A Technique for Rapid Estimation of the Charge Distribution of Submicron Aerosols under Atmospheric Conditions

Abstract

A portable technique is presented for rapid estimation of the charge distribution of submicron aerosols under atmospheric conditions, using two Differential Mobility Analyzer (DMA) systems in parallel. Simultaneous measurement of the aerosol mobility and size distributions are made by using one DMA with a neutralizer and the other without. An estimate of the aerosol charge is obtained by a fitting procedure, in which the size distribution and an expression for the charge distribution are used to calculate the mobility distribution of the sample. The parameters in the theoretical charge distribution are varied iteratively until the calculated and measured mobility distributions match. Validation was undertaken with separate measurements of ion mobility and concentration used in the charging expression. Results are presented for ambient indoor air, unipolar ion production by an ionizer and downwind of a high-voltage overhead AC powerline.

INTRODUCTION

The charge state of aerosols is a parameter which has been long studied both theoretically and experimentally, at least in part due to its importance in obtaining size distributions from measurements of electrical mobility. Measurement of charge for the purpose of aerosol characterization, either produced in the laboratory or by industrial processes, or present in an ambient environment, can be important in terms of the design and operation of measurement devices (Liu et al. 1985) or appropriate filtration or precipitation techniques (Yoo et al. 1997), and the effect on aerosol coagulation rates (Matsoukas 1997). Also of concern are the potential implications of elevated aerosol charge for adverse human health effects (Melandri et al. 1983; Yu 1985) and optimization of pharmaceutical drug delivery (Balachandran et al. 1997).

Techniques and devices for measurement of particle charge were reviewed by Hochrainer (1985) and Brown (1997), who classified methods in two categories: (a) static or direct (absolute measurement of charge), and (b) dynamic (charge information obtained by measuring electrical mobility). The historical development of instrumentation to measure aerosol mobility and size distributions is discussed in a review of electrical aerosol measurements by Flagan (1998). The most widely used of these devices in the submicron size range is the Differential Mobility Analyzer (DMA), as described by Knutson and Whitby (1975). Conversion from the mobility distribution obtained using the DMA to a size distribution requires knowledge of the aerosol charge state. In practical use this is achieved by imposing charge neutrality on the aerosol sample by means of a source of bipolar ions, often a radioactive substance. Previous studies of aerosol charging (for example, Liu and Pui 1974; Covert et al. 1997; Ji et al. 2004) have been concerned with determining the efficiency of these neutralizers in bringing an aerosol of unknown and/or elevated charge distribution to a charge-neutral state, as defined by Fuchs (1963) theory and subsequent workers (Hoppel and Frick 1986; Wiedensohler 1988). This charge-neutralized steady-state charge distribution shall hereafter be referred to as charge-neutral.

The basis of many dynamic systems for determination of aerosol charge is measurement of both mobility and size, allowing charge information to be obtained. Examples of such methods include the integral or cumulative mobility analyzer (Forsyth et al. 1998), or electrostatic elutriator (Johnston 1983), followed by a particle counter. Measurements of the aerosol charge distribution using DMAs have largely been achieved by what is known as the Tandem DMA (TDMA) method, whereby one DMA selects monomobile aerosols, which then pass through a neutralizer and a second DMA to give the size distribution of the selected particles. This allows contributions from particles of different size and charge, but same initial mobility, to be resolved. This method has been applied successfully in several studies (Kim et al. 2005; Maricq 2006). Emets et al. (1991) describe a similar experimental method, which uses one DMA for mobility selection followed by a laser analyzer for particle size measurement. In the TDMA system, successful resolution of the charge distribution requires a relatively high particle concentration, since only a limited mobility range (and therefore a fraction of the total number) will be selected by the first DMA. Also, to build up a complete charge distribution over a range of particle sizes, different initial mobilities must be selected, each with a subsequent size measurement in the second DMA. This makes the process time-consuming, precluding its use when aerosol concentration fluctuates on time scales shorter than the time for measurement.

