Method to assess performance of scanning mobility particle sizer (SMPS) instruments and software

EDITOR:

• Jingkun Jiang

Introduction

The Scanning Mobility Particle Sizer (SMPS) (Wang and Flagan 1990) is the most commonly used instrument for measuring size distributions of sub-0.5 µm aerosol particles. However, insufficient attention has been paid to assessing the quality of SMPS data. This is largely because suitable methods have not been developed, accepted, and routinely used by aerosol scientists. In this Letter we describe a method that determines to high accuracy whether or not the SMPS mobility classifier, condensation particle counter, and data acquisition/analysis software are performing properly.

An SMPS consists of a bipolar aerosol charger (neutralizer), a differential mobility analyzer (DMA) to size the particles and a condensation particle counter (CPC) (or aerosol electrometer) to detect the particles. Our technique is to challenge the SMPS with particles having a narrow and known mobility distribution from an independent reference DMA, as illustrated in Figure 1. Measurements are carried out with particles that are sufficiently large to ensure that diffusional broadening of the DMA transfer functions and losses are small. This mobility-classified aerosol is sampled, either in parallel or sequentially, by the SMPS being calibrated and a second reference CPC that has been independently calibrated. Our method allows determining the accuracy of SMPS particle counting and sizing, and also provides information on the validity of the DMA transfer function. However, because we bypass the SMPS charger, our approach cannot identify errors due to improper charging, a noteworthy limitation.

Figure 1. SMPS performance test setup.

Wiedensohler and co-workers at the Leibniz Institute for Tropospheric Research (TROPOS) have implemented an excellent, comprehensive quality assurance program for mobility particle size spectrometers (MPSS) (Wiedensohler et al. 2018). Our alternative approach is in several regards less comprehensive than that used at TROPOS. However, it can be implemented using instrumentation that is readily available in many aerosol laboratories and it is amenable to use in the field. To assess sizing accuracy, we rely on consistent sizing by both DMAs, rather than using certified PSL spheres as is done at TROPOS. When used properly, PSL provides a rigorous and citable size standard. However, uncertainties are introduced when PSL solutions degrade with age; laboratories that do not have a reliable method for maintaining PSL size standards may get more reliable results using the tandem DMA method. Our approach also provides a validity criterion for the DMA transfer function, information that would not necessarily be revealed by methods used at TROPOS. The TROPOS method, however, incorporates a means to assess the performance of the neutralizer. Their approach also assesses instrument performance over a range of sizes, while our approach focuses on a single size.

We have encountered various problems with SMPS systems. For example, we've encountered DMAs with transfer functions that were degraded (i.e., broadened) by flow distortions caused by particle deposition within the classifier tube (including the DMAs that were used to acquire the data described in this letter–e.g., compare data in Table 1 for runs done before and after the DMAs were cleaned), sizing errors due to errors in flowmeter calibrations or leaks, CPC concentration errors due to improper pulse counting, and continuity failure in the DMA high voltage connection. Furthermore, during collaborative intensive field campaigns we've observed discrepancies between parallel measurements done using independent SMPS systems. These problems have been encountered using both commercial and laboratory-built SMPSs. The method we propose would have allowed us to identify and resolve these issues.

Table 1. SMPS recovery results^a.

Run^b
Measurements Completed Before Cleaning DMAs (CPC1 and SMPS operated in Parallel)
4kv5m,pre	−8.2	−0.1	0.0261	1.173	0.0268	1.183
Measurements Completed After Cleaning DMAs
Parallel
6kv5m	−6.5 → −3.3	−1.7 → −1.4	0.0155 → 0.0161	1.066 → 1.071	0.0163 → 0.0169	1.073 → 1.078
6kv2m	−4.0 → −2.8	−0.7 → −0.4	0.0142 → 0.0145	1.056 → 1.058	0.0151 → 0.0153	1.063 → 1.065
4kv5m	−3.9 → −2.2	+0.4 → +0.9	0.0088 → 0.0118	1.022 → 1.039	0.0108 → 0.0134	1.033 → 1.049
4kv2m	−1.7 → −0.2	+0.9 → +1.0	0.0115 → 0.0128	1.037 → 1.046	0.0131 → 0.0143	1.047 → 1.056
Sequential
6kv5m	−2.4 → +1.6	−1.6 → −1.0	0.0182 → 0.0206	1.090 → 1.114	0.0189 → 0.0212	1.097 → 1.121
6kv2m	−2.6 → −0.5	−0.7 → −0.6	0.0133 → 0.0146	1.049 → 1.059	0.0142 → 0.0155	1.056 → 1.066
4kv5m	−6.7 → +9.4	−0.4 → −0.2	0.0149 → 0.0157	1.061 → 1.068	0.0161 → 0.0169	1.071 → 1.078
4kv2m	−5.3 → +0.4	+0.5 → +0.7	0.0119 → 0.0131	1.039 → 1.047	0.0134 → 0.0145	1.050 → 1.058

