Performance of diethylene glycol-based particle counters in the sub-3 nm size range

When studying new particle formation, the uncertainty in determining the “true” nucleation rate is considerably reduced when using condensation particle counters (CPCs) capable of measuring concentrations of aerosol particles at sizes close to or even at the critical cluster size (1– 2 nm). Recently, CPCs able to reliably detect particles below 2 nm in size and even close to 1 nm became available. Using these instruments, the corrections needed for calculating nucleation rates are substantially reduced compared to scaling the observed formation rate to the nucleation rate at the critical cluster size. However, this improved instrumentation requires a careful characterization of their cut-off size and the shape of the detection efficiency curve because relatively small shifts in the cut-off size can translate into larger relative errors when measuring particles close to the cut-off size. Here we describe the development of two continuous-flow CPCs using diethylene glycol (DEG) as the working fluid. The design is based on two TSI 3776 counters. Several sets of measurements to characterize their performance at different temperature settings were carried out. Furthermore, two mixing-type particle size magnifiers (PSM) A09 from Airmodus were characterized in parallel. One PSM was operated at the highest mixing ratio (1 L min −1 saturator flow), and the other was operated in a scanning mode, where the mixing ratios are changed periodically, resulting in a range of cut-off sizes. The mixing ratios are determined by varying the saturator flow, where the aerosol flow stays constant at 2.5 L min−1. Different test aerosols were generated using a nano-differential mobility analyser (nano-DMA) or a highresolution DMA, to obtain detection efficiency curves for all four CPCs. One calibration setup included a high-resolution mass spectrometer (APi-TOF) for the determination of the chemical composition of the generated clusters. The lowest cut-off sizes were achieved with negatively charged ammonium sulfate clusters, resulting i cut-offs of 1.4 nm for the laminar flow CPCs and 1.2 and 1.1 nm for the PSMs. A comparison of one of the laminar-flow CPCs and one of the PSMs measuring ambient and laboratory air showed good agreement between the instruments.


Introduction
Roughly 50 % of the global cloud condensation nuclei (CCN) are thought to originate from secondary aerosol production in the atmosphere (Merikanto et al., 2009).Therefore, one major topic in atmospheric sciences is the detailed study of the nucleation processes.As atmospheric new particle formation happens in the size range below 2 nm, there has been a growing demand to extend the range, where direct measurements are possible also, below that.The lower size limit of a condensation particle counter (CPC) is generally described by D. Wimmer et al.: Sub-3 nm counters the diameter at which the counter still detects half of the particles.This diameter is called the cut-off diameter, or d 50 .Using condensation particle counters with low cut-off sizes enables detection of particles right after they are formed, even when the initial growth rate is slow.This also allows for obtaining information on the particle formation rate close to or even at the critical cluster size (Kulmala et al., 2012(Kulmala et al., , 2013)), without the need to scale down the measurement data of CPCs with larger cut-off sizes by using assumptions about the particle growth rate and the loss mechanisms.It has been proposed (Sipilä et al., 2010) that the inability of reproducing atmospheric nucleation rates in the laboratory could be partly explained by the slow growth of particles together with the relatively large cut-off sizes of the instrumentation used in most experiments.
Condensation particle counters are the most commonly used instruments for measuring the total particle number concentration in the sub-micrometre range (McMurry, 2000).The working principle of a condensation particle counter is to expose the aerosol sample to a supersaturated vapour, which condenses on the particles, thereby making them large enough to be detected optically.At least three different methods have been used for creating the required supersaturation: adiabatic expansion (Saghafifar et al., 2009), thermal diffusion in a laminar flow (Stolzenburg and McMurry, 1991) or mixing of two flows with different thermodynamic properties (Vanhanen et al., 2011).
The overall detection efficiency of a CPC depends both on the losses of particles inside the instrument as well as on the activation probability of the particles (Stolzenburg and McMurry, 1991).
where η sam is the sampling efficiency, which is defined as the ratio of particle concentrations exiting and the concentrations extracted from the sample flow; η act is defined as the activation efficiency; and η det is defined as the counting efficiency of the particles in the optics.The activation probability, in turn, mainly depends on the supersaturation of the condensing vapour which the particles are exposed to and also on the activating vapour.Besides the size of the particles, their surface curvature (Kelvin effect), their chemical composition and their charging state can have an influence on their activation (Kulmala et al., 2007b;Winkler et al., 2008).The cut-off size of a CPC can be lowered mainly by increasing the supersaturation, but also to some extent by minimizing the diffusional losses of particles inside the instrument.The first CPCs designed specifically for ultrafine particles were developed in the 1990s with a cutoff size around 3 nm (Stolzenburg and McMurry, 1991).The demand to measure even smaller particles -mainly to study atmospheric nucleation -has led to further CPC development, and by now several different instruments have been reported to measure in the sub-3 nm size range (Seto et al., 1997;Sgro and Fernandez de la Mora, 2004;Mordas et al., 2005;Kulmala et al., 2007a;Sipilä et al., 2008Sipilä et al., , 2009;;Iida et al., 2009;Lehtipalo et al., 2009Lehtipalo et al., , 2010;;Saghafifar et al., 2009;Vanhanen et al., 2011).
Here we characterize four diethylene glycol-based CPCs: two laminar flow DEG CPCs (modified TSI 3776) and two mixing-type particle size magnifiers (Airmodus A09 PSM), and the focus is on the validation of their performance in the sub-3 nm size range through precise laboratory calibrations.In addition, two of the instruments of different type were inter-compared while measuring ambient air.All of the four instruments were used in the CLOUD experiments at CERN (Kirkby et al., 2011), and the calibration data are crucial for evaluating and understanding their performance during the experiments.

