Caution with spectroscopic NO2 reference cells (cuvettes)

Spectroscopic measurements of atmospheric trace gases, for example, by differential optical absorption spectroscopy (DOAS), are frequently supported by recording the trace-gas column density (CD) in absorption cells (cuvettes), which are temporarily inserted into the light path. The idea is to verify the proper functioning of the instruments, to check the spectral registration (wavelength calibration and spectral resolution), and to perform some kind of calibration (absolute determination of trace-gas CDs). In addition, trace-gas absorption cells are a central component in gas correlation spectroscopy instruments. In principle DOAS applications do not require absorption-cell calibration; however, in practice, measurements with absorption cells in the spectrometer’s light path are frequently performed. Since NO2 is a particularly popular molecule to be studied by DOAS, and at the same time it can be unstable in cells, we chose it as an example to demonstrate that the effective CD seen by the instrument can deviate greatly (by orders of magnitude) from expected values. Analytical calculations and kinetic model studies show the dominating influence of photolysis and dimerization of NO2. In particular, this means that the partial pressure of NO2 in the cell matters. However, problems can be particularly severe at high NO2 pressures (around 105 Pa) as well as low NO2 partial pressures (of the order of a few 100 Pa). Also, it can be of importance whether the cell contains pure NO2 or is topped up with air or oxygen (O2). Some suggestions to improve the situation are discussed.


Introduction
There are a number of reasons for using absorption cells in conjunction with instruments measuring trace-gas column densities (CDs) by absorption spectroscopy, e.g. by differential optical absorption spectroscopy (DOAS).These include the verification of the overall functioning of the instrument, stray-light determination, or a check of the instrument's absolute wavelength calibration.
Field calibration of a spectrometer is not necessary for UV-visible absorption spectroscopy (see e.g.Platt and Stutz, 2008), since the instrument can be calibrated by using highresolution absorption cross-section spectra of the particular gases.This is accomplished by (1) determining the instrument function (IF) and (2) convoluting a high-resolution trace-gas cross-section spectrum with this IF and then (3) fitting the resulting trace-gas cross section to measured spectra in order to obtain the trace-gas CD.The details of this process are explained in studies, e.g. by Platt and Stutz (2008).However, it may be tempting to perform the calibration process simply by recording the CD of an absorption cell filled with a known amount of trace gas brought into the light path of the instrument.This approach complicates the measurements and may introduce additional errors due to uncertainties in the trace-gas CD in the cell.Nevertheless such procedures may work for a series of gases, like O 2 , CO, CO 2 , and CH 4 , which do not (at ambient temperature) undergo self-reaction and which are neither photolysed by ambient solar radiation near the Earth's surface nor by the radiation typically used for their absorption spectroscopic measurement.
Published by Copernicus Publications on behalf of the European Geosciences Union.
On the other hand, if a trace-gas cell is used to determine absolute wavelength calibration of a spectrometer, the absolute trace-gas CD in the cell is usually not critical.
In addition, gas correlation spectroscopy measurements (e.g. Ward and Zwick, 1975;Sandsten et al., 1996Sandsten et al., , 2004;;Kebabian et al., 2000) require absorption cells containing the gas to be measured at CDs leading to optical densities around unity.
In general, there are a number of issues with using gas cells for these purposes, including the following: optical problems with the cell stability of the gas in the cell due to photolysis and/or other chemical reactions temperature dependence of chemical equilibria within the cell temperature dependence of the optical density.
In the following we discuss the above problems for the case of NO 2 -absorption cells; however some of the discussed issues will also apply to cells with other gases.

Optics of cells
In principle the introduction of an absorption cell into the optical path of a remote-sensing instrument (e.g. a spectrometer) is straightforward.The cell is mounted in front of the entrance optics, and in the first approximation the absorption due to the trace gas in the cell (i.e.due to the trace-gas CD) is added to the trace-gas absorption seen without the cell.While this view is correct in some approximation, in detail there are a number of problems that need investigation.

