Particle charge-size distribution measurement using a differential mobility analyzer and an electrical low pressure impactor

ABSTRACT

We introduce a particle charge-size distribution measurement method using a differential mobility analyzer and an electrical low pressure impactor in tandem configuration. The main advantage of this type of measurement is that it is suitable for a wide range of particle sizes, from approximately 30 nm up to a micrometer, and for high charge levels, which have been problematic for previously used methods. The developed charge measurement method requires information on the particle effective density, and the accuracy of the measurement is dependent on how well the particle effective density is known or estimated. We introduce the measurement and calculation procedures and test these in laboratory conditions. The developed method has been tested using narrow and wide particle size distributions of a known density and well-defined particle charging states. The particles have been produced by the Singly Charged Aerosol Reference (SCAR) and an atomizer and charged with the previously well-characterized unipolar diffusion chargers used in the Nanoparticle Surface Area Monitor (NSAM) and in the Electrical Low Pressure Impactor (ELPI+). The acquired charge-size distributions are in good agreement with the reference values in terms of the median charge levels and widths of the charge distributions.

Copyright © 2017 American Association for Aerosol Research

EDITOR :

• Jing Wang

Introduction

As listed below, the electrical charge level of particles (charging state) is important information in many applications of aerosol technology. The size and concentration measurement of nanoparticles relies heavily on particle charging to a known level. Diffusion charging is commonly used to produce controlled charge levels (Intra and Tippayawong 2011), and it is used in combination with electrical detection in instruments measuring particle concentration, for instance the Nanoparticle Surface Area Monitor (NSAM; Fissan et al. 2007), the Partector (Fierz et al. 2014), and the PPS-M (Rostedt et al. 2014). The operation principles of various particle sizing instruments, including the Scanning Mobility Particle Sizer (SMPS; Wang and Flagan 1990), Electrical Low Pressure Impactor (ELPI; Keskinen et al. 1992; Marjamäki et al. 2000), and Engine Exhaust Particle Sizer (EEPS; Johnson et al. 2004), require that particles are charged to a known level. Electrostatic precipitation is widely used in industry and power generation to reduce harmful particle emissions. The collection efficiency of these precipitators depends on the charging efficiency and the final charging state of the particles (Zhuang et al. 2000). In aerosol medicine, the charge level affects the lung deposition because of image and space charge effects (Balachandran et al. 1997). In engine exhaust aerosol measurements, the charge level gives information on the particle formation conditions (Maricq 2006; Lähde et al. 2009), and in outdoor aerosol studies, elevated electric charge levels have been found for particles originating from engine exhaust (Hirsikko et al. 2007; Tiitta et al. 2007; Lee et al. 2012; Jayaratne et al. 2014). While bipolar charge levels in normal conditions can be rather accurately predicted theoretically (Fuchs 1963; Wiedensohler 1988), unipolar charging levels and high temperature bipolar charging levels must be experimentally measured.