General considerations
One limiting factor in lowering the cut-off diameter of a CPC is homogeneous nucleation inside the instrument.If the saturation ratio is too high, homogeneous nucleation of the working fluid can occur, which leads to a too high count rate in the CPC due to the internally produced particles.Iida et al. (2009) evaluated different working fluids for CPCs and showed that by selecting a working fluid with high surface tension but low enough saturation vapour pressure, one can achieve high supersaturations without considerable homogeneous nucleation.In that study, diethylene glycol was identified as a fluid with very favourable properties, and it has been demonstrated that it can be used to activate particles even close to 1 nm (Jiang et al., 2011b;Vanhanen et al., 2011).Another method to not only measure the total particle concentration in the range below 3 nm in diameter but also to retrieve information about their size is the SANC (size analysing nuclei counter), which is an expansion-type CPC, and by using the CAMS (constant angle Mie scattering) method, information about the particle size can be determined (Winkler et al., 2008).
The calibration of a CPC requires being able to produce a monodisperse aerosol with known size, chemical composition and charging state, which is not straightforward in the size range below 3 nm.CPCs are calibrated by using an aerosol generator and a differential mobility analyser (DMA) downstream, where the aerosol is classified according to the electrical mobility of the particles.As a reference instrument usually an electrometer is used.One major topic in aerosol nucleation studies is the question of how far the nucleation process is affected by the presence of ions (Kirkby et al., 2011).In the atmosphere, ions are always present, and therefore the measured formation rates will include both the neutral and the charged component if no ion filter is used in front of the CPCs.Therefore, it is useful to calibrate CPCs with charged particles of both polarities, but calibration measurements using neutral particles would also be desirable.
Usually charged particles of different compositions are used for calibrating CPCs.
Measurements in the sub-3 nm size range need to achieve a stable and sufficient concentration of aerosols for each selected size.Furthermore, significant diffusional losses have to be considered.Even if one manages to produce large amounts of 1 nm particles, a sufficient concentration needs to reach the aerosol counters after charging and transfer through the DMA.

