 % NO x oxygen) decreases to only 11 % of NO x oxygen.
The final NO x δ-value was calculated based on the oxygen mole fractions (f ) of NO 2 and NO and their respective final δ-values at the end of the dark simulation period of two hours, ) and ( 2) Two effects occur during the dark phase simulation reactions that impact the final NO x isotope composition.The first is the NO 2 -NO equilibrium (Sharma et al., 1970).In both the light and dark simulations, at all time steps (in the model we chose each step to be ∼60 s) there was a constant offset between the NO 2 and NO δ 18 O values (42 ± 1.2 ‰) but the 17 O values were essentially equal within ± 0.1 ‰.This re-flects the mass dependent nature of the equilibrium for the pair's isotopic exchange and suggests that under the experimental conditions, the NO x isotope exchange occurred on a time scale faster than the oxidation of NO.The second effect was that the final dark simulation NO x δ 18 O and 17 O values were reduced relative to the "light" simulation values and this reduction was proportional to the amount of NO that was oxidized by O 2 in the dark.This was because the O 2 δ 18 O and 17 O values are defined as 0 ‰ relative to tank, which are much lower than the same values in NO x at the end of the light simulation.During the 500 torr simulations, the dark simulations resulted in isotope dilution that  remained fairly constant, with the NO x δ 18 O value decreasing by an average of −11 ± 1.6 ‰ and its 17 O decreasing by −5 ± 0.9 ‰.This corresponds to 18 ± 0.03 % of the final NO x oxygen atoms arising from the 2NO + O 2 reaction.The constant mole, variable pressure experiments have a wider range of this reaction contribution to NO 2 (from 7 to 22 %).

Constraint on O 3 formation rate constants
The observed isotope values in NO x were used to constrain the O 3 isotopologue formation rate constants in the model.First, the rate coefficients for reactions O + OQ + M → OOQ + M and O + OP + M → OOP + M were selected that would reproduce closely the δ-values reported by Morton et al. (1990) and Mauersberger et al. (2005) for pressures 50,75,100,150,200,300,400,500,600,700, and 750 torr of O 2 .These two isotopologue rate factors are denoted r 18 and r 17 (Table 5) and their reaction rate constants are obtained by multiplying the O + OO + M → OOO + M rate constant by these factors (Table 4).The Kintecus model was run with these pressure dependent rate constants while keeping the NO 2 amount at 20 µmole.As an example, at a pressure of 50 torr the chosen enrichment factors were: r 18 = 1.450 and r 17 = 1.335 (Table 5).The resulting 60 min Kintecus NO x -O 3 light simulation resulted in O 3 δ 18 O and δ 17 O values of 128.0 ‰ and 112.5 ‰ which match exactly the experimental values of Morton et al. (1990) and Mauersberger et al. (2005).The model predicted a 17 O value of NO x of 4.2 ‰, which compares well with the observed value of 3.0 ‰ (Table 2).Across all simulations the differences between the modeled and experimental O 3 δ / values were minimal (Table 5), smaller than 0.8 ‰ for both δ 18 O and δ 17 O (Fig. 6) and 0.5 ‰ for 17 O.We note that the experimental values O 3 δ values reported by Morton et al. (1990) and Mauersberger et al. (2005) have large dispersions and we used a logarithmic function to fit the data points in order to estimate the enrichments at specified pressures (