There are several other methods relying on measurement of electrical mobility and size, or related properties, usually by applying an electric field to cause differential motion for charged and uncharged particles. Kousaka et al. (1981a, b) measured visually the motion of particles under the influence of an electric field and gravity to determine the electrical mobility and size, a method which was used to calibrate the DMA (Kousaka et al. 1981b). The electrical single particle aerodynamic relaxation time analyzer (E-SPART, Mazumder et al. 1991) uses oscillatory acoustic excitation, with a superimposed electric field. Kulon et al. (2003) employed Phase Doppler Anemometry (PDA), in which particle size is obtained from the linear relationship with phase shift between the light scattered at different angles at the intersection of two laser beams. Again, an external electric field is used to give an additional velocity to electrically charged particles. This technique can deal with a large number of particles (>1000 s⁻¹) obtaining charge distributions quickly, and was successfully operated to characterize the charge on aerosols of 0.5–3 μm, but is clearly unsuited to a portable application.

Health implications for those working with submicron, ultrafine or nano-structured particles are currently the subject of concern (Maynard and Kuempel 2005). The techniques outlined above are well suited for measuring the charge on these laboratory- or industry-generated aerosols and subsequently estimating any health impact they may cause. However, when considering human exposure to environmental aerosols, which are generally present at considerably lower concentrations outside the laboratory, these techniques are not always applicable or practical. In this article we present a technique to estimate, with short sampling time, the charge distribution of polydisperse submicron aerosols using two DMAs in parallel. The present technique is suitable for portable applications, for low aerosol concentrations and avoids the necessity for long sampling times. Experimental verification of the method was undertaken with separate measurements of ion mobilities and concentrations used in the calculation of the charge distribution. The technique was applied in several indoor and atmospheric environments.

THEORY

The DMA utilizes electrical classification to separate particles according to their electrical mobility. It consists of a cylindrical central electrode and a coaxial cylindrical housing. Filtered, dry sheath air is supplied in the annular region around the central electrode with sampled atmospheric air passing a single-stage impactor then though a thin annular ring adjacent to the outer cylinder. Charged particles deflect in the electric field due to the potential applied on the central electrode. At the end of the central electrode particles of desired mobility pass through a slit to be subsequently counted. By changing the potential applied to the central electrode, different mobilities can be sampled to give the mobility distribution of the aerosol under investigation.

Measured mobility data can be converted into a size distribution if the charge distribution of the aerosol is accurately known. This is achieved by bringing the aerosol into charge equilibrium with the ionic atmosphere in a bipolar diffusion charger (neutralizer) prior to the measurement of the mobility distribution. The fractions of charged particles of given size can then be calculated by means of existing bipolar charging theories.

Several theories for the bipolar diffusion charging of spherical aerosol particles have been reported, with the limiting sphere approach by Fuchs (1963) the most widely used over an extended size range. In this work, for an aerosol in charge-neutral state, the fraction of particles carrying up to two charges is calculated using Fuchs theory with the parameters outlined in Wiedensohler (1988): (1) ion mobility ratio, μ₊/μ₋ = 0.875 (Wiedensohler et al. 1986); (2) ion masses from Hussin et al. (1983); and (3) the correction of the α-parameter (collision probability of ions with the particle) following Hoppel and Frick (1986). The fraction of particles with three or more charges is calculated using the analytical solution derived by Gunn (1955).

The measured mobility equivalent size distribution of the classified sample aerosol, F_c (d_p ), from the DMA at voltage V, is related to the original number size distribution function, F(d_p ), by the following equation (Heim et al. 2004),

where N_c is the number concentration, α(d _p , j) is the charge distribution of the particles (Gunn 1955; Fuchs 1963), Tr(Z(d _p , j)) is the ideal transfer function and E(d_p ) is the system detection efficiency. Thereby with knowledge of the number size distribution and the charge distribution of the classified sample aerosol, Equation (1) can be solved analytically to give the original number particle size distribution.