The laminar flow DEG CPCs
Diethylene glycol (DEG) is very well suited for activating aerosol particles smaller than 3 nm in diameter, but as its absolute saturation vapour pressure at typical saturator temperatures is low, the particles grow only to sizes of about 90-100 nm, and are thus too small for direct optical detection (Iida et al., 2009;Vanhanen et al., 2011).This means that a special setup consisting of two growth stages is required.In the first stage the particles are activated and grown by DEG; in the second stage they grow further by condensing another liquid and the actual counting of the particles takes place.For the second stage a commercial CPC can be used, which will be termed the "booster" CPC in the following according to the nomenclature given by Iida et al.In the work presented here, two butanol-based CPCs, a TSI 3776 (d 50 = 2.5 nm), a TSI 3010 (d 50 = 10 nm) and an isopropanol-based TSI 3007 (d 50 = 10 nm) were used as booster CPCs.The total flow through the DEG stage is set to 0.3 L min −1 , but the booster can have a higher inlet flow rate.In this case an additional adjustable dilution flow after the DEG stage is required.Iida et al. (2009) used a total inlet flow rate into the CPC of 0.3 L min −1 .The condenser temperature was at 10 • C, and the saturator temperature was set to 50 • C. The wick that is installed inside the saturator was replaced by a 14 cm ×14 cm cellulose sheet.However, in the work presented here, two standard TSI 3776 ultrafine butanol CPCs were modified: after removing the wick, a cellulose filter was wrapped around a perforated stainless steel tube housed in the saturator part of the CPC.Since the TSI software does not allow for controlling the saturator temperature to values larger than 50 • C, an additional temperature control was installed.It consists of a Pt1000 attached directly outside the saturator block and a PID (proportional-integral-derivative) heat control unit (EZ-Zone, PM 6CICK-2AAAAAA).The optics part of the CPC was removed and instead an adapter was attached to the outlet of the condenser in order to connect it to a booster CPC.
Test measurements were performed to determine the highest saturator temperature where no homogeneous nucleation occurs while having the condenser at a fixed temperature of The setup is based on the commercially available TSI 3776.For the DEG CPC 2 a valve and a pump were added to give the possibility to increase the inlet flow.The flow and temperature settings for each CPC are shown in magenta for the DEG CPC 2 and in green the DEG CPC 1. 10 • C.This saturator temperature was found to be 52 • C. One of the DEG CPCs was always operated with these settings, and is here termed DEG CPC 1.During these measurements, a high-efficiency particle filter was installed at the inlet of the CPCs (using laboratory air as carrier gas) while stepping up the saturator temperature.With the temperatures of 10 and 52 • C the homogeneous nucleation was about 0.01-0.02cm −3 min −1 .
For the DEG CPC 2 the same modifications were performed, but with two additional changes.The flow rate through the aerosol capillary was increased (from 40-50 to 90-100 cm 3 s −1 ), which allowed for raising the saturator temperature to 55 • C before substantial homogeneous nucleation occurred.This was verified by applying the same procedure as mentioned before, and the same particle formation rate by homogeneous nucleation was achieved.Another change was made by implementing a needle valve and an external pump (see Fig. 1).Thereby, the inlet flow rate of the CPC could be increased up to 1.8 L min −1 .In the following, this setup will be referred to as DEG CPC 2.
Details for the systems, displaying the flow schemes and temperatures, are shown in Fig. 1.Labels in green font represent the working conditions for the DEG CPC 1; magenta represents the settings used for the DEG CPC 2. Similar modifications were reported by Kuang et al. (2011).They showed that with these modifications the detection efficiencies of the CPCs were improved significantly, when using negatively charged sodium chloride (NaCl) as a test aerosol.) 2.48 nm 2.07 nm 1.77 nm 1.48 nm 1.33 nm 1.24 nm Fig. 2. Detection efficiency of the PSM as a function of the saturator flow rate for negatively charged ammonium sulfate particles at different sizes.The different lines are measurements with differently sized particles and determine the saturator flow rate which is needed for achieving the corresponding cut-off diameters.

The particle size magnifier
The particle size magnifier (PSM; Airmodus A09) is a mixing-type condensation particle counter in which the supersaturation required for activating particles is achieved by turbulently mixing the sample with clean air saturated with diethylene glycol.A regular commercial CPC (TSI 3772 or TSI 3010) was used for further growing and counting the activated particles.Details of the instrument are described by Vanhanen et al. (2011).The cut-off size of the PSM can be varied by changing the mixing ratio of the saturator and sample flow rate, which determines the supersaturation achieved in the mixing section.Therefore, using the PSM in a scanning mode, also information about the particle size distribution can be obtained.One scan starts at the lowest mixing ratio, continues up to the highest and then back down again; one full scan takes 4 min.The relationship between the mixing ratio and activation diameter of particles is based on laboratory calibrations.Figure 2 shows how the detection efficiency of differently sized negative ammonium sulfate clusters change when varying the PSM saturator flow rate.Particles above 2 nm in diameter are detected already with very small saturator flow rates (mixing ratio < 0.07), whereas 1.2 nm clusters require a mixing ratio higher than 0.22 before they are detected.The ammonium sulfate clusters were produced with the setup described in Fig. 3 (see next Sect.3.3).

