The calibration unit is depicted in Fig. 1. The core piece is a 250 µL sample loop connected to a six-port valve allowing well-defined gas standard injections into the PTR-MS instruments. A small flow (∼10 mL min-1) of carrier gas transports the content of the sample loop (i.e. a multi-component gas standard containing approximately 1 µmol mol-1 per compound in N2) to a T connection where it is mixed into a larger flow (0.2–2 L min-1) of dry or humidified carrier gas. The small flow is tuned to produce a pulse duration of approximately 1 s. The larger flow is used for diluting the gas standard to ∼5 nmol mol-1 for the Vocus, to ∼2 nmol mol-1 for the PTR3 (additional extra dilution), and to ∼50 nmol mol-1 for all other instruments. In order to avoid wall loss, the sample loop, six-port valve, and dilution system are operated at approximately 80 ∘C, and all materials in contact with the gas standard are either stainless steel with Sulfinert^® coating (Restek Inc.) or Teflon PFA. The sample loop approach allows one to perform full calibrations very quickly (within 1–2 s). Multiple calibrations in a row can be performed to assess the quality of the calibrations directly and/or to explore different operating conditions (e.g. humidified or dry gas, E/N settings).

After dilution the mixing ratios are large enough to ensure good counting statistics but also small enough to avoid saturation effects. In Fig. S1 in the Supplement, we show the standard addition protocol. In essence, the sequence consisted of 50 sample loop injections, i.e. 5 sets of 10 injections using dry nitrogen, dry air, humidified air, humidified nitrogen, and dry nitrogen as carrier gas, respectively. On selected instruments and occasions, calibrations were performed sequentially at different E/N values to investigate their effect on the calibrations. During the campaign, we used two different gas standards produced by Apel Riemer Environmental, Inc., USA (AR), which was used until 22 September 2017, and the National Physical Laboratory, UK (NPL), which was used from 23 September onwards. Both gas standards contained compounds that are entirely detected at their protonated mass as well as a few compounds that partially fragment during protonation (e.g. monoterpenes, siloxanes, and isoprene). The compounds in the gas standards cover the mass-to-charge (m/Q) range 33–373 Th. Details on the gas standards are given in Tables S1 and S2. Figure 2 shows an example of the raw signal (in counts per second, cps) during the 50 injections of the calibration on the TOFqi LIL instrument on 21 September 2017, which is representative for all calibrations and instruments. The 16 compounds in the gas standard produce 22 ions which are all shown in the panels of Fig. 2. The different colours indicate the carrier gas. The reproducibility was tested by totalling the signal of individual injections and calculating the standard deviation of the 10 injections using the same carrier gas. This analysis showed that the reproducibility was typically 1 % unless counting statistics were the limiting factor (see percent values printed in the charts of Fig. 2).

All basic data processing of PTR-MS instruments with a time-of-flight (TOF) mass analyser was done with PTRwid (Holzinger, 2015). For the subsequent analyses we used the raw data output files that provide time series of ion signals (in cps) for all ions that were auto-detected in the mass spectrum. These raw data closely correspond to the raw data obtained from PTR-MS instruments using a quadrupole mass spectrometer (QMS), allowing TOF and QMS instruments to be directly compared.

All transmissions shown in Fig. 3 have been retrieved from the first 10 injections that used dry N2 as carrier gas. Transmissions obviously vary between instruments but also over time for individual instruments. However, instruments that were operated under constant conditions (e.g. TOF8000 UHEL, and QMS LSCE) exhibited little variation in transmission over time. We find that typically “flatter” transmissions (smaller parameter a in Eq. 1) were retrieved when the instruments were (deliberately) operated at lower E/N (thin lines in Fig. 3). Considering that higher water clusters of the hydronium ion (H3O+(H2O)n, with n>1) could provide significant fractions of the primary ion signal at lower E/N (which is not accounted for in our algorithm), we would expect to retrieve “steeper” transmissions (larger parameter a in Eq. 1) in the range 20–50 Th. However, we do not observe this effect, so we conclude that we did not miss a significant fraction of the primary ion signal. On the other hand, flatter transmissions were also retrieved from gas standard injections that used humidified carrier gas. An example is shown in Fig. S3. This suggests that several compounds in the gas standard must be detected with lower sensitivity than expected. The cause for reduced sensitivities includes slower proton transfer with hydronium clusters, as reported for benzene (Warneke et al., 2001), as well as more complicated ion chemistry involving back reaction of protonated compounds with water vapour as has been reported for formaldehyde (Hansel et al., 1997). Together with evidence presented below we suggest that the flattening of transmission with lower E/N is caused by slower proton transfer with hydronium clusters.

