Extending the Capabilities of Single Particle Mass Spectrometry: II. Measurements of Aerosol Particle Density without DMA

Abstract

Particle density is an important and useful property that is difficult to measure because it usually requires two separate instruments to measure two particle attributes. As density measurements are often performed on size-classified particles, they are hampered by low particle numbers, and hence poor temporal resolution. We present here a new method for measuring particle densities using our single particle mass spectrometer, SPLAT. This method takes advantage of the fact that the detection efficiency in our single particle mass spectrometer drops off very rapidly as the particle size decreases below 100 nm creating a distinct sharp feature on the small particle side of the vacuum aerodynamic size distribution. Thus, the two quantities needed to determine particle density, the particle diameter and vacuum aerodynamic diameter, are known. We first test this method on particles of known compositions and densities to find that the densities it yields are accurate. We then apply the method to obtain the densities of particles that were characterized during instrument field deployments. We illustrate how the method can also be used to measure the density of chemically resolved particles. In addition, we present a new method to characterize the instrument detection efficiency as a function of particle size that relies on measuring the mobility and vacuum aerodynamic size distributions of polydisperse spherical particles of known density. We show that a new aerodynamic lens used in SPLAT II improves instrument performance, making it possible to detect 83 nm particles with 50% efficiency.

INTRODUCTION

One of the most informative physical properties of atmospheric particles is the particle density. Knowledge of particle densities is needed to calculate aerosol mass loading and yields of secondary organic aerosol (SOA) formation from measured particle volumes. The density is related to the particle composition and in the absence of composition measurements can even be used, in field measurements, to estimate an average aerosol composition (McMurry et al. 2002). Monitoring changes in aerosol densities due to changes in their composition can be used to follow heterogeneous chemical reactions (Katrib et al. 2005; Zelenyuk et al. 2010). Particle densities are also correlated with their optical properties (Moffet and Prather 2005; Tang and Munkelwitz 1994) and hygroscopic growth factors (Zelenyuk et al. 2008a).

With the advent of single particle mass spectrometry simultaneous measurements of particle compositions and densities have become possible (Murphy et al. 2004; Spencer et al. 2007; Zelenyuk and Imre 2009; Zelenyuk et al. 2008a, 2008c, 2008d). The simultaneous measurements of densities and internal composition for the same individual particles make it possible to obtain quantitative information on particle composition (Zelenyuk et al. 2008a; Zelenyuk et al. 2008c) and aid in particle identification (Hering and Stolzenburg 1995; McMurry et al. 2002; Zelenyuk et al. 2008a). Furthermore, particle densities were shown to be particularly useful for quantifying water retention by particles composed of inorganic salts coated with organic surfactants (Zelenyuk et al. 2007) and SOA (Zelenyuk et al. 2010). Monitoring density changes of coated particles makes it possible to detect organic coatings less than a monolayer (Zelenyuk et al. 2010, 2007).

Particle densities, or effective densities for aspherical particles (DeCarlo et al. 2004), are typically determined from measurements of two particle attributes using two different instruments (Alfarra et al. 2006; Bahreini et al. 2005; DeCarlo et al. 2004; Hand and Kreidenweis 2002; Hering and Stolzenburg 1995; Kelly and McMurry 1992; McMurry et al. 2002; Morawska et al. 1999; Murphy et al. 2004; Pitz et al. 2003; Schleicher et al. 1995; Spencer et al. 2007; Stein et al. 1994; Virtanen et al. 2004; Zelenyuk et al. 2005, 2008a, 2008d). These measurements are carried out either in series on the same particle, or in parallel on the same aerosol population. McMurry et al. (2002) have used a differential mobility analyzer (DMA) to classify particles of a single mobility diameter, d_m , and then measured their mass with an aerosol particle mass analyzer (APM). To reduce sampling time and achieve higher transmission Malloy et al. (2009) have reversed the order of the traditional DMA-APM system, by selecting particles of a given mass with the APM and analyzing them with a DMA. Murphy et al. (2004) have used their single particle mass spectrometer to measure density of individual particle on the basis of the ratio of particle vacuum aerodynamic diameter and particle diameter obtained using light scattering intensity.