Reference instrument
The detection efficiencies shown in the following were derived from the ratio of the concentrations measured by a CPC and an electrometer, which was normalized to 1 at larger sizes to account for small differences in the setups.Two different electrometers (Grimm Aerosol Technik, FCE -Grimm model 5.705 and TSI model 3068B) were used as reference instruments.An inter-comparison showed that the two instruments agreed within 0.5-1 %.The comparison was done by selecting a certain diameter in the DMA while the two electrometers were measuring the concentrations in parallel.Also the offset was measured for both instruments and subtracted.The concentrations measured by the electrometer were corrected for the offset by setting the voltage at the centre electrode of the DMA to zero, which prevents particles from reaching the exit.Since the offset can vary with time, the zero measurement was done regularly.The concentrations were also corrected for diffusional losses (Chen and Pui, 2001) for each CPC/electrometer individually since they have different inlet flow rates.All the fitting curves for the counting efficiencies shown in the following are based on the function proposed by Stolzenburg and McMurry (1991) except for Fig. 7a.The maximum uncertainty in the selected mobility diameter using the nano-differential mobility analyser (nano-DMA) was 10 % at 1 nm, where the highresolution DMA had a resolution of about 20 (Jiang et al., 2011a).The instrument mobility resolution is defined as the reciprocal of the normalized full width at half-maximum, as described in (Flagan, 1999).

Generation of test aerosols
The main focus of this work is to characterize and compare the detection efficiencies of the DEG CPCs and the PSMs.Therefore, detailed calibration measurements were carried out using six methods for providing monodisperse aerosol particles in the size range between 1 and 10 nm.
The first setup is shown in Fig. 3a, where a nano-DMA (Grimm Aerosol Technik, S-DMA, 55-100) was used for size-selecting the generated aerosol particles.In this case the DMA was running in a closed loop arrangement with a sheath air flow rate of 20 L min −1 .Two different types of aerosol generators were used in this configuration.These are (a) a tungsten oxide generator (Grimm Aerosol Technik, NANO WO x Generator, 7.860) and (b) a sulfuric acid particle generator (Middlebrook et al., 1997).The sulfuric acid particle generator consists of a small heated quartz glass tube containing a ceramic vessel filled with sulfuric acid (Carl Roth GmbH + Co. KG, 95 %).The temperatures of the heater were varied between 55 and 77 • C. For these experiments the carrier gas was not conditioned, except for placing a high-efficiency particle filter in front of the aerosol generation unit.Therefore it is likely that the particle composition changes before the particles reach the calibration setup, e.g. by uptake of ammonia and other trace gases contained in the laboratory air.In this setup there was no mass spectrometer available to provide more detailed information about the exact particle composition.The high-resolution DMA (Herrmann et al., 2000) was operated in two different modes.The first one is shown in Fig. 3b, where the high-resolution DMA was running in an open loop arrangement, and the DEG CPC 1 was calibrated against an electrometer.In the second mode (Fig. 3c), the high-resolution DMA was operated in a closed loop arrangement, while one DEG CPC and one PSM at a time were calibrated in parallel against an electrometer.All four instruments were calibrated using this setup.The main difference between running a DMA in open or closed loop mode is the way the sheath air is controlled.In the closed loop setup, the sheath air is recirculating.When using an open sheath air setup, on the other hand, the air is drawn in from ambient and depending on the conditioning of the laboratory air the conditions in the sheath flow will change.Detailed information about the different methods can be found in Kangasluoma et al. (2013).A high-resolution mass spectrometer capable of analysing the composition of the clusters (atmospheric pressure interface -time of flight APi-TOF, Junninen et al., 2010) was measuring in parallel to verify that the composition of the aerosol was free of impurities and did not change during the calibration measurements.By using pure nitrogen as carrier gas (5.0), the aerosol sample was observed to be bisulfate clusters with only a few contaminant substances at low levels, while contaminant levels were considerably higher when filtered lab air was used.Since no direct measurement of the high-resolution DMA sheath gas flow rate was available, ions from an electrospray source with known electrical mobility were used to calibrate the voltage-mobility relation flow prior to each measurement (Fernandez de la Mora et al., 2005).For a better overview over the different calibration setups used, in Table1 an overview over the DMAs and their operations and the generators used is given.

