For the mc-CPC we used three commercial SKY-CPCs (Model 5411, Grimm Aerosol Technik GmbH, Germany). The SKY-CPC is a state-of-the-art condensation particle counter that has been designed for airborne applications. The measurement technique is based on the growth of aerosols through the condensation of a working fluid on an aerosol particle. The instrumentation consists of three modules. The saturator is held at temperatures Tsat so that the working fluid (e.g. an alcohol) evaporates and mixes with the sample flow. In the condenser, the temperature Tcon is lower than Tsat to create supersaturation of the working fluid on the aerosol particles and thus activating their growth to optically detectable sizes. The third module is the photo-optical detection cell where the enlarged aerosols are detected through light scattering (Sinclair and Hoopes, 1975; McMurry, 2000). Each particle that has a sufficiently large diameter is detected by the CPC. The smallest size at which particles are activated by the given working fluid is called the Kelvin equivalent size or critical diameter dKelvin (Seinfeld and Pandis, 2016). Aerosols that are smaller than this threshold value dKelvin cannot be activated by the working fluid due to the Kelvin effect. The aerosol diameter at which 50 % of all aerosols are activated and measured is defined as the cutoff diameter or d50. This diameter size depends on various conditions. For example the temperature difference between the saturator and condenser regime, the temperature dependent vapor pressure of the working fluid itself, the pressure in the system and the sample flow rate (Banse et al., 2001).

By default, the SKY-CPC is operated with 1-butanol (CAS: 71-36-3) as its working fluid and the saturator and condenser temperature are set to 36 and 10 °C, respectively, which results in a cutoff diameter of 4 nm at ambient pressures of ∼ 1000 hPa. We set two of the three SKY-CPCs to a saturator temperature of 41 °C and a condenser temperature of 5 °C, yielding a ΔT of 36 °C. The third CPC was operated at 35 and 20 °C for saturator and condenser, respectively (ΔT = 15 °C). The instruments have a constant flow rate QCPC of 0.6 L min⁻¹ that is maintained by a critical orifice, which is located downstream of the detection cell inside the channel block.

Butanol is a highly flammable and hazardous alcohol with a strong odor. Most of the CPCs used in ground-based research are running with butanol because it is well-proven for many applications as a reliable working fluid (Wlasits et al., 2020; Sem, 2002). It has a rather high vapor pressure of 6.7 hPa at 25 °C (Carl Roth GmbH + Co. KG, 2024), resulting in sufficiently low and well-defined cutoff diameters that increase at low pressures (Hermann et al., 2005; Banse et al., 2001; Weigel et al., 2009; Bauer et al., 2023). Due to its high flammability, aircraft certification of butanol for a CPC is challenging. Therefore, we decided to use perfluorotributylamine (Fluorinert™ FC-43, 3M Performance Materials, St. Paul, Mn, USA, CAS: 311-89-7). Nevertheless, there are some disadvantages of FC-43 compared to butanol. For one, Fluorinert has an extremely high global warming potential (GWP) of ∼ 7000 (Hong et al., 2013), which demands responsible handling. The other disadvantage is the comparably low vapor pressure of 1.92 hPa at 25 °C (3M, 2019). Even though the saturation vapor pressure at typical saturator temperatures for the two fluids are in the same order of magnitude (Table 1), the evaporation of FC-43 is lower, potentially suppressing the activation of the aerosol particles. With a ΔT of 36 °C, butanol can activate aerosols with a diameter of 2 nm whereas the particles that can be activated by FC-43 need to have a diameter of 5 nm (Hinds, 1999). However, some studies showed that the latter problem can be circumvented by decreasing the pressure in the CPCs, which facilitates the evaporation of FC-43, or by increasing the saturator temperature (Williamson et al., 2018; Weigel et al., 2009; Hermann et al., 2005; Gallar et al., 2006). FC-43 has already been used as a working fluid in several airborne CPCs. In Williamson et al. (2018) cutoffs down to 3 nm could be realized by keeping the internal pressure constant at 120 hPa and by increasing ΔT to 36.4 °C. Hermann et al. (2005) did a comparison between butanol and FC-43 operated TSI CPCs at different internal pressures, ranging from 200 to 1000 hPa. They demonstrated that the cutoff of the FC-43 CPC decreased with decreasing pressures while the maximum detection efficiency increased (highest counting efficiency compared to a reference instrument). The CPC operated with butanol showed the opposite effect in this study. Furthermore, Weigel et al. (2009) and Gallar et al. (2006) also used Fluorinert-operated CPCs at different pressures, but these were both custom made. Grimm SKY-CPCs have also been tested at low pressures, but only with butanol, dimethylsulfoxide (DMSO) and water as a working fluid (Hermann and Wiedensohler, 2001; Bundke et al., 2015; Weber et al., 2023b, a; Bauer et al., 2023). As far as we know, the application of FC-43 with a Grimm SKY-CPC has not been tested yet.