Comparison of model and observed NO x δ 18 O and 17 O values
The model predicted 17 O and δ 18 O values for a chosen set of experimental conditions, are given in Fig. 3/Table 1 (for Set 2) and Fig. 4/Table 2 (for Set 3) along with the observed values.There was excellent agreement between the observed 17 O values and those derived by the model for both the sets (compare columns 7 and 10 in Table 1 and columns 8 and 11 in Table 2).For Set 3 the agreement was, on average, within 2 ‰ and the model-observed fit had a slope of 0.97 with a r 2 = 0.97.In Set 2 experiments, the model-observed agreement for 17 O values was even better, typically within 0.1 ‰, with a model-observed slope of 1.06 (r 2 = 0.99).In general, the agreement between the model and observations was better at the low and high pressure conditions.The maximum model-observed 17 O difference was 4 ‰ (about a 10 % offset from the observed value) and occurred for the 400 torr case (Table 2).Considering an estimated error in experimental determination of 17 O value to be 1.9 ‰ the observed mean difference is within the expected range and attests to the validity of the model.
Both data sets show a decrease in the 17 O value of NO x with an increase in the ratio NO 2 / O 2 and the modeled 17 O values reproduce this feature quite well (Fig. 5).It is clear that there is opposing effect of oxygen pressure (or amount) and initial NO 2 amount on the final 17 O value of NO x .As the O 2 pressure increases the O 3 formation rate increases.For example, the Kintecus output shows that for increase of pressure from 100 torr to 700 torr the average O 3 formation rate increases from 1.0 × 10 11 to 2.1 × 10 12 (molecules s −1 ).This increase results in enhanced O 3 oxidation of NO and subsequently a larger 17 O values in NO x .When the initial amount of NO 2 is increased at a fixed O 2 pressure, the O 3 formation rate is constant but the exchange of O-atom with NO 2 increases, which reduces the 17 O.It is therefore clear that when the original reservoir of NO 2 is large, any effect introduced by the O 3 oxidation step would be relatively small compared to the case when the NO 2 reservoir is smaller.The effect of each of these reactions can be explored by the Kintecus model quantitatively.

Sensitivity tests for exchange reactions
A number of simulations for evaluating the sensitivity of the exchange reactions were carried out to test the abovementioned isotope dilution via Reaction (R7a and Reaction (R10) (NQ+O←→NO+Q) (Table 6).This was accomplished by alternatingly reducing the rate constant of one of the above reactions to 10 −6 of its value (Table 4), which essentially eliminates it from the reaction scheme.The relative importance of the exchange reactions was evaluated using two cases of NO x / O 2 ratios: Case 1: 20 µmol/500 torr compared to 237 µmol/500 torr (for amount variation) and Case 2: 20 µmol/500 torr compared to 20 µmol/50 torr (for pressure variation).The exchange reactions did have a major impact on the simulated isotope values as expected.For example, when all four isotope exchange mechanisms (Reactions R7a, R7b, R9, and R10) were eliminated the NO x 17 O value stabilized at 68.0 ‰, 48.0 ‰, and 48.0 ‰ for the 20 µmol/50 torr and 237 µmol/500 torr and 20 µmol/500 torr cases respectively.These values are in good agreement with the O 3 17 O values obtained at these two pressures (Tables 1 and 2) multiplied by 3/2 required by the terminal atom transfer assumption.In other words, in the absence of NO x exchange reactions the δ 18 O and 17 O values in the product NO x are the same as that of the terminal O atoms in O 3 .
The simulations that compared the amount effect (constant P = 500 torr) provided insight into which exchange reactions were important under changing NO x mixing ratios (Table 6).For comparison, a 17 O dilution parameter was introduced here which is defined as: 1-( 17 O eq / 48 ‰), where 17 O eq is the 17 O value of NO x at equilibrium for simulations that had one or more of the exchange pathways removed and 48 ‰ is the expected NO x value when all exchanges were removed.For the 20 µmol case, the 17 O dilutions were, 0.07 (Reaction R7a off), 0.12 (Reaction R7b off), 0.09 (Reaction R9 off), 0.07 (Reaction R10 off), and 0.12 when all exchanges were included (Table 6).This indicates that under these conditions no single exchange reaction is dominant and in concert they induce only about a 10 % reduction relative to NO x equilibrium value (48 ‰).In contrast, for the 237 µmol and 500 torr case the 17 O dilutions were much higher (0.54 ± 0.075) and fell into two groups.[O] the overall exchange is much higher under the elevated mixing ratios.
The pressure comparison (50 versus 500 torr at 20 µmol NO 2 ) also showed that only two of the exchange pathways were important, but their effects were not the same as in the amount comparison (Table 6).In the 50 torr case the 17 O dilutions (1-17 O eq / 68‰) averaged 0.86 ± 0.11, which were much higher than the high pressure case that averaged 0.095 ± 0.026.The R7b (off), R9 (off) and all exchange (on) simulations had the same 17 O dilution of 0.92, while Reaction (R7a) (off) was slightly lower (0.87) and Reaction (R10) (off) having 0.66 value was the most sensitive reaction.This was traced back to the dependence of Reaction (R7b) on [M] which is ten times lower at 50 torr relative to 500 torr.This limited NO 2 production via Reaction (R7b) and resulted in NO / NO 2 ratio of 6.3 at 50 torr compared to 0.86 at 500 torr.The roughly ten fold higher concentration of NO then leads to accelerated oxygen exchange via Reaction (R10).Since pressure already limits ability of Reaction (R7b) to produce NO 2 , eliminating it from the exchange scheme had no effect.Thus we conclude that 17 O variations in the simulations can be explained by exchange reactions whose relative importance shifts depending on production of NO x and odd oxygen as mixing ratio and pressure change.

