# Size resolution of the Airmodus A10 particle size magnifier with purified clusters

Juan Fernandez de la Mora, Juha Kangasluoma, Michel Attoui

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Juan Fernandez de la Mora, Juha Kangasluoma, Michel Attoui. Size resolution of the Airmodus A10 particle size magnifier with purified clusters. Journal of Aerosol Science, 2022, 160, pp.105916. 10.1016/j.jaerosci.2021.105916. hal-04379591

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# 1. Introduction.

Condensation particle counters (CPCs) are widely used as detectors for aerosol particles due to their ability to sense individual particles, by turning them into visible drops via condensation of a supersaturated vapor. Whether or not a small particle is activated (grown to larger sizes) by the CPC depends steeply on the vapor concentration and temperature distribution in the CPC, characterized, for instance, by the maximal saturation ratio $S_{max}$ within the instrument. Therefore, by scanning over $S_{max}$, a cumulative size distribution may be obtained. This approach has been demonstrated primarily with turbulent mixing CPCs (Gamero-Castaño et al., 2000, 2002; Figure 7 of Vanhanen et al., 2011), but also with thermally diffusive CPCs (Wiedensohler et al. 1994; Gallar et al. 2006; Liu et al., 2021; Kuldinow et al. 2021), and is a subject of considerable current interest.

A key issue in condensation-sizing is the size resolution achievable, determined by the steepness of the dependence $P(S_{max}, d_p)$ of the activation probability on $S_{max}$ and the particle diameter $d_p$. Based on classical heterogeneous nucleation predictions, as well as on a few available experiments, this potential resolution appears to be quite high (Fernandez de la Mora, 2011). However, in practice, the actual resolution is often limited by the finite range of maximum $S$ values encountered by particles in most CPCs; and the measured resolution is further limited by lack of uniformity in size, shape and chemical composition of the seed particles used. The first problem is not easy to avoid in most CPCs, except in specialized facilities relying on the impulsive adiabatic expansion of a gas (Tauber et al. 2018). The second problem has been overcome by certain aerosol generation techniques such as electrospray (Fenn et al., 1989) of salt clusters with charge reduction followed by high resolution mobility classification (Gamero-Castaño et al., 2000, 2002, Winkler et al. 2012, Tauber et al. 2018). Comparison of activation curves obtained with such purified seeds with those mobility-selected at high resolution from more conventional aerosol sources (such as heated wires), confirms that purified electrosprayed clusters produce considerably steeper activation curves (Fernandez de la Mora, 2011). It would accordingly seem that a systematic study of the activation characteristics of existing CPCs with purified cluster seeds would provide a faithful indicator of their potential sizing resolution.

Along these lines, Liu et al. (2021) have probed the response of KanomaxFMT’s commercial Fast CPC Model 3650 to several particles in the size range down to 1.5 nm. Their seed particles were all classified at high resolution by a Half-Mini DMA (Fernandez de la Mora, 2017), and included small Tetraheptylammonium Bromide (THA-Br) clusters, polyethylene glycol and the product from the evaporation of a nichrome wire in air. They report relatively steep activation curves $P(d_p)$ as a function of particle diameter $d_p$. In terms of the width parameter