The mc-CPC was designed for the Learjet TPEx campaign. In Fig. 1 the flow schematic of the mc-CPC, including internal and external structure of the housing is depicted. The instrument consists of a 19 in. (48.3 cm) aircraft rack module including three individual commercially available SKY-CPCs (each 16.5 cm × 21.5 cm × 27 cm), accessory components, a bypass flow system to regulate and reduce the internal pressure and a common inlet system. The mc-CPC has a weight of 34.5 kg and the dimensions are 48 cm × 35 cm × 40 cm and needs to be connected to an external pump to enable a constant flow through the system. This was realized by using a dry scroll pump (IDP-3, Agilent IDP3D01). The mc-CPC as well as the pump are operated at a power supply voltage of 24 V.

Each SKY-CPC has a removable O-ring sealed 8 mm inlet tube that can be easily plugged in and out. To avoid leakages during low pressures, we replaced the inlet with a leak tight fitting (0.25 in. (6.35 mm) NPT male to 0.25 in. (6.35 mm) tube). The SKY-CPCs were installed in parallel into the rack. Because of the limited space in the housing, the length of each CPC inlet is different (Table B1).

The containers for the working fluid are made of PEEK material (Polyether ether ketone) and both, the reservoir and waste container, have a volume of 200 mL and are attached to the front panel of the instrument (Fig. 1). They can be easily filled or emptied via quick connectors. In order to provide an equal flow to the individual CPCs, we installed an inlet manifold, that connects the individual CPC 0.25 in. (6.35 mm) sampling lines with the overall aerosol port, an 8 mm stainless steel tube. Due to space restrictions, the sampling lines outside the mc-CPC housing needed to be strongly bent. Due to these circumstances, the total lengths of the individual CPC inlet lines, measured from the inlet manifold to the CPC entrance were 58 cm (channel 1), 46.5 cm (channel 2) and 60 cm (channel 3) (Table C1). The data logging of the particle concentration and several other parameters was realized using the Grimm nanoSoftware alongside a LabView-based custom solution.

For the pressure reduction we implemented an 8 mm ball valve in front of the mc-CPC common inlet, that included two interchangeable orifices (0.45 and 0.65 mm). The bypass line of the pressure regulation system consists of two pressure sensors P1 and P2 (Keller Model 23SY, see Fig. 1), a 10 L min⁻¹ flow sensor F (Omron, Model D6F-10A6-000) and a 10 L min⁻¹ solenoid control valve (MKS, 248D). The pressure sensors are installed upstream and downstream of the MKS valve. The control valve is regulated with a PID-controller on the pressure measured by P1, regulating the pressures pCPC inside the CPCs. P2 is recording the pressure in the exhaust line. The flow sensor provides information about the additional flow that is needed to maintain a low and constant pressure at P1. The IDP-3 pump provides the flows Qbypass and QCPC through the bypass and the SKY-CPCs, respectively. For the pressure regulation and the data logging of the pressure and flow sensors we used a LabView program.

