The effect of carrier gas contaminants on the charging probability of aerosols under bipolar charging conditions

Abstract

This work concentrates on the experimental determination of the properties of ionic molecular clusters that are produced in the bipolar ionic atmosphere of a radioactivity based ²⁴¹Am charger. The main scope of this study was to investigate the dependency of the ions' properties on carrier gas contaminants caused by the evaporation of trace gases from different kinds of frequently encountered tubing materials. A recently developed high resolution mobility spectrometer allows the precise determination of the ions' electrical mobility; an empirical mass-mobility relationship was used to approximate the corresponding ion masses. It was found that impurities in the carrier gas dramatically change the pattern of the ion mobility/size distribution, resulting in very different ion properties that strongly depend on the carrier gas composition. Since the ion properties control the charging process of aerosols, it was further investigated how the different ion properties affect the calculation of the charging probabilities of aerosols. The results show that despite large variations of the ions' properties, only a minor effect on the calculated charging probabilities can be found.

Highlights

► High resolution mobility measurements of airborne molecular clusters. ► Ion properties in the charger are strongly affected by carrier gas contaminants evaporating from different tubing material. ► Charging probabilities depend only weakly on ion properties. ► Mobility size distributions determined with a DMA are almost independent of ion properties.

1. Introduction

In recent years, the precise determination of the properties of molecular clusters has become more and more of interest for many scientific fields. For example in atmospheric sciences, they are of special importance for fundamental investigations on heterogeneous as well as homogeneous nucleation (Winkler et al., 2008) and studies related to particle formation in the atmosphere (Kulmala et al., 2007) and in recently performed chamber studies (Kirkby et al., 2011). For sure, this list could be expanded by many more fields of application, not only relevant for atmospheric studies. However, one of the most important applications that are related to atmospheric studies and depend on the knowledge of the properties of molecular ions is the Electrical Mobility Spectrometry (EMS)—one of the most reliable sizing methods in aerosol science, where the properties of the ions that are responsible for the charging of the aerosols have to be known.

The EMS relies on a well defined charging state on the aerosol particles of interest. As a stable saturation charging state on the aerosol cannot be assumed a priori, charging devices have to be used to produce a large number of ions to ensure the condition of a stable saturation charging state on the particles, no matter what its charging state was before the charging process. Furthermore one can speak of a uniquely defined charging probability; a probability for the amount of elementary charges on the particles. However, the ions generated in the charging device also limit the applicability of the EMS method to sizes approximately >2 nm (Manninen et al., 2011). Below that size limit, it is hard to distinguish between the charger generated ions and the freshly charged aerosol particles. In aerosols science, the most commonly used ionizers rely on radioactive sources, corona discharges, UV radiation and more recently on soft x-ray photo ionizers. Radioactive sources, corona discharge as well as the soft x-ray ionizers bear the advantage of diffusion charging which is almost independent upon aerosol material. In contrast, the charging mechanism based on UV radiation strongly depends upon particle composition and is therefore only suitable for very specific investigations.

No matter what charging mechanism is governing the actual charging on the particles, in all cases, an ion source ensures the ionization of the carrier gas molecules to form primary ions. These primary ions will combine with the most abundant compounds, according to their gas phase basicity (their proton affinity), and polar molecules (mostly water) to form larger clusters. Ultimately, these larger clusters will combine with the aerosol to bring it into a defined charging state.

In the case of a bipolar ionic atmosphere where approximately the same numbers of positive and negative ions are present, some particles that are initially neutral will acquire charges from these ion clusters by collisions due to their random Brownian motion. Aerosols that are initially charged will lose their charge or their charging state will be reduced as their charge attracts ions of the opposite polarity. For large aerosols with diameters >100 nm, these competing processes lead to a stationary charging state of the particles called Boltzmann equilibrium (an equilibrium between ions and particles), that assumes a continuous distribution of the energy states on the particles. However, according to Fuchs (1963), generally the situation is much better described by a steady state equilibrium, especially for ultrafine particles<100 nm where a continuous energy distribution is definitely inapplicable and a kinetic method is required to calculate the rate of diffusion of the ions towards the particle.