Particle charge levels can be experimentally studied by various methods. An aerosol electrometer can be used to measure the net charge of the particle size distribution (Kulvanich and Stewart 1987; Murtomaa and Laine 2000). The ELPI can be used to measure the net charge-size distributions by bypassing the charger or by simply turning off the internal unipolar diffusion charger and the ion trap (Kwok and Chan 2008; Kuuluvainen et al. 2015; Simon et al. 2015). Another method is to conduct electrical mobility based measurement in which, particles are led to an electric field resulting in a constant drift velocity according to their electrical mobility. The electrical mobility is dependent on the particle size and charging state. In the case of a narrow size distribution of known diameter, direct measurement by differential mobility analyzer (DMA) followed by a particle counter may be used to analyze particle charge levels (Hewitt 1957). More advanced techniques combine electrical mobility analysis and particle size measurement. Mobility analyzers accompanied with an optical particle size and concentration measurement have been applied to measure the charging state of larger particles (Emets et al. 1991; Forsyth et al. 1998; Vishnyakov et al. 2016). In the case of nanoparticles, a straightforward solution is to measure the particle size distribution by an SMPS and then bypass the neutralizer to study the original charge of the particles (Maricq 2004). The latest and the most accurate methods are based on two DMAs used in tandem configuration (Kim et al. 2005; Maricq 2005). In the tandem configuration, the particles are classified in the first DMA according to their electrical mobility, which is determined by their initial charging state and size. After the first DMA, the particles are brought to a known charging state in a bipolar diffusion charger and classified by the second DMA, which is followed by a detection instrument, a condensation particle counter (CPC) or an aerosol electrometer. The tandem-DMA measurement provides accurate three-dimensional (concentration as a function of size and charge) information, but the method has some limitations. Tandem-DMA measurement requires a long measurement time, and as a result, the aerosol source must be stable over a long period of time. In addition, the charge level must be well defined before the second DMA, which can be difficult to achieve if the particles were initially highly charged (de La Verpilliere et al. 2015). Thus, the tandem DMA method is most suitable for nanosized particles from 1 to 100 nm, for which the initial particle charge levels can be expected to be relatively low. It is notable that the tandem DMA method with a CPC is the only applicable charge measurement technique for studying the nanoparticle charge in low number concentration environments. For particle sizes larger than 1 µm, the charge-size distributions can be measured for instance with a bipolar charge analyzer (BOLAR; Yli-Ojanperä et al. 2014).

In this study, we introduce a charge measurement method intended to be used mainly in the sub-micrometer size range. The favorable measurement application is highly charged particles of a known density. We introduce the charge measurement method and present the calculation routine for the determination of charge-size distributions. The performance of the developed method is verified experimentally by using particles of a known size and two different charge conditions: singly charged and charging state resulting from the unipolar diffusion chargers. The charger designs are those used in the Nanoparticle Surface Area Monitor (NSAM) and in the Electrical Low Pressure Impactor (ELPI+). We also test the developed method using wide size distributions subjected to unipolar diffusion charging.

Charge measurement concept

Concept of operation

The new charge-size distribution measurement concept is illustrated in Figure 1. The concept combines electrical mobility selection with aerodynamic size classification accompanied with electrical detection of the collected particles. The first step is conducted with a DMA and the second step is conducted with an ELPI. Let us consider what happens when a polydispersed aerosol size distribution with an unknown electric charge (bipolar or unipolar) enters the DMA, which is operated at a constant voltage difference between electrodes. In this case, the output of the DMA consists of particles with nearly the same electrical mobility. The output particles may have 1, 2, …, n number of elementary charges. Each different number of elementary charges corresponds to a different particle size (mobility diameter) and, consequently, to a different aerodynamic diameter. The DMA is followed by the ELPI. The ELPI charger is switched off because, in this way, the detected current is not affected by the charging efficiency. The particles with a different number of elementary charges represent different aerodynamic diameters and are distributed to different impactor stages and thereby detected as an electric current with separate electrometers. If the density of the particles is known, it is straightforward to calculate to which impactor stages the penetrated particles with a different number of elementary charges are distributed at any given DMA voltage setting. This enables the determination of the particle number concentrations at each impactor stage based on the measured electric currents. In other words, a measurement at one DMA voltage results in pairs of a number of elementary charges n and corresponding number concentrations N, one pair for each particle size. By conducting the described measurement routine at different DMA operating voltages, the number of elementary charges and corresponding number concentrations measured by the impactor stages change while the particle sizes collected by the individual impactor stages remain the same.

Figure 1. The principle of the DMA-ELPI charge measurement system.

As a result, number concentrations as a function of the number of elementary charges are obtained for the particle sizes collected at different impactor stages. By combining the obtained information, the initial charge-size distribution of the inlet aerosol can be calculated from the results. A thorough description of the calculation procedure will be given in the section “Calculation of charge-size distribution.”