Path length in an isolated cell
In a realistic cell, partial reflection (reflectance R) occurs at the cell windows.For simplicity we assume an index of refraction of n = 1.5 for the cell window material and accordingly (Fresnel formula) i.e. about 4 % reflection per surface for near-normal incidence (see Fig. 1).The reduction of the incoming intensity by (1−R) 4 , or about 15 %, is probably of minor importance; however (if we neglect the absorption by the trace gas in the cell) a fraction of about (1 − R) 2 • (R + R) 2 ≈ 0.59 % of the incoming radiation and 0.69 % of the transmitted radiation passes the cell three times (this effect will be lower at high trace-gas optical densities and also could be reduced by adding anti-reflective coatings to the cell windows).Due to this multiply reflected light the total absorption of the cell (and thus the trace-gas slant column density -SCD -S C ) Figure 1.Sketch of the optics of a gas absorption cell; parallel rays are assumed, and the (small) tilt of the incoming ray with respect to the cell axis is introduced to distinguish the rays.The described effect will also be there at strictly normal incidence.We assume an index of refraction of n = 1.5 for the cell window material and accordingly 4 % reflection per surface (for near-normal incidence).Note that a fraction of about 0.69 % of the transmitted radiation passes the cell three times, thus adding ≈ 2 % to the total absorption (if the trace-gas absorption in the cell is small).
will be enhanced by about 2 % over the CD S 0 for a single traverse.We note that the case of nearly normal incidence is quite realistic in many cases; for instance multi-axis DOAS (MAX-DOAS) instruments (e.g.Hönninger and Platt, 2002;Platt and Stutz, 2008) have total aperture angles of the order of 1 • , i.e. incidence angles of −0.5 to +0.5 • .A typical use of a cell would be to mount it just in front of the instrument's telescope.In this arrangement the enhancement of the light path inside the cell (and thus the trace-gas column density S C ) due to the finite aperture angle of the radiation passing the cell will vary according to S C = S 0 / cos(ϑ), with S 0 denoting the trace-gas CD for rays parallel to the cell axis.An angle of ϑ = 0.5 • would lead to an enhancement in S C /S 0 of ≈ 1.000038 or 0.004 %.
Thus a slight (few degrees) tilt of the cell will not lead to noticeable light path extension in the cell, but already a 1 • tilt, leading to 0.015 % light path extension, would be sufficient to direct the multiple reflected light outside the field of view of the telescope.Thus, the additional 2 % cell absorption would disappear.On the other hand, larger tilts of the cell, for example of 10 • , would increase the cell absorption again by 1.5 % and should therefore be avoided.This could be accomplished by a rigid mount which fixes the (removable) cell at a defined angle with respect to the cell optical axis (normal of the windows), e.g. at 2 • .
As will be discussed below, the acceptance angle of the cell to ambient direct or scattered sunlight can play a significant role.Therefore, this small aperture angle allows for shielding the cell from sunlight, since solar radiation only needs to enter from a small solid angle (of the order of 10 −3 sr), for instance, by mounting the cell inside a relatively long tube made of nontransparent material.

Path length in a cell as part of an optical system
In Sect.2.1 we discussed the behaviour of an isolated cell; however the idea is to incorporate an absorption cell into an optical system, i.e. to just hold it in front of a MAX-DOAS instrument.In this case there can be interaction between the cell and the entrance optics of the instrument (for instance due to reflection of light at the surface of the telescope lens).As described by Lübcke et al. (2013) this can further enhance the trace-gas CD in the cell as seen by the instrument looking through it.
In the case of using gas cells in imaging instruments, for instance imaging spectrometers (e.g.Lohberger et al., 2004) or gas correlation instruments (e.g. Ward and Zwick, 1975), a larger aperture angle is required.This causes two potential problems.First, the aperture angle of the cell has to be much larger than in the case of a one-pixel (narrow field of view) instrument, for instance, typically a 30 • total angle.Thus the acceptance angle for solar radiation becomes considerably larger (e.g.0.22 sr instead of 10 −3 sr), and consequently the photolysis frequencies for the gases inside the cell will be enhanced (see below).Second, the trace-gas CD of the cell becomes dependent on the observation angle ϑ (angle between the optical axis and the actual viewing direction within the field of view) as described above.For a total aperture angle of 30 • this would amount to an enhancement of the S C (15 • ) over S 0 = S C (0 • ) of about 3.5 %.

Chemistry in NO 2 -absorption cells
Nitrogen dioxide (NO 2 ) is a quite reactive gas (see rest of the section); therefore a series of chemical processes in an absorption cell can occur.Since they can alter the NO 2 concentration -and thus the NO 2 CD in the cell -considerably, they have to be watched.In the following subsections we discuss the relevant chemical processes, starting with important reactions and then proceeding to further reactions which are only relevant under certain conditions or if high accuracy is required.
We first discuss simplified chemistry, just encompassing the pertinent reactions, and then we proceed to a more comprehensive discussion of the chemistry in the following subsections.