Furthermore, the experimental data presented by some other authors (e.g. Reischl et al., 1983; Hussin et al., 1983; Wiedensohler & Fissan, 1991) show that the Boltzmann charge distribution clearly underestimates the number of charged particles below 30 nm diameter, indicating that the theory by Fuchs is the best to describe the diffusion charging process.

As stated by Reischl et al. (1996), the “beauty” of Fuchs' theory is that only two ion parameters have to be known to calculate the particles' charging probabilities: the ions' electrical mobility and their mass. All other ion input parameters can be derived from the latter two properties.

There is an intense scientific discussion on the actual nature of the clusters produced in an aerosol charger. In the literature (Cabane & Playe, 1980; Eisele & Tanner, 1990; Nagato et al., 2006), NO₃⁻ HNO₃ and HCO₃⁻ HNO₃ as well as hydrates of the form NO₂⁻ (H₂O)_n, NO₃⁻ (H₂O)_n, NO₃⁻ HNO₃ (H₂O)_n and HCO₃⁻ HNO₃ (H₂O)_n are proposed and observed configurations for the ionic clusters of negative polarity. For positive polarity, (H₃O)⁺ (H₂O)_n, and NH₄⁺ (H₂O)_n are suggested to be the most abundant cluster species produced in air (Huertas et al., 1971; Eisele & Tanner, 1990; Nagato et al., 1999, Parts and Luts, 2004). Unfortunately, very little is known on the effect of contaminations or impurities on the formation of ion clusters within an aerosolcharger. Therefore, the goal of this work is to experimentally determine the properties of the charging ions that are needed for using the Fuchs theory and to evaluate the effect of impurities on these properties. Ultimately, the different ion properties are used to calculate the aerosol charging probabilities to investigate their influence on Fuchs' charging theory.

2. Experimental method

In this work an aerosol charger (tapcon ID: “tapcon minicharger”) purchased from “Tapcon & Analysesysteme”, equipped with an ²⁴¹Am source was used to investigate the properties of the generated ion clusters (Fig. 1). ²⁴¹Am decays by alpha emission with an energy of 5.5 MeV and a small by-product of gamma rays to ²³⁷Np with a half live of about 2 million years. The most evident advantage of ²⁴¹Am chargers, compared to other radioactive chargers equipped with ²¹⁰Po or ⁸⁵Kr, is its long half life of 432.2 years (²¹⁰Po: 138.2 days, ⁸⁵Kr: 10.8 years). Therefore, a decrease of ion production can be almost completely neglected within our comparably short human lifetime.

Fig. 1.

Schematic cross section of the “Tapcon and Analysesysteme” aerosol charger. It is equipped with an ²⁴¹Am source with an activity of approximately 60 MBq and has a total volume of about 32 cm³.

The radioactive material is embedded in a gold matrix coated on a strip that is housed in a massive stainless steel body. The ²⁴¹Am source has an activity of 60 MBq—the only major drawback in the use of ²⁴¹Am as this activity is far above the (Austrian) permitted limit of 100 kBq and requires special permits for handling and transport. However, this high activity is necessary to ensure a sufficient ion production to meet the prerequisite of a N⋅t product (N is the number of ions produced be the ionizing source per unit time and t the residence time of particles in the charging chamber) of approximately 10⁷ (Liu & Pui, 1974).