Figure 4 shows that the measured sensitivities for all instruments and compounds in the gas standards cover the range 1–2×105 cps ppb-1. Note that identifying the best instrument was not the purpose of this study. Some instruments were deliberately operated outside the optimal range in terms of tuning (sensitivity) or energetics in the drift tube/reactor (E/N). In general, we note that the large difference in sensitivity for the PTR-MS instruments is rooted in different tuning and ion optics, or innovative concepts that further boost the sensitivity of the Vocus and PTR3 instruments. For many compounds the PTR3 instrument is at least 1 order of magnitude more sensitive than any other instrument. This is due to the very different conditions under which the PTR3 instrument is operated: the PTR3 instrument gains sensitivity by allowing for longer reaction times and a higher pressure in the reaction chamber rather than by boosting the primary ion signal. As a result, reagent ions undergo approximately 1000 times more collisions with the analyte gas molecules compared with the other instruments. While this concept overall leads to greatly enhanced sensitivities, it also complicates quantification: deprotonation reactions of the form RH++H2O → H3O++R limit the sensitivity for a broader range of species, while in other instruments this is only the case for formaldehyde and a few other compounds with proton affinities just slightly above that of water. Furthermore, the PTR3 is operated at a reduced electric field strength of 60±5 Td; therefore, the primary ion distribution is dominated by water hydronium clusters. Thus, ligand switching reactions with internal proton transfer dominate over direct proton transfer from the hydronium ion. Both effects lead to relatively poor and uncertain sensitivities for compounds having a low proton affinity and/or low dipole moment, both preventing efficient ligand switching reactions. This explains that the measured sensitivities of the different compounds cover several orders of magnitude for the PTR3 instrument, whereas for all other instruments the measured sensitivities are typical within 1 order of magnitude (Fig. 4). The lower sensitivity of the QMS LSCE instrument for higher m/Q values is a property of the quadrupole mass analyser that is used in this instrument. Figure 4 reveals lower-than-expected sensitivities in the Vocus instrument for methanol, acetonitrile, acetaldehyde, 3F-benzene, and 3Cl-benzene. For the three lighter compounds the reason is a very sharp high mass pass filter

Position and sharpness of the filter are adjustable. The default factory settings aim at optimizing the detector lifetime.

Further insights can be obtained from looking at the ratio of measured to expected sensitivity, which should be unity if the reaction kinetics are accounted for correctly and if there are no additional losses. Figure 5 shows this ratio for all compounds in the gas standard and for all instruments. Data from all injections using dry carrier gas (N2 or air), except those that were used to retrieve the transmissions, are included in Fig. 5. For many compounds the ratio deviates much less than ±30 % from unity; the boundary of this range is indicated by the black horizontal lines in Fig. 5. In principle, this demonstrates the potential of PTR-MS to quantify organic compounds without calibration. However, some limitations emerge from the data shown in Fig. 5.

Above 150 Th spreading between instruments becomes larger. The likely reason for this is that transmissions are less constrained in this range. Most calibrations were done with the NPL gas standard that contained only two compounds above m/Q=150 Th (D4 and D5 siloxanes). There are indications that these two compounds are sticky (note that Fig. 2 shows a poorer reproducibility of these compounds), and thus these results are vulnerable to surface artefacts. Moreover, the combination of Eqs. (1), (2), and (3) may not be the best choice to replicate the real behaviour of all of the mass analysers used. The latter is clearly the case for quadrupole mass analysers, when considering the D4 siloxane ratio for the QMS LSCE instrument (low blue point at 300 Th in Fig. 5). Many instruments show a dipole between D4 and D5 siloxanes (D4 low and D5 high), because the ratios measured to expected sensitivity were inconsistent with the spectrum of retrievable transmissions (dictated by Eqs. 1–3). Such a case is shown in Fig. S2a, where the algorithm minimized the error by distributing the inconsistency between D4 (too low) and D5 (too high), whereas Fig. S2b shows a case with ratios consistent with possible transmissions.

These issues are likely resolvable with an improved gas standard that contains more compounds in the range 150–400 Th.

Methanol is detected with a lower sensitivity than expected in most instruments. A close inspection revealed that injections using humidified carrier gas clearly produced higher signals, and the injections using dry carrier gas exhibited significant tailing. Both features are visible in the top left chart of Fig. 2. We suggest that this issue is caused by wall effects in the instruments and/or their inlet lines and that the issue is less pronounced under humidified conditions. A similar issue, but less pronounced, was observed for MVK and MEK for the TOF8000 UHEL instrument. These features demonstrate that surface effects in the PTR-MS instruments and their inlet systems can jeopardize quantitative detection of organic compounds.

For the Vocus instrument the ratio measured to expected sensitivity was biased high for acetonitrile and low for acetaldehyde, isoprene, benzene, 3F-benzene, and 3Cl-benzene. The high bias of acetonitrile may be an artefact of the transmission algorithm that tried to compensate for the inconsistency caused by lower-than-expected sensitivity of acetaldehyde. Correcting the bias would further decrease the ratio obtained for acetaldehyde. With respect to other instruments, the Vocus is unique because the reaction chamber contains approximately 30 % of water vapour. Therefore we suggest that lower-than-expected sensitivities of these compounds are the result of reactions of protonated compounds with water vapour. The higher E/N compared to other instruments is another factor that helps to overcome the energy barrier for these reactions and makes deprotonation more efficient.

The results shown in Fig. 5 suggest that, in principle, PTR-MS is able of quantifying compounds without calibration based on simple reaction kinetics and a correctly retrieved transmission, if surface effects and unknown fragmentation can be excluded. However, in addition to the aforementioned reservation, the dependence of the retrieved transmissions on E/N is another concern. In this section, we will further discuss to what extent PTR-MS is capable of performing quantitative measurements of uncalibrated compounds. The results from all gas standard measurements and all instruments are shown in Fig. 6 for acetone as an example. Similar figures for the other compounds are provided in Figs. S4–S18. First-row panels in Fig. 6 show the ratio of primary ions H2OH3O+ to H3O+ as well as operating conditions of the instruments, and the second-row panels show the measured sensitivities for acetone as displayed in Fig. 4. The third-row panels in Fig. 6 show that the normalized sensitivities, SN, are within 1 order of magnitude (6–50 cps ppb-1). This demonstrates that the reagent ion signal is the primary factor that determines the sensitivities of individual PTR-MS instruments. The bottom-row charts in Fig. 6 show that measured and expected sensitivities typically agree within less than 10 % (standard deviation) for all instruments, with some exceptions visible for measurements that used humidified carrier gas.

The data shown in Fig. 5 represent idealized conditions because the dry carrier gas suppresses the production of water hydronium clusters. Such conditions cannot be achieved in many common applications of PTR-MS. Therefore, we show the ratio of measured to expected sensitivities for the humidified calibrations in Fig. 7. The main message is that for many compounds the ratio is still within ±30 % of unity; however, the spreading between instruments is larger compared with dry gas standard injections. For some instruments the spreading between individual measurements is increased as well (error bars in Fig. 7 compared with error bars in Fig. 5). A closer inspection of Fig. 7 reveals the following.

We observe no significant changes for the Vocus instrument. This is expected because the humidified carrier gas does not add significant extra humidity to the 30 % water vapour that is present in the reactor anyway. Besides the Vocus, the instruments TOF8000 UU, TOF8000 UHEL, QMS LSCE, and TOFqi BHAM also produce very similar results with dry and humidified carrier gas. These instruments were operated at relatively high E/N values in the range 100–135 Td (except one measurement with TOFqi BHAM). The chosen operating conditions for these instruments resulted in relatively low levels of water hydronium clusters, so that the expected sensitivities produced accurate results. The results for methanol even improved slightly, showing that the surface effects are eased a bit under humid conditions. The same holds for MVK and MEK measured with TOF8000 UHEL.

The ratios for benzene and 3F-benzene are lower. This is likely due to the well-documented fact that these compounds are not efficiently protonated by water hydronium clusters (Warneke et al., 2001).

The instruments TOFqi LIL, and to a lesser extent TOFqi CEH, were biased low by typically 10 %–30 % for all compounds except the siloxanes (D3, D4, and D5) and methanol for TOFqi LIL.

For the instruments TOF1000 UU and TOF8000 FZJ, the spread between individual gas standard measurements is much increased. A closer inspection revealed that measured and expected sensitivities were generally consistent for measurements done at E/N levels above 100 Td. However, measurements at E/N levels below 100 Td revealed significant inconsistencies between measured and expected sensitivities. This has also been the case for other instruments during occasional measurements at low E/N (see deviations from unity in bottom row charts of Fig. 6, and Fig. S4–S18). We note that the inconsistency at low E/N results in sensitivities that are measured lower than expected, except for the TOF800 FJZ instrument where the opposite was observed.

Points 3 and 4 warrant further discussion. Figure 8 summarizes the results of a comparison of dry and humidified gas standard injections. The panels in Fig. 8 show the ratios of different parameters measured with humidified versus dry carrier gas. Data printed in red, yellow, and blue are the ratios of (i) the primary ion signal (H3O+ + H2OH3O+) corrected by the transmission , (ii) the uncorrected H3O+ signal, and (iii) the measured sensitivities, respectively. The latter has been calculated as the mean measured sensitivity of a core set of compounds (acetonitrile, acetaldehyde, acetone, isoprene, MVK, MEK, xylene, trimethylbenzene (TMB), and monoterpene) that all exhibited very similar trends (see Figs. S4–S18). For all instruments that performed gas standard measurements at E/N levels below 100 Td we observed that the measured sensitivity decreased for the core set compounds when the carrier gas was humidified. The likely cause is a reduced reaction speed with water hydronium clusters, which could be taken into account in more advanced models to calculate the expected sensitivity. At humidified conditions and an E/N around 80 Td, less than a few percent of the primary ions are present as H3O+ (de Gouw et al., 2003), which is the likely reason for very low measured sensitivities of benzene (Fig. S9) and 3F-benzene (Fig. S13). Note that only the TOF1000 UU instrument measured low fractions of H3O+ as expected (ratios F37/F19 are in the range 6–9 for humidified injections at 80 Td); in all other instruments the cluster distribution was not preserved during the transfer from the drift tube into the mass spectrometer (F37/F19 always lower than 1.5; see top panels in Fig. 6).

The ratio of measured to expected sensitivity is not sensitive to the humidity of the sample if both the measured sensitivity and the transmission-corrected primary ion signal vary in the same way; i.e. the blue and red data overlap in Fig. 8. For the reasons discussed above, this is not the case for measurements at low E/N. Another process that causes separation of red and blue data is best visible in the TOFqi LIL chart of Fig. 8. This chart clearly shows that the cause is not a change in the sensitivity, but that for unknown reasons the primary ion signal is recorded higher during humidified measurements. Since the uncorrected H3O+ signal (yellow data in Fig. 8) is recorded higher in the TOFqi LIL instrument as well, we reject the possibility that this may be caused by an artefact in the transmission retrieval. Instead, we think that for unknown reasons primary ions are extracted to the mass analyser more efficiently under humidified conditions. The TOFqi CEH instrument shows a similar but less pronounced effect. An opposite effect was observed for the TOF8000 FZJ instrument: during humidified low E/N measurements the primary ion signal was recorded lower for unknown reasons, but the measured sensitivity did not decrease correspondingly.

In response to the question posed in this section we state the following.

Quantitative detection (better than ±30 %) is possible for E/N values above 100 Td if artefacts associated with the transmission of primary ions can be ruled out. The reasons for the artefacts are not explored in this study, but they may be associated with ion optics in the interface between the drift tube and mass spectrometer or with surface ageing (coating) in this region. These artefacts can be detected by comparing gas standard additions using dry and humidified carrier gas, respectively. A required condition is that most of the primary ion signal is present as H3O+ ion, which may require controlling water leakage from the ion source. Alternatively, higher E/N values can be applied to suppress the formation of water hydronium clusters.

Backward reactions can significantly reduce the sensitivity for compounds with a proton affinity relatively close to that of water. This effect is well known and studied for formaldehyde (Hansel et al., 1997) but can also affect the detection of other compounds in instruments/setups that allow for many collisions of protonated compounds with water molecules as it is the case for the PTR3 instrument (low E/N and high drift tube pressure; see Appendix A) and to a lesser extent for the Vocus instrument (due to high levels of water vapour in the reaction chamber).

Reliable quantification for E/N values below 100 Td becomes more complicated because increasing fractions of the primary ions are present in the form of water hydronium clusters. For a number of compounds, this resulted in reduced sensitivities up to 50 % (see Figs. S4–S18), and even larger reductions were observed for benzene and 3F-benzene.

We note that an improved kinetic ion chemistry model that accounts for the cluster distribution, different reaction rates with clusters, the humidity, and the back reaction can expand the limits of quantitative operation of PTR-MS. In this study we did not explore dissociative proton transfer reactions because in traditional PTR-MS applications that focus on volatile organic compounds fragmentation of compounds is the exception rather than the rule (e.g. Lindinger et al., 1998). However, there are indications that this changes dramatically in new fields of application such as the analysis of semi-volatile organic compounds, condensed organics, and dissolved organics (Holzinger et al., 2010; Eichler et al., 2015; Materic et al., 2017). A recent intercomparison study (Gkatzelis et al., 2018) revealed that operating PTR-MS at lower E/N values strongly reduces the fragmentation of these compounds, which likely will make measuring at lower E/N an appropriate choice, especially if the disadvantages of that can be compensated for with an improved reaction kinetic model. Finally, we note that the mentioned new fields of applications mostly concern compounds in the range 150–400 Th, which highlights the need to better constrain the transmission in this m/Q range.