The (initial) NO 2 -only chemistry -simple case
In a cell (initially) filled only with NO 2 we can expect a series of reactions to occur, which are described in the following (bi-molecular rate constants are given in cm 3 molec.−1 s −1 , termolecular rate constants are given in cm 6 molec.−2 s −1 for 25 • C and 1000 hPa, and details on temperature and pressure dependence as well as literature references can be found in Table 1).In fact, when buying NO 2 from a manufacturer, some of the described reactions can already proceed in the initial gas, which therefore might already contain impurities (e.g. of NO, HONO, and HNO 3 ).
Usually cells are exposed to sunlight or radiation needed for the measurement; thus NO 2 in the cell can be photolysed: The above value for J 1 is reached in full sunshine around noontime (see e.g.Jones andBayes, 1973 or Kraus andHofzumahaus, 1998).Of course this figure (and in fact all photolysis frequencies in the cell; see Table 1) is highly variable, depending on solar zenith angle (i.e.latitude, season, and time of day), cloudiness, atmospheric turbidity, and the shading situation at the measurement site.In the case of active DOAS systems the photolysis frequencies will depend on the intensity of the light source and on the fraction of the cell cross-section area covered by the light beam.Nevertheless, it is frequently seen that calibration cells are used in full sunshine without any shielding; moreover, as is shown below (see Sect. 4), the effects on the NO 2 chemistry are similar over a wide range of photolysis frequencies.
In the following, ground-state oxygen atoms O( 3 P) will be denoted by O.The threshold wavelength for Reaction (R1) is about 398 nm (e.g.Johnston and Graham, 1974;Burkholder et al., 2015); however, due to vibrational excitation of the ground-state molecule there is noticeable photolysis up to about 430 nm.If the cell is only illuminated with radiation of a wavelength longer than 430 nm, NO 2 will not photolyse and J 1 will be essentially zero.
Although it is only a small effect it is worth noting that the photolysis frequency inside a cell is not different from the value in the air surrounding the cell despite reflectance of the cell walls, as described by, for example, Bahe et al. (1979).
The oxygen atoms produced in Reaction (R1) can (1) recombine However, this is a slow process, because the O-atom concentration will be very low (see Figs. 4 to 8).Alternatively, (2) O atoms may react with the wall where they predominantly recombine (see e.g.Cartry et al., 2000): Also, (3) O atoms can react with NO 2 to form NO: Further, (4) oxygen atoms also may react with NO to form NO 2 : The final possibility, (5) formation of NO 3 -as well as further reactions, will be addressed in Sect.3.4 below.
In addition there is the termolecular reaction of the O 2 formed in Reactions (R4) or (R2) (or added to the cell filling) that oxidizes NO to NO 2 : In an attempt to obtain a first-order quantitative understanding of the processes in the cell, we just consider a pure NO 2 initial filling and Reactions (R1) (NO 2 photolysis), (R4) (O + NO 2 ), and (R6) (2NO + O 2 ).
From the combination of Reactions (R1) and (R4) we derive the rates of NO and O 2 formation under illumination, which ultimately (i.e. in the stationary state) must equal the rate of NO destruction, D(NO) and NO 2 formation, and P (NO 2 ) due to Reaction (R6): Since P (O 2 ) ≈ 0.5 • P (NO) and the concentration of both species are zero initially, we have and equating P (NO) with D(NO), we obtain Further substituting or This cubic equation can be solved for the stationary-state NO concentration [NO] S as a function of the initial [NO 2 ] 0 as given in Appendix A. Examples.
(1) As an example, and to obtain a first idea of what might be happening in the cell, we assume about 1 atm (1000 hPa) of pure NO 2 (initially); i.e. the initial NO 2 concentrations in the cell will be [NO 2 ] 0 ≈ 2.4 × 10 19 cm −3 and the very simple chemical system just comprising Reactions (R1), (R4), and (R6).As we show below, the simplified reaction system -with the exception of the NO 2 dimer (N 2 O 4 ) formation (see Sect. 3.2) -is quite adequate.Also, such a cell would have a peak optical density (at around 440 nm) of about 14 at 1 cm length but much lower at other wavelengths.
In the dark (J 1 = 0) nothing will happen, while in sunlight (J 1 = 8 × 10 −3 ): NO + O formation will take place followed by Reaction (R4) of NO 2 with O. Thus the (initial) rate of NO formation P (NO) will be This will lead to an initial decay time The stationarystate NO concentration can be calculated according to Eq. ( 7) and the solution given in Appendix A to be [NO] S ≈ 2.57 × 10 18 molec.cm −3 , or about 10.7 % of the initial NO 2 level.In other words, the NO 2 concentration will be reduced to 89.3 % of its initial value [NO 2 ] 0 .The corresponding NO rate of destruction will be from NO 2 photolysis .
(2) We give a further example using about 1 hPa of pure NO 2 (initially) corresponding to [NO 2 ] 0 ≈ 2.4 × 10 16 cm −3 , and the same simple chemical system, just comprising Reactions (R1), (R4), and (R6), as above.Such a cell would have an initial differential optical density in the vicinity of 450 nm of about 2.4 × 10 −3 and would thus appear ideal to test the sensitivity of an NO 2 spectrometer.
In sunlight we have D(NO 2 ) ≈ 1.92 × 10 14 cm −3 s −1 .In this case, the resulting stationary-state NO level becomes [NO] S ≈ 2.4 × 10 16 , or about 100 % of the initial NO 2 .In other words after illumination the remaining NO 2 concentration and thus the NO 2 CD of the cell will only be a very small fraction of the expected value ).After a short (of the order of 1 min) exposure to sunlight the NO 2 in the cell will practically vanish.
On the other hand, in this simplified calculation, the NO reconversion, D(NO), to NO 2 will be much slower than the initial photolysis: Recovery from illumination.A further interesting question concerns the time for the chemical system to recover from a period of photolysis.Equation (4) gives the rate of NO destruction as a function of [NO].In the case of example (1), above NO would decay with an initial rate of D(NO)/[NO] ≈ 0.11 s −1 (ca.11 % per second, suggesting a 9 s time constant for recovery).However, D(NO) varies with the third power of [NO].When, for example, 90 % the NO is consumed (i.e.1.4 % of [NO] is still left) the time constant would increase by a factor of 1000 to around 3 h.In the case of example (2), the initial reconversion rate would only be 5.6 × 10 −6 s −1 (or ≈ 49 % per day), which would seem to imply a recovery time of somewhat more than 2 d.But again the dependence on the cube of the NO concentration means that the recovery time becomes much longer later on.For some model results, see Fig. 9.