For the investigation of ion molecules in the size range around 1 nm, high resolution mobility measurements are necessary to separate individual ion species. Additionally, the high flow DMAs, with a sheath air flow rate above 500 L/min (8.3e-3 m³/s), typically used for high resolution measurements, reduce the residence time of the clusters in the DMA's classification channel and therefore minimize diffusion losses—a crucial feature for a proper detection of molecular ions. More information on the high resolution DMA used in this work can be found elsewhere (Steiner et al., 2010). The so called “UDMA” achieves a resolution up to R=50 at optimal conditions (2% relative FWHM of its transfer function) at 1.4 nm mobility equivalent diameter. As the resolution of the UDMA strongly decreases with decreasing particle size, the mobility resolution for the ions studied in this work was around R=25 (∼4% relative FWHM of the DMA transfer function). For the operation of the UDMA, a closed loop arrangement (Jokinen & Mäkelä, 1997) for sheath air and excess air is used to prevent contaminations of the sheath air that would be possible when using the open loop configuration (sheath air is drawn in from the ambient lab air and not recycled) which is also often used in high flow high resolution mobility spectrometry. Since the sheath air flow is continuously enriched with particle free air and the ions exiting the UDMA with the excess air flow will be rapidly lost in the highly turbulent regions in the excess air pipes (latest in the blower), and no interfering effects on the mobility classification where observed during the experiments, the sheath air flow is not filtered before re-feeding it to the inlet of the UDMA. For the measurements, a comparably high aerosol inlet flow rate of 17 L/min (2.83e-4 m³/s) was chosen to catch the ions early after their initial formation (reducing their residence time in the charger) and to reduce diffusion losses on the way to the UDMA.

For measurements related to atmospheric studies, air will be the most important carrier gas for the investigation of the properties of newly produced ionic molecules. Therefore, pressurized air supplied by a compressor is purified in a first stage by means of an oil extractor, freeze drier and high flow (HF) HEPA filter and in a second stage purified by two ultra fine active carbon filters (ACF_fine), a standard active carbon filter (ACF), at least three silica gel diffusion driers and a HEPA filter (AF). This way, the pressurized air entering the ²⁴¹Am charger can be considered as ultra pure and dry, with a relative humidity (r.H.) of approximately 1%, close to the detection limit of the used digital humidity sensors (Sensirion, SHT75) with an accuracy of 1.8% r.H. and a repeatability of 0.1% r.H.

Two experimental setups where in use during this study as schematically shown in Fig. 2: for the first one, the purified pressurized air is fed via a short connection tube made of PTFE of approximately 10 cm length to the ²⁴¹Am charger which is mounted directly in front of the inlet of the high resolution UDMA. The ion clusters produced by the ionizing radiation immediately enter the UDMA for classification and are detected by a fast Faraday Cup Electrometer (FCE_VIE-f), an updated version of the one described by Winklmayr et al. (1991), with a response time of typically 100 ms. For the first set of experiments, only air ducts of stainless steel or PTFE were in use. To ensure clean conditions for the whole system, the charger and air ducts as described above were flushed with the purified and dried air for a time period of 3 weeks—7 days a week and 24 h a day—before the start of the experiments. Only this way the influence of contaminants and trace gases led through the charger housing in the past can be reduced to a minimum.

Fig. 2.

Experimental setup for the high resolution mobility measurements. Carefully, by means of two stages (ACF=Active Carbon Filter; HEPA=High Efficiency Particulate Airfilter), purified pressurized air is used as carrier gas for ions that are generated in the ²⁴¹Am charger. These ions are subsequently analyzed according to their electrical mobility in a high resolution mobility analyzer called “UDMA” and detected by a Faraday Cup Electrometer (FCE). In the first set of experiments with clean and dry carrier gas conditions, only stainless steel or PTFE tubing and a short 10 cm PTFE tube between gas purification and charger was used. For additional experiments focusing on the influence of carrier gas contaminations, 2 m of different tubing material are inserted between the gas purification and the charger.