$$ \Delta d_p = P_{max}/(dP/\Delta d_p)_{max}, \qquad (1) $$

we infer from their data $\Delta d_p$ values as small as 1.4 nm for 4.3 nm particles and 2.2 nm for 2.5 nm particles, both generated by a NiCr wire heated in air. The corresponding value with tetraheptylammonium cluster cations is 0.96 nm with 1.8 nm particles. We have recently extended the study of Liu et al. (2020) with KanomaxFMT’s fast CPC using a wider range of THA-Br clusters. We found $\Delta d_p$ values as small as 0.35 nm by increasing the fraction of CPC sheath gas used from 50% to 96% (Kuldinow et al. 2022). Recently, Brilke et al. (2020) have evaluated three commercial CPCs relying on DMA-purified singly charged cluster anions and cations of THA-Br and tetrabutylammonium iodide (TBA-I) produced by a bipolar electrospray source. They provide four activation curves for each CPC in the form $P(d_p)$, obtained from the positive and negative cluster ions of their two salts. Corresponding $\Delta d_p$ values have been collected in Table 2 of Kuldinow et al. (2022), and are re-elaborated and expanded in our Table 1. Table 1 includes also
one $\Delta d_p$ value from the 5 values inferred by Kuldinow et al. (2022) from Figure 2 of Keshavarz et al (2020) for the A10 particle size magnifier (PSM) tested with cluster anions of the ionic liquid 1-Ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (EMI-Im). This PSM is a particular kind of CPC relying on turbulent mixing of a cold aerosol flow and a hot flow saturated with diethylene glycol vapor. Note that the $d_p$ and $\Delta d_p$ values reproduced in Table 1 for EMI-Im were based by Kuldinow et al. (2022) on the standard collision cross section, which assumes elastic collisions, uses a reference temperature of 0 °C, and uses the effective binary collision mass rather than the mass of the gas molecule. These diameters therefore differ from the more commonly used mobility diameters (Friedlander, 1977) with which these and other related data will be reanalyzed below. Kuldinow et al. (2022) have compared the data of Brilke et al. (2020) included in Table 1 for the A10 PSM with a variety of other data, including those of Keshavarz (2020). They conclude that the values from Brilke et al. (2020) cannot be representative of the best resolving power of the A10.

<table><caption>Table 1: Size resolution parameters for the A10 PSM inferred by Kuldinow et al (2022) from various sources. $d_p$ is the particle diameter at $P=0.5$, $\Delta d_p$ is defined in (1).</caption><thead><tr><th></th><th>d<sub>p</sub> (nm)</th><th>Δd<sub>p</sub> (nm)</th><th>Δd<sub>p</sub>/d<sub>p</sub></th></tr></thead><tbody><tr><td>THA-Br<sup>+a</sup></td><td>1.67</td><td>0.62</td><td>0.371</td></tr><tr><td>THA-Br<sup>-a</sup></td><td>1.55</td><td>0.655</td><td>0.423</td></tr><tr><td>TBA<sup>+a</sup></td><td>1.3</td><td>0.5</td><td>0.385</td></tr><tr><td>TBA-I<sup>-a</sup></td><td>1.5</td><td>0.4</td><td>0.267</td></tr><tr><td>EMI-Im<sup>-b</sup></td><td>1.80</td><td>0.205</td><td>0.114</td></tr></tbody></table>

<sup>a</sup> From Table 2 of Kuldinow et al (2022) based on measurements from Brilke et al. (2020). <sup>b</sup> From Figure 7 of Kuldinow et al (2022) drawn from data of Keshavarz et al. (2020) with EMI-Im cluster anions, with $d_p$ and $\Delta d_p$ based on standard collision cross sections rather than the mobility diameter.

In order to resolve this discrepancy, here we collect data from a more extensive evaluation of the A10 PSM carried out with salt clusters during a campaign at Yale in September 2018. These data were originally intended to generate basic heterogeneous nucleation information, which required reliable calculations of temperatures and vapor concentrations within the PSM. However, given the instrument's relatively complex geometry and flow field, we were unable to complete these calculations satisfactorily. As a result, except for Figure 2 in Keshavarz et al. (2020), this information had remained unpublished and is presented here for the first time.