If the number of singly charged particles of given size and polarity N(d_p , ±1), is known, then the size distribution can be simply calculated using:

The key to de-convolving the size distribution of the aerosol population from the measured mobility equivalent size distribution of the classified sample aerosol is in the use of the impactor on the aerosol inlet of the DMA (Figure 1). The highest voltage applied to the central electrode of the DMA is set so that the lowest mobility to be measured is equivalent to that of the largest particle size to pass the impactor carrying a single charge. The impactor therefore ensures that at this voltage there are no contributions from larger, multiply-charged particles of equivalent mobility. However, subsequent lower voltage (higher mobility) measurements will include contributions from larger, multiply charged particles which are small enough to pass the impactor, in addition to the singly charged particles of interest. These contributions must be removed to obtain the number of singly charged particles for a given voltage measurement, and are calculated by reference to the known charge fraction at given size, α(d _p , j), and the actual measurements made at larger mobility bins.

FIG. 1 Schematic diagram of parallel DMA system used to measure the aerosol mobility and size distributions in the estimation of the aerosol charge distribution. Example measurements of indoor air with negative ionizer.

We present a technique whereby the charge distribution of atmospheric aerosols can be estimated from parallel measurements of the natural and charge-neutralized mobility distributions of the aerosol population, using two DMAs side-by-side. From the size distribution measured with one DMA, F(d_p ), if a charge distribution, α(d _p , j), is fixed, then the “natural” mobility distribution, N(d_p , j), can be calculated using

in a similar process to that of size distribution calculation. As this mobility distribution is measured using the second of the two DMAs, for which the charge distribution is unknown as it does not employ a charge neutralizer, the charge distribution α(d _p , j), can be chosen so that the predicted and measured mobility distributions match. The relationship between these measured and unknown parameters is outlined schematically in Figure 1.

Charge Distribution Calculation

The approach of Fuchs (1963) uses a numerical procedure to obtain a charge distribution. However in the current work the analytical solution for bipolar aerosol charging of Clement and Harrison (1991, 1992) is used, as this allows a much simpler calculation for obtaining charge distributions.

The approach of Clement and Harrison (1992) uses a modification factor to the Boltzmann equilibrium based on theoretical consideration of ion-aerosol attachment processes. The aerosol charge is determined using

where for a monodisperse aerosol of radius a, there is a number concentration N_j of particles carrying j charges. n ₊ and n ₋ are the bipolar ion concentrations with associated mobilities μ ₊ and μ ₋, e is the electronic charge, k is the Boltzmann constant, and ε ₀ the permittivity of free space. The corresponding mean charge 〈 j〉 for the aerosols is

For a given particle size, the key variable in Equations (4) and (5) is the asymmetry ratio x, defined as

This Modified Boltzmann Distribution (MBD) was derived for use in steady-state monodisperse conditions. However, a polydisperse aerosol can be represented as a superposition of monodisperse aerosols of different mean diameters, allowing the use of this expression in the present application. The MBD has previously been applied in a variety of situations including unipolar negative aerosol charging by a domestic room ionizer (Harrison 1996), volcanic plume electrification (Mather and Harrison 2006), and Venusian cloud formation (Aplin 2006). Comparison of theoretical predictions of aerosol charging using the MBD and experimental measurements found reasonable agreement (Harrison and Carslaw 2003; Gensdarmes et al. 2001).

METHOD AND VALIDATION

The charge estimation technique utilizes two identical sequential mobility particle sizer and counters (SMPS+C, Grimm Aerosol Technik GmbH) with size range 10.5–1100 nm, each comprising of a Vienna type DMA (model 5.500) and condensation particle counter (CPC, model 5.400). However, the technique could be applied to any two identical DMAs.

Figure 1 shows the experimental set up. The two systems are run in parallel: DMA-1 with an ²⁴¹Am charger (Neutralizer 5.522, Grimm Aerosol Technik GmbH) to give the aerosol particle size distribution and DMA-2 without charge neutralization, to measure the aerosol mobility distribution. Both devices make measurements at 22 voltage steps logarithmically down from +10000 V to +5.8 V over a 3-minute cycle (fast stepping mode of operation). Measurements are made at 1 s intervals, with 9 measurements made on each voltage channel. Only measurements in the last 5 s per voltage are used in the subsequent data analysis to allow for the finite time response of the system. Only a positive potential can be applied to the central electrode, therefore only negatively charged particles will be selected. A mobility distribution consisting of 44 mobility bins is then calculated from the raw data, system transmission efficiency and DMA response function.