Model performance and r-values
The excellent agreement between the model predictions and the observations allows us to constrain the variation in the r 17 and r 18 rate coefficients as a function of the O 2 (total) pressure (Table 5 and Fig. 7).There is decrease in both these factors with increasing pressure consistent with the observed decrease in MIF of O 3 at high pressure (Thiemens and Jackson, 1990).The decrease for r 18 was from 1.450 to 1.330 for a pressure increase from 50 to 750 torr.We can speculate in the light of Gao-Marcus model that the main reason for this decrease is an increase in collision frequency which lowers the life time of the transition state of the asymmetrical O 3 iso-topomer (known to be the factor responsible for MIF).This factor causes large change in asymmetrical O 3 abundance as expected.For example, at 50 torr the modeled O 3 δ 18 O values were: 150 ‰ (asymm) and 85 ‰ (symm) whereas at 750 torr the values were 93 ‰ (asymm) and 85 ‰ (symm).Correspondingly, the modeled 17 O value of bulk O 3 changes from 44.5 to 30.6 ‰.Applying these adjusted r 17 and r 18 rate coefficients the best fit line between observed and model predicted values (Fig. 6) was improved yielding very similar slopes of 1.03 (NO x ) and 0.95 (O 3 ).This provides an additional validity to the proposed transfer mechanism.
The model also does a good job of predicting NO x δ 18 O values for low NO x mixing ratios, but not as well when mixing ratios increase.In the constant amount experiments (set 2), the model (y) versus observed (x) best fit, when forced through zero, was y = 1.01x (r 2 = 0.96) (Table 1 and Table 2) indicating excellent agreement between the kinetic model's and experiment's NO x δ 18 O values when NO x was at 20 µmol.In the constant pressure experiments (set 2), however, the model (y) versus observed (x) best fit was y = 0.75x + 13 (r 2 = 0.96).Additionally, in the constant pressure experiments there is a strong negative correlation between observed NO x 17 O values and the difference between the "light" model's predicted NO x δ 18 O value and the observed NO x value.In other words, as the NO x mixing ratio became smaller, the "light" model NO x δ 18 O values approach the observed values, whereas they diverge as the mixing ratio increases.Any KIE occurring during the reactions in the dark phase, like NO + O 2 or NO-NO 2 isotope exchange can be ruled out as the cause of this divergence because the correlation exists without the former, and the latter simply alters isotope distribution between NO 2 and NO without changing the bulk NO x isotope composition.This suggests that the equilibrium values used in the O +NO x exchange reactions may be incorrect and the divergent isotope effect becomes more obvious when isotope exchange becomes more important at the high NO 2 mixing ratios.The 13 ‰ offset generated by the model may reflect the fractionation factor associated with such an exchange.Regardless, it appears from both data sets that as the NO 2 mixing ratio approaches ambient levels (much less than ppm), the model does an excellent job of predicting the observed NO x δ 18 O values.