Although measurements at clean and dry carrier gas conditions can be easily compared to each other and will most probably describe the “genuine” mobility size distribution of ions produced by the ionizing radiation, in reality, aerosol measurements always involve contaminations and impurities to some extent. Therefore, a more interesting and realistic scenario focuses on the investigation of the properties of ionic molecular clusters produced during the presence of trace gases or impurities within the carrier gas by the ionizing radiation in the charger. As indicated in Fig. 2 by the dashed line in front of the charger, different kinds of frequently encountered contaminations were added to the system by placing different tubing material of two meters length in front of the charger—a quite untypical but very practical approach; The inner surfaces of the tubing materials evaporate trace gases and thereby influence the formation of ionic cluster species in the neutralizer. As the contaminated carrier gas enters the charger, the additional chemical components represent new bonding partners for the primary ions to form larger clusters.

3. Results

3.1. Clean and dry carrier gas conditions

Although the important parameter of interest are the ions' electrical mobilities, and also the UDMA classifies the clusters according to their electrical mobility, all mobility distributions will be converted into size distributions according to Milikan's relationship with the slip correction coefficients form Fuchs (1964). Of course, correlating a molecular cluster with a diameter is worthy of discussion, but as we are speaking of the electrical mobility equivalent diameter—a commonly used concept in aerosol science—this conversion still seems to be reasonable as it allows a direct comparison of the small cluster size to commonly known sizes of aerosol particles.

For extremely clean and dry operating conditions and only using the short 10 cm PTFE line between the gas purification and the ²⁴¹Am charger. Fig. 3 shows very typical size distributions of positive (black line) and negative (gray line) ion clusters produced in air by the ionizing radiation in the charger.

Fig. 3.

Typical size spectrum of positive (black line) and negative (gray line) ions produced in clean and dry purified air in the ²⁴¹Am charger. In this experiment, only the short 10 cm PTFE tubing is used between the gas purification and the charger.

During the very clean gas conditions, the size spectrum of positive ions is dominated by a “main” peak at 1.11 nm, but there are at least two additional separate peaks at smaller clusters sizes at 1.00 nm and 1.05 nm and some larger, not that well pronounced peaks at a.1.21 nm, 1.32 nm and 1.42 nm. For the negative ions, again a sort of “main peak” can be found but at smaller sizes compared to the positive ions. The negative “main” peak seems to consist of at least two cluster species with sizes very closely situated to each other at 0.96 nm and 0.98 nm. At larger sizes, rather broad peaks can be found at 1.05, 1.22 and 1.31 nm. Note that Fig. 3 is plotted with a logarithmic size scale for the electrometer current (proportional to the ion cluster concentration). Accordingly, the main peak at 0.96 or 0.98 nm almost exclusively dominates the size spectrum for negatively charged clusters produced in air.

3.2. Contaminated carrier gas conditions

The measured size distributions of positive ions produced by an ²⁴¹Am α-source in purified pressurized air using different tubing materials as air duct in front of the charger are shown in Fig. 4. In total, three additional tubing configurations where investigated: tubing made of polycarbonate, polyurethane, and a PVC fabric hose. The data indicated in the following as “clean and dry” always refers to the experiments with the short 10 cm PTFE-connection tube in front of the charger. These tubing materials were chosen as they represent the typical air ducts used in experimental setups for aerosol measurements.

Fig. 4.

Comparison of the size distribution of positive ion clusters produced during the presence of various tubing materials in front of the charger. The different tubing materials evaporate impurities to the system that are causing a dramatic change in the pattern of the mobility/size distribution of the ions generated in the ²⁴¹Am charger. With contaminants present, the mean mobility equivalent diameter is shifted towards bigger sizes.

The black line again represents the measurements performed under very clean and dry conditions, as explained in the previous section. Using polycarbonate or polyurethane tubing in front of the charger dramatically changes the pattern of the size distribution and results in the formation of additional ion cluster species at sizes of 1.24 nm and 1.34 nm leading to a trimodal size distribution where the smallest clusters below 1 nm disappear.

A completely different pattern can be found using the PVC fabric hose: the “main” peak at 1.11 nm becomes almost 2 orders of magnitude higher than any other cluster species. This indicates that either the fabric hose adds contaminants with a higher proton affinity than any other compound present in the carrier gas, yielding this single peak size distribution, or (rather unlikely) the fabric hose shows a sort of denuder effect that scavenges impurities and contaminations to purify the carrier gas.