We demonstrate the charge distribution estimation technique with the following example. Figure 1 shows the negative aerosol mobility distributions measured on a single cycle with DMA-1 and DMA-2. The experiment was carried out in a room with a negative corona discharge ionizer to create a unipolar ion imbalance. Also shown in Figure 1 is the corresponding number particle size distribution, calculated using Equations (1) and (2).

A mobility equivalent size distribution is calculated using the measured size distribution (DMA-1) and calculated charge distribution (Equation [4]). The initial charge distribution is calculated assuming a positive to negative ion mobility ratio of 0.875 (Wiedensohler 1988) and equal ion concentrations (x= 0.875). The asymmetry ratio x, is the only variable in the calculation of the charge distribution of the polydisperse aerosol, and itself is dependent only on the positive and negative ion concentrations and mobilities. By iteratively altering x, the best fit between the predicted mobility distribution and that measured using DMA-2 (with no neutralizer) can be found. The best fit is assessed using the probability associated with the paired, two-tailed Student's t-test. Significance is assumed at the 95% confidence level, which we term a good fit. If a fit cannot be achieved at this level then the result is discarded.

Figure 2 shows the predicted mobility equivalent size distributions obtained from the size distribution given in the earlier example, and charge distributions calculated using varying values of x. The best match to the mobility distribution measured with DMA-2 is found using x= 0.0097 (Pearson's correlation coefficient, R ²= 0.993). Assuming a mobility ratio, μ ₊ /μ ₋ of 0.875, this corresponds to a 90-fold excess of negative ions compared to positive ions. The corresponding charge distribution for 200 nm particles is shown in Figure 3.

FIG. 2 Measured mobility distribution (DMA-2, single cycle) of indoor air with negative ionizer compared to fitted mobility distribution (calculated from DMA-1 measurement and different charge distributions).

FIG. 3 Charge distribution of 200 nm particles for different measurement environments.

Vana et al. (2006) used simultaneous measurements of aerosol size distribution and air ion mobility distribution to ascertain the charging state of atmospheric nanoparticles in the size range 2.6–40 nm during particle nucleation events. Under normal conditions particles of this size would hold a maximum of ±1 charge. The ratio of the measurements made with and without charge neutralization for a given size thus immediately gives the charging probability. This procedure is not directly applicable to larger particles capable of holding multiple charges, but information on the charging state over the whole measureable size range (10.5–1100 nm) can be gained. By comparing the total number of particles counted with DMA-1 over one cycle with that measured using DMA-2, the level of negative charging of the aerosol compared to charge-neutral can be ascertained.

Figure 4 shows scatterplots of the total concentration of negatively charged particles (10.5–1100 nm), N _−meas , measured using DMA-2 with the total concentration of negatively charged particles after charge neutralization N _−neut , measured with DMA-1, for three different charging situations. Charge-neutral is represented by a gradient of 1 because the neutralizer should have no additional effect. Values <1 represent undercharged particles and values >1 overcharging of the particles compared to charge-neutral. During operation of the negative ionizer, the gradient of the scatterplot is 3.7, indicating excess negative unipolar charging in agreement with the fitted charge distribution.

FIG. 4 Total number of negatively charged particles (10.5–1100 nm) measured with DMA-1 versus that measured with DMA-2 for different atmospheric environments.

The asymmetry ratio x, is the only variable in the calculation of the charge distribution using the MBD outlined in Equation (4). Under steady-state conditions, validation of the estimated charge distribution is possible by comparison of the fitted asymmetry ratio with that calculated using ion mobility and concentration measurements. Positive and negative ion concentrations and mobilities were obtained using an Aspiration Condenser Ion Mobility Spectrometer (ACIMS) described by Fews et al. (2005) simultaneously with the indoor ambient charge estimation measurements. In the present article, small ions are defined as those particles of mobility greater than 0.5 cm² V⁻¹ s⁻¹ (smaller than ∼1.8 nm in size). Corresponding to the measurements in Figure 5 for a one hour period, positive and negative ion concentrations of 392 cm⁻³ and 280 cm⁻³, respectively, and positive and negative ion mobilities of 1.62 cm²V⁻¹s⁻¹ and 2.27 cm²V⁻¹s⁻¹, respectively, were observed. These correspond to the asymmetry ratio, x= 0.999, which compares reasonably well to that fitted using the charge distribution estimation technique (x= 0.962). Analysis for other one-hour periods also yielded good agreement.