To estimate the performance of a CPC, two parameters are commonly used. The counting or plateau efficiency ηmax⁡ and the cutoff diameter d50. To derive the counting efficiency ηmax⁡ of the individual mc-CPC channel, the particle number concentration of the respective CPC at a specific diameter is compared to a reference instrument, in our case a TSI 3776 CPC (GUF) and a Grimm 5.705 FCE (FZJ). This leads to the following equation, which is dependent on the aerosol diameter dp: 3ηidp=NiNTSI,FCEwithi=channel1,2,3 The so-called cutoff curve, which can be retrieved from the comparison between the counting efficiency ηi and the particle diameter, can be represented by a logistic sigmoid fit function: 4ηidp=ηmax⁡+ηmin⁡-ηmax⁡1+dpd50d0 Here d50 refers to the aerosol diameter at which the counting efficiency between the mc-CPC channel i and the reference instrument reaches 50 %. d0 describes the onset diameter at which the particles get initially activated and dp is the aerosol diameter selected by the DMA. The efficiency ηmax⁡ stands for the plateau region, where the counting efficiency ηi reaches its maximum value and remains stable with increasing dp. ηmin⁡ on the other hand refers to the lowest detection efficiency derived by equation 4 and is usually zero. Note that the sigmoid function can still be used to calculate the cutoff d50 at 50 % of the efficiency range between ηmin⁡ and ηmax⁡ even when ηmax⁡ is not 1, which is the case for many CPC calibrations (Hermann et al., 2005; Weigel et al., 2009). A discussion on this formula can be found in Appendix D.

During the TPEx aircraft campaign, the flow rates of the SKY-CPCs were critical for only 16 % of the measurements. This raises two questions: (1) is the cutoff diameter influenced by the changing flows and (2) how is the data quality affected by it. To answer the first question we determined mc-CPC cutoff diameters at the GUF laboratory (Sect. 3.1) for different combinations of four pressures and four flows.

Figure 4 depicts the averaged counting efficiencies for each size bin from channel 1 at an internal CPC pressure of 250 hPa and an external pressure pexternal of 1000 hPa. In Fig. 4a the counting efficiency is displayed without the flow correction. The asymptotic counting efficiency ηmax⁡ for the lowest flow of 0.39 L min⁻¹ or FF 1.2 reaches a maximum value of 57 % only. The critical flow of roughly 0.6 L min⁻¹ gives a maximum efficiency of 81 % and a d50 of 11.9 nm. Figure 4b represents the same data as Fig. 4a but includes the flow correction (as described in Appendix C). All data points that were measured at FF < 1.9 are now in line with the target cutoff curve at FF ≥ 1.9 (dark blue). Here, the difference in the asymptotic efficiencies is less than 5 % between the individual cutoff curves. Regarding the cutoff diameter, the largest difference of 0.8 nm occurs between the target flow and FF = 1.2, where the cutoff is slightly higher for lower flows. Still, the deviation is small and within the uncertainty, pointing to the importance of applying the flow correction. This result is also representative for channel 2 and 3 of the mc-CPC. This leads to the conclusion that the prolonged residence time of the aerosols in the CPC system is not affecting the cutoff diameter. Furthermore, the results demonstrate that the flow correction is valid for the laboratory calibration measurements and that the reduction of the sample flow has a negligible influence on the d50 and was therefore disregarded. Consequently, the cutoff characterization in the following plots is only discussed for the flow corrected parameters.

Here, we present the results of the mc-CPC characterization at the Goethe University Frankfurt (GUF) and at the Forschungszentrum Jülich (FZJ). In Fig. 5a the cutoff measurements of channel 1 at GUF are shown at a constant external pressure of 1000 hPa and a varying pCPC in the range of 200 to 750 hPa. Figure 5b depicts comparable measurements from FZJ with a pexternal of 400 hPa and pCPC from 200 to 315 hPa. All data points shown in Fig. 5 and also in the following plots are normalized by their plateau efficincy ηmax⁡ (see Fig. E1 for the raw data). The cutoff diameters and plateau efficiencies derived from the raw data are listed in Table 2. The focus here is on the pressure range between 200 and 350 hPa, as these were the pressures at which the mc-CPC was operated during the TPEx campaign. Note that the differences in the measurement setups arise due to technical limitations, which mainly concern the differences in the external pressures and the test aerosol.