Similar results were obtained for negative ions (Fig. 5). At clean conditions, almost only a single peak at 0.96 or 0.98 nm characterizes the size distribution of negatively charged ions. Using different tubing materials, that evaporate various chemical compounds from their inner surface into the previously carefully purified air, again strongly alters the ions' size distribution. For polycarbonate and polyurethane tubing, the initially unimodal size distribution now features three different well pronounced size peaks. The PVC fabric hose again shows a little bit different pattern, but this time with additionally generated clusters at larger sizes with less pronounced corresponding peaks, indicating a larger amount of evenly distributed cluster species.

Fig. 5.

Comparison of the size distribution of negative ion clusters produced during the presence of various tubing materials in front of the charger. Similar to the positive ions, the pattern of the size distribution changes with contaminants present in the system. Again, the mean mobility equivalent diameter is shifts towards bigger cluster sizes.

As can be clearly seen, there exists a strong dependence of the ions' formation on the chemical composition of the carrier gas. The different mobility spectra always show a general pattern but with distinctly different relative abundances of the individual cluster species.

Depending on the generated cluster species, the mean ion mobility and therefore also the respective mean mobility equivalent diameter is shifted towards bigger or smaller sizes.

Unfortunately, high resolution mobility spectrometry can only derive one important property of aerosol particles or molecular clusters: the electrical mobility. A second crucial parameter for describing a particle or molecular cluster is its mass. If genuine mass spectrometric instrumentation is not available, empirical derived mass-mobility relationships are a useful alternative for the mass determination, allowing the calculation of the respective mass out of a measured mobility distribution. It has to be mentioned, that there exists no generally excepted conversion from mobility into mass, as especially for molecular clusters also the finite size of the carrier gas molecules, the added drag associated to ion dipole interaction, also referred to as the polarization effect, and the size dependent accommodation coefficient have to be taken into account (Tammet, 1995; Ku & Fernández de la Mora, 2009).

However, the most frequently used mass mobility relationship goes back to Kilpatrick (1971) who determined the electrical mobility of twenty five different positive and negative ion molecules with a plasma chromatograph in clean and dry air and/or nitrogen. The masses of the very different molecule species ranged from about 35 Da–2211 Da. Due to technical reasons, in Kilpatrick's studies, the mobility of the molecular clusters was determined at a temperature of about 200 °C. Therefore, his original data was converted into a “reduced” mobility Z₀ calculated by the commonly used expression in Eq. (1), and referring to a temperature of 273 K and a pressure of 760 Torr (101325 Pa).

$$Z_0=Z\frac{p}{760}\frac{273}{T}$$ (1)

In Kilpatrick's original publication the data was fitted with a line to guide the eye but without any mathematical background. For a more convenient use of Kilpatrick's empirical data set, Mäkelä et al. (1996) fitted a function to Kilpatrick's data given in Eq. (2),

$$Z=\exp [-0.0347{(\ln (m))}^2-0.0376\ln (m)+1.46662$$ (2)

where m denotes the ion mass in [Da] and Z the ion mobility in [cm²/Vs].

An inverted conversion, for given mobility, related to Mäkelä's fit, can be expressed as following:

$$m=\exp [-0.27{(\ln (Z))}^2-2.2\ln (Z)+6.008]$$ (3)

This way, the experimentally determined mobility distributions of positive and negative ions can be converted—keeping in mind its limitations—into a corresponding mass distribution. The averaging over the mobility and mass distributions readily allows the calculation of the mean values for the ion mobilities and ion masses; providing the two necessary input parameters for Fuchs' charging theory.

The resulting mean mobility values of both ion polarities during the experiments with the different tubing material are shown in Fig. 6. For comparison, the graphs also show the mean mobility values presented by Reischl et al. (1996) as a reference for typically used input parameters for Fuchs' charging theory.

Fig. 6.