The
There is a thermal decay of the dimer, leading to an equilibrium with the equilibrium constant (298K; from Atkinson et al., 2004), Note that the time to attain the equilibrium is shorter than 1/k 8 ≈ 7 µs (at 298 K and 1000 hPa).Thus, one can assume that there is always equilibrium between NO 2 and N 2 O 4 .From this follows, for the What is usually most interesting is the fraction of NO 2 of the total amount of NO 2 + N 2 O 4 (i.e.pressure during filling) in the cell.The fraction is given by which can be transformed into and solved for [NO 2 ], with the only positive solution: or The relationship between NO 2 and For example, [M] = 2.4 × 10 19 (1000 hPa or ca. 1 atm of total pressure, at 298 K), resulting in [NO 2 ] 1 ≈ 8.29 × 10 18 molec.cm −3 and [NO 2 ] 1 /[NO Z ] ≈ 0.344.Thus, filling a cell from an NO 2 reservoir (e.g. an NO 2 tank) to 1 atm of total pressure will lead to only 34 % of this pressure being present as NO 2 (see also Fig. 2).
At 100, 10, and 1 hPa (ca.0.1, 0.01, and 0.001 atm) of NO 2 + N 2 O 4 , the corresponding figures for [NO 2 ] 1 /[NO Z ] would be 0.717, 0.95, and 0.995, respectively.These figures are independent of an additional topping with air or oxygen to a full atmosphere of total pressure, as is described below.In other words, unless the NO 2 partial pressure is below around 10 Pa, the actual NO 2 partial pressure (and thus the concentration of NO 2 ) will be below expected levels by two-digit percentages.
A further problem associated with the NO 2 -N 2 O 4 equilibrium is the marked temperature dependence of the equilibrium constant.In the usual Arrhenius expression, it is given as with A = 1.07 × 10 −28 cm −3 molec.−1 and B = 6400 K (see Table 1).The (relative) temperature dependence of K Eq is given by and with the above values for A and B, we obtain, for the relative change in the equilibrium constant, In other words the equilibrium constant is reduced by more than 7 % K −1 of heating.Fortunately the effect on NO 2 is somewhat smaller, ranging from nearly zero change at very small NO 2 levels to about a 3 % increase per degree of heating at 1000 hPa (see Appendix B).