The direct comparison between the two calibration setups of Fig. 5a and b shows that the overall fit progression follows a similar trend. Still slight differences in the plateau efficiencies as well as in the cutoffs are visible. However, the measurements taken at FZJ show much higher efficiencies throughout all pressure stages compared to the GUF measurements, i.e. when the data is not normalized by ηmax⁡ (see Table 2). At a pCPC of 250 hPa ηmax⁡ is 94 % for FZJ and 82 % for GUF, respectively. This difference of roughly 10 % stays rather constant at comparable internal pressures, which results in a difference in the cutoff diameter as well. When obtaining the cutoff diameters from Fig. 5a for the GUF measurements at 250 hPa internal pressure, channel 1, 2 (operated at ΔT = 36 °C) and 3 (operated at ΔT = 15 °C) reached cutoff diameters of 12.4, 12.1 and 16.4 nm, respectively (Figures for channels 2 and 3 are presented in Appendix E). The experiments at FZJ for the same channels showed d50 values of 11.2, 12 and 14.7 nm. The cutoff diameter is therefore in agreement for both setups for all three channels when considering the uncertainties Δd50 of the cutoff determination listed in Table 2.

Both laboratory experiments show that with increasing internal pressures the plateau efficiency increases while the cutoff decreases, but this effect is stronger at GUF than at FZJ (Table 2). This is true for all three channels in the given pressure range of 200–350 hPa. For the FZJ experiments the cutoff diameter shifts by ∼ 1 nm to smaller values when increasing the pressure from 200 to 315 hPa, where the differences are in the range of uncertainty. Moreover, the ratio between the channels with smaller cutoff diameters (1 and 2) and the channel with larger cutoff (3) stays rather constant within 1 nm (Table E2). At GUF we saw a decrease of less than 2 nm in d50 while changing pCPC from 200 to 350 hPa, though the differences become larger when increasing the pressure even further. This is similar to the results from Bauer et al. (2023) who noted the same trend with identical Grimm instruments using butanol as the working fluid. Previous studies using FC-43 with CPCs from other manufacturers indicate that the cutoff of the respective instrument shifts to smaller sizes at lower internal pressures (Williamson et al., 2018; Hermann et al., 2005; Weigel et al., 2009).

Figure 5 illustrates that the increase of pCPC leads to an enhanced CPC performance and this behavior was reproduced for both experimental setups. Furthermore, the d50 changes only slightly for the pCPC pressure range of 200–350 hPa. At FZJ we also changed the external CPC pressure pexternal to mimic different flight levels, which could not be done at GUF. As the FZJ measurements are thus more representative for the conditions during the TPEx flight campaign, we will proceed with discussing these results, but comparable measurements, which were performed at GUF, are documented in the Appendix for completeness.

One reason for the discrepancy between the data shown in Fig. 5 could be caused by the particle losses in the inlet system due to the pressure-reducing orifice. To verify how large its influence on the cutoff diameter and the counting efficiency of the CPCs is, we removed the orifice and did diameter scans for pressures listed in Table 3 which represent flight altitudes between 11 500 and 3000 m. For these measurements the electrometer and the mc-CPC were operating at the same pressures, where Δp = pexternal-pCPC = 0.