Mean ion mobility ${\overline{Z}}^{+}$and ${\overline{Z}}^{-}$ of positive and negative ions for different tubing materials placed in front of the charger compared to values given by Reischl et al. (1996).

For the positive ions, the data by Reischl et al. (1996) gives the lowest mean ion mobility (${\overline{Z}}^{+}$=1.15 cm²/Vs)—apparently considering larger ion clusters compared to those observed in this study. For the measurements performed during this work, the differences between the mean mobility of positive ions can be up to 30% when comparing the experiments performed during clean and dry conditions (${\overline{Z}}^{+}$=1.65 cm²/Vs) and the polycarbonate tubing in front of the charger (${\overline{Z}}^{+}$=1.27 cm²/Vs). For negative ions, the mean mobility values are generally higher as the ion molecules form smaller clusters with a maximum mean ion mobility for clean and dry conditions of ${\overline{Z}}^{-}$=2.09 cm²/Vs, but also here, differences up to 40% can be found for the mean electrical mobility of the ions.

When converting the mean ion mobilities into the mean ion masses, the differences between the results for the different tubing materials become even worse (Fig. 7). For positive ions, a maximum difference of 90% can be found by comparing the estimated mean ion masses for the operating conditions with the PVC fabric hose in front of the charger (${\overline{m}}^{+}$=160 Da) and the polycarbonate tubing in front of the charger (${\overline{m}}^{+}$=303 Da). For negative ions even a maximum difference of more than 200% can be found for the mean ion masses (${\overline{m}}^{-}$=109 Da for clean and dry conditions and ${\overline{m}}^{-}$=236 Da using the polyurethane tubing in front of the charger).

Fig. 7.

Mean ion mass ${\overline{m}}^{+}$ and ${\overline{m}}^{-}$ of positive and negative ions for different tubing materials placed in front of the charger compared to values given by Reischl et al. (1996).

With the experimentally determined ion mobilities and the approximated ion masses, the remaining ion properties that are necessary for Fuchs's charging theory (Fuchs, 1963, also summarized by Reischl et al., 1996) can be calculated. According to Eq. (4), the mean thermal velocity ${\overline{c}}^{\pm }$ can be written as

$${\overline{c}}^{\pm }=\sqrt{\frac{8k_{B}T}{\pi {\overline{m}}^{\pm }}}$$ (4)

where k_B is Boltzmann's constant, T the absolute temperature and ${\overline{m}}^{\pm }$ the mean ion mass. Its determination is important for calculating the mean free path λ^± of the ionic clusters which can be expressed by

$${\lambda }^{\pm }=\frac{16\sqrt{2}}{3\pi }\frac{D^{\pm }}{{\overline{c}}^{\pm }}{\left(\frac{M}{M+{\overline{m}}^{\pm }}\right)}^{1/2}$$ (5)

where M represents the mass of the carrier gas molecules.

The diffusion coefficient D^± of the charging ions can be determined from the Einstein relation

$$D^{\pm }=B^{\pm }{k}_{B}T$$ (6)

where B is the ions' mechanical mobility that is proportional to the electrical mobility Z

$$Z^{\pm }=B^{\pm }{e}_0$$ (7)

with e₀, the elementary unit of charge.

This way, the properties of the ions produced by ²⁴¹Am α-radiation can be extended by three additional parameters per polarity: the ions' mean thermal velocity ${\overline{c}}^{\pm }$, their mean free path λ^± and their diffusion coefficient D^±. An overview is listed in Table 1.

Table 1.

Comparison of ion cluster properties ${\overline{c}}^{\pm }$, λ^± and D^±, calculated from mean ion mobility ${\overline{Z}}^{\pm }$ and mean ion mass ${\overline{m}}^{\pm }$.