Estimation of uncertainty in r-values
We note that the rate coefficient ratios r 17 and r 18 of ozone formation are inferred based on trial and error method and are subject to some uncertainty.The initial choice is based on fitting literature data on pressure variation of δ-values during ozone formation.These values are then slightly modified to fit the pressure variation data of NO x obtained in the present experiment.
The pressure variation data as available in literature (summarized in Mauersberger et al., 2005) have large scatter not only due to experimental limitations but also due to the fact that they combine data from various methods and sources.As discussed, to obtain a consistent set of pressure variation data in digital form that can be used for our purpose we fitted a smooth curve through the points and read out the δ-values at each of the eleven pressures (50, 75, 100, 150, 200, 300, 400, 500, 600, 700 and 750 torr).Based on the smoothing error and the dispersion associated with the data points we estimate that each of the ozone δ-values should have an uncertainty of about ± 4 ‰.Since we are using these δ-values to derive the r-values which, in turn, are used to fit the observed experimental δ-values of NO x the overall uncertainty should be reflected in the goodness of fit of the NO x δvalues.The model δ-values do differ from the observed ones; the maximum absolute difference in both δ-values is about 8 ‰ and the maximum absolute difference in the 17 O values is 4.9 ‰ (see Table 2).Therefore, the uncertainty in the ozone δ-values gets reflected in the NO x δ-values.Based on these considerations, we assign error of 4 ‰ (1σ ) in each of the fitted ozone δ-values as a reasonable estimate of the error.To determine the corresponding uncertainty in each of the eleven r-values, the Kintecus program was varied in order to match the high and low limit of ozone δ-values in each case.A reasonable estimate of the total error in each r-value can then be obtained by using half of the difference between the corresponding high and low r-values.As an example, at 200 torr pressure the δ 17 O and δ 18 O values (in ‰) are 95.3 and 105.4 with fitted values of 95.2 and 105.6 corresponding to r 17 and r 18 values of 1.282 and 1.382.Assigning error of 4 ‰ in both δ 17 O and δ 18 O values we obtain uncertainty of 0.012 in each of the two r-values i.e., 1.282 ± 0.012 and 1.382 ± 0.012 (Fig. 7).For comparison, the difference between the r 18 values corresponding to 50 and 750 torr is: 1.450-1.335= 0.115.So the uncertainty in r 18 value in this case is of the order of 10 % of the total variation.