NO 2 + O 2 chemistry
The addition of O 2 (or air) to the NO 2 filling can greatly help with stabilizing the NO 2 concentration in a cell under certain conditions.
In the presence of molecular oxygen, following the photolysis of NO 2 , ozone is formed in the cell: This in turn can react with NO to form NO 2 :  The reaction scheme encompassing the reaction pathways discussed above is sketched in Fig. 3.
Here we can distinguish two regimes.The first regime assumes comparable concentrations of O 2 and NO 2 , i.e.
[O 2 ]/[NO 2 ] around unity.In this case the termolecular oxidation of NO by O 2 dominates.This is similar to the situation discussed in Sect.3.1; however we can take the O 2 concentration [O 2 ] to be essentially constant.This reduces the third-order kinetics of Eq. ( 7) to pseudo-second-order or second-order kinetics, and we obtain For example we may assume 0.5 atm (500 hPa) each of pure NO 2 and O 2 (initially); i.e. the initial concentrations of either species in the cell will be In sunlight we have NO 2 photolysis (Reaction R1) followed by O + NO 2 (Reaction R4) plus oxidation of NO by O 2 ; From this stationary-state assumption we can calculate [NO] s : Thus, the NO 2 concentration would be reduced by only 5.4 % from its initial value once the cell is exposed to sunlight.
The second regime assumes a high [O 2 ]/[NO 2 ] ratio (for instance larger than 10 4 ) so that the reaction of O atoms formed in NO 2 photolysis is much more likely to react with O 2 than with NO 2 .In this case for each molecule of NO 2 photolysed nearly one molecule of O 3 is formed, which will react with the NO molecule produced in the NO 2 photolysis.The O 3 concentration will rise until its reaction with NO balances the rate of NO 2 photolysis: For instance at [NO 2 ] = 2.4 × 10 15 cm −3 and about 1 atm (1000 hPa) of O 2 , the stationary-state NO level would be [NO] ≈ 4.4 × 10 13 cm −3 , or about 1.8 % of the initial NO 2 concentration.Note that a small fraction (about 10 −4 in this example) of the O atoms produced in the NO 2 photolysis would still react with NO 2 and form NO without a corresponding O 3 production (rate about 2 × 10 9 cm −3 s −1 ); thus the NO fraction in the cell would slowly grow until Reaction (R6) balances this process.At the above NO level the rate of NO 2 formation would be around 10 9 cm −3 s −1 ; thus the NO level would slightly grow (by about 50 %) during several days of continuous illumination of the cell.

The (initial) NO 2 -only chemistry -some complications
In addition to the three reactions described above, O atoms can recombine with NO 2 to form nitrate radicals, NO 3 : k 11 (298 K, 10 5 Pa) ≈ 2.5 × 10 −11 cm 3 molec.−1 s −1 . (R11) The NO 3 radicals formed in Reaction (R11) can be photolysed: The threshold wavelength is much longer than in the case of NO 2 (J 1 ), and the photolysis is much faster.Alternatively, NO 3 may react with NO (from Reaction R1) to re-form NO 2 , or undergo self-reaction, Finally, and typically most likely, NO 3 will react with NO 2 to form dinitrogen pentoxide, N 2 O 5 : k 15 (298 K, 10 5 Pa) ≈ 1.34 × 10 −12 cm 3 molec.−1 s −1 .(R15) Dinitrogen pentoxide is thermally unstable and decays: In the absence of water (dry system) N 2 O 5 will just be another reservoir potentially sequestering some of the NO 2 .On the other hand, N 2 O 5 is the anhydride of nitric acid and may react with water to form HNO 3 .While the reaction of N 2 O 5 plus water vapour appears to be exceedingly slow in the gas phase, it may react with a layer at the cell surface; details are given in Sect.3.5.Analysing the above system of reactions, one notices that loss of O atoms other than by Reactions (R4) or (R11) are of minor importance.This is underlined by the results of the model calculations using the full chemical system (see Table 1) presented in Sect. 4.
Therefore, we can summarize that each photolysis Reaction (R1) is followed by a conversion of NO 2 to NO (Reaction R4) or to NO 3 (Reaction R11).However, NO 3 is largely converted back to NO 2 by Reactions (R12a), (R13), and (to a minor extent) (R14); thus, in effect each photolysis act of NO 2 leads to the loss of approximately two NO 2 molecules.Essentially NO 2 would be converted to NO + O 2 .In bright sunshine with J 1 ≈ 8 × 10 −3 s −1 , this would lead to an NO 2 lifetime in the cell of τ (NO 2 ) ≈ 1/(2 • J 1 ) ≈ 63 s, or roughly 1 min.Even if the cell is kept in the shade or is only exposed to indoor illumination where J 1 could be estimated to be 10 times (shade) to 100 times (indoor) smaller than in bright sunshine the conversion could be expected to proceed within around 10 min (shade) to 100 min (indoor) or even faster.