FIG. 5 Hour-averaged measured mobility distribution (DMA-2) compared to fitted mobility distribution for ambient indoor air. (Error bars shown are of the standard deviation of the single cycle measurements.)

The aerosol charge estimation technique was applied in 3 different environments. DMA-1 and DMA-2 were run simultaneously on 3-minute cycles in a room located on the 4th floor of a building in central Bristol, U.K. The ACIMS was also run on 15 min cycles, with positive and negative ion concentrations and mobilities taken from one hour averages of the measured data. Laboratory measurements were made on 4 separate occasions, two of which covered a full 24 h period. A negative ionizer was used for one 5 h measurement period, located approximately 50 cm from the DMA inlets. Measurements were also made over a period of 2 h, 270 m downwind of a 400 kV AC powerline near Cheltenham, U.K. Corona ion generation from high voltage (HV) AC overhead powerlines, which could alter the charge state of atmospheric aerosols, is a well documented phenomenon (Chalmers 1967; Fews et al. 1999, 2002; Bracken 2005). The DMA inlets were 10 cm apart and approximately 1 m above the ground. The wind speed and direction were stable over the 2 h measurement period.

RESULTS

Figure 5 shows the calculated negative mobility distribution fitted to the average negative mobility distribution measured overnight in the laboratory using DMA-2 between 04:30 and 05:30 in the morning. The fit corresponds to a charge distribution with asymmetry ratio x= 0.962, with the two distributions correlating well (R ²= 0.994). x values in the range 0.961 and 0.963 correspond to a good fit at the 95% confidence level, over which there is a 0.01 e difference in the average charge on a 200 nm particle, 〈j〉 _200 nm .

When the ionizer was used, typical positive and negative ion concentrations of 32 and 1200 cm⁻³ s⁻¹ were measured, respectively, using the ACIMS. The optimum fitted mobility distribution (R ²=0.995) for the time period 12:10 to 13:10 is shown in Figure 6. The fitted mobility distribution corresponds to an asymmetry ratio x = 0.0131 (negative to positive ion concentration ratio of ∼70), and 〈j〉 _200nm = −8.4 e (Figure 3). Again, the range of x values which correspond to a good fit is small (x=0.0129 – 0.0133) and corresponds to a 0.06 e difference in 〈j〉 _200 nm .

FIG. 6 Hour-averaged measured mobility distribution (DMA-2) compared to fitted mobility distribution for negative ionizer. (Error bars shown are of the standard deviation of the single cycle measurements.)

For the measurements made downwind of the HV powerline, the fit to the average measured negative mobility distribution for one hour (14:20 to 15:20, 20 SMPS+C cycles) is shown in Figure 7, corresponding to an asymmetry ratio x=1.706, which to 3 significant figures is the only x value which corresponds to a significant fit at the 95% confidence level. For particles larger than 25 nm, the correlation between the two distributions is very good (R ²= 0.999 for 25 to 1100 nm particles). However, at smaller sizes the distributions diverge, with fewer particles measured with DMA-2 than expected for x=1.706. The divergence increases as particle size decreases, this will be discussed later.

FIG. 7 Hour-averaged measured mobility distribution (DMA-2) compared to fitted mobility distribution for measurements made at ground level downwind of a HV overhead powerline. (Error bars shown are of the standard deviation of the single cycle measurements.)

Table 1 and Figure 4 show the correlation between the total number of negatively charged particles (10.5–1100 nm) measured directly with DMA-1 and DMA-2, for each of the environments investigated. Under ambient conditions in the laboratory the gradient is very close to 1, while with the ionizer switched on an almost 4-fold increase in the number of negatively charged particles is observed as previously discussed. Downwind of the powerline, undercharging (i.e., fewer negatively charged particles) by approximately half compared to charge-neutral was observed. Each of these results corresponds well with the fitted charge distributions (Figure 3).