Atmospheric applications
The present model can be used to predict the expected oxygen isotope composition of NO x in the atmosphere when it is generated by only NO x -O 3 chemistry.The isotopologue rate constants are the crucial input to the model and they have been shown to be independent of NO x / O 2 mixing ratios and accurately predict the resulting δ 18 O and 17 O values in NO x .The photolysis model (only the light reactions) was run for a range of NO x mixing ratios typical of the troposphere, which can widely vary depending on the proximity to NO x sources; urban regions are typically 10's of ppbv, while remote ocean regions can be below 10 pptv.For standard temperature and pressure and typical NO 2 j coefficient (0.007), the NO x -O 3 only isotope equilibrium model predicts the nearly same steady state NO 2 17 O and δ 18 O values of 45 ± 0.2 ‰ and 117 ± 5 ‰ respectively (relative to VS-MOW), regardless NO x mixing ratios (model runs ranged from 10 pptv to 10 ppbv).This NO 2 δ 18 O value was based on the model prediction of 92 ± 5 ‰ enrichment relative to the reactant O 2 δ 18 O value, which in the case of the tropospheric O 2 is 23 ‰ relative to VSMOW.This suggests that, to a first approximation, the NO x -O 3 equilibrium value used in atmospheric nitrate 17 O models can be initialized using a single NO 2 17 O value of 45 ‰, regardless of local NO x concentrations.This 17 O value is 5 ‰ higher than a previous 1-D model (Lyons, 2001), which differs significantly in its estimation of the O 3 terminal O atom isotope enrichment (78 ‰) compared to the present model (48 ‰) at 750 torr.This arises primarily because Lyons assumes that the symmetric / asymmetric branching ratio is fixed, while ours vary with pressure (Janssen, 2005; Table 5).If the higher O 3 17 O value (Lyons, 2001) is assumed in our model the predicted NO x 17 O value would be ∼ 70 ‰, significantly higher than the observed value.In addition, it is unclear why, in that model, there was decrease in the NO x 17 O values with decreasing altitude in the troposphere.We infer that this was due to an assumed isotopic exchange between NO 2 and H 2 O, a process not considered in our model.
Transport of stratospheric O 3 could potentially alter tropospheric NO x -O 3 isotope equilibrium δ / values.Remote tropospheric O 3 mixing ratios are often dominated by cross tropopause mixing of stratospheric O 3 .This O 3 would have an isotopic composition that reflects the stratospheric pressure and temperature conditions where it was formed and would alter tropospheric NO 2  17 O values since the NO x -O 3 isotope equilibrium depends on the isotopic composition of the O 3 .This influence, however, is expected to be minor because while the chemical lifetime of O 3 in a clean troposphere may be months, the isotopic lifetime would be much less.Ozone photolysis and reformation in the troposphere would reset its isotopic composition, and this recycling rate will be limited by O 3 photolysis lifetime of τ = 1/j O3 .Ozone j coefficients in the troposphere vary depending on the overhead total O 3 column, latitude, time of day, and other phenomena that change photon fluxes, but have a daily average ∼1 × 10 −4 s −1 resulting in a τ ∼3 hours.Thus, in much less than a day any stratospheric O 3 transported to the troposphere would have its isotope composition reset to values based on T-P of the air mass in which it photolyzes and reforms.However, in regions where stratospheric O 3 mixing is high but its photolysis rate is low, such as polar winters, stratospheric O 3 may still influence NO x 's isotopic composition.Yet, minimal sunlight in polar winters would also inhibit NO x recycling itself (discussed below), so the net isotopic effect is unclear and would require more detailed 3D chemical transport modeling.
It is emphasized that the model predicted δ 18 O and 17 O values are those for NO 2 produced by NO x -O 3 isotope equilibrium only and would not likely represent the actual tropospheric NO 2 values.Under low NO x conditions, hydroperoxy and organo-peroxy radicals are the main oxidants that convert NO into NO 2 .These radicals form mainly when H and organic radicals (R) react with air O 2 , which has a 17 O value of about zero.If one assumes that the product peroxy One set denotes the case of low ozone and low NO x : 5 ppbv O 3 , 30 pptv NO x , and a NO 2 j coefficient of 0.00033 s −1 and demonstrates that under these conditions equilibrium occurs after 9 h.The second set denotes the case of high ozone and high NO x : 50 ppbv O 3 and 10 ppbv NO x (typical of urban and suburban pollutant levels) and a NO 2 j -coefficient of 0.007 s −1 .In this case, the equilibrium is reached in about 60 min.radicals also have near zero 17 O values and that the NO oxidation process itself follows mass dependent isotope fractionation rules, then the NO 2 produced during peroxy radical oxidation of NO should have a 17 O value of zero.Therefore, the final 17 O (and δ 18 O) value of tropospheric NO 2 will depend on the proportion of NO oxidized by peroxy radicals relative to oxidation by O 3 (Michalski et al., 2003;Morin et al., 2008).This dilution effect is incorporated into isotope mass balance models used to predict atmospheric nitrate 17 O values (Michalski et al., 2003;Morin et al., 2008;Alexander et al., 2009).However, these models require an estimate of the 17 O value of NO 2 generated by NO x -O 3 equilibrium, which has a value of ∼45 ‰ as shown here.
While the NO x -O 3 isotopic equilibrium δ 18 O and 17 O values are nearly the same regardless of NO x mixing ratios (at ppbv levels), the timescale reach isotopic equilibrium can be significantly different (Fig. 8).Simulations run at 20 ppbv to 10 pptv NO x predict NO x -O 3 equilibrium times of hours to several days.These longer equilibrium times predicted by the present model are gross overestimations because at pptv mixing ratios in a NO x only system (no organics) the model shows that [NO] ∼ [O 3 ] as per R5 (Pandis and Seinfeld, 1998).Thus in our model using pptv levels of NO x the result is pptv levels of O 3 , which results in significantly slower isotope recycling rates, mainly via slow NO oxidation by O 3 .In the real world, even in remote regions of the troposphere, O 3 mixing ratios below 10 ppbv are rare, and they are typically 5 times higher than NO x (Crutzen and Lelieveld, 2001;Faloona et al., 2000;Jaegle et al., 2000;Liu et al., 1987), which would greatly accelerate the equilibrium process.Simulations initialized to urban to rural O 3 and NO x mixing (10-50 ppbv and 1-10 ppbv, respectively) equilibrate in less than an hour or two (Fig. 8).However, even at these high O 3 mixing ratios the timescale to equilibrium can be sufficiently slow such that NO x -O 3 equilibrium may not be reached and may manifest itself in the isotopes of atmospheric NO − 3 if the NO x -O 3 equilibrium is slower than conversion to HNO 3 .The lifetime for daytime conversion of NO 2 into HNO 3 by reaction by hydroxyl radical at typical OH mixing ratios (1 × 10 6 molecules/cm 3 ) is τ = 1/[OH]2.4× 10 −11 cm 3 / molecules s, which is on the order of 10 h, so there may be situations in remote regions where NO x -O 3 only chemistry does not reach isotope equilibrium before the NO x is converted to nitric acid.For example, when initializing our model under conditions observed by Morin et al. (2007) (i.e., 5 ppbv O 3 , 20 pptv NO x (assumed), and NO 2 J coefficients of 1.7 × 10 −3 (29 March, noon) or 5.6 × 10 −4 (29 March, 6 p.m.)), it requires 4 h before NO x -O 3 isotopic equilibrium is achieved.The lack of NO x -O 3 isotope equilibrium would be exacerbated with approaching polar winters and nights when j NO 2 becomes small since this rate ultimately controls the isotope recycling rate in the NO x -O 3 .The NO 2 lifetime at night is controlled by NO 3 / N 2 O 5 chemistry that in turn depends mainly on aerosol types and their surface area, but has value similar to that of the OH reaction.Under these conditions NO x -O 3 equilibrium may be sufficiently slow relative to HNO 3 production to impact the 17 O values of NO − 3 .For example, the NO 2 J coefficient for Alert, Nunavut, Canada (82 • 30 N, 62 • 19 W) on 7 October at noon is 0.00033 s −1 and using the same O 3 mixing ratios as observed by Morin et al. (2008) the resulting time to equilibrium is roughly 9 h.Given there are only ∼5 h of daylight at this time of year at this latitude, daytime NO x -O 3 equilibrium is not likely to be achieved before there is some nighttime conversion of NO x into HNO 3 .Therefore, we predict that there should be significantly lower NO 2 δ 18 O and 17 O values in polar regions, especially those that have high winter NO x emissions relative to NO x / NO − 3 transport (mid latitudes or the stratosphere) where NO x -O 3 equilibrium would have been complete.However, this prediction of lower NO x (NO − 3 ) δ 18 O/ 17 O values in polar winters may not be realized in observations because of the possibility of dark NO x oxidation by isotopically heavy stratospheric O 3 (as mentioned above), the influx of stratospherically derived equilibrated NO x , and because the NO −