Measurement procedure

As mentioned earlier, the measurement setup consists of a DMA and of an ELPI, which are connected in tandem configuration. During one charge-size distribution measurement, the classification voltage of the DMA is changed in a stepwise manner, beginning from low values and proceeding towards larger values. Each stepwise voltage change is followed by a stabilization period, during which the ELPI electrometer signals stabilize.

The stabilization period is followed by a measurement period, during which the electric current signals are recorded and an average current value for each stage is calculated. As a result, the electric current values and also number concentrations are obtained as a function of the DMA voltage separately for each impactor stage. In Figure 2a an example of the charge-size measurement procedure is shown. In this example raw electrometer signals from two impactor stages and the DMA voltage are recorded as a function of time.

Figure 2. Example of the measurement data (a), results after the calculation (b), integrated charge distribution (c) and three-dimensional charge-size distribution (d). Only two impactor stages, 1 and 2, are shown. Data from (b) is either summed to produce an integrated charge distribution over the entire size distribution, (c) or particle concentrations are shown as a function of both particle size and charging state (d).

Calculation of charge-size distribution

For one measurement point, the DMA defines the particle electrical mobility and the ELPI defines the current distribution as a function of particle aerodynamic diameter, which compose the basis of the calculation. The collection efficiency function parameters for the ELPI+, which is used in this case, are given in Järvinen et al. (2014), except the stage cut diameters and pressures, which are impactor specific and are taken from the manufacturer calibration datasheet. In the first stage, the impaction collection efficiency functions of the ELPI+ are converted from aerodynamic to mobility diameter by assuming an appropriate constant density for the particles. Next, the diffusion part of the collection efficiency functions, not dependent on particle density, are added and the kernel (response) functions are formed. The values of the kernel functions are calculated at certain particle sizes, which is explained later. This results in response terms a_k,m for each impactor stage m and particle size k. The particle charging state, the number of elementary charges per particle n_k, is calculated from the DMA parameters for the particle size of index k based on basic DMA equations, given in the online supplemental information (SI). It is now possible to represent the electric currents measured by the ELPI stages by a simple group of equations[1] where I_m is the electric current measured by stage m and x_k is the particle concentration (electric current) term for particle size k. The K is the number of particle size bins used in the calculation. This group of equations forms an inversion problem that can be solved by conventional methods. In this case, the Tikhonov regularization method (Hansen 1998) was used. Constant values of 14 and 1 were used for the number of size bins and the Tikhonov regularization parameter, respectively. Finally, the particle number concentration N for the specific size and charge combination is given by equation[2] where e is the elementary charge and Q_DMA is the DMA sample flow rate. Instead of the ELPI flow rate, the sample flow of the DMA is used in the equation because it defines the amount of particles entering the measurement system. The presented calculation is conducted for all of the measurement points (DMA voltages) separately, and as a result, the particle charging state is obtained for each of the impactor stages (see example in Figure 2b). The particle concentrations acquired are presented as arbitrary units because a zero-width DMA transfer function is used to simplify the calculation. In further analysis the results are combined into a single charge distribution and divided into integers of elementary charge (0.5 to 1.5 are counted as 1 and so on). An example is given in Figure 2c. Another option is to present the results in a three-dimensional figure. In this case, particle concentration is shown as a function of both mobility diameter, based on selected particle sizes, and the particle charging state (Figure 2d).

The calculation requires the selection of the particle sizes of index k, which has not yet been discussed. A straightforward solution is to use the mean diameters of the impactor stages to solve the group of equations, but this may result in unstable computational results especially when the useful signal is concentrated on only a few stages. To remedy this, at the first stage, the measured data from the entire measurement is analyzed by checking which of the impactor stages collect charge during the entire measurement. The size range used in the calculation is then limited to cover these stages. First, the maximum charge values over an entire measurement for all of the stages are searched. Then, the stages are selected for which the stage maximum value is more than 10% of the highest value over an entire measurement. To capture all of the required signal, adjacent stages are also considered. The size range used in the calculation is then selected logarithmically so that the first and last sizes are the mean diameters of the adjacent stages. For instance, if the 10% limit is exceeded for stages 5, 6, and 7, the size range is a logarithmic series from the mean diameter of stage 4 to the mean diameter of stage 8, with 14 different particle sizes. The limitation of the size range affects the solution through changes in the collection efficiency terms a_k,m.