Cut-off measurements
In the following, the results of the cut-off measurements are presented.The diameters reported here are electrical mobility equivalent diameters because the DMA measurement principle is based on electrical mobility.When the mobility is converted into a diameter, the use of the mobility diameter is most direct, while the conversion to a mass equivalent diameter introduces additional uncertainties (Ki Ku and Fernandez de la Mora, 2009;Ehn et al., 2011).
Figure 4 shows the counting efficiency as a function of the saturator temperature for the DEG CPC 1.For each setting the condenser temperature was kept constant at 10 • C, whereas the saturator temperature was varied between 40 • C (dark-blue line) and 55 • C (red line).The plot clearly shows that the counting efficiencies of the DEG CPC 1 vary with the temperature difference between saturator and condenser.For the smallest temperature difference between the saturator and the condenser, the d 50 was found to be 2.7 nm.For the temperature of 52 • C, the 50 % counting efficiency was 2.0 nm and for 55 • C 1.8 nm.These two temperature settings are used for the DEG CPC 1 and 2 respectively, but the highest temperature difference could only be realized with the higher capillary flow rate while avoiding significant homogeneous www.atmos-meas-tech.net/6/1793/2013/nucleation.The fact that the curves shown in Fig. 4 reach different plateau values is most likely due to internal losses inside the DEG CPC 1 and 2 and to incomplete activation of particles which travel through regions of the condenser with lower saturation ratio (Stratmann et al., 1994).The calculations of the uncertainties for the counting efficiency measurements are at least 10 %, from the flow uncertainty plus the contribution from statistical counting uncertainties; sample error bars included in Fig. 4. For particles larger than 5 nm, sulfuric acid was used as test aerosol.The tungsten oxide measurements stop at 4nm, because with the applied settings for the highresolution DMA, the biggest size that can be selected is 4 nm.Mobility standards are not included for the fit.
Figure 5 shows the counting efficiency of the DEG CPC 1 applying the methods of generating test aerosols according to Fig. 3a and b.The circles show the measurements performed with the nano-DMA and the triangles with the highresolution DMA (in the open loop configuration).By using this configuration, a d 50 of 2.0 nm was achieved.The results of the measurements performed providing sulfuric acid particles (according to setup Fig. 3a) are shown in Fig. 6.Here one data point at 1.7 nm is higher than expected, and similar calibrations did not reproduce this high point; therefore it is regarded as an experimental outlier.A d 50 of 2.0 nm was achieved also for sulfuric acid test aerosol.
Figure 7a shows a comparison of the counting efficiencies for PSM 1 and 2 as well as DEG CPC 1 and 2 using the setup from Fig. 3c.The PSM 1 was set to the highest saturator flow, so it was operating at the lowest cut-off diameter, whereas the PSM 2 was in scanning mode and the results shown here are achieved, by using the channel with the highest mixing ratio.The figure shows the results for a set of measurements where negatively charged ammonium sulfate particles were used as test aerosol; here a sigmoid fit function was applied, since the fit proposed by Stolzenburg and McMurry (1991) did not represent the data properly.Surprisingly, the cut-off of the DEG CPC 1 (1.4 nm) seems to be considerably lower (by 0.6 nm) than shown in Fig. 5, whereas the DEG CPC 2 has a 50 % counting efficiency of 1.3 nm.The fact that the cut-off of the DEG CPC 1 is significantly shifted towards lower sizes compared to the calibration measurements using tungsten oxide and sulfuric acid particles is unexpected, since the results for the other measurements all showed a cutoff diameter of ∼ = 2 nm.Nevertheless, similar results for the d 50 (1.4nm) for negatively charged ammonium sulfate particles are reported by Iida et al. (2009).The PSMs here also show the lowest cut-offs that have been achieved throughout the measurements and have a d 50 counting efficiency of 1.1/1.2nm.
Figure 7b shows the counting efficiencies for both PSM 1/2 and DEG CPC 2 using the setup Fig. 3c.The aerosol used here was positively charged ammonium sulfate.According to these measurements the DEG CPC 2 had a 50 % counting efficiency at 1.7 nm.The PSMs here agree nicely with each other.Both have a cut-off of 1.6 nm, which were the highest cut-offs that have been measured with the PSMs within this study.Figure 7c shows the counting efficiencies for both PSM 1/2 and DEG CPC 1/2 applying the setup shown in Fig. 3c where negatively charged sodium chloride particles were generated.These data show 50 % counting efficiencies of 1.7 nm for the DEG CPC 2 and 2 nm for the DEG CPC 1 respectively.The cut-off for both PSMs for sodium chloride was 1.2 nm.
One reason for the differences in the cut-off sizes of the CPCs for the different test aerosols might be the following: when using an APi-TOF in parallel, to measure the cluster composition, we found out that, if the aerosol sample and the measurement setup is not cleaned carefully, it will contain molecular impurities, which seem to affect the measurement at sizes smaller than about 1.7 nm.The cleaning was done by heating the tubes, and purging them with nitrogen.Also, for each substance always the same tubing was used.Details concerning the procedure can be found in Kangasluoma et al. (2013).Especially when generating positively charged aerosol particles, it turned out that it was impossible to produce a completely clean test aerosol without organic impurities in our setup, which could explain the higher cut-off size (by 0.5 nm) for positive ammonium sulfate.The effect of a lower counting efficiency for positively charged clusters has been shown by various other studies, and even for different working fluids (Winkler et al., 2008;Iida et al., 2009;Kuang et al., 2011).One possible explanation might be that aerosol particles consisting of a considerable amount of organic compounds are less soluble in the organic vapours that are mostly used as working fluids.Another explanation could be that in the positive polarity where the ions produced in the charger are bigger, they can have an influence on the counting efficiency curves, as their activation properties are different to the sample ions (Sipilä et al., 2009;Kangasluoma et al., 2013).The overall question comes up of whether the lower counting efficiency for positively charged aerosols is due to the charge sign or due to the fact that in the positive case the organic contribution is always higher than in the negative case.These two effects are very likely not to be completely decoupled from each other.
The 50 % counting efficiency diameters are summarized in Table 2 and the overall results indicate that the effect of the aerosol type on the counting efficiencies is in general non-negligible.It seems that when dealing with aerosol particles/clusters in the sub-3 nm size range, the chemical composition of the clusters and the purity of the sample have a significant impact on the counting efficiencies.The fact that a range of cut-off diameters exists and that the shapes of the counting efficiency curves are different makes it more difficult to determine the formation/nucleation/growth rates unambiguously.It is not obvious which cut-off diameter to choose if a calibration with exactly the same particle composition is not possible.