In Fig. 6a and b the normalized counting efficiencies for channel 1 and channel 3 are depicted, respectively, color-coded by the pressure. The results for channel 2 are included in Table 3. Similar to Fig. 5b, the dependence of the pressure on the CPC performance changes, at least for channel 1 and 2. For 200 hPa we determined a d50 of 11.9, 11.7 and 13.5 nm for all three channels, which leaves only a difference of less than 3 nm between the “small” and the “large” CPC channels. Still, the values are in a similar size range as the cutoffs determined with the default mc-CPC setup (Tables 2 and E2). The smallest cutoff diameters of 8.2 and 8.8 nm were reached for channel 1 and 2 at 700 hPa. During the pressure increase, the counting efficiency for the two channels reaches a maximum of 100 % (±5 %) for all pressure stages, which is higher than for the orifice-including measurements. This suggests that the critical orifice installed before the mc-CPC inlet causes particle losses. Especially particles in the size range were the plateau efficiency reaches its maximum seem to be affected. This could explain the small difference between the cutoff diameters measured with and without orifice and the larger differences regarding the plateau efficiency.

However, this behavior is not fully reproducible for channel 3. At 550 hPa and 700 hPa, the trend reverses and the onset diameter as well as the cutoff moves to larger diameters. From the raw data in Table 3 we can also determine that the plateau efficiency stays rather constant between 200 and 550 hPa but decreases drastically to 56 % at 700 hPa. We cautiously suggest that the drop in the CPC performance at 700 hPa is due to a reduced FC-43 diffusion rate in the saturator and a small ΔT. The diffusion rate is highly dependent on the pressure, being enhanced at lower pressure levels. By increasing pCPC to 700 hPa we possibly also decreased the diffusion of FC-43 into the center of the saturator, which consequently could have had an unfavorable effect on the particle activation. The much higher saturator temperature of channel 1 and 2 may have balanced out the effect of the high pressure. Note, that these are assumptions, which need further investigation. Nevertheless, the trend of an increased CPC performance at increased pressures up to 400 hPa is reproducible even without the orifice, which leads to the conclusion that the limiting factor is not the particle loss through the orifice but the geometry of the inlet line.

In Fig. 7 the normalized counting efficiencies of all three channels at a constant internal CPC pressure of 250 hPa and at four external pressures are depicted. The cutoff diameters as well as the plateau counting efficiency of the raw data are listed in Table 4. For the graphical representation of the raw mc-CPC data, see Appendix F.

From Table 4 one can directly derive a dependency of the counting efficiency with the external pressure, which is reproducible for all three mc-CPC channels. The higher pexternal and thus the higher Δp, the lower is the plateau efficiency. This can probably be explained by increased inlet line losses resulting from the higher pressure drop and thus the higher flow that is provided by the mc-CPC bypass system. However, the differences between pressure levels are rather small. The smallest counting efficiency could be derived at pexternal 1000 hPa being the same for each channel at 87 %. The maximum ηmax⁡ is associated with the lowest pexternal of 300 hPa (Δp = 50 hPa) and gives values from 94 % to 96 % for channel 1–3, respectively. In total the change in efficiency is less than 10 % for all channels in the external pressure range of 300 to 1000 hPa.

Note that the cutoff diameters determined for the different pressures are relatively constant. In case of channel 1, d50 ranges from 11.1 to 11.4 nm which is within the uncertainty, while the deviations for channel 2 and 3 were somewhat larger, ranging from 12 to 12.6 nm and from 14.7 to 15.2 nm, respectively, which is still within their uncertainty. The differences in the channels are probably due to statistical deviations.

The measurements indicate that the cutoff diameters are not strongly dependent on the external pressures and also the plateau efficiency is only to a minor degree influenced by pexternal. For our aircraft measurements, this means that varying altitudes do not alter the cutoff but the plateau efficiency changes slightly with altitude. Hence, the measurement data of the research flight presented in Sect. 5 were corrected by the raw counting efficiency according to the pCPC and the ambient pressure pexternal (see Fig. G1 for the summarized data).

Figure 8a depicts the cutoff diameters of the three CPCs at varying internal pressures. The color code refers to the Δp between upstream (pexternal) and downstream (pCPC) pressure of the critical orifice. With an increase in CPC pressure the cutoff decreases. In the displayed measurement range of 160 to 700 hPa the cutoffs of channels 1 and 2 decrease by about 5 nm. This relation arises for channel 3 as well, but only at lower pressures of up to 400 hPa. The cutoffs of all channels seem to be rather independent of the pressure change between pexternal and pCPC although the counting efficiency shows higher values when Δp is low. During the TPEx campaign the pressure difference between the ambient and the CPC pressure was most of the time lower than 200 hPa which leads to a difference in ηmax⁡ of 5 %–10 % (Fig. G1).