Measurements

The measurement setup is described in Figure 3. The mobility classification is achieved using a 280 mm long Vienna type DMA (Winklmayr et al. 1991) operated with a closed sheath flow loop. A sample to sheath flow ratio of 1/10 was used. The ELPI+ (Dekati Ltd., Finland) requires a sample flow of 10 l/min, which is far higher than the DMA inlet flow (2 l/min in all charge distribution measurements). As shown in Figure 3, the setup has an additional bypass loop to ensure that the inlet flow rate stays constant if the DMA flows are changed. The flow rate through this bypass loop is adjusted with needle valves, and the particles are removed using a HEPA filter. The ELPI+ was operated with the charger and the ion trap switched off, and the particles were collected in the impactor into aluminum foil collection substrates, which were covered by a thin layer of vacuum grease (Apiezon L, M&I Materials Ltd., UK).

Figure 3. Measurement setup.

The measurement routine consisted of scanning the DMA voltage and measuring the particles with the ELPI+. The DMA voltage was logged directly by the ELPI+ analog input channel to assemble all of the data into a single file. One measurement point consisted of 10 s stabilization and 10 s measurement periods. There were 20 measurement points, resulting in a total time of 400 s for one charge distribution. Data processing was conducted in a Matlab environment (Matlab 2015a, Mathworks Inc., MA, USA).

To study the performance of the developed method, laboratory measurements were conducted using particles of a known size, charging state and material properties. Singly charged particles were used to test that the method is capable of estimating low numbers of elementary charges per particle. The singly charged particles were generated by the Singly Charged Aerosol Reference (SCAR; Yli-Ojanperä et al. 2010). This is a reliable reference method because practically all particles are singly charged (Högström et al. 2011). The particles were composed of an approximately 10 nm NaCl or Ag seed particle surrounded by liquid diethylhexyl sebacate (DEHS). Size distributions were acquired by measuring the total electric current from the ELPI (charger and ion trap switched off) during the DMA scan. Because particles were known to be singly charged, there was a one-to-one correspondence between the total electric current and the particle number concentration in this special case. The size distributions, measured using the DMA, are shown in Figure S1a (see the SI). The generated particle sizes were 50, 100, 200, and 500 nm, with rather narrow size distributions, the Geometric Standard Deviations (GSD) ranged between 1.06 and 1.15. Because the particle sizes are significantly larger than the seed particle size, the seed particle has a minimal effect on the density. Thus, the particle density was approximated by the bulk density value of pure DEHS, which is 0.914 g/cm³.

The method was also tested with the same narrow size distributions of particles with higher charge levels. Particles were generated by the SCAR and then neutralized using a Kr-85 aerosol neutralizer (3077A, TSI Inc., Shoreview, MN, USA) followed by an electrostatic precipitator and finally charged by corona-based diffusion chargers. The ELPI+ charger was selected to provide higher charge levels. Järvinen et al. (2014) report the charging efficiency of this charger over a wide particle size-range. The charger was operated at the standard corona discharge current value of 1 μA. In addition, another charger based on Medved et al.'s (2000) design was used to produce charged particles. This mixing-type diffusion charger is used in electrical aerosol instruments (Electrical Aerosol Detector, Model 3070A, and Nanoparticle Surface Area Monitor, Model 3550, TSI Inc., MN, USA). Qi et al. (2009) and Kaminski et al. (2012) have characterized the charger, the latter reporting particle charge distributions. The charger in this study was operated using the same flow rates (1.5 L/min aerosol and 1.0 L/min ion jet flows) and the same 1 μA corona current as in Kaminski et al. (2012).