^a Using methods described in the online supplemental information, the effects of diffusion were taken into account when calculating and . and were calculated with Equations (4[4] )–(6[6] ), assuming that diffusion was negligible.

^b Run “6kv5m” corresponds to V_DMA1 = 6 kV with 5 min SMPS scan time.

Methodology

The apparatus used for this method is shown in Figure 1. An inherent assumption of the standard SMPS data analysis is that the measured size distribution function () may be approximated as constant over the width of the DMA transfer function. For the case of a narrow distribution such as the proposed mobility-classified challenge aerosol, this assumption is violated and the accuracy of the SMPS recovered size distribution may be compromised. Stolzenburg and McMurry (2018) have analyzed the accuracy of the recovered moments¹ of narrow size distributions with the following results:[1] [2] [3] where the relative variance of the DMA transfer function for non-diffusing particles is:[4] and , and are the total number concentration, (arithmetic) mean mobility and mobility standard deviation, respectively, of the challenge aerosol. The subscript “r” denotes values recovered from SMPS inversions assuming a broad distribution function. The DMA transfer function parameters are given by the flow ratios and (Knutson and Whitby 1975; Stolzenburg 1988). and are the DMA aerosol in and out flows while and are the sheath in and excess out flows. Distortion of the DMA transfer function due to fast scan rates is not considered in this analysis.

Equations (1[1] ) and (2[2] ) show that the bias between inverted (recovered) values of number concentrations and mean mobilities and their true values is determined by . For typical SMPS operation, the DMA inlet and outlet aerosol flows are equal () and most often a tenth of the sheath flow (). In almost all instances, such that . Thus, in the case of negligible diffusional broadening of the transfer function, and the errors in the total number (Equation (1[1] )) and mean mobility (Equation (2[2] )) are less than 0.7% and 1.3%, respectively. This level of error is well within typical flow measurement uncertainties for the SMPS DMA and detector, which also affect and .

For the relative mobility variance in Equation (3[3] ), the error can be seen as an offset given by . However, it is also instructive to note that the relative variance of the recovered distribution is simply the sum of the relative variances of the input distribution and the SMPS DMA transfer function. (Note the similarity to the analysis of propagation of independent errors.) Thus, the width of the recovered distribution will only be accurate if the width of the transfer function is small compared to that of the input distribution. This is not the case for the narrow input distributions considered here.

In the case of a tandem DMA experiment² where DMA2 is part of an SMPS system and where both DMAs are performing according to theory, Equation (3[3] ) becomes for nondiffusing particles:[5] where it is assumed , the centroid mobility of the upstream DMA transfer function. If the SMPS DMA is performing with sub-optimal resolution, then the second equality expressed in Equation (5[5] ) will be significantly violated. To quantify the degree of this effect, the last term in this equation representing the SMPS DMA can be augmented with an adjustable parameter to account for the extra spread in the transfer function. Following Stolzenburg (2018), the augmented version can take two possible forms as shown on the right sides of Equation (6[6] ),[6] In the first form is an absolute measure of the increase in the relative variance of the SMPS transfer function while in the second gives the measure of this increase relative to the original non-diffusing width of the transfer function. The first term on the left side of Equation (6[6] ) is the square of the relative mobility standard deviation of the SMPS recovered distribution. As demonstrated in Stolzenburg and McMurry (2018), this can be well approximated as[7] where is evaluated at the DMA1 centroid diameter, and and are the geometric standard deviations of the recovered mobility and diameter distributions, respectively.

A method to incorporate diffusional broadening in Equations (1[1] )–(6[6] ) is described in the online supplemental information (SI), and its effects for the experiments described below are tabulated. In practice, neglecting diffusion leads to sufficiently accurate results provided that the DMA voltages exceed about 4 kV.