Conclusion
The isotope systematics of the NO x -O 2 -O 3 photochemical cycle has been investigated by experiment and kinetic modeling.The experiments confirm that photochemical cycling between NO x and O 3 generate high δ 18 O and 17 O values in NO x as a result of rapid effective equilibration of O 3 and NO x .The good agreement between the predictions of the model that uses literature experimental rate constants (for ozone formation and other reactions shown in Table 4) and the observations suggests that the NO oxidation by O 3 occurs primarily through the terminal atom extraction as predicted by ab initio calculations.The 17 O and δ 18 O values of tropospheric NO x (relative to VMOW) generated by NO x -O 3 only chemistry were estimated to be 45 ‰ and 117 ‰ based on this model.These values should be used as the basis for isotope mass balance models that aim to predict 17 O values in atmospheric NO − 3 .

Figure 1 .
Figure 1.Experimental set up for study of isotopic changes in NO x produced during Leighton cycle involving isotopologues of O 2 -NO x -O 3 .The symbols are, A: Xenon Lamp, B: Quartz window, C: Reaction chamber (∼20 L), D: U-trap, E: Oxygen tank, F: Pressure gauge, G: Pirani vacuum gauge, H: NO 2 flask, I: Spiral trap, J: Tesla Discharge chamber, K: Molecular sieve chromatography column, L: Sample tube with Molecular sieve, M: Baratron Gauge, N: Turbo-molecular pump and O: Rotary Pump.

Figure 3 .
Figure 3. Change in the steady state δ 18 O and 17 O values of NO x as function of the initial NO 2 amount as a result of photochemical cycling in a 20 L chamber at O 2 pressure of 500 torr.Isotopic exchange between O and NO x suppresses the δ -values at high NO 2 concentrations as seen by close agreement with the model predictions (see text for details).