The developed charge measurement method was also subjected to wide particle size distributions of charged particles. Particles were generated by atomizing DEHS from solutions at different concentrations (1%, 10%, and 100% by volume). HPLC-grade 2-propanol was used as a solvent in the case of the 1% and 10% solutions. The wide size distributions generated by atomizing DEHS solutions are shown in Figure S1b. The distributions range to super-micron diameter and were measured using a standard ELPI+. The median mobility diameters according to lognormal fitting are 135, 224, and 430 nm for 1%, 10%, and 100% DEHS solutions. The GSD's for the atomized particle size distributions range between 2.0 and 2.4. After the generation, the aerosol was diluted with filtered air and neutralized by alpha radiation neutralizer (Am-241, 29.6 MBq, residence time 1.9 s). The final charging was performed by the same ELPI+ charger as in the previous measurements and using the same 1 μA corona current.

Results

For singly charged particles the calculation was performed as in Figure 2c, by calculating the charging state over the entire size distribution. The particles were mostly detected to carry one elementary charge by the developed method (Figure 4). At the 50 nm particle size, small amounts of other charge levels were detected, especially doubly charged particles. This effect likely arises from the low electric currents measured and from the narrow size distribution detected only by two ELPI channels. In the case of the 100 and 200 nm particles, the calculated fraction of particles with more than one elementary charge was minimal, less than 5%, which implies that the method is suitable for singly charged particles. The charge distribution for singly charged 500 nm particles is not shown because the particle concentrations were too low for the calculation.

Figure 4. Charge distributions from singly charged particles of different sizes. The fraction is calculated from the charged particles only.

The higher charge levels, produced by a separate ELPI+ charger installed in line, were studied with the same distributions presented in Figure S1a. The results for the unipolar diffusion charged aerosol are presented in Figure 5. Modal values of 2, 5, 10 and 36 elementary charges were observed, while the particle diameters were 50, 100, 200, and 500 nm. If a lognormal fitting is conducted for the charge distributions, median values of 2.41, 5.09, 10.5, and 37.1 are obtained. The corresponding Pn-values, penetration multiplied by the number of elementary charges per particle, for the ELPI+ charger used were 1.75, 4.08, 9.54, and 29.3 (Järvinen et al. 2014). The Pn-values include the particle losses and should be somewhat lower than the presented charge number values. Taking this into account, the values from the developed method match the Pn-values well. The measured values and the reference values for the test measurements are shown in Table 1.

Figure 5. Charge distributions of unipolarly diffusion charged particles. The particles were charged by a separate corona charger similar to the one used in the ELPI+. The vertical line represents the charger Pn-value at the corresponding particle size.

Table 1. Measured and reference charge distribution parameters for the ELPI+ and the mixing-type chargers. The n refers to the number of elementary charges per particle. For the ELPI+ charger, separate values for narrow (N) and wide (W) size distributions are presented.

	ELPI+							Mixing-type
	n mode		n median			n GSD
dp (nm)	N	W	N	W	n ref^a	N	W	n mode	n median	n ref^b	n ref^c	n GSD	n GSD ref^c
50	2	2	2.41	1.92	1.75	1.31	1.38
100	5	4	5.09	4.57	4.08	1.21	1.36	3	3.18	2.90	2.67	1.40	1.46
200	10	10	10.5	9.82	9.54	1.22	1.25	8	6.98	6.31	5.83	1.35	1.40
500	36	33	37.1	34.7	29.3	1.18	1.20

^a Pn-value, Pn = 68.531·D_p(μm)^1.225 (Järvinen et al. 2014).

^b Average, n = 0.0167·D_p(nm)^1.12 (Kaminski et al. 2012).