<table><caption>Table 2: List of the salts [$C^+A^-$] (and their abbreviations) used to generate clusters</caption><tr><td>1-Ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide</td><td>EMI-Im</td></tr><tr><td>1-Ethyl-3-methylimidazolium tris(pentafluoroethyl)trifluorophosphate</td><td>EMI-FAP</td></tr><tr><td>Vinilenebis(triphenylphosphonium) Bromide</td><td>Vinilene</td></tr></table>

## 2. Experimental

The experimental approach has been described in detail by Keshavarz et al. (2020). Briefly, two identical solutions of methanol with approximately 1 mM of dissolved salt [$C^+A^-$] are electrosprayed from two confronted pulled silica capillary tips held one at positive and the other at negative polarity. Recombination between originally multiply charged cluster anions and cations
results primarily in a mixture of neutral and singly charged clusters $(C^{+}_{n \pm 1}A^{-}_{n})^{\pm 1}$ of both polarities (Fernandez de la Mora and Barrios, 2017). A list of the salts used is included in Table 2 with their abbreviations. One of these cluster anions or cations is selected in a Half-Mini-p differential mobility analyzer (DMA) with a resolving power greater than 40 (Fernandez de la Mora 2017).

<figure><img src="image_2.png" /><figcaption>Figure 1: Representative size spectrum of EMI-FAP in positive polarity showing well resolved peaks of $(\text{EMI}^{+}_{n}\text{FAP}^{-}_{n-1})^{+1}$, corresponding from left to right to $n=1,2,3,\dots$.</figcaption></figure>

A representative size spectrum obtained for cluster cations of the salt EMI-FAP is given in Figure 1, showing that relatively pure clusters can be isolated up to $n=10$, with some impurity levels of neighboring clusters present in the classified aerosol at larger $n$. The horizontal scale in the original mobility spectrum is based on the mobility of the $\text{EMI}^{+}$ ion (appearing at 0.98 nm in Figure 1), given by Larriba et al. (2011) as 2.083 cm$^2$/V/s. Mobilities at the small sizes involved here are converted into mobility diameters via the free molecule limit of Millikan's law: $d_p=(2.02/Z)^{1/2}$, with $Z$ in cm$^2$/V/s and $d_p$ in nm. The classified aerosol is then split into two streams. One, going through an electrometer (Fernandez de la Mora et al. 2017), is used to determine cluster concentration. The other is introduced in the A10-PSM to determine the concentration of activated particles. The activation probability is usually defined as the ratio of these two concentrations, sometimes with corrections for possible differences in diffusive losses in both instruments. Here, given the typically large losses of our small clusters at the entrance of both detectors, we have alternatively assumed that the activation probability reaches unity at the highest PSM saturated vapor flow rate, and normalize the data so that the activation probability is unity at the highest flow rate. While this normalization is often objectionable in CPC studies, it is justifiable in our case by the well-defined horizontal asymptote obtained in most of our data. This is shown in Figures 2a and 2c for EMI-FAP and EMI-Im, and applies similarly to all data taken. The largest particles lack a well-defined upper asymptote, and are subject to a greater indeterminacy. Nevertheless, this circumstance has no effect on our conclusions, as the largest resolutions reported do not correspond to the largest particles. The variable $S_{\text{max}}$ measurements are carried out by scanning over the ratio of the two flow rates used by the CPC: the saturated vapor flow rate $Q_{\text{sat}}$ varies typically between 0.05 and 1.3 L/min, while the classified aerosol flow rate is held constant at $Q_{\text{aer}}=2.5$ L/min.

The CPC has two controllable temperatures corresponding to the saturator $T_s$ and the growth tube $T_g$. These were used only in two different settings referred to as *high* ($T_s=82$ °C and $T_g= 2$ °C) and *low* ($T_s=70$ °C and $T_g= 2$ °C). Figure 2a shows a representative saturation scan in the form of activation probability versus $Q_{\text{sat}}$. Each line corresponds to a different cluster anion of EMI-FAP, with associated mobility diameters $d_p$ (nm) shown in the caption. These diameters are inferred
from the mobilities by use of Millikan's drag law (Friedlander 1977), without any corrections for
polarization or for the finite size of the air molecules.