Looking at the internal pressure range of 200–350 hPa it becomes apparent that the cutoff changes only slightly. For Channel 1 this means a decrease of ∼ 1 nm with increasing pCPC, channel 2 drops about 1.6 nm and channel 3 decreases 1.2 nm. This indicates that the overall decrease in cutoff with pCPC is rather constant for all channels, at least in the relevant pressure range. We therefore decided to use only one characteristic cutoff diameter per channel for the pressure range of 200–350 hPa. With the most commonly observed pressures of pCPC during TPEx at around 250 hPa (46 %) and pexternal of 300–400 hPa (23 %), the cutoffs are determined to be 11.3 nm regarding channel 1, 12.3 nm for channel 2 and 14.9 nm for channel 3, as shown in Fig. 8b. The channels 1 and 2 have the same ΔT of 36 °C, which should in theory result in a comparable cutoff. With our measurements, we show that this is true within the range of uncertainty. Note that the cutoff difference between the smallest and the largest channel is only 3.6 nm. This is rather small regarding the large difference in ΔT. We also observed that the performance of the CPC (cutoff diameter and plateau efficiency) is decreasing at low pressures and not the other way around, as Hermann et al. (2005), Weigel et al. (2009) and Williamson et al. (2018) presented. As another striking feature it needs to be pointed out that at a pressure of 550 hPa the cutoff of channel 3 suddenly increased with the pressure, which we have not seen for the other channels. First, we want to emphasize that the previous studies that investigated the enhanced efficiency of FC-43 at lower pressures used different CPC instruments than we did (e.g. TSI CPCs). Furthermore, there are studies that examined the behavior of Grimm CPCs at low pressures (Weber et al., 2023b; Bauer et al., 2023) and observed a similar relationship as we did, but were using butanol as the working fluid. Due to the different measurement setups, these studies cannot directly be compared to ours. Currently, we can only speculate about the reasons for this behavior in our system. We tentatively propose that altering diffusion rates in combination with the relatively long mc-CPC inlet lines could have caused the dropping CPC performance for all three channels with decreasing pressures in the range of 200 to 400 hPa. However, also the increasing cutoff sizes observed for channel 3 at pCPC > 400 hPa could be a result of varying diffusion rates. The diffusion of gases is dependent on the temperature and the pressure; low pressures and high temperatures are most favorable. On the other hand, the diffusion losses of aerosols to the wall are also affected by these parameters and additionally by the length of the inlet lines. The diffusion losses of small particles are high at low pressures (in the size range of 2–35 nm five times higher for 200 hPa than for 1000 hPa). Our inlet line is rather long, which enhances the particle losses even further. This could explain the large cutoffs that we observed even at the highest ΔT. When increasing the pressure in the range of 200 to 400 hPa, the aerosol diffusion coefficient decreases, which could have led to lower cutoff diameters. We assume that saturator temperatures of 41 and 35 °C, respectively, in this pressure regime are high enough for the FC-43 to reach the center of the saturator and to reach supersaturation (Hermann et al., 2005). A further increase of pCPC could have caused unsaturated sections in the saturator due to a lowered FC-43 diffusion rate (Hermann et al., 2005; Bauer et al., 2023). This seems to have an effect only on the performance of channel 3, as the cutoff diameters of channel 1 and 2 still decrease with increasing pCPC (Fig. 8a).

With these results, we can conclude that the mc-CPC in this configuration is best suitable for low internal pressures. For aircraft campaigns that focus on different flight levels, a pressure regulation seems to be useful. Especially when flying in the UTLS region it might be appropriate to remove the orifice and thus the pressure regulation to avoid the additional particle losses.