TABLE 1 Correlation parameters of the total number of negatively charged particles (10.5–1100 nm) measured with (DMA-1) and without neutralization (DMA-2) for single cycle measurements made in the 3 environments investigated

	DMA-1 / DMA-2 correlation
Measurement	N	Linear regression line	R ^2
Lab	1207	N −neut = 1.10N −meas – 33	0.991
Lab with ionizer	129	N −neut = 3.75N −meas – 45	0.919
Powerline	40	N −neut = 0.48N −meas + 37	0.887

DISCUSSION

Results have been presented for three different atmospheric situations, for which charge distributions using the MBD were calculated, showing good agreement between the measured size (DMA-1) and mobility distributions (DMA-2). The physical quantities measured are the aerosol mobility distributions, with and without charge neutralization. Here we discuss the errors involved in the measurements and their subsequent propagation through the analysis.

Heim et al. (2004) found the number response of the CPCs used in this work to have a maximum error of 20%. Assuming the error is the same for both systems and all sizes of particle, then applying the same fractional correction to both measured mobility distributions (with and without charge neutralization) has no effect on the estimated charge distribution.

A comparison between measurements made with the two DMA systems was carried out; both systems measured the same mean diameter to within 1.5 nm, with a maximum relative difference in total concentration of 6.8% for single cycle measurements. This difference is reduced when data is averaged prior to analysis. Again for the measurements shown in Figure 5, correcting for a relative error of 3% between the two systems (typical value found for averaged data) by adding 3% to the neutralized data set results in a fitted charge distribution with x=0.987 (〈j〉_{200 nm} = –0.03) compared with x = 0.962 (〈j〉 _{200 nm} = −0.08).

Obtaining a charge distribution from measurements made on the two DMA systems requires the assumption that the size distribution obtained from measurements in DMA-1 is the same as that which passes through DMA-2. Following charge neutralization of the aerosol sampled in DMA-1, there may be a significant disparity between the level of aerosol charging in DMA-2 compared with DMA-1, resulting in a possible difference in the response of the two DMAs due to image- and space-charge effects. The threshold value of the space charge parameter, ζ, defined by Alonso et al. (2000), above which significant shifting of the classification voltage from the ideal voltage occurs, is given by

where N ₀ is the aerosol concentration at the inlet, Z is the electrical mobility and τ is the residence time in the DMA. For operating conditions and DMA geometry similar to those in the present study, with maximum aerosol concentrations in the present study (2 × 10⁴ cm⁻³) and assuming an extreme aerosol charging scenario (entirely singly charged 10 nm particles), the space charge parameter obtained was ζ = 1.5 × 10⁻⁴, two orders of magnitude below the threshold value, therefore space charge effects are unlikely to occur. Image charge effects inside the DMA column can also be ignored, as the particle drift velocity in the applied electric field is always much greater than that due to electrostatic image force.

Likewise, particle losses due to image charge deposition (calculated from the empirical expressions of Yu 1985) in the region of sample flow between the neutralizer and DMA column were evaluated for charging asymmetry ratios of 100 (extreme case for unipolar charging by an ionizer) and 2 (typical of measurements near to overhead powerlines). The expected difference in image charge deposition between elevated-charge and charge-neutral aerosol is <1.3% and <0.3% for all particle diameters for x= 100 and x= 2, respectively.

The overall difference in deposition between flow through DMA-1 (with the neutralizer fitted) and through DMA-2 (with no neutralizer fitted) was also experimentally verified by comparing aerosol concentrations measured using the CPC with either neutralizer fitted or not fitted at the inlet. The relative difference was found to be ∼2.5% in concentration, in agreement with theoretical calculations which accounted for diffusional and image charge deposition (Yu 1985), which predicted losses of 2.5% for 10 nm particles and losses <1% for particles of sizes >25 nm. Ideally, a dummy chamber identical to that containing the ²⁴¹Am neutralizer would be used, but was not available during the present study. Accounting for these losses in the neutralized mobility distribution measured in the lab under ambient conditions (Figure 5) by artificially adding 2.5% to the data set for particles <25 nm lead to negligible difference in the fitted charge distribution (x=0.9623, 〈j〉 _200 nm =−0.08) compared to when losses are unaccounted for (x = 0.9620, j>200 nm=−0.08). The error in the two systems when used with and without charge neutralization can therefore be considered the same.