NO
Since water is by far the most abundant (typical mixing ratios around 1 %) reactive trace gas in the ambient atmosphere (not counting nobel gases, CO 2 , H 2 , or N 2 O), it may be possible that if traces of water enter the cell when it is filled, then a series of additional reactions may play a role (see e.g.Bahe et al., 1979): Followed by quenching of O( 1 D) to O( 3 P) or the formation of hydroxyl (OH) radicals, In an NO 2 cell, OH radicals are most likely to react with NO 2 (or NO) to form nitric acid (or nitrous acid; see below): OH + NO 2 + M → HNO 3 + M, k 19 (298 K, 10 5 Pa) ≈ 1.05 × 10 −11 cm 3 molec.−1 s −1 .(R19) Nitric acid is photolysed very slowly, and also its reaction with OH (to form NO 3 ) is slow; thus it will constitute a final sink of NO 2 (and water) in the cell.Alternatively, OH may react with NO to form nitrous acid: which -in turn -is lost by photolysis, In addition, N 2 O 5 , formed in Reaction (R15), can react with (liquid) water adsorbed at the wall of the cell, also forming HNO 3 :  Finally NO 2 is also known to heterogeneously react with water: Although this reaction appears to be second order in NO 2 , several studies (e.g. by Kleffmann et al., 1998) found a firstorder dependence of HONO formation on the NO 2 concentration probably because the NO 2 reaction with NO 2 adsorbed at the wall is rate limiting.Therefore, heterogeneous reactions of N 2 O 4 with water are probably not important.HNO 2 will photolyse relatively quickly to form OH + NO (with OH in most cases reacting according to Reaction R19); and HNO 3 from the above two reactions will remain.Our model calculations actually show that all H 2 O is ultimately (typically after a few hours in full sunshine) converted to HNO 3 , sequestering equivalent amounts of NO 2 and water; thus no HONO will remain after this time.
For example a cell having been filled with a very small amount of NO 2 (e.g. 10 hPa or 2.4 × 10 17 molec.cm −3 ) is topped with ambient (e.g.laboratory) air (which is of course not recommended; see Sect.5.2) at 25 • C and 70 % relative humidity.Thus the approximate amount of water admitted is 70 % of the saturation vapour pressure of H 2 O at that temperature (70 % of 31.6 hPa = 22.1 hPa or 5.3 × 10 17 molec cm −3 ).Some of this water will form a film at the inside of the cell and allow heterogeneous Reactions (R22) and (R23), converting NO 2 into HNO 3 , although it is hard to judge how fast this process will proceed.In addition, upon illumination with UV-radiation Reactions (R9), (R17), (R18), and (R19) will provide (relatively slow) gas-phase conversion of NO 2 to HNO 3 .Since the amount of H 2 O in this example exceeds the amount of NO 2 it is likely that ultimately all NO 2 is converted to HNO 3 , as can be seen in Figs. 4 to 8.  1).Same as Fig. 4, but with initial O 2 assumed; (a) logarithmic scale and (b) linear scale.