Figure 7 .
Figure 7. Variation of rate coefficient ratios of asymmetric heavy ozone formation as a function of pressure.r 18 values and r 17 values denote rate factors of OOQ formed by O + OQ + M → OOQ and OOP formed by O +OP + M → OOP relative to the formation of OOO, respectively.These values are derived by trial and error method using the Kintecus model such that the simulated δ-values of O 3 match the experimental values in Mauersberger et al. (2005).

Figure 8 .
Figure 8.Time variation of modeled NO x isotope ratios to show timescale to NO x -O 3 isotopic equilibrium for different initial concentrations.The curves denote δ 18 O and 17 O values of NO x (relative to tank O 2 in ‰).One set denotes the case of low ozone and low NO x : 5 ppbv O 3 , 30 pptv NO x , and a NO 2 j coefficient of 0.00033 s −1 and demonstrates that under these conditions equilibrium occurs after 9 h.The second set denotes the case of high ozone and high NO x : 50 ppbv O 3 and 10 ppbv NO x (typical of urban and suburban pollutant levels) and a NO 2 j -coefficient of 0.007 s −1 .In this case, the equilibrium is reached in about 60 min.
are also controlled by N 2 O 5 , NO 3 , OH and BrO oxidation pathways.Nevertheless, this does suggest that NO − 3 isotopes may be useful for delineating between local and stratospheric NO x oxidation.Likewise, we predict that NO − 3 produced by nighttime NO x emissions would have lower NO 2 δ 18 O and 17 O values relative to daytime and result in lower δ 18 O and 17 O values in atmospheric NO − 3 .This may be detectable by rapid (hourly) collection and analysis of NO − 3 δ 18 O/ 17 O values in urban areas with high nighttime NO x emissions and thus may give insight into the lifetime of nocturnal NO x .
O 3 or 16 O 18 O 16 O and 16 O 17 O 16 O), which more readily undergoes unimolecular decomposition back to O + O 2 .Recent quantum calculations by

Table 1 .
Mauersberger et al. (2005)n of NO x modified by ozone in a NO x cycle experiment where the O-atom is supplied by dissociation of NO 2 by UV (Leighton cycle) with O 2 pressure at 500 torr and exposure time of 60 min.The δ-values refer to total NO x produced and are relative to the tank oxygen in ‰ to express enrichment.The model values are obtained using coefficients 1.352 and 1.252 for formation of OOQ and OOP as discussed in the text.Predicted ozone δ-values (in ‰) are: 84.7 (δ 17 O), 95.2 (δ 18 O) and 34.3 ( 17 O) in close agreement with enrichment values 86.0, 96.6 and 34.9 obtained by interpolation using data fromGuenther et al. (1999)andMauersberger et al. (2005).

Figure 2. The time scale for NO x to achieve isotopic equilibrium in δ 18
O and 17O is approximately 30 min based on NO x cycling experiment run with NO 2 / O 2 ratio of 23 × 10 −6 (23 ppmv) at O 2 pressure of 750 torr in a 20 L chamber.

Michalski et al.: NO x cycle and the tropospheric ozone isotope anomaly
Change in δ -values of NO 2 as a result of photochemical cycling achieved with 20 µmole of NO 2 at oxygen pressures ranging from 50 to 750 torr in a 20 L chamber.As the O 2 pressure increases the ozone formation rate increases imparting higher enrichment to NO 2 .
The highest (relative to tank O 2 ) NO x δ 18 O values, 84.2 ± 4 ‰ (n = 3), were from the experiments conducted at pressures around 750 torr (typical atmospheric pressure), with corresponding 17 O values of 39.3 ± 1.6 ‰ (Table2).We could not investigate enrichments for mixing ratios lower than 20 ppmv NO 2 because of minimum sample size G.

variable pressure) 500 torr O 2 (variable NO 2 ) Figure 5. 17
O of NO 2 based on combined data from Table1(open symbols for variable initial NO 2 ) and Table2(filled symbols for variable O 2 pressure) plotted as a function of NO 2 / O 2 mixing ratio.As the NO 2 mixing ratio decreases, the 17 O values increase until they remain constant at a value of about 40 ‰ when the NO 2 mixing-ratio reaches about 20 ppmv (seen for both data sets).At the same mixing ratio, but higher O 2 pressure, the ozone formation rate increases resulting in more ozone oxidation of NO and larger 17 O values in the product NO 2 (the filled symbols).

