The CLOUD chamber at CERN is a 26 m3 cylindrical vessel that is used to study aerosol processes such as new particle formation. The inner surfaces consist of electropolished stainless steel. Great effort is made to minimize contamination by any condensable substances that may influence new particle formation. The chamber and its components have been described in detail before (Kirkby et al., 2011; Kupc et al., 2011; Voigtländer et al., 2012). For this study results are reported from the CLOUD7 and CLOUD10-T experiments (October–December 2012 and April–May 2015) in which the aerosol nucleation for the sulfuric acid–water–dimethylamine system was investigated (Almeida et al., 2013; Kürten et al., 2014). All measurements were carried out at a temperature of 278 K and a relative humidity of 38 % in the chamber.

A schematic drawing of the gas system and the CLOUD chamber is shown in Fig. 1. A specially designed gas system has been implemented at CLOUD for precisely controlling the amount of dimethylamine which is fed into the chamber. The gas system for each individual trace gas includes three calibrated mass flow controllers (MFCs) and several valves for diluting a mixture from a gas bottle with clean air before it is fed into the chamber close to the lower mixing fan.

The amount of DMA introduced into the chamber can be calculated from the fraction B of DMA inside the gas bottle (B=0.01) and the MFC flow rates (see Fig. 1). When the bypass valve is closed, which was the case at all times during CLOUD7 and CLOUD10-T, the following amount of DMA enters the chamber: ADMA=MFC1⋅MFC3MFC1+MFC2⋅B. The flow rates (denoted with MFC1, MFC2, and MFC3) have units of cm3 s-1 (at standard temperature and pressure – STP – in this case 293.15 K and 1013 hPa), and the quantity ADMA is the flow rate of DMA. The volume mixing ratio (VMR) of DMA (in pptv) inside the CLOUD chamber can be derived from the following differential equation: dVMRDMAdt=ADMAVch⋅1012pptv-kwall⋅VMRDMA-kdil⋅VMRDMA. Here, Vch is the chamber volume (2.61 × 107 cm3, where Vch denotes a physical volume), kwall is the wall loss rate constant for DMA, and kdil is the dilution rate constant. The dilution rate constant can be calculated from the ratio of the clean gas flow rate that is required to replenish the gas taken by the instruments and the chamber volume. In this study, the flow rate of air into the chamber is 160 L min-1 at standard temperature and pressure, which yields a dilution rate constant (assuming homogenous mixing) of 1 × 10-4 s-1. Assuming that the walls act as a perfect sink the wall loss rate can be assumed to be proportional to the square root of the gas-phase diffusion coefficient for an aerosol chamber (Crump and Seinfeld, 1981). For sulfuric acid the wall loss rate constant was experimentally determined as 2.2 × 10-3 s-1. For DMA it should be higher because it is a lighter molecule compared to sulfuric acid and has a higher diffusivity. The value for sulfuric acid therefore provides a lower limit for the wall loss rate of DMA.

Assuming steady state in Eq. (2) yields VMRDMA=ADMA⋅1012pptvVch⋅kwall+kdil=MFC1⋅MFC3MFC1+MFC2⋅B⋅1012pptvVch⋅kwall+kdil=Fkwall+kdil. The factor F describes the addition of DMA to the chamber in units of pptv s-1. The unknown quantity kwall could in principle be derived from Eq. (3) by calibration experiments if a reference instrument for the measurement of DMA were used. Alternatively, the wall loss rate can be determined from the decay rate of the signal, which is used to calculate the DMA mixing ratio in this study (see Sect. 3.1).

It should be noted that the effect of DMA condensation on aerosol particles, which are formed during nucleation experiments, is not taken into account in Eqs. (2) and (3). For the data shown in this study, either no sulfuric acid was generated when the DMA calibration measurements (see Sect. 3.2) were performed or the sulfuric acid and the associated condensation sink was so low that it had no effect on the DMA mixing ratio.