Change in the aerosol size distribution due to coagulation of particles in the neutralizer is unlikely to occur for low aerosol concentrations (Maisels et al. 2004). The efficiency of the ²⁴¹Am neutralizer must also be confirmed, especially where the sample aerosol may be highly charged. Liu and Pui (1974) report that an nt product of 6 × 10⁶ cm⁻³ s (where n is the bipolar ion concentration and t the residence time within the neutralizer) is sufficient to neutralize aerosols initially at the Rayleigh charging limit, much greater than the charging experienced in the present study. The manufacturers of the ²⁴¹Am source used here quote nt ∼10⁷ cm⁻³ s, which should be adequate for complete neutralization of aerosols throughout this study. Experimental verification was undertaken by comparing the size distribution after passing the aerosol through one neutralizer alone and through two neutralizers, in sequence. After accounting for additional particle deposition in the extra neutralizer, minimal difference was observed both for ambient indoor and ionizer measurements. Significantly higher aerosol concentrations would reduce the efficacy of the neutralizer in this regard.

For an averaged data set (e.g., Figures 5, 6, and 7), there is a corresponding spread in concentration due to the variation of aerosol characteristics over time. Consequently there may be a corresponding range of charge distributions. To give an indication of this range, charge distributions were estimated using the two average mobility distributions (with and without charge neutralization) from Figure 5, minus and plus their standard deviations respectively. This provides a lower and upper bound on possible values of x of 0.958 and 0.965 for this data set.

Data presented in Figures 5, 6, and 7 correspond to 1 h averages of individual DMA cycles. Charge distributions have also been successfully fitted to measurements over shorter time periods, with good correlation still found for single cycle measurements (for example, Figure 2). Analysis of the same data set at different time resolution was undertaken. Table 2 shows the asymmetry ratios and correlation coefficients for a 1 h period split into different analysis periods, under ambient indoor conditions and with the use of a negative room ionizer. Under ambient conditions, where the variability in ion production rate and ion-aerosol interaction is low, the charge distribution estimation procedure displays a better fit for longer time averages. In contrast, with the ionizer, where the ion production rate is variable, lengthening the analysis period does not improve the fit achieved. The rapid resolution of the technique presented allows investigation of the variation in the charge distribution over time, for example with an ionizer (Figure 8).

FIG. 8 Variation of 1/x before, during, and after the use of a negative ionizer.

TABLE 2 Asymmetry ratios and correlation coefficients for different time resolutions for a 1 h period under ambient indoor conditions and with the use of a negative room ionizer

	Indoor ambient		Indoor with ionizer
	(01:00 to 02:00)		(10:30 to 11:30)
Time resolution	Average x	R ^2	Average x	R ^2
1 h	0.896	0.995	0.0128	0.992
30 min	0.898	0.994	0.0124	0.992
15 min	0.900	0.992	0.0136	0.992
6 min	0.900	0.991	0.0123	0.992
3 min	0.901	0.986	0.0122	0.989

The 3 min time resolution achievable in the present work compares favorably with the TDMA technique. The TDMA technique is appropriate for controlled laboratory-based experiments, but the short time resolution achievable in the present work means that variation in aerosol parameters during measurements is less likely to cause a problem than in TDMA work. This work uses sequential, stepwise, variation of the applied voltage to the DMA column (Heim et al. 2004). Devices have been developed which scan across the voltage range (Wang and Flagan 1989), achieving a size distribution in under a minute. The present technique could be extended for use with such devices with the inclusion of the appropriate transfer functions and deconvolution to correct for the finite time response of the detector. The present technique is also suitable for use in low particle concentrations (for example in this work concentrations as low as 280 cm⁻³ were observed, compared to concentrations of the order 10⁶cm ⁻³ and above reported in literature regarding TDMA measurements (Larsson et al. 2007). Particle charge measurements using the TDMA technique were undertaken in the present study for indoor ambient conditions, but consistent detection of multiply charged particles was not possible due to the low concentrations encountered.