^c Median from lognormal fit (Kaminski et al. 2012).

The charge distributions after the mixing-type charger were tested using 100 and 200 nm narrow particle size distributions, similar to those shown in Figure S1a. The charge distributions are presented in Figure 6 accompanied by the results from the Kaminski et al.'s (2012) empirical model. The developed charge measurement method produces mode values of 3 and 8 and median values of 3.2 and 7.0 elementary charges per particle for 100 and 200 nm particles. These median values are calculated by fitting a lognormal function to the final charge distributions. In comparison, a similar fitting method gives 2.67 and 5.83 elementary charges per particle median values according to the model by Kaminski et al. (2012). Average values for the same particle sizes using a simple power equation by Kaminski et al. (2012) are 2.9 and 6.3. Thus, the values from the developed charge measurement method are slightly higher than those predicted by the model, which is also shown in Figure 6. The GSD values according to the charge measurement method are 1.40 and 1.35, and the corresponding values from the model are 1.46 and 1.40, which indicates that the width of the charge distribution is detected quite well by the developed method in comparison to the model.

Figure 6. Charge distributions of unipolarly charged particles after the mixing-type charger. The bar plot is the distribution according to the developed method, and the line represents results from the semi-empirical model by Kaminski et al. (2012).

Typical particle size distributions are rather wide compared to the test aerosols shown in Figure S1a. To study more realistic measurement application, wide distributions were generated by atomizing DEHS (size distributions in Figure S1b). This aerosol was neutralized and then charged using the same ELPI+ charger as in the case of the narrow size distributions. This type of measurement generates a three-dimensional output, in which particle number concentration is presented as a function of particle size and charging state. In Figure 7, the results for three different particle size and charge distributions are given. The pattern observed in Figure 7 closely resembles the Pn-curve of the ELPI+ charger (Järvinen et al. 2014), which is also plotted in the figure, from 30 nm up to a 1 μm particle size. This result confirms that the method is capable of measuring the charging state of wide particle size distributions and performs well in wide size range from tens of nanometers up to a micrometer.

Figure 7. Charge-size distributions after the ELPI+ corona charger in the case of three wide size distributions generated by atomizing 1% (a), 10% (b), and 100% (c) DEHS solutions. The line in the figure represents part of the Pn-curve of the ELPI+ corona charger (Järvinen et al. 2014).

To more closely study the charge-size distribution of Figure 7, specific particle sizes were selected, and the charge distributions are shown for these selected particle sizes in Figure 8. Because the selected particle sizes are not the specific sizes used in the calculation, the results are based on the interpolation of the distribution. To compare the values, the same particle sizes were selected as in Figure 5, which were supplemented by additional 30 nm and 800 nm sizes. The 30, 50, and 100 nm charge distributions were calculated as cross-sections from Figure 7a, and the 200 nm charge distribution from Figure 7b. The two largest charge distributions, 500 and 800 nm, were calculated from Figure 7c. The modal values in Figure 8 are 1, 2, 4, 10, 33, and 54 elementary charges per particle, and the median values of 1.29, 1.92, 4.57, 9.82, 34.7, and 56.6 were achieved through lognormal fitting. The Pn-values for the same particle sizes are 0.93,1.75, 4.08, 9.54, 29.3, and 52.1 (Järvinen et al. 2014). The charge values obtained from the wide size distribution are actually closer to the Pn-values than those obtained from the narrow size distributions shown in Figure 5. In general, the charge distributions from the wide size distributions are in good agreement with those measured from the narrow size distributions (Table 1).

Figure 8. Charge distributions of unipolarly diffusion charged particles from wide size distributions. The charge distributions presented are cross-sections from the charge-size distributions presented in the Figure 7 at the selected particle sizes. The vertical line represents the charger Pn-value at the corresponding particle size.