Evaluation of the diffusional losses in a laminar flow CPC
The design of the ultrafine TSI 3776 with its rather low aerosol flow rate inside the capillary (50 cm 3 min −1 ; see Fig. 1) indicates that it has non-negligible internal losses.In addition, the comparison of the cut-off curves for the DEG CPCs and the PSMs underline this assumption.From Fig. 7 it can be seen that the PSMs 1 and 2 have steeper slopes in the counting efficiencies, and reach an efficiency close to 100 % at smaller sizes compared to the DEG CPCs, which might be due to the fact that the DEG CPCs have larger internal losses.To quantify the effect of the internal losses, a set of measurements was carried out.The setup used is shown in Fig. 3d and consists of an aerosol generator (tube furnace with sodium chloride) and a Grimm nano-DMA for classification of the particles.Behind the DMA, a three-way valve is located where the flow is directed either to the DEG stage or to a flexible conductive tubing before being sampled by the CPC.The tube length was adjusted until the CPC showed the same concentrations no matter whether the aerosol was going through the DEG stage or through the tube.To determine the final effective tube length, the length of the condenser was estimated (8 cm).This has to be subtracted from the total length, since the particles at this stage can be considered big enough not to be substantially affected by diffusional losses any more.Prior to these measurements the DEG CPC was dried carefully and the saturator temperature was set to 30 • C to avoid any activation of the particles.This way, the effective length was evaluated to be 19 cm at a flow rate of 0.3 L min −1 through the tube.Figure 8 shows the calculated penetration efficiencies according to Gormley and Kennedy (1948) for the size range 1-10 nm using the experimentally determined tube length and flow rate.The detection efficiencies, applying these corrections of the DEG CPC 1 (red symbols) and the uncorrected points (green symbols) are shown in Fig. 9.The fact that the 100 % efficiency line is reached for particles larger than 3 nm indicates that the corrections applied are appropriate.As a comparison the data points from the PSM 2 for the positively charged sodium chloride clusters are added to this figure (black symbols).It shows that after correcting for the internal losses, the slopes of the counting efficiency curves of the laminar-flow CPC are comparable  to the mixing-type CPCs, in which the diffusional losses of particles are considerably lower.Thus the red symbols (corrected data) represent the activation efficiency of particles in the DEG CPC 1.
As the internal losses are rather significant (approximately 50 % at 2 nm), it needs to be discussed as to how far the results from DEG CPC measurements such as the nucleation and formation rates need to be corrected to account for these internal losses.However the same applies to all continuousflow CPCs when measuring close to their cut-off sizes.Usually it is not possible to correct the data without knowing the exact size distribution of the measured particles, because the diffusional losses are size dependent.Therefore, in our data analysis, the uncorrected counting efficiency is used.