Tubing material/gas condition	${\overline{Z}}^{+}$ (cm²/Vs)	${\overline{m}}^{+}$ (Da)	${\overline{c}}^{+}$ (m s−1)	λ+ (nm)	D+ (m2 s)
Clean and dry	1.65	167	192.62	19.98	4.17 E-6
PVC fabric hose	1.61	160	196.86	19.41	4.07 E-6
Polycarbonate	1.27	303	142.99	15.94	3.22 E-7
Polyurethane	1.41	249	157.95	17.44	3.55 E-7
Reischl et al. (1996)	1.15	290	146.26	14.36	2.90 E-7
	${\overline{Z}}^{-}$ (cm²/Vs)	${\overline{m}}^{-}$ (Da)	${\overline{c}}^{-}$ (m s−1)	λ− (nm)	D− (m2 s)
Clean and dry	2.09	109	240.25	24.47	5.34 E-6
PVC fabric hose	1.90	129	220.22	22.59	4.84 E-6
Polycarbonate	1.61	212	171.77	19.89	4.11 E-6
Polyurethane	1.53	236	163.07	18.98	3.90 E-6
Reischl et al. (1996)	1.43	140	211.58	17.08	3.64 E-7

With the necessary input parameters available, the charging probabilities for aerosol particles that have been exposed to a bipolar ionic atmosphere can be computed according to Fuchs's theory. To unambiguously represent the calculated charging probabilities. Fig. 8 shows only the most extreme data sets for both ion polarities for singly charged particles. It has to be noted that according to Fuchs' theory, there already is a significant amount of doubly charged particles in the size range from 30 to 100 nm. However, to avoid an “overload” of information and to keep the picture as simple as possible, we focus on the calculated charging probabilities for only singly charged particles. For positive polarity, the ion properties determined while using the PVC fabric hose in front of the charger deliver the highest charging probability; the data corresponding to the polycarbonate tubing give the lowest charging probabilities. For negative polarity, the ion properties given by Reischl et al. (1996) yield the highest charging probability, the dataset involving the polyurethane tubing shows the lowest charging probabilities. All the other calculated charging probabilities, corresponding to the other ion properties determined while using the other tubing material, would lie in-between the displayed calculations.

Fig. 8.

Most extreme data sets for the calculated charging probabilities only considering singly charged particles. Just minor differences in the charging probabilities are found despite the very different ion properties used for the calculation.

4. Discussion

As can be seen, only minor differences in the calculated charging probabilities can be found. Although the input parameters determined from the different ion measurements were completely different (Table 1), the charging probability converges for large particles around 100 nm and splits up only slightly for both polarities with decreasing particle size. Generally, negative ions show a slightly higher charging probability compared to the positive ions.

However, the minor effect of the different ion properties on the calculated charging probabilities can be easily explained by looking in more detail into Fuchs' charging theory (Fuchs, 1963). There, the ions' mean mobilities and masses are used to calculate the ions mean thermal velocity ${\overline{c}}^{\pm }$ (see Eq. (4)) and further the ions' diffusion coefficient D^± (see Eq. (6)). These parameters are needed to calculate the mean free path λ^± of the ions (Eq. (5)) which controls the radius δ^± of the limiting sphere (Eq. (8))

$${\delta }^{\pm }=\frac{a^3}{{\lambda }^{\pm 2}}\left[\frac{1}{5}{(1+\frac{{\lambda }^{\pm }}{a})}^5-\frac{1}{3}(1+\frac{{\lambda }^{\pm 2}}{a^2}){(1+\frac{{\lambda }^{\pm }}{a})}^3+\frac{2}{15}{(1+\frac{{\lambda }^{\pm 2}}{a^2})}^{5/2}\right]$$ (8)

In Eq. (8), a stands for the radius of the geometric cross section of the particle and λ^± for the mean free path of the ions. The limiting sphere's radius δ^± is in the order of one ionic mean free path larger than the particle and divides the space around a spherical particle into two regions: outside the limiting sphere, the ions move according to the continuous diffusion equation; inside the sphere, the ions are assumed to travel without collisions with gas molecules as in a vacuum. Accordingly, the larger the mean free path of the ions, the larger the radius of the limiting sphere will become.