The measurements of particle vacuum aerodynamic diameter, , and mobility diameter, d_m , are also commonly combined to obtain particle density (Alfarra et al. 2006; Bahreini et al. 2005; DeCarlo et al. 2004; Katrib et al. 2005; Spencer et al. 2007; Zelenyuk et al. 2005, 2008d). When d_m and distributions are measured separately, the transmission functions of both instruments must be considered. Moreover, the average density is calculated under the assumption that particle density is size-independent. Size-resolved density can only be obtained by measuring vacuum aerodynamic diameters of DMA-classified particles (Spencer et al. 2007; Zelenyuk et al. 2005, 2006a, 2008a, 2008d). This approach reveals that ambient particles are often composed of rich and complex mixtures, with size-dependent compositions and, hence, densities (Spencer et al. 2007; Zelenyuk et al. 2008a). This method also yields more precise particle densities (Zelenyuk et al. 2005, 2008d) and in some cases the measurements that yield density can be used to obtain particle shape, phase, and dynamic shape factors (Vaden et al. 2010; Zelenyuk and Imre 2007; Zelenyuk et al. 2008c).

The particle shape itself may play a role in measurements of densities. It is common to treat asphericity by defining a quantity called effective density, , identical to density in the way it is calculated, except that it denotes that particles could be aspherical (DeCarlo et al. 2004; Zelenyuk et al. 2006a). Since the majority of atmospheric particles are either spherical or only slightly aspherical (Salcedo et al. 2006) the differences between density and effective density are relatively small making the assumption of particle sphericity reasonable. Cases of dust and soot particles, in which shape plays an important role, can easily be identified based on the particle mass spectra and need to be treated separately. When the method presented here is used to determine the average density of an ensemble of internally and externally mixed particles, we rely on a newly developed approach to characterize the asphericity of ensembles of particles in real-time with high temporal resolution (Vaden et al. 2011) to assess whether shape plays an important role in determining the calculated density.

We begin by introducing a new method to obtain particle density directly from the vacuum aerodynamic size distributions measured by our single particle mass spectrometer, SPLAT II (for simplicity, just SPLAT (Zelenyuk et al. 2009a)). This method requires no DMA and yields particle density as a byproduct of routine measurements of polydisperse particle size and composition, enabling facile real-time monitoring of particle densities during field measurements with minimal assumptions or approximations about the ambient particle population. We test the approach on laboratory-generated particles and then apply it to ambient aerosol population composed of a mixture of internally and externally mixed particles and to particles of specific compositions.

We present data obtained with a new aerodynamic lens, whose improved performance significantly increases detection efficiency of small particles. In addition, we illustrate a new, fast, and simple method to measure the instrument size-dependent detection efficiency. We show how a detailed analysis of measured vacuum aerodynamic size distributions for polydisperse spherical particles of known size distributions and densities can be used to characterize the instrument detection efficiency as a function of particle size. We use this approach to obtain the detection efficiency curve of SPLAT equipped with the new aerodynamic lens inlet and show that with this lens SPLAT's 50% detection point was improved from 109 nm to 83 nm.

Experimental

Sodium nitrate particles were generated from a 0.1 M aqueous solution of NaNO₃ (Fisher Scientific, >99.5% purity) with an atomizer (TSI Inc., Model 3076), and dried using two diffusion driers (TSI Inc., Model 3062) in series before being loaded into a 100 L Teflon bag. These particles were further dried by mixing/diluting with dry (Relative Humidity (RH) less than 0.5%) particle-free air using dilution ratio of ∼100, which resulted in particle number concentration of particle/cm³. Number concentrations and size distributions of NaNO₃ particles as well as particles sampled directly from the ambient air were measured using a condensational particle counter (CPC, TSI Inc., Model 3786) and a scanning mobility particle sizer (SMPS, TSI Inc., Model 3936), respectively. Particle distributions for the NaNO₃ particles, as well as for ambient laboratory particles, were measured with SPLAT, as has been described in detail elsewhere (Zelenyuk and Imre 2009; Zelenyuk et al. 2009a). Briefly, particles enter into the instrument through an aerodynamic lens inlet used to transport the particles from the ambient air into the vacuum system with extremely high efficiencies (Zelenyuk et al. 2009a). The aerodynamic lens forms a low divergence particle beam and imparts on each particle a velocity that is a narrow function of the (Zelenyuk et al. 2009a). Individual particles are detected by light scattering at two optical detection stages located 10.5 cm apart. The particle time of flight (PTOF) between the two stages is used to calculate particle velocity and determine the with 0.5% precision (Zelenyuk and Imre 2005; Zelenyuk et al. 2009a). The particle detection event and the PTOF are then used to generate triggers to fire the IR and UV lasers for particle evaporation and ionization, respectively (Zelenyuk et al. 2009c). Individual particle chemical compositions are determined from the acquired mass spectra using an angular reflectron time-of-flight mass spectrometer (Zelenyuk et al. 2009a, 2009b). High-precision density measurements of NaNO₃ and ambient laboratory particles, by size-selecting particles with the DMA and measuring their with SPLAT as described in detail elsewhere (Zelenyuk et al. 2005; Zelenyuk and Imre 2009; Zelenyuk et al. 2008d).