Instrument comparison in ambient conditions
In this section, measurements of outdoor air in Helsinki (in Kumpula university campus area, ca. 4 km from Helsinki city centre) as well as indoor air from the aerosol laboratory are shown.The left-hand side of Fig. 10 shows the comparison of total particle concentration measured with the DEG CPC 2 and the PSM 1 in scanning mode, measuring lab air for a time period of approximately 10 h.The different colours of the lines represent the different flow settings for the saturator flows of the PSM.The right half of the figure shows outdoor air measurements.The two channels with the highest mixing ratios (lowest cut-off diameter) of the PSM (green and blue line) show a slightly higher concentration than the other channels, especially when the overall particle concentration was low, leading to a lower condensation sink for small particles.The difference in concentration between the flow settings was larger in the indoor air measurements, which might be due to the fact that a lot of small particles were present in the laboratory air as the aerosol generation setup was running.It is worth noting that all the settings of the scanning PSM show very similar concentrations during the outdoor air measurements.Therefore, it can be concluded that no significant amount of nucleation mode particles was present D. Wimmer et al.: Sub-3 nm counters during this measurement period.The sudden increase of the particle concentration around 04:30 UTC (06:30 LT -local time) might be due to the beginning of the morning traffic, as the measurement place is close to a big road.In the inset of the figure a scatter plot shows the correlation between the total concentrations measured by the DEG CPC and the PSM during the ambient measurement period.It shows good agreement (R 2 = 0.95) between the DEG CPC 2 (d 50 = 1.5-1.8nm) and the 0.55 L min −1 setting (d 50 = 1.5 nm) of the scanning PSM.

Conclusions
We investigated the performance of CPCs which are sensitive to particles below 3 nm in mobility equivalent diameter.Four different ultrafine CPCs which all use diethylene glycol as the working fluid were studied.Two different calibration setups and in total six different methods of generating test aerosols were used.
The determination of the exact detection efficiency functions of the CPCs is important when measuring concentrations close to the cut-off sizes.If the cut-off function is shallow, both the nucleation rates and the growth rates can be affected by the shape of the detection efficiency curves.Our results show that the 50 % detection efficiency diameters of the diethylene glycol-based particle counters differ depending on the composition of the particles.Even though the two DEG CPCs are slightly different from earlier work, their detection efficiency results agree well with the ones developed and characterized in other laboratories (Jiang et al., 2011a;Kuang et al., 2011;Iida et al., 2009).Iida et al. (2009) achieved a cut-off diameter of 2 nm using negatively charged silver particles, and roughly 1.3 nm for negatively charged ammonium sulfate particles, and Jiang et al. (2011a) achieved the same result by using negatively charged sodium chloride particles.Kuang et al. (2011) acquired cut-offs of 1.5 nm with a temperature difference of 50 K for negative sodium chloride particles.In this study we found a cut-off diameter of 1.4 nm for negatively charged ammonium sulfate for both laminar flow DEG CPCs and 1.2 and 1.1 nm for the PSMs.Using negative sodium chloride particles resulted in d 50 of 1.7 and 1.5 nm for the DEG CPCs and 1.2 nm for the PSMs.In the laboratory the chemicalcomposition-dependent counting efficiencies are not a problem as there the particle composition is typically known, but in the real atmosphere the composition is unknown.This leads to a higher uncertainty in the data obtained with the atmospheric nanoparticles.
The CPCs capable of detecting particles in the range of 1 to 2 nm are highly important when studying atmospheric nucleation because the corrections for calculating the "true" nucleation rates are considerably reduced and information about particle growth rates in the size range between 1 and 3 nm can be obtained.Also seemingly redundant measurements with multiple sub-3 nm CPCs are highly useful, since matching data from several CPCs with independent operating principles adds greatly to the confidence in the measurements, allows for rapid and reliable determination of data quality and helps to identify any instrumental problems.When comparing the mixing-type CPCs with the laminar-flow DEG CPCs, they agree fairly well based on our experiments.The measurements at CLOUD have underlined the good agreement of the two counter types and the importance of using low cut-off counters for the nucleation measurements (Kirkby et al., 2011;Kulmala et al., 2013).