Gas kinetic simulations
We performed a series of gas-kinetic-simulation calculations in order to illustrate the behaviour of the reaction system described above under various conditions of initial NO 2 and amounts of added O 2 .In a one-box model, the system of coupled ordinary differential equations resulting from the above reactions was solved numerically.This allows following the temporal evolution of the concentration of the individual gases in the cell under given conditions.Our full model includes Reactions (R1) to (R23), except (R3) and (R22) of Table 1 (marked with an asterisk in column 1).The heterogeneous Reaction (R23) was included in the simulation, with the parameterization proposed by Kleffmann et al. (1998) k 23 = 0.25•S/V •v •γ , with uptake coefficient γ = 10 −6 , the molecular velocity of NO 2 v, and the surface-to-volume ratio S/V ).We assumed a typical cell (cylindrical, radius of 1 cm, and length of 5 cm, S/V = 240 m −1 ) as well as estimates of the amount of H 2 O in this cell from assuming a monolayer of water at the inner surface of the cuvette.Of course -given the uncertainties in heterogeneous reactions -this approach can only provide a rough estimate of the HONO concentration in the cell.
Also some runs with a subset of the reactions were performed as described in Appendix B in order to check on the simplified analytical calculations in the previous section.Table 2 shows a comparison of the NO 2 reduction after 1000 s given by the analytical calculations and the simplified model.
Further calculations encompass the full range of Reactions (R1) to (R23), except (R3) and (R22) as given in Table 1 (marked with an asterisk), where an analytical solution is not practical or is probably even impossible.Figures 4 to 8 show the results of these model runs for NO 2 , NO, O atoms, O 2 , N 2 O 4 , NO 3 , O 3 , N 2 O 5 , H 2 O, OH, HNO 3 , and HONO in an illuminated NO 2 cell for initial, N 2 O 4 -equilibrated [NO 2 ] 0 of 1, 10, 71, and 344 hPa (2.4 × 10 16 , 2.4 × 10 17 , 1.7 × 10 18 , and 0.84 × 10 19 molec.cm −3 ).In Fig. 4 no initial O 2 was assumed, and the remaining figures (Figs. 5 to 8) show time se-     Atkinson et al. (2004).c Data from Tsang and Hampson (1986).d Data from Trebs et al. (2009).e Data from Bahe and Schurath (1978).f Data from Alicke et al. (2002).The reactions marked with * are included in the kinetic model; see Sect. 4. In order to study the effect of different photolysis frequencies, we also performed model runs with all J values scaled to 1/10 of the figures given in Table 1.The resulting temporal evolutions of NO 2 are also included in Figs. 4 to 8 (note that the time series of all other species are for the J values as given in Table 1).As can be seen from these figures there  is still a rather large loss of NO 2 , even with J being only 1/10 of its value in full sunshine.This is due to the fact that the NO 2 loss scales only with the second or third root of the photolysis frequency (see analytical solutions in Sect. 3 and Appendix A).
As discussed in Sect.3.1 the recovery of NO 2 in the dark after initial illumination (e.g.due to a use of the cell in a measurement) is an important question.Figure 9 shows model calculations of the temporal evolution of NO 2 , NO, and O 2 according to the full model (Reactions R1 to R23, except Reactions R3 and R22 -see Table 1; at 298 K).The NO 2 cell is initially illuminated for 1500 s and then left in the dark afterwards for initial, N 2 O 4 -equilibrated [NO 2 ] 0 of 1, 10, 71, and 344 hPa (2.4 × 10 16 , 2.4 × 10 17 , 1.7 × 10 18 , and 0.84 × 10 19 molec.cm −3 , respectively).At the two highest [NO 2 ] 0 levels the initial NO 2 was chosen such that total pressures of 100 and 1000 hPa were reached.It can be seen that the NO 2 recovery at low NO 2 levels can take days to hours.Adding O 2 to the cell again has a strong impact on the [NO 2 ] evolution (see thin blue lines in Fig. 7), reducing the recovery time to a fraction of the NO 2 -only case.For larger initial   1).The NO 2 cell is initially illuminated for 1500 s and then left in the dark afterwards.Initial [NO 2 ] 0 of 1, 10, 71, and 344 hPa (2.4×10 16 , 2.4×10 17 , 1.7×10 18 , and 0.84×10 19 molec.cm −3 ).The blue thin line in the plots for 1, 10, and 71 hPa show [NO 2 ] for O 2 -topped-up cell.
NO 2 concentrations (e.g.71 hPa) and added O 2 , a hysteresis between initial [NO 2 ] and equilibrium [NO 2 ] in the dark can be observed; i.e. the NO 2 level does not return to its initial value after illumination.This is due to the formation of N 2 O 5 in the illuminated period.

Summary and conclusions
We conclude that the use of NO 2 cells requires careful consideration, in particular when quantitative measurements of the NO 2 CD in the cell are desired.If unfortunate parameters are chosen (e.g.rather low NO 2 pressures or no O 2 or air added), practically no NO 2 might be found in the cell at all.Also, one cannot conclude that particularly high or low NO 2 concentrations in the cell are the superior choice.At high NO 2 concentrations (approaching atmospheric pressure) a large fraction of the NO 2 is converted to the dimer N 2 O 4 , which not only reduces the NO 2 CD way below expected values but also introduces a large temperature dependence (up to 3 % per degree) of the NO 2 CD in the cell (also, there might be some additional uncertainty due to uncertainty of the equilibrium constant, as pointed out by Roscoe and Hind, 1993).On the other hand, at low NO 2 levels (e.g. 1 hPa) photolysis may convert much (if not virtually all) of the NO 2 to NO.Although NO 2 eventually recovers, this process may take long (days) to complete.Thus, the actual NO 2 CD of the cell may become dependent on the illumination and recovery history of the cell and may be rather unpredictable for a particular cell.
Unfortunately, the two described effects are not even the full story; therefore the potential problems are listed below.Fortunately, there are ways to minimize the problems, like oxygen addition to the cell and choosing the right NO 2 concentration, which may help in reducing the uncertainty of the NO 2 CD of a given cell to the single-digit percentage range.