These four deduced ion properties govern the attachment coefficient η that represents the combination rate of ions and particles from Eq. (9)

$${\eta }_i^{\pm }=\frac{\pi {\delta }^{\pm 2}{\overline{c}}^{\pm }{\alpha }_i^{\pm }\exp \left[-\frac{{\Phi }_i({\delta }^{\pm })}{k_{B}T}\right]}{1+\exp \left[-\frac{{\Phi }_i({\delta }^{\pm })}{k_{B}T}\right]\frac{{\delta }^{\pm 2}{\overline{c}}^{\pm }{\alpha }_i^{\pm }}{4D^{\pm }a}{\int }_0^1\exp \left[\frac{{\Phi }_i(a/x)}{k_{B}T}\right]dx}$$ (9)

Φ_i(δ^±) or Φ_i(a/x) stand for the electrostatic potential energy of an ion in the field of a charged particle in a distance of δ^± or a/x, where x is an integration variable.

As determined by the conversion from mobility to mass, higher mean ion mobility values implicate a lower mean ion mass and vice versa.

Therefore, according to Eq. (9) with increasing mean ion mobility, the diffusion coefficient D^± of the ions will become larger and the attachment coefficient ${\eta }_i^{\pm }$ will be increased, resulting in a higher charging probability. At the same time, the attachment coefficient ${\eta }_i^{\pm }$ is reduced by a relative smaller mean thermal velocity ${\overline{c}}^{\pm }$ of the ions as their mean mass becomes lower with increasing mobility.

Accordingly, inertial interaction will dominate the charging process for low ion mobilities and large ion masses because of the higher kinetic energy of the ions. For low ion masses and high ion mobilities a diffusive interaction between ions and aerosol particles is promoted.

This way, the influence of the different ion parameters, triggered by the mean ions' mobilities and masses, that are causing the increase and decrease of the attachment coefficient ${\eta }_i^{\pm }$ almost cancels out, resulting in a very weak dependence of the calculated particle charging probabilities on the ions' physical properties.

Nevertheless, Fig. 9 shows the maximum uncertainties for the calculated charging probabilities of aerosols, calculated as the mean difference of the most extreme datasets for the ions with different properties. At large particle sizes of 100 nm, the differences between the calculated charging probabilities vanish and converge into each other. For decreasing particle size, the uncertainties increase with a maximum value of ±8.1% for negative ions and ±6.3% for positive ions.

Fig. 9.

Maximum uncertainties for the calculated charging probabilities for different ion properties. For decreasing particle size, the uncertainties increase more and more with a maximum value of ±8.1% for negative ions and ±6.3% for positive ions. The “hump” in the data for positive polarity originates from a glancing intersection of the minimum and maximum dataset.

5. Summary and conclusions

In this study, a newly developed high resolution mobility spectrometer was used to experimentally investigate the properties of ionic molecular clusters, produced in a radioactivity based ²⁴¹Am aerosol charger. It was seen, that for very clean carrier gas conditions, the size/mobility spectrum of the ions is almost exclusively presented by one dominating peak—for positive ion polarity as well as for negative ions. As soon as contaminats are added to the system, in this work realized by placing different tubing material in the carrier gas duct infront of the charger, additional ion species are formed, leading to a much more complex size/mobility spectrum. The observation of the change in the ion properties lead to the assumption that also the charging probabilities for aerosols will be affected by the different ions caused by impurities.

However, when using the experimental data derived in this work for the calculation of the charging probabilities, the results show that the Fuchs charging theory is very insensitive on variations in the ion properties. This result essentially means that if incorrect ion properties are used for the calculation of the charging probabilities, a measured particle number size distribution that relies on properly calculated charging probabilities will be under- or over-estimated in maximum by ±8.1% or ±6.3%, respectively. This clearly underlines the versatile applicability of the bipolar charging of airborne particles for laboratory as well as atmospheric measurements.