Fig. 1 .
Fig. 1.A detailed overview of the setup for DEG CPC 1 and 2. The setup is based on the commercially available TSI 3776.For the DEG CPC 2 a valve and a pump were added to give the possibility to increase the inlet flow.The flow and temperature settings for each CPC are shown in magenta for the DEG CPC 2 and in green the DEG CPC 1.

Fig. 3 .
Fig. 3. Overview of the different configurations used for the calibrations.The aerosol generators used together with the nano-DMA are shown in (a).The measurement configurations using the high-resolution DMA in the open loop mode are shown in (b) and for the closed loop mode in (c); (d) shows the setup for quantifying the internal losses of the DEG CPCs.

Fig. 4 .
Fig. 4. Detection efficiencies for DEG CPC 1 at different temperature settings, using tungsten oxide particles.The condenser temperature was 10 • C, and the saturator temperature was varied from 40 • C (blue) up to 55 • C (red).The black symbols show the setting of 52 • C, which was used throughout all the experiments shown in this work.The fit curves to the data are based on the parameterization byStolzenburg and McMurry (1991).

Fig. 5 .
Fig.5.Detection efficiencies for the DEG CPC 1 for different particle types of both polarities classified with a nano-DMA and a highresolution DMA in open loop.For particles larger than 5 nm, sulfuric acid was used as test aerosol.The tungsten oxide measurements stop at 4nm, because with the applied settings for the highresolution DMA, the biggest size that can be selected is 4 nm.Mobility standards are not included for the fit.

Fig. 6 .
Fig. 6.Detection efficiencies for the DEG CPC 1 using negatively charged sulfuric acid particles classified with a nano-DMA.

Fig. 7 .
Fig. 7. Detection efficiencies for the DEG CPCs compared to the PSMs using negatively charged ammonium sulfate (a), positively charged ammonium sulfate (b) and negatively charged sodium chloride particles (c) produced in the closed loop high-resolution setup.

Fig. 8 .
Fig. 8. Calculated penetration efficiencies as a function of size for the experimentally determined parameters (flow rate and tube length).They were derived by measuring the concentrations of sizeselected aerosols (3, 4 and 6 nm) once after passing a flexible tube and once after passing through an empty laminar flow CPC (model TSI 3776).

Fig. 9 .
Fig. 9. Detection efficiencies of DEG CPC 1 before correcting for internal losses (green symbols) and after the correction (red symbols).As a comparison the (uncorrected) data from the PSM 2 from Fig. 7c is shown here in black.

Fig. 10 .
Fig. 10.Comparison of the scanning PSM and DEG CPC 1 measuring the total particle concentration indoors and outdoors.The different coloured lines for the scanning PSM show the different flow rate settings for the saturator flow.The scatter plot shows the correlation between the 0.55 L min −1 saturator flow setting for the scanning PSM and the DEG CPC 1.The slight spread of the data for higher concentrations might be due to coincidence in the DEG CPC.

Table 1 .
Summary of DMAs, calibration setups and aerosol generators used.

Table 2 .
Summary of the 50 % detection efficiencies of the four CPCs for different types of aerosols.When using tungsten oxide as test aerosol the smallest size that can be produced was about 1.5 nm, where the PSMs still detected roughly 60 %.Type of aerosol Polarity d 50 DEG CPC 1 d 50 DEG CPC 2 d 50 PSM1 d 50 PSM2