Although characterization of the aerosol charge distribution is possible with the MBD, explicit information on the ion mobilities and concentrations is not available and only in steady-state can the asymmetry ratio be assumed to correctly describe the ion properties. It is assumed that for indoor ambient air (when no direct aerosol sources are present), the ion-aerosol interactions are in a steady-state, and therefore there is little variability in aerosol charge distribution. This allows validation of the charge estimation technique using ACIMS ion mobility and concentration measurements. When using a negative ionizer, if continuous ion production is assumed, after a time one would expect a steady state at a different aerosol charging level (significant aerosol coagulation is unlikely to occur due to increased charge for low aerosol concentrations [Matsoukas 1997; Maisels et al. 2004], therefore the size distribution will be unaffected by unipolar ion production). Validation was not possible here due to the high negative ion concentration exceeding the measurement limit of the ACIMS. Even in a non-steady-state situation (such as downwind of HV powerlines) the fit obtained is still statistically good, showing that the calculated charge distribution can describe the aerosol charging probability at that instant. In terms of health effects related to additional aerosol charging, this is the relevant quantity to consider, and whether or not the aerosol charge is in steady state is unimportant.

For a particular volume of air blown past a HV powerline in a crosswind, there is a discrete influx of ions from the line. Therefore as this air is transported away from the line, ion recombination and attachment to aerosols are the dominant processes, as there is no further ion production. The divergence at sizes below 25 nm between the fitted and measured mobility distributions observed at the powerline site (Figure 7) may be due to the respective ion-aerosol attachment coefficients of the different sized particles. The ion-aerosol attachment coefficients are lower for smaller particles. For example, the coefficient (ion mobility 1.2 cm²V⁻¹s⁻¹, ion mass 150 amu) for a neutral 10 nm particle is 0.220 × 10⁶ cm³s¹, while for a neutral 50 nm particle it is 1.87 × 10⁻⁶ cm³s⁻¹ (Hoppel and Frick 1986). Therefore, for the smallest particles, the ion-aerosol attachment process may not be completed in the transit time from powerline to measurement site (∼100 s), resulting in lower than expected charging compared to the larger particles.

The environments investigated in this work involve either measurement in an ambient situation or during the production of ions only. When an aerosol source is present, the charge state of the newly produced aerosol may differ from that of the background aerosol population. In such a situation the TDMA technique can be used to calculate the charge distribution, if particle concentrations are high. If the appropriate charge distribution for the two aerosol modes can be resolved, the charge distribution estimation technique presented here could be extended to such situations.

CONCLUSIONS

A portable technique has been presented for rapid estimation of the charge distribution of submicron aerosols under atmospheric conditions, using two DMA systems in parallel. The method involves making independent aerosol size distribution and mobility distribution measurements. By using an expression for aerosol charge (Clement and Harrison 1992) a predicted mobility distribution can be obtained from the size distribution measurement. The charge distribution is estimated by altering the parameters in this expression until the fit between the predicted and observed mobility distributions is optimized.

The time taken for measurement is limited by the capability of the DMA and CPC systems used, which in the present study was 3 min, but it is demonstrated that a reliable estimate of the aerosol charge distribution can be obtained at this time resolution. This reduces the likelihood of a significant change in aerosol properties or concentration over the measurement period, an issue with some laboratory-based methods. Charge distributions at low aerosol concentrations (as low as 280 cm⁻³ in the present study) can be obtained. The present method could be applied to any two identical devices capable of measuring mobility and size distributions.

Validation was undertaken with separate measurements of ion mobility and concentration used in the charging expression, resulting in similar values for the asymmetry ratio x when examined over one hour periods in indoor air. Further results are presented for ambient indoor air, unipolar ion production by a corona discharge ionizer and outdoors downwind of a high-voltage AC overhead powerline.

This work was supported by CHILDREN with LEUKAEMIA, registered charity No. 298405 (UK). The authors are grateful to R. G. Harrison at the Department of Meteorology, University of Reading, UK for helpful discussions.