<figure><img src="image_3.png" /></figure>

Figure 2: Activation probability data $P(Q_{sat}, d_p)$ for clusters anions (a,b) and cations (c, d) of EMI-FAP. They are represented either versus saturator flow rate $Q_{sat}$ (left) with $d_p$ as a parameter, or versus mobility diameter (right) with $Q_{sat}$ as a parameter. The legends shows either the fixed mobility diameters $d_p$ in nm (a,c) or the fixed $Q_{sat}(L/min)$ (b,d). T_s=70 °C. (d) includes *Error Function* fittings (gray) to the five data sets exhibiting a complete transition with a single step. The corresponding $Q_{sat}$ are, from right to left, 0.2, 0.3, 0.4,...,1,1, 1.2, 1.3 Lit/min

Activation curves such as those shown in Figure 2 (a) and (c) have originally a large number of
pairs ($P, Q_{sat}$) for each particle diameter. These curves are not directly useful for our purposes due
to the difficulty in converting the CPC condenser and saturator temperatures and variable $Q_{sat}$ into
theoretically relevant quantities such as temperature and vapor concentration profiles within the
CPC. For this reason, we have selected a number of discrete $Q_{sat}$ values and formed a matrix of
$P(d_p, Q_{sat})$ values. Only the data in this matrix are shown in Figures 2 (a) and (c) and other similar
data sets reported in this article. These same data can alternatively be represented with $Q_{sat}$ as a
parameter, and $d_p$ as the independent variable, as shown in Figure 2 (b) and (d). These curves
provide directly the sizing characteristics of the CPC at various CPC settings, without the need for
any theoretical interpretation (other than the Millikan law to convert mobility into size). The
method used here to determine the size resolution variable $\Delta d_p$ defined in Equation (1) is to
compute the discrete slopes defined in $P(d_p)$ curves based on two neighboring particle diameters,
and selecting from the various slopes the largest one for each CPC setting. $P_{max}$ is taken in all cases
to be unity. In order to quantify the error involved in this discrete slope determination we have
alternatively computed $\Delta d_p/d_p$ by fitting the data for EMI-FAP⁺ to curves of the form $1/2\{1+\text{Erf}[a(x-d_p)]\}$ (Figure 2d), and determined $\Delta d_p/d_p$ as $\pi^{1/2}/(a d_p)$. Figure 3 collects the corresponding data
obtained for cluster cations of EMI-FAP by this fitting method (open circles) as well as from the maximum discrete slopes formed by adjacent data points (Filled circles). The fitting method facilitates inferring activation curve widths at more mean particle diameters, but the results of both approaches are quite similar. From this comparison we conclude that the error involved in activation curve width determination is at most 10%. One can also see in Figure 3 that the variation of $\Delta d_p/d_p$ with cluster diameter is relatively modest, though with a clear tendency for the largest particles to have relatively wider structures.

<figure><img src="image_4.png" /><figcaption>Figure 3: Widths of the activation curves for EMI-FAP cations obtained from either the maximum discrete slopes formed by adjacent data points (Filled circles) or by fitting to an error function (open circles). The horizontal variable is the particle diameter at the middle point of the activation curve ($P=0.5$).</figcaption></figure>

### 3. Results and Discussion

The structure of the $P(d_p)$ curves seen in Figures 2 (b) and (d) is peculiar on its left end, in that the minimal activation probability achieved does not drop to zero at $Q_{sat}$ values above approximately 0.6 L/min, not even for the smallest particles. This means that, for that particular low setting of instrument temperatures, the ability to discriminate the smallest particles deteriorates quickly below about 2.8 nm. Classical ion nucleation theory has that same qualitative feature, because small ions solvate and acquire a solvated size independent of the bare ion size. Ions smaller than this equilibrium solvation size therefore theoretically behave all identically. In view of this effect, CPC settings producing $P(d_p)$ curves not decaying to $P$ near zero at small sizes are poorly suited for high resolution sizing, and will not be used to infer $\Delta d_p$