Summary of problems
As discussed above, the NO 2 concentration in a cell -and thus the NO 2 CD of the cell -can deviate from expectations due to a number of reasons: 1. Optical effects, namely multiple reflection in the cell and tilt of the cell with respect to the optical axis, can enhance the light path and thus the apparent NO 2 CD.
2. Photolysis of NO 2 can reduce the NO 2 CD in the cell.
3. Sequestration of NO 2 as N 2 O 4 due to the thermodynamic equilibrium between the two species can reduce NO 2 in the cell and cause temperature dependence of the NO 2 CD.
4. Formation or re-formation of NO 2 from NO in the cell leads to slow recovery of NO 2 .
5. Irreversible conversion or conversion of NO 2 to HNO 3 can lead to long-term loss of NO 2 .
6. Wall loss of NO X species like N 2 O 4 or N 2 O 5 can lead to long-term loss of NO 2 5.2 Some ideas to remedy the situation One approach for minimizing loss of NO 2 in the cell is certainly to reduce the photolysis of NO 2 (Reaction R1); this can be achieved by a series of measures.
1.Only expose the cell to measurement radiation by, for example, putting it in a nontransparent tube.
2. Minimize exposure time by, for example, putting the cell in a light-tight box when not in use.
3. Use a filter in front of the cell which only admits radiation at wavelengths > 450 nm; this, however, may interfere with the measurements.
Also, it may be good to avoid ozone photolysis in the cell to minimize OH formation by using a UV-nontransparent cell material, e.g.glass instead of quartz.In addition, it is a good idea to keep the gas in the cell as dry as possible to avoid formation of HNO 3 or HNO 2 and to further minimize OH formation.Furthermore, it may be a good idea to illuminate a freshly filled cell initially (for a few hours) to allow all remaining water to be converted to HNO 3 , thus (1) minimizing later changes in the NO 2 concentration due to HNO 3 formation and (2) avoiding HONO formation.
A further important measure is to add O 2 to the cell in order to enhance reconversion of any NO formed to NO 2 .
The problems associated with excessive N 2 O 4 formation in the cell (reduction of the NO 2 CD, temperature dependence of the NO 2 CD, and HNO 3 formation) can be reduced by using lower NO 2 concentrations in the cell.The length of the cell may need to be extended to still achieve a desired NO 2 CD.In principle the cell may also be heated to lower the amount of steady-state N 2 O 4 .
Problems with the optics of the cell are also difficult to avoid; fortunately they usually lead to changes in the NO 2 CD of < 10 %.In principle wedged cell windows or antireflective coatings could be used on the cell windows to minimize the problems described in Sect. 2. Another approach would be to tilt the entire cell with respect to the optical axis; thus reflected radiation would not reach the entrance optics of the spectrometer.
Data availability.The model data can be obtained from the authors upon request.
in NO 2 (thin blue line) of about 16 % due to this temperature rise.

Figure 2 .
Figure 2. NO 2 concentration (black line in units of 10 19 molec.cm −3 and hPa; left axes) and fraction of NO 2 (red line; right axis) of the total [NO Z ] = [NO 2 ] + [N 2 O 4 ] as a function of [NO Z ] (given in pressure units for 25 • C).At atmospheric pressure (1000 hPa) in the cell, only about 34 % of the total NO Z (or ≈ 344 hPa partial pressure) exists as NO 2 .

Figure 3 .
Figure 3. Scheme of the chemical reactions in an illuminated NO 2 cell; (a) only basic reactions and (b) complete system excluding the formation of OH.

Figure 5 .
Figure 5. Results of calculations with the full model (reactions marked with * in Table 1).Same as Fig. 4, but with initial O 2 assumed; (a) logarithmic scale and (b) linear scale.

Table 1 .
Summary of reaction rate constants.
* b Data from

Table 2 .
Comparison of the analytical calculations and the simplified model encompassing Reactions (R1), (R4), and (R6).The left and right panels have logarithmic and linear concentration scales, respectively.Comparison of the result with the data in Figs. 5 to 8 shows that there are no fundamental differences in the NO 2 time series between the simple model and the full model (see also Table2).