Here, we present an approach that takes advantage of the distinctive feature of the SPLAT measured particle vacuum aerodynamic distributions that is a reflection of the rapid drop-off in instrument detection efficiency on the small-particle side. To avoid confusion we use to denote the true particle vacuum aerodynamic size distribution and define , to denote the SPLAT measured vacuum aerodynamic size distribution that depends on the distribution and the SPLAT detection efficiency curve.

The ability to use the left-edge of the distribution to estimate particle densities necessitates knowledge of the detection efficiency curve for particles with diameters between ∼50 and ∼150 nm. The data presented in this article were obtained with two different aerodynamic lens inlets. SPLAT equipped with the older lens inlet configuration (Zelenyuk and Imre 2005) was carefully characterized by measuring the SPLAT detection efficiency of NIST-certified size standards (spherical polystyrene latex spheres) of known diameters, whose concentrations were determined with a condensation particle counter (CPC) (Zelenyuk et al. 2009a); this measurement yielded a 50% detection efficiency at d_p =109 nm.

A new aerodynamic lens system was used for some of the experiments presented here. Like the old lens, it has outer diameter of 0.500 inches, and contains six apertures with the same diameters ranging from 3 mm to 5 mm that are placed at the same positions as before. What is different is that the inner diameter (ID) of the new lens is 0.3735 inches as compared with the old lens whose ID was 0.402 inches, and the apertures in the new lens are designed to assure their precise, reproducible positioning during lens assembly. This is accomplished by machining each aperture to be an integral part of a sleeve that is only 0.0015 inches smaller than the lens ID, as compared with the old design, in which the apertures were 0.01 inches thick flat disks and 0.007 inches smaller in diameter than the tube ID, leaving some room for misalignment. The combined effect of tight tolerances and precise machining assures exact, reproducible alignment of the aerodynamic beam.

Below we demonstrate the application of a new, much simpler approach to obtain the instrument's detection efficiency vs. d _p curve by measuring the distribution of polydisperse aerosol population composed of spherical particles of known density, for which the particle size distribution is measured with a DMA. We apply this procedure to the new lens using dry NaNO₃ particles and find that the instrument's new detection probability drops to 50% at d_p = 83 nm.

Field measurements of aerosol particles presented here were conducted during the Indirect and Semi-Direct Aerosol Campaign (ISDAC), in which SPLAT was deployed onboard the Canadian National Research Council Convair 580 aircraft (McFarquhar et al. 2010; Zelenyuk et al. 2009a) and during the recent Carbonaceous Aerosols and Radiative Effects Study (CARES) field campaign that took place in Sacramento, CA in June 2010.

Simulations of the Distribution and Its Use in Determining Particle Density

We begin by pointing out that the vacuum aerodynamic size distributions of polydisperse aerosol, as measured by SPLAT, , have a distinctive line-shape (McFarquhar et al. 2010; Zelenyuk and Imre 2005). For the vast majority of atmospheric particles the large-particle side of is determined by the particle vacuum aerodynamic size distribution while in contrast, the sharp drop-off on the small-particle side reflects the fact that the instrument detection efficiency decreases rapidly as particle true size, d_p , decreases below ∼100 nm (Zelenyuk et al. 2009a). The instrument's detection sensitivity is a function of the particle true diameter and SPLAT measures vacuum aerodynamic diameter, . Therefore, the sharp drop-off on the left edge of the curve is almost entirely determined by the instrument detection efficiency, which is a known function of d_p . The combined knowledge of d_p and can be used to calculate particle density, ρ _p , or for aspherical particles effective density, ρ (DeCarlo et al. 2004; Zelenyuk et al. 2005; 2006a; Zelenyuk and Imre 2009) using Equation (1):

where ρ ₀ is a unit density, d_p is the particle diameter and is the vacuum aerodynamic diameter.

The instrument (SPLAT) detection efficiency as a function of particle diameter can be fit using an approximate form given in Equation (2):

where a and b can be empirically fit to experimental data. The resultant curve, fit to measured detection efficiency using the older lens inlet (Zelenyuk et al. 2009a), is shown in Figure 1a. The a-parameter corresponds to the d_p , for which 50% of particles that enter the instrument are detected (i.e., the halfway point), and b determines the gradient, or the sharpness of the curve. As shown in Figure 1a, for the older aerodynamic lens d_p = 109 nm. Note that while it might be possible to use a more complex function that fits the observed data points more precisely, the calculated particle density will not be affected.

FIG. 1 (a) A fit of the experimental small-particle detection efficiency curve (Zelenyuk et al. 2009b) using Equation (1); (b) A typical log-normal size distribution (red) and the corresponding SPLAT detected vacuum aerodynamic size distribution (

assuming spherical particles with ρ= 1.0 g cm⁻³ (c)

curves of particles with density indicated in the legend. Also shown are the densities estimated from the halfway points of the left-edge of the

distributions. See text for details.

The effect of this sharp decrease in detection efficiency for small particles on a typical log-normal particle size distribution is shown in Figure 1b. The curve is a product of the particle sizedistribution and the particle detection efficiency curve, i.e.,

where A is the total particle number concentration, σ is the geometric standard deviation, ρ _p is the particle density, or effective density, and d^avg _p is the average particle diameter. This curve, which is simply the log-normal distribution (red line in Figure 1b) multiplied by the function in Figure 1a, is shown in blue in Figure 1b for d^avg _p = 100 nm, ρ _p =1.0 g cm⁻³, and ln σ=0.7. Figure 1b illustrates how the detection efficiency curve leaves its distinct signature on the curve in the form of a sharp left-edge of the size distribution.

It is possible to obtain a relatively accurate particle density from Figure 1b by noting that the at the 50% point (on the left-edge) is 110 nm and knowing that the instrument detection efficiency drops to 50% at 109 nm to calculate a particle density of 1.01 g cm⁻³, which is only 1% different from the true value, ρ _p .

Simulated distributions for particles with different densities are shown in Figure 1c. These curves are generated using Equation (3) with the same parameters as in Figure 1b, but with increasing values of ρ _p as indicated in the legend of Figure 1c. The shape of the left-edge does not change with density, because only the position of the distribution is affected by density under constant d^avg _p and ln σ. The density values estimated from the 50% point on the left-edges are shown at the bottom of the figure, and are all within 1% of the exact particle density.

Figure 1 demonstrates that once the halfway point of the detection efficiency curve is determined (for a given instrument configuration), accurate estimates of particle densities can be obtained from the halfway point of the left-edge of the distribution. One reason for the high accuracy of the estimated densities shown in Figure 1 is the fact that in this case d^avg _p = 100 nm, which is very close to the halfway point of the detection efficiency curve (109 nm). For particles with d^avg _p much larger or much smaller than 109 nm, the shape of the left-edge of will be slightly impacted by d^avg _p and the density estimate would be expected to be less accurate. This is illustrated in Figure 2, in which simulated curves with ρ _p = 1.0 g cm⁻³ and ln σ=0.7, and increasing d^avg _p values as indicated in the legend are shown. Note that while d^avg _p changes by a factor of 5, from 50 nm to 250 nm, the densities estimated from the left-edge of all curves changes only from 0.93 g cm³ to 1.13 g cm⁻³. These densities, shown at the bottom of Figure 2b, are all reasonably close to the exact density (1.0 g cm⁻³).

FIG. 2 (a) Calculated

curves of polydisperse aerosols with ρ= 1.0 g cm⁻³ and log-normal size distributions peaking at the values (d^avg _p ) indicated in the legend; (b) Expanded view of the left-hand edges of the

curves, showing estimated particle densities; (c) A plot of the error in the estimated densities as function of d^avg _p . This plot is used to correct the estimated density. See text for details.

Nevertheless, a number of ways exist by which the accuracy of the estimated density can be improved. The most obvious is to take the effect of d^avg _p and σ on the shape of the observed into account by fitting the observed distribution with Equation (3). This approach will be illustrated in the next section below. An alternative approach is to generate a correction curve in which the errors in estimated densities as a function of d^avg _p and σ are quantified. The error curve generated for the estimated densities in Figure 2b is shown in Figure 2c. For d^avg _p below 109 nm, the errors are negative, i.e., the estimated densities based on the 50% point are underestimated, and for d^avg _p above 109 nm, the errors are positive, i.e., the densities based on the 50% point are overestimated, and the further d^avg _p is from 109 nm, the larger the required corrections. Note, however, that even for particles with d^avg _p as large as 250 nm, when nearly the entire aerosol population (98% and 96.5% for ln σ=0.7 and 0.5, respectively) are detected by SPLAT, the uncorrected density estimates are still less than 15% too high. Most importantly, the density obtained based on the 50% point can be used to calculate a fairly precise value for d^avg _p using the observed and the 50% point estimated density. For example, consider a curve with a maximum at nm and a 50% point at 131 nm, which yields an estimated density of 131/109 = 1.2 g cm⁻³. This approximate density is used to calculated^avg _p ∼200/1.2=167 nm. d^avg _p = 167 is then used to obtain, from Figure 2c a 2.5% correction factor that needs to be applied to the density estimate of 1.2 g cm⁻³, yielding an improved density estimate of 1.17 g cm⁻³.

Improved Detection Probability of Small Particles and a New Method for Establishing the Instrument Detection Efficiency Curve

We now proceed to apply the above methodology to estimate particle densities from laboratory aerosol measurements. However, as we have mentioned above the instrument in its new configuration has a new aerodynamic lens inlet, for which a detection efficiency curve has not been established yet. To apply the method described above we must first establish the new SPLAT detection efficiency vs. d _p curve. We start with dry, spherical NaNO₃ particles, but because the exact density of these particles depends on the drying process (Zelenyuk et al. 2005, 2010) we first establish their density under present drying conditions with a high-precision method using a DMA and SPLAT connected in series. The measurements performed for DMA-classified particles with diameters 100 and 200 nm (not shown) yield a density of 2.07 ± 0.02 g cm⁻³, which is consistent with our previous measurements (Cai et al. 2006; Zelenyuk et al. 2005, 2010, 2007).

The mobility size distribution of the polydisperse NaNO₃ aerosol is shown in Figure 3a (blue curve). The curve of the NaNO₃ aerosol shown in Figure 3b (blue curve) clearly has a similar shape to that simulated in Figure 1b. In principle, the high-precision density and the log-normal distribution of the aerosol mobility size distribution could be used to fit the data in Figure 3b with Equation (3) to obtain parameters a and b. We choose instead to test whether it is possible to use alone to obtain the detection efficiency curve, particle density, and even the mobility size distribution. The results are shown as the red curves in Figures 3a and 3b and the derived parameters are listed in Table 1.

FIG. 3 (a) Mobility size distribution of polydisperse NaNO₃ particles obtained with a SMPS (blue) and a fit using parameters listed in Table 1 (red). See text for details; (b) Experimentally observed

of the polydisperse NaNO₃ particles (blue) and a fit of the data using Equation (3) and the parameters listed in Table 1 (red).

TABLE 1 Parameters obtained by fitting the NaNO distribution with Equation (3)

Parameter	Value
ln σ	0.53
d^avg p	79 nm
ρ	2.06 g cm^−3
a	83 nm
b	5.7 nm

The excellent fits shown in Figure 3 indicate that the line-shapes determined by Equation (3) are good representations of which include the new SPLAT detection efficiency curve and the particle size distributions. The d^avg _p of 79 nm obtained from the SPLAT data alone compares very well with the 80 nm value from the SMPS measurement. Similarly, this procedure yields a particle density of 2.06 g cm⁻³, which is in excellent agreement with the high-precision measurement of NaNO₃ density. The same fit also yields the new 50% detection efficiency point of 83 nm, for SPLAT with the new aerodynamic lens configuration, which is 24% lower than the 109 nm value obtained with the older lens. This indicates a significant increase in SPLAT's detection efficiency of smaller particles with the new configuration.

With this example, we have outlined a new simple method for establishing a detection probability curve for small particles. This method uses a polydisperse aerosol, composed of particles of known density and with known particle size distribution that peaks near the halfway point of the detection probability. Measurement of the vacuum aerodynamic size distribution with good signal-to-noise allows for an accurate fit, which is carried out assuming that can be described with a sharp drop-off detection efficiency function multiplied by the measured mobility size distribution and shifted by the known density. As we show below, once a new curve is obtained it can be tested on another polydisperse aerosol sample of known density.

The Densities of NaNO₃ and Ambient Particles

From Table 1, the estimated density for the NaNO₃ particles based on the simulated curve is 2.06 g cm⁻³. Alternatively, we can use the newly established halfway point of d_p = 83 nm together with the observed halfway point of which is 168 nm (shown in Figure 3b) to yield an estimated density (before correction) of 2.02 g cm⁻³, which differs by only 2% from the exact value. Considering the relevant error correction curve, we find that the estimated density needs to be increased by 1% to yield a density of 2.04 g cm⁻³, which is only 1% off the true particle density.

With the new detection curve established based on the NaNO₃ particles, the next step is to test how well the analysis works for different particles. The curve measured for ambient laboratory air particles is shown in Figure 4a (black trace), with a fit to the data (red curve). These data were fit with Equation (3), in which the 50% detection point (a in Equation (2)) was fixed at d_p = 83 nm to yield a particle density of 1.38 g cm⁻³. As with the NaNO₃ particles, we measured for these particles their precise density using DMA-classified particles and SPLAT. The results of these measurements for 100 nm, 151 nm, and 200 nm DMA-classified particles are shown in Figure 4b, and yield an effective density of 1.4 g cm⁻³, in excellent agreement with the density of 1.38 g cm⁻³ from . We note that the observed d_va distributions of the monodisperse ambient laboratory particles are rather broad and asymmetric, which is especially true for the larger particles with mobility diameter of 200 nm. This line-shape indicates either that these particles are aspherical (Zelenyuk et al. 2008d), in which case the density measurements yield effective particle densities, or that the particles have a range of compositions and hence densities. The asphericity parameters measured for these particles (Vaden et al. 2011) indicate that a significant fraction of these particles are aspherical, which is consistent with the line-shape of the smaller particles. The broader line-shapes of larger particles indicates the presence of a mixture of particles with a range of compositions and hence densities.

FIG. 4 (a) Experimentally observed

of ambient room-air particles (black) and fit to the data (red) using Equation (3); (b)

distributions of DMA-classified room-air particles and the calculated high-precision particle density. The particles with d_m = 154 nm are doubly charged particles detected during the measurements of 100 nm particles.

Notable in the case of the polydisperse room-air particles is that on the small-particle side the shape of the mobility size distribution was found to be very different from a log-normal distribution. Yet the fit, used to extract a relatively accurate density, works extremely well despite the fact that it assumes log-normal distribution. The reason is that since the small particle side of is strongly dominated by the SPLAT detection efficiency, the exact shape of the d_p distribution on the small particle side is not that important.

Before we precede to present field data measurements, we apply the simple method of locating the halfway point on the left-edge to the ambient particle data (as opposed to fitting the data with Equation (3)). The observed 50% point is d_va = 118 nm yielding an estimated effective density of 1.42 g cm⁻³. Since the particle size distribution peaks at 110 nm the error correction is −1%, yielding again a density estimate with 1% accuracy.

Application to Field Measurements and the Densities of Composition-Resolved Particles

The density measurements for the DMA-classified ambient laboratory particles presented in the section above indicate that their density was nearly size-independent, making the interpretation of the density calculated from rather straightforward. However, ambient particles can present more complex scenarios, in which the particle compositions, and hence densities, are size-dependent. In these cases, the interpretation of the density calculated from the sharp, small particle edge is not so obvious.

In Figure 5, we present data obtained on June 25, 2010 at 10 am during CARES field campaign, when the number concentration of particles larger than 14 nm was ∼5,000 particles cm⁻³, and the number concentration of particles detectable by SPLAT was 700 particles cm⁻³. Figure 5a shows that the mobility size distribution peaks at 37 nm and has a second smaller mode at ∼220 nm, providing the first indication that more than one type of particles is present. Figure 5b shows the results of the density measurements of DMA-classified particles with diameters 80, 100, 119, 151, and 200 nm. The figure reveals a simple pattern, in which particle densities increase from 1.3 to 1.6 g cm⁻³ as the particle size increase from 80 to 200 nm. The line-shapes of the distributions of the monodisperse particles in Figure 5b are also informative. They show that the majority of smallest particles have a density of 1.3 g cm⁻³, and as the particle size increases the line-shape broadens, indicating that a mix of particles with densities between 1.3 and 1.6 g cm⁻³ are present, and that the density of most of the 200 nm particles is 1.6 g cm⁻³.

FIG. 5 (a) Mobility size distribution of particles measured in Sacramento, CA during the CARES field campaign; (b) Density measurements of DMA-classified particles with diameters of 80, 100, 119, 150, and 200 nm; (c) The

distribution of the particles whose mobility size distribution is shown in (a).

The analysis of individual particle mass spectra and sizes reveals that vast majority of the particles are composed of organics mixed with sulfate and that particles with higher density have larger fraction of sulfate.

Figure 5c is a plot of the measured , showing the characteristic sharp drop-off at the small particle side and three peaks at 142, 220, and 340 nm. The first is most likely due to the drop in detection efficiency, and the third is consistent with the ∼220 nm, minor peak in the mobility size distribution and the measured density of 1.6 g cm⁻³. The presence of three distinct peaks in provides an indication that the particle compositions are most likely size-dependent. It is clear that the average particle density calculated from the sharp detection drop-off for this distribution cannot be representative of all the particles.

Figure 5c shows also that the 50% point is at d_va = 118 nm, which translates to a density of 118/83 = 1.42 g cm⁻³. For a density correction, we note that the size distribution shows multiple peaks with the most intense peak at 142 nm, which yields a particle size of 142/1.42 = 100 nm, which with the new lens translates to no correction. It is important to point out that despite the fact that the instrument was transported from the laboratory to the field, where it was reassembled, realignment, and recalibrated, the 50% detection point remained at d_p = 83 nm.

Looking at the size-resolved particle densities, shown in Figure 5b, we find that a density of 1.42 g cm⁻³ is a reasonable representation of the densities of particles that are between 80 and 120 nm—the range of sizes that affect the position and shape of the sharp drop-off we used to calculate the particle density.

This example illustrates the fact that even in complex cases, where the particle densities are size-dependent and the mobility and distributions exhibit multiple peaks, it is possible to obtain useful and relatively accurate average density. It is important to keep in mind that the calculated values represent an average density of particles that are between 80 nm and 120 nm in diameter. When the data provide indication that particle compositions vary with particle size, it is best to apply this method to the distributions of the chemically resolved data. Below we demonstrate an application of this approach to data collected on one of 27 ISDAC flights.

We apply the data analysis methodology presented above to aerosol populations measured during the ISDAC, in which SPLAT was deployed onboard of an aircraft to continuously sample atmospheric particles. Figure 6a shows the curve of a representative aerosol measurement taken over a few minutes of flight, from which we calculate an average particle density of 1.39 g cm⁻³, using the sharp drop-off on the left side of the curve. We can test this calculated density by comparing to the size distribution measured by the Passive Cavity Aerosol Spectrometer Probe (PCASP) that was also used to monitor the aerosol size distribution during the ISDAC. Because the PCASP cannot detect particles smaller than 100 nm, the density is calculated by comparing the large particle side of the SPLAT and PCASP size distributions to yield 1.4 g cm⁻³, which is clearly in excellent agreement with the density obtained based on the small particle size estimate.

FIG. 6 (a)

of aerosol sampled during part of flight 26 of the ISDAC field campaign; (b) Expanded view of the left-hand edge used to estimate particle density; (c) Expanded views of the left-hand edges of the

distributions of composition resolved particles as indicated in the legend that lists their estimated densities as well.

One of the most important features of SPLAT and all other single particle mass spectrometers is their ability to measure simultaneously the vacuum aerodynamic diameter and mass spectrum of each detected particle. This enables the separate and simultaneous characterization of distributions for different types of particles by classifying their mass spectra into a number of classes (Zelenyuk et al. 2006b; 2008b) and separately obtaining the distributions of particles that belong to each of these classes. Classification of the mass spectra (not shown) recorded during this flight segment shows that the majority of the particles belong to the following six classes: organics, biomass burning (BB) aerosol, three types of sulfates mixed with organics, and sulfates mixed with BB.

Figure 6c shows the left-hand sides of the distributions obtained for six classes listed above. The density values calculated from each composition-resolved curves is shown in the figure legend. The density of the organic particles that are mostly composed of the oxygenated organics is found to be 1.2 g cm⁻³, which is in good agreement with typical SOA particle densities (Zelenyuk et al. 2008d) and the density of the oxygenated organics component of atmospheric particles previously measured using high-precision methods (Zelenyuk et al. 2008a). The calculated density of BB particles of 1.3 g cm⁻³ also falls within the 1.2–1.4 g cm⁻³ range of densities reported for dry biomass burning particles (Reid et al. 2005).

The estimated densities of 1.4, 1.5, and 1.6 g cm⁻³ of the particles composed of organics mixed with sulfates can be used to calculate their corresponding sulfates and organics weight fractions (Zelenyuk et al. 2008a). Using densities of 1.8 and 1.2 g cm⁻³ for sulfate and organics, respectively, we calculate the weight fractions of organics in these three classes to be 56%, 38%, and 22%, respectively. Similarly, the density of particles composed of sulfate mixed with BB whose estimated density is 1.7 g cm⁻³ indicates that these particles have only 10% BB by mass.

In addition to the six classes discussed above, there were a few dust particles, and small number of fresh and process sea-salt particles. However, the number of particles in these classes was significantly smaller than the ∼1000 particles required to obtain distributions that can be used to estimate particle density.

Conclusions

Typical density measurements require measurement of two different particle properties, which is usually accomplished by two separate instruments. We have shown here that in SPLAT the sharp decrease in detection efficiency of small particles gives rise to a reproducible, distinctive line-shape of the curve. While the sharp drop-off is determined by the particle true diameter, the curve is a measure of particle vacuum aerodynamic diameter, making it possible to deduce, based on SPLAT data alone, the aerosol density or effective density. The only requirement is that the particle size distribution is sufficiently broad and that it has significant population with diameters close to the sharp detection probability drop-off point.

We have illustrated two different practical methods to take advantage of this feature and to estimate particle density with good precision. In one, the measured SPLAT detection efficiency curve is simulated with a simple function and the overall particle population is assumed to have a log-normal distribution. The measured is then fit as the product of these two functions using the density as one of the fitting parameters. The other, somewhat simpler, approach uses the ratio of particle diameter at the 50% detection efficiency point and the vacuum aerodynamic diameter on the small-particle side where the observed distribution drops to half of its maximum value, to estimate the particle density. We showed that it is possible to generate an error correction curve to improve the accuracy with which the density is estimated. Both methods were tested with particles of known densities.

The method presented in this article can be utilized by any single particle mass spectrometer that uses particle optical detection. It is suitable for field studies of atmospheric aerosols, which often require high temporal resolution and real-time monitoring. We illustrated the application of this analytical methodology to field data acquired by SPLAT during ground and aircraft-based deployments. The overall density derived for an aerosol sample was found to be in good agreement with the density obtained by other methods. The density analysis of the composition-resolved particles using their distributions alone reveals density values consistent with known values for typical atmospheric particles and was used to quantify the relative fraction of constituents of internally mixed particles. This method is therefore highly useful in complex data analyses that are typically required for interpretation of field measurements.

This article also presents the first data obtained with a new aerodynamic lens inlet that improves the detection efficiency of small particle, making it possible to detect 83 nm particles with 50% efficiency. The improved lens was designed and machined to assure that the positioning of the apertures is reproducible and precise. We have also shown that it is possible to reverse the approach used to measure particle density and deploy polydisperse spherical particles of known density and size distribution to determine the instrument detection efficiency. The application of this method to SPLAT, equipped with the newly designed aerodynamic lens inlet, shows a significantly improved detection efficiency of small particles, as the 50% detection point of the new lens is 83 nm as compared with 109 nm for the older lens.

Acknowledgments

This work was supported by the U.S. Department of Energy (DOE) Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences and Office of Biological and Environmental Research (OBER). Part of this research was performed in the Environmental Molecular Sciences Laboratory, a national scientific user facility sponsored by the DOE's OBER at Pacific Northwest National Laboratory (PNNL). PNNL is operated by the U.S. DOE by Battelle Memorial Institute under contract No. DE-AC06-76RL0 1830.

We thank the ISDAC and CARES teams for their incredible help during these field campaigns. ISDAC and CARES were supported by the U.S. DOE Atmospheric Radiation Measurement (ARM) Program Climate Research Facility, the DOE Atmospheric Sciences Program, the National Research Council of Canada and Environment Canada. Some of the data were obtained from the ARM program archive, sponsored by DOE OBER Environmental Science Division.