Table 2 .
Oxygen isotopic composition of NO x modified by ozone formed by UV in presence of oxygen with O-atom supplied by dissociation of NO 2(Leighton cycle); the δ-values show enrichment of produced NO x relative to tank oxygen in ‰.Model values are calculated by Kintecus with coefficients chosen for 18 O and 17 O asymmetric ozone formation to match the observed values of isotopic enrichment as given in Table5.The experiments that produced the highest NO x δ 18 O and 17 O values can be qualitatively explained by the isotopic distribution within the O 3 molecule (i.e., the isotope mass balance assumption that 17 O-terminal O 3 = 3/2 * 17 Obulk O 3 ) and transition state during the NO + O 3 reaction.
(Thiemens and Jackson, 1990;Mauersberger et al., 2005).Tank Oxygen δ-values: −5.69 (δ 17 O) and −10.84 (δ 18 O) in ‰ relative to VSMOW.* 17 O= 1000•ln(1+δ 17 O/1000)−0.516•1000•ln(1+δ181000) measures the magnitude of mass independent enrichment.xoxidationandexchange reactions during the cycle.The inset shows good agreement (slope = 0.997; r 2 = 0.991) between model predictions of ozone 17 O with experimentally observed values by Mauersberger et al. (2005)O 2 (∼0.4 mole).However, the similarity between the product NO x δ 18 O and 17 O values and those in previous O 3 experiments(Thiemens and Jackson, 1990;Mauersberger et al., 2005)suggests that isotope enrichment in O 3 is no different when the O atom that generates O 3 is supplied by NO 2 dissociation via lower energy photons compared to high energy dissociation of O 2 (UV photolysis/electron impact).Therefore, it appears that the O 3 isotope enrichment process, including the MIF, is insensitive to the initial energy distribution of the O-atoms.
for NO 2 and NO the δ-values in the model can be defined based on species ratio as usual for mass spectrometric measurements.Therefore, in this case we use: P/O= [PNO]/{2[ONO]}

Table 3 .
Description of dominant oxygen species used in the Kintecus chemical reaction model to simulate the NO x -O 3 cycling experiment (O= 16 O, P= 17 O, Q= 18 O).It is assumed that three major species together constitute close to 100 % and other minor species can be neglected in the model.δ-values are relative to VSMOW in ‰.

Table 4 .
Adopted rate constants of reactions involving isotopomers of the species taking part in photolysis of NO 2 in presence of oxygen at 50 torr.The factors for the formation rates of heavy ozone isotopologues are given in Table6and discussed in the text.

Table 5 .
Mauersberger et al. (2005)tive to the source oxygen as obtained from literature at various pressures of oxygen.The two coefficients for asymmetric ozone formation as a function of pressure are also given and they are chosen such that the model predicted δ-values match the experimental values within 1 ‰.The 1σ error on each r-value is about 0.012.The experimental values used for fitting are taken fromGuenther et al. (1999)andMauersberger et al. (2005).* * * 17 O = 1000 • ln(1+δ 17 O/1000)−0.516• 1000 • ln(1+δ 18 O/1000) measures the magnitude of mass independent enrichment.

Table 6 .
Test of sensitivity of the isotope anomaly 17 O (NO x ) in the model due to four reactions involving NO x including exchanges.These reactions dilute the full anomaly expected from transfer of ozone anomaly as seen from values of dilution defined for 50 and 500 torr pressure, i.e., fractional deviation from 68 and 48 ‰ respectively.Zero value indicates no dilution whereas 0.92 indicates 92 % dilution.
Table 5).Additionally, their experiments refer to the photolytically produced O 3 δ-values in an O 2 -N 2 system whereas the modeled values in this study refer to O 3 formation where the O-atoms are supplied by NO 2 dissociation.Unlike those studies, this O atom and O 3 can exchange/react with NO and NO 2 .The rate constant values that were obtained by this fitting technique may have some limitation in application to O 3 formed in pure O 2 -N 2 .However, they should be appropriate in case of atmospheric applications.