As mentioned above, these results were derived assuming the triangular (or trapezoidal) DMA transfer function described by Knutson and Whitby (1975), which applies to a fixed DMA voltage. However, in most cases, as was done here, the measurements are obtained by scanning the DMA2 voltage exponentially, as is done with the SMPS. Collins et al. (2004) and others have shown that scanning distorts the transfer function, and this affects measurements of number concentration, mean mobility, and DMA resolution or variance. Errors caused by scanning are determined by the value of the non-dimensional parameter, , the ratio of the mean gas residence time in the classifier to the time constant for the exponential voltage scan rate. For , and , the effects of scanning on and are negligible (well less than 1%) relative to other sources of uncertainty while and are increased by about 2% of or (see Figs. 9, 10, and 5 of Collins et al. 2004). This corresponds to an increase in of about 0.01 which is seen to be within the run-to-run variability of the data presented below. Thus, represents a reasonable upper limit for the SMPS scan rate for this performance test. Scanning errors depend on the flow ratio so the limit for may need to be adjusted for significantly different flow ratios (see Figure 14 of Collins et al. 2004). To minimize and errors due to scanning, we recommend scanning slowly over a narrow range of voltages.

SMPS performance testing

As shown in Figure 1, the test equipment includes a stable aerosol source such as an atomizer with dryer and neutralizer, a differential mobility analyzer (DMA1) followed by a Condensation Particle Counter (CPC1) and the SMPS to be tested in parallel.³ DMA1 and CPC1 are used as transfer standards and need to be well-characterized in terms of efficiency and near ideal performance for the DMA1 resolution. The SMPS system consists of a charger/neutralizer followed by DMA2 and CPC2. For this test, the SMPS charger must be bypassed, or a dummy charger substituted in its place, and a charge fraction of 1 used in the SMPS data analysis.

The parallel simultaneous measurements by CPC1 and the SMPS as shown in Figure 1 are ideal for dealing with a varying concentration from a potentially unstable aerosol generator. By using ratios of raw SMPS data to raw CPC1 readings before applying the standard SMPS analysis, the effects of the variations in the aerosol source can be largely canceled out. However, the addition of makeup flow to an aerosol stream followed by a flow split, as indicated in Figure 1, can often be problematic, leading to unequal concentrations in the two flow splits. An alternative approach is to make alternating sequential measurements with CPC1 and the SMPS. If the aerosol generation is sufficiently stable, this approach is much simpler to execute.

It is important to note that in the case where diffusional broadening of the DMA transfer function and diffusional transport and detection losses are negligible, the fraction of multiply charged particles coming from the upstream DMA has no effect on the results. All particle sizes have the same electrical mobility, experience exactly the same transfer functions in traversing each DMA and are counted in the detectors with maximum efficiency. Under these conditions no correction is needed for multiply charged particles.

Such a system following both the parallel and sequential procedures was used to test a TSI Model 3080 SMPS system with a Model 3081 DMA followed by a Model 3772 CPC. Identical equipment was used for the upstream components in Figure 1. This CPC has a nominal sample flow of 1.0 L/min and both DMAs were operated with nominal flows of 10 L/min sheath and 1.0 L/min aerosol (= 0.00167). All flows were calibrated directly with a Gilian Gilibrator II bubble flowmeter. TSI AIM software (Ver. 9) was used to recover the SMPS data as well as record the CPC1 concentrations.

Measurements were made at two calibration sizes, 168 and 215 nm, corresponding to DMA1 classifier voltages of 4 and 6 kV, respectively. The atomizer produced a distribution with peak around 46 nm and geometric standard deviation of about 2.0. The CPC2 detection efficiency relative to CPC1 after correction for actual calibrated flows was measured to be 0.996, well within the margin of flow calibration uncertainties. SMPS scan (and CPC1 averaging) times of 5 and 2 min were used, corresponding to values of about 0.006 and 0.016, respectively. Each combination of experimental parameters was run 2 to 4 consecutive times. After our initial measurements, which revealed degraded DMA resolution, the DMAs were cleaned prior to completing instrument performance assessments.