Discussion and conclusions

While calculating the charge-size distribution results presented in this study, a zero-width DMA transfer function was used for simplicity. In the experiments, a sample to sheath flow ratio of 1/10 was used. At this flow ratio, the DMA transfer function is narrow compared to the particle size range collected by individual ELPI impactor stages, which justifies the use of the zero-width DMA transfer function approximation. Should the ratio be increased for a better signal to noise ratio, it might be necessary to include the actual DMA transfer function in the calculation.

The accuracy of the developed charge measurement method depends, among other things, on how accurately the density or effective density of the particles is known. In the case of liquid particles, the bulk density of the liquid can usually be used as an accurate estimate of the particle density. Estimating the effective density of solid particles may result in large errors. According to the equations used to calculate the charge-size distributions, an error in effective density produces an error in the charge results. The magnitude of the error depends on the particle size. For example, if the effective density is half or twice the real value, the error would be +226% or −72% at the 30 nm particle size and +77% or −50% at the 300 nm particle size. However, an estimate of the effective density of the particles as a function of particle size can be determined experimentally, using, for instance, the tandem DMA-ELPI setup (Maricq and Xu 2004) or the tandem setup with multiple charge correction (Bau et al. 2014). These tandem setups are almost the same as in this charge measurement method, only a neutralizer is added in front of the DMA. Another option is to use the parallel DMA-ELPI measurement setup presented by Ristimäki et al. (2002). Based on Ristimäki et al.'s (2002) and Bau et al.'s (2014) results, the accuracy of the reported effective density values is approximately ±20%. In the case of 30 nm particles, a ±20% error in the effective density causes +49% or −28% errors in the charge level. If the particle size is 300 nm, the error in the charge level decreases to +22% or −16%.

It is common that the particle effective density changes according to particle size. For agglomerated particles, the density is the highest for the smallest (primary) particles, while the density lowers as the agglomerates come larger. If the effective density has such a strong dependency on particle size, this charge measurement method should be used with caution. A strong change in effective density widens the particle size range collected by the individual impactor stages in mobility space, which reduces the accuracy of the final charge distribution. In the case of a small change in effective density, the constant effective density that is currently used in the calculation can be replaced by a particle size dependent density profile.

In conclusion, a DMA-ELPI charge measurement method was developed and found to produce similar values with the references used. The singly charged particles were mostly detected to carry a single elementary charge by the developed method. Values for the unipolarly diffusion charged particles were mostly the same as those reported in the literature. The method was also found to work for wide particle size distributions generated by the atomizer. Both wide and narrow size distributions produced comparable charge levels when particle charging was achieved using the same ELPI+ charger. In the case of the mixing-type charger, the measurement method produced slightly higher charge levels than Kaminski et al.'s (2012) model, but the widths of the charge distributions were almost the same.

The size and charge range in this study is difficult for the conventional tandem DMA methods, due to the second DMA's multiple charging issues. The developed method does not suffer from this issue, because the size classification does not depend on the particle charge level.

The measurement is rather fast compared to the tandem DMA methods and could likely be tuned for faster total measurement time. By optimizing tubing between the DMA and the ELPI, stabilization could perhaps be reduced to 5 s, and the measurement period of 5 s would most likely be enough to acquire a stable signal. These modifications might enable halving the total measurement time, but this has not been tested yet. Note that although it is not reported here, it is of course possible to measure both polarities in sequence using a bipolar voltage supply for the DMA.

The main advantage of the developed measurement method is that it is suitable for a wide particle size range of approximately 30 nm up to a micrometer and for high charge levels, which have been problematic for previously used methods. The measurement is truly two-dimensional and generates particle charge-size distribution, in which particle concentration is seen as a function of both particle size and charging state.

Acknowledgments

The authors thank Dr.-Ing. Christof Asbach from Institut für Energie- und Umwelttechnik e. V. (IUTA) for providing the mixing-type charger used in this study.

Funding

The authors acknowledge Dekati Ltd. for financing this study under the project name CHARM.