The assumption that the DMA mixing ratio is at equilibrium inside the pipes once the chamber valve is opened, i.e., that wall loss is negligible for the DMA inlet lines, is justified due to the following reasons. First, the gas lines are conditioned over a duration of at least 24 h before DMA is added to the chamber for the first time. During this time the purge valve is open and the chamber valve is closed (Fig. 1). Only the last ∼ 23 cm between the chamber valve and the point where the DMA enters the chamber are therefore not conditioned. Second, the mixing ratio of DMA inside the gas lines is generally higher than several tens of ppbv even though the DMA inside the chamber is in the pptv range due to the strong dilution inside the chamber. The high DMA mixing ratio enables a rapid equilibration of the short unconditioned section of the gas lines.

The CI-APi-TOF mass spectrometer has been described previously (Jokinen et al., 2012; Kürten et al., 2014). The CI-APi-TOF combines an atmospheric pressure chemical ionization source based on the design by Eisele and coworkers (Eisele and Tanner, 1993) and a high-resolution atmospheric pressure interface time-of-flight mass spectrometer (Tofwerk AG, Switzerland). The ion source uses a corona discharge for the primary ion generation (Kürten et al., 2011). Nitrate ions (NO3-⚫(HNO3)x) are generally used for the detection of sulfuric acid and sulfuric acid–amine clusters but more recently it was found that they also allow for the detection of ELVOCs (see, e.g., Ehn et al., 2014). Owing to the high mass resolving power (∼ 4500 Th Th-1) and the high mass accuracy (better than 10 ppm) of the CI-APi-TOF these ions can be unambiguously identified in this study if additional information like the isotopic pattern is taken into account. These features will minimize potential interferences especially in field measurements, where a lot of unknown compounds are potentially present.

One important aspect to consider is sampling line losses when evaluating the DMA signals. During CLOUD10-T the CI-APi-TOF was connected to the chamber by its own sampling line, while in CLOUD7 the instrument was sharing the sampling line with another instrument. Therefore, a y-splitter was used. For this kind of inlet the sampling line losses cannot be easily calculated in the same way as for a straight tube and laminar flow. Instead, the effective length method (Karlsson and Martinsson, 2003) was used after comparing the sulfuric acid concentrations measured by a CIMS and the CI-APi-TOF simultaneously. Since the CIMS was connected to the CLOUD chamber with its own dedicated sampling line, the loss rate could be quantified for sulfuric acid. Taking into account the independently determined calibration constant regarding sulfuric acid for the CIMS and the CI-APi-TOF (Kürten et al., 2012, 2014) an effective length of ∼ 1.5 m could be determined for the CI-APi-TOF sampling line at a flow rate of 8.5 L min-1 (at STP) for sulfuric acid. These values are used in the next section for deriving the transmission efficiency of DMA to the CI-APi-TOF.

In contrast to the detection of gaseous sulfuric acid (H2SO4) by a proton transfer reaction which leads to the formation of bisulfate ions (HSO4-, Eisele and Tanner, 1993), dimethylamine is detected due to its ability to cluster with the NO3-⚫(HNO3)x=1-3 primary ions: DMA+NO3-⚫(HNO3)→NO3-⚫(HNO3)⚫(DMA)DMA+NO3-⚫(HNO3)≥2→NO3-⚫(HNO3)≥2⚫(DMA). The association Reactions (R1) and (R2) could both occur in the ion–molecule reaction zone (∼ 50 ms reaction time) of the CI-APi-TOF; however, DMA is mainly detected at integer mass m/z 170 Th (NO3-⚫(HNO3)⚫ (DMA) ions) and integer mass m/z 233 Th (NO3-⚫(HNO3)2⚫ (DMA)) (Fig. 2c and c). In addition, a small signal at m/z 296 Th (NO3-⚫(HNO3)3⚫ (DMA)) is also visible in the mass spectra at high DMA mixing ratios (Fig. 2d). Since fragmentation could occur in the APi section, it is possible that this fragmentation is responsible for a high signal at m/z 170 Th although Reaction (R2) could be dominant. Regarding the identification and quantification of the mentioned signals it should be noted that even though integer masses are mentioned, the CI-APi-TOF mass spectra are evaluated using high-resolution data. The data are processed using tofTools developed by the University of Helsinki (Junninen et al., 2010).

To quantify the DMA concentration, the sum of the two most intense DMA signals is normalized by the primary ion count rate at m/z 188 Th (NO3-⚫(HNO3)2). Tentatively, we have chosen the NO3-⚫(HNO3)2 ion as the reference because it seems likely that this produces more stable cluster ions compared to NO3-⚫(HNO3) due to an efficient acid–base stabilization mechanism (1:1 ratio between acid and base if the NO3- is regarded as a Lewis base). In previous CLOUD studies a similar scheme has been observed for ion clusters involving sulfuric acid and ammonia or dimethylamine (see Kirkby et al., 2011; Almeida et al., 2013; Kürten et al., 2014; Bianchi et al., 2014). Furthermore, Ortega et al. (2014) reported that a cluster of two acid molecules and one base molecule (e.g., (H2SO4)2⚫ DMA) will only be stable in the neutral case. As soon as this cluster is negatively charged it becomes unstable and the base molecule will evaporate rapidly. In contrast, a cluster containing two acids besides the ion and a base molecule (HSO4-⚫(H2SO4)2⚫ DMA) will be much more stable. Although, the acid is in our case HNO3 and not H2SO4 we believe that qualitatively the ion cluster chemistry for the two acids is similar. Future studies will show to what extent this assumption holds true. This leads to the following equation for the DMA concentration: DMA=C⋅SL⋅ln⁡1+(CR170+CR233)CR188≈C⋅SL⋅(CR170+CR233)CR188. The factor C (in molecule cm-3) can be derived from calibration measurements using the CLOUD chamber. Generally DMA mixing ratios are reported rather than concentrations and therefore the calibration factor has a different unit than in Eq. (4). However, the derived calibration constant can be converted to molecule cm-3 (see Sect. 3.2). An additional factor, SL (inverse of the penetration usually used to characterize sampling line losses of aerosol particles and molecules in tubes), is required to take into account losses of DMA molecules in the CI-APi-TOF sampling line during the transport from the chamber to the instrument; the parameters CR170, CR233, and CR188 denote the count rates at the exact masses for the NO3-⚫(HNO3)1,2⚫ (DMA) and the NO3-⚫(HNO3)2 ions, respectively. The factor SL has a value of ∼ 2.5 for CLOUD10-T. During CLOUD7 the factor has a value of ∼ 4 and was evaluated based on the effective length method mentioned in the previous section. For the evaluation of SL it was assumed that the diffusivity of H2SO4 at 278 K and 38 % relative humidity equals 0.07 cm2 s-1 (Hanson and Eisele, 2000). For DMA a value of 0.10 cm2 s-1 was assumed, which follows when scaling the reported value in Freshour et al. (2014) to the temperature of this study using a power dependency of 1.75 for the temperature dependence of the diffusion coefficient.

To our knowledge the existence of ion clusters containing amines and nitrate has been reported only once by Luts et al. (2011). They added diethylamine (CH3CH2NHCH2CH3, DEA) to ions created from ambient air and identified the cluster NO3-⚫(HNO3)⚫ (DEA) (m/z 198 Th). Additionally, signals at m/z 261 and m/z 334 Th were observed, which were tentatively assigned to the clusters NO3-⚫(HNO3)2⚫ (DEA) and NO3-⚫(HNO3)2⚫ (DEA)2. This study is in agreement with the findings by Luts et al. (2011) regarding the clusters containing one amine molecule; however, we did not observe a cluster containing two DMA molecules. Combining the results of the present study and the one by Luts et al. (2011) indicates that nitrate chemical ionization mass spectrometry should likely be capable of detecting various other amines and not just DMA or DEA.

Figure 2 shows high-resolution mass spectra for the m/z values corresponding to the NO3-⚫(HNO3)0-3⚫ (DMA) ions when different amounts of DMA were added to the CLOUD chamber (the indicated mixing ratios are discussed further below). Clearly it can be seen that the NO3-⚫ (DMA) ion never exceeds the background level (Fig. 2a), indicating that this ion is very unstable and breaks up either in the ion drift tube or inside the CI-APi-TOF vacuum chamber. For the other signals the intensity increases with increasing DMA mixing ratio.

The data shown in Fig. 3 were used experimentally to determine the wall loss rate of DMA in the CLOUD chamber during CLOUD7. The same procedure was repeated for CLOUD10-T. The red line shows the sum of the signals for NO3-⚫(HNO3)1⚫ (DMA) and NO3-⚫(HNO3)2⚫ (DMA) normalized by the count rate from the NO3-⚫(HNO3)2 primary ion. Additionally, the setting of the DMA flow into the CLOUD chamber is shown in arbitrary units (shaded area in Fig. 3). When the DMA flow is shut off, a clear decrease in the DMA signal can be seen. This decay is due to two different loss processes: (1) wall loss, which is fast, and (2) mainly loss due to dilution, which is a slow process (see Sect. 2.2). However, this latter loss process is influenced by re-evaporation of DMA from the chamber walls. Fitting the decay with a double-exponential function yields a value for the wall loss rate of 2.3 × 10-3 s-1. Comparison to the wall loss rate of sulfuric acid (2.2 × 10-3 s-1) confirms that the derived wall loss rate for DMA is reasonable. One expects a slightly higher loss rate for DMA because it is the lighter molecule and therefore diffuses faster. The fact that the wall loss rate for DMA is slightly faster than the one found for sulfuric acid implies that the walls act as a perfect sink for DMA under these experimental conditions (i.e., low DMA mixing ratios, short exposure time, 278 K, and 38 % RH). Furthermore, this assumption should be justified by the fact that the calibration lines (discussed in Sect. 3.2) show no steepening when going from low mixing ratios to higher values, which is evidence that no wall saturation occurs. However, when measuring higher mixing ratios over a long time it will probably be necessary either to clean the sampling line occasionally or to calibrate with a known amine concentration. The re-evaporation of DMA mentioned above therefore seems to have only a small effect and comes into play only when the flow of DMA into the chamber is shut off and the DMA concentration reaches very low values. The DMA wall loss rate of 2.8 × 10-3 s-1 for CLOUD10-T is slightly higher due to a different configuration of the mixing fans inside the chamber resulting in a different thickness of the diffusion layer.

Using the derived wall loss rate, the DMA mixing ratio can be calculated according to Eq. (3). The error in the targeted mixing ratio during CLOUD7 is calculated based on the 1 σ standard deviations for the parameter τ1 (τ1 is the average decay time, i.e., the inverse of the wall loss rate, τ1=432±48 s) from the double-exponential fit which was made with the software IGOR. Furthermore, a 5 % error in the MFC flow rates is taken into account in the error analysis.

Different flow rates of DMA were applied to the chamber during both CLOUD campaigns and for certain periods the DMA was completely shut off. The periods when the chamber was flushed with clean air for extended times, can be used to determine the background signal for the NO3-⚫(HNO3)1-2⚫(DMA) cluster ions. We believe that this background is caused by electronic noise, since no DMA was detected in the clusters for the nucleation experiments conducted during these periods (Kürten et al., 2014). Since the CI-APi-TOF uses the same clean gas as the CLOUD chamber for the sheath gas it is also unlikely that there is any source of DMA inside the instrument.

Figure 4 shows the time series of the normalized DMA signal (red line) during CLOUD7 and CLOUD10-T together with the calculated DMA mixing ratio (shaded area) according to Eq. (2). It can be seen in Fig. 4a that even at the lowest set point of ∼ 2.2 pptv DMA the signal is significantly elevated compared to background conditions. Further increase of the DMA flow leads to correspondingly higher signals.

The data from Fig. 4 and from other periods (not shown) have been averaged over sufficiently long periods where a constant DMA mixing ratio was applied to the chamber. These averaged normalized signals are shown as a function of the calculated DMA mixing ratio in Fig. 5. A linear fit has been applied to the data from each calibration, yielding a correlation coefficient close to 1 (R2=0.99). This indicates that the applied methodology is capable of quantifying DMA at low mixing ratios in the pptv range. However, note that for mixing ratios below 7 pptv additional effects of the CLOUD chamber itself, like re-evaporation of DMA from the chamber walls and conditioning of the DMA inlet lines, might enhance the equilibrium time significantly and therefore introduce additional uncertainty.

The slopes of the calibration line from Fig. 5 are a measure of the sensitivity of the nitrate CI-APi-TOF towards DMA. After converting the mixing ratio of DMA into a concentration (1 pptv corresponds to 2.61 × 107 molecule cm-3 at 278 K and 1 bar), the calibration constant from Eq. (4) can be evaluated as C=1.48 × 1011 molecule cm-3 for CLOUD7 and C=3.45 × 1011 molecule cm-3 for CLOUD10-T from the slope of the individual linear fit. Compared to the calibration constant for sulfuric acid this value is about 1 to 1.5 orders of magnitude higher (Kürten et al., 2012, 2014) and therefore indicates a lower sensitivity for DMA compared to sulfuric acid. One explanation for this behavior could be that the evaporation rate of the NO3-⚫(HNO3)1-2⚫ (DMA) clusters regarding DMA is non-negligible. It is still an open question whether this evaporation occurs inside the ion source, where the temperature is close to the chamber temperature or within the APi section (first stage which is below ambient pressure), where a higher effective temperature is expected due to energetic collisions of the ions (that are accelerated by electric fields) and neutral gas molecules. In order to avoid ambiguity due to changes in the primary ion count rate distribution over time, routinely performed calibration measurements are therefore recommended (Freshour et al., 2014). In this case, the method should yield accurate and reproducible results despite the yet unknown details of the ion–molecule clustering and declustering processes involved.

The data shown in Fig. 5 can be used to determine the LOD for the DMA measurements with the nitrate CI-APi-TOF. The average background signal together with the 3 σ standard deviation is indicated by the light blue band in Fig. 4. The second step in Fig. 4a (4.4 pptv of DMA) during the CLOUD7 calibration yields an average signal that is outside the blue band. By use of the 3σ standard deviation the LOD during the CLOUD7 campaign was below 2.6 pptv for a 10 min integration time.

Since the CI-APi-TOF sampling line in CLOUD7 leads to a factor of 4 reduction in the DMA concentration reaching the instrument, a considerably lower detection limit (∼ 0.7 pptv) would result for a situation where sampling line losses are negligible. While zero wall loss cannot be realized in reality, a considerable reduction in the sampling line losses can be achieved in field studies. The CLOUD sampling lines are relatively long (∼ 1 m in total) and the instrument operated at a low flow rate (∼ 8.5 L min-1). In the field there is no restriction on the available amount of air that can be drawn; therefore reduced line losses may be realized. During the CLOUD10-T calibration (Fig. 4b) the first step (5.8 pptv of DMA) is clearly above the LOD. This is supported by the determination of the LOD which was below 1.7 pptv for the CLOUD10-T campaign. Taking the sampling loss of a factor ∼ 2.5 into account yields an LOD of ∼ 0.7 pptv, which matches very well with the value obtained for CLOUD7.

One important aspect of the present study is that the DMA mixing ratios are calculated for the CLOUD chamber from the evaluated wall loss rate for DMA and the MFC settings. A comparison to DMA mixing ratios measured directly using an ion chromatograph (IC; see Praplan et al., 2012) yields generally reasonable agreement for the CLOUD7 data for the time periods when both instruments where operated in parallel with the settings reported here (Fig. 6). The DMA average mixing ratio (averaged for the time period displayed) was 17 pptv for the IC and 22 pptv for the CI-APi-TOF. During the CLOUD10-T measurements the IC was not available. Note that the displayed DMA mixing ratios from the IC for CLOUD7 have been multiplied by a factor of 1.8 to account for the efficiency of the cation trap column. This correction was not considered in previous publications and therefore some of the reported DMA mixing ratios should be scaled up by a factor of 1.8. Some of the high concentration points reported in Almeida et al. (2013) are from CLOUD7 and need to be scaled up, while the low concentration points (≤ 5 pptv) are from CLOUD4 and are correct. The correction of the high concentration points from CLOUD7 therefore relates to data where nucleation rates were saturated with respect to DMA, and therefore the change does not affect any of the conclusions. Similarly, Kürten et al. (2014) reported DMA mixing ratios between 5 and 32 pptv during measurements of neutral sulfuric acid–DMA clusters. Applying the correction factor these values increase correspondingly. Since the exact DMA mixing ratios were not used in the data analysis by Kürten et al. (2014) the adjustment of the reported DMA values does not imply a significant change of the conclusions of Kürten et al. (2014).

Detection of amines by means of nitrate chemical ionization has the benefit that other substances relevant for new particle formation, such as sulfuric acid and ELVOCs, can be measured simultaneously with the same instrument. This is demonstrated in Fig. 7 for sulfuric acid concentrations up to 1.5 × 107 molecule cm-3 and DMA at 46 ± 12 pptv (i.e., 1.15 × 109 molecule cm-3), which shows that both compounds can be measured at the same time (data from CLOUD7) and that the DMA signal is not affected by the presence of H2SO4 in this example. In situations where the DMA concentration is similar or lower than the sulfuric acid concentration, not all DMA molecules might, however, be detected due to clustering between sulfuric acid and DMA (see discussion further below). Figure 7 only shows the normalized DMA signals and no DMA mixing ratios because during the early phase of CLOUD7 the CI-APi-TOF was tuned differently and therefore the calibration curves from Fig. 5 could not be applied. In conclusion, it is crucial to calibrate the instrument for each instrumental setting.

Jen et al. (2015) have also performed measurements using nitrate chemical ionization while sulfuric acid and DMA were simultaneously present in a flow tube. However, they did not report signals at m/z 170 and m/z 233 Th, indicating that the nitrate DMA clusters were not present. We have no definitive explanation why Jen et al. (2015) could not observe these clusters but it might be related to the fact that they used rather high sulfuric acid concentrations (4 × 109 molecule cm-3, i.e., ∼ 160 pptv). DMA was also present at a relatively high mixing ratio (110 pptv); however the ratio between DMA and sulfuric acid was only about 0.7. From the paper by Jen et al. (2015) it is not evident whether the DMA mixing ratio was measured during the presence of sulfuric acid or before sulfuric acid was added. Assuming that the reported DMA mixing ratio was determined without sulfuric acid would probably mean that the actual DMA (free DMA molecules not bound to any other molecule or cluster) during the experiment with added sulfuric acid could be significantly lower because sulfuric acid monomers and clusters of sulfuric acid would efficiently deplete DMA at such a low DMA to sulfuric acid ratio (Ortega et al., 2012; Jen et al., 2014; Kürten et al., 2014). In the case that the DMA molecules are not “free” but attached to sulfuric acid (or to sulfuric acid clusters), they might not lead to a signal for NO3-⚫(HNO3)1,2⚫ (DMA) but rather end up in a cluster involving the bisulfate ion associated with sulfuric acid and DMA. Such mixed clusters (bisulfate, sulfuric acid, and DMA) were detected by Jen et al. (2015). In summary, the depletion of DMA by sulfuric acid and clusters could be responsible for the missing signals at m/z 170 and m/z 233 Th. If this was the case nitrate chemical ionization would yield accurate results for DMA measurements as it would only measure the free (unbound) portion of the amines and not the amine molecules clustered to sulfuric acid.

In terms of measuring the total amine concentration, the technique presented here will instead provide a lower limit when the sulfuric acid to amine ratio is on the order of 1 or larger. However, the same applies to the measurement of total sulfuric acid, which will also be higher than the sulfuric acid monomer concentration when several pptv of DMA are present because a significant fraction of sulfuric acid monomers can be incorporated in clusters (Rondo et al., 2016).