The ranges of errors in the recovered values for and are shown in Table 1. The error in is based on comparison to the concentration measured by CPC1. Note that SMPS total concentrations were typically within 5% of those measured by CPC1, although there was one outlier of 9.4% for the sequential measurements. Neither the AIM diffusion correction nor any other adjustment was made to account for diffusion losses in the SMPS plumbing. These are expected to be minimal, resulting in only a slight bias in the reported errors in the recovered total number. The error in is based on comparison to the centroid diameter of DMA1, . The table uses the recovered geometric mean diameter, but the arithmetic mean differs by less than 0.1%. The errors in recovered diameter are all less than 2%, within the uncertainty range of the flows. Based on these measurements we conclude that this SMPS measured concentration and size with accuracies of about 5% and 2%, respectively.

To determine DMA2 resolution, the SMPS-reported values of the geometric standard deviation in diameter space, , were plugged into Equation (7[7] ) and the results of that into Equation (6[6] ) to obtain values for and as shown in Table 1. Criteria for acceptable performance suggested by Stolzenburg (2018) are or .⁴ Before cleaning the DMAs these criteria were not met. After cleaning, these criteria were met for all measurements but one outlier in the sequential data set. During cleaning, evidence of asymmetrical particle deposits in the flow straightener near the exit to the classifying tube was observed. As there was no visible evidence of significant aerosol deposition elsewhere, we believe those deposits led to the degraded values of and that were initially observed.

In order to measure the DMA resolution, data must be recorded with adequate resolution. SMPS programs often report size distribution data and calculate integral parameters based on data size resolution (e.g., 64 channels per decade) significantly less than the original raw data resolution. As is demonstrated in Table S1 (see the SI), sufficiently accurate values of and are recovered for a data resolution of 64 channels per decade. However, a resolution of at least 512 channels per decade, or 36 channels across the width of the peak, was needed to obtain accurate values of and .

The quality assurance program of Wiedensohler et al. (2018) specifies target criteria of acceptable performance as accuracy for total number on a direct CPC comparison and for SMPS diameter compared to a PSL standard. As we are bypassing the charger and the uncertainty of charge fractions, this same number standard might reasonably be applied to here as long as diffusion and detection losses are negligible. The same size standard could similarly be adopted for here. As noted above, Stolzenburg (2018) has suggested or as criteria for acceptable DMA resolution performance. Though all these criteria were readily met here under laboratory conditions, only experience will determine if the same criteria can be reasonably maintained under field conditions.

Supplemental material

The theory is generalized to account for the effects of diffusional broadening, and a suggested step-by-step experimental procedure is described. The need to analyze data that were recorded with sufficiently high resolution for accurate recovery of DMA sizing resolution is also discussed.

Additional information

Funding

This work was supported by the US Department of Energy's Atmospheric System Research program, an Office of Science, Office of Biological and Environmental Research, under grant number DE-SC0011780.

Notes

¹ It is common practice to characterize sharply peaked distributions using the mode and resolution. These parameters are nominally based on just three isolated points of the distribution. Moments, as integrals over all the data in the form of mean and standard deviation, are more amenable to mathematical manipulation as in Stolzenburg and McMurry (2017) and also far more robust in rejecting measurement noise.

² Our analysis assumes that the aerosol entering DMA1 has a broad size distribution (e.g., an atomized NaCl solution). Our method could also be applied to polystyrene latex spheres (PSL), for example, although DMA1 would still be required to remove atomized residue particles. Sharply peaked PSL distributions would penetrate through DMA1 with nearly 100% efficiency at the peak voltage. The first term on the right side of Equation (5[5] ) would then be replaced by the relative variance of the PSL (or, ideally, the variance of the product of the DMA1 transfer function and the PSL mobility distribution). For a perfectly monomobile aerosol, the first term would equal zero.

³ Our method would work equally well if electrometers were used as detectors, provided, of course, that concentrations are sufficient to ensure adequate measurement accuracy. However, because multiple charging would lead to an unknown relationship between particle number concentration and electrical current, the use of one CPC and one electrometer would lead to errors.

⁴ The work of Stolzenburg (2018) indicates a small bias (∼−7%) in the conversion of a fitted f_β to σ_distor using Equation (6[6] ) compared to a direct fit of σ_distor. Applying these results to the reverse conversion as used here, the bias in the calculated values of (f_β−1) of Table 1 is estimated to be on the order of +15% relative to values from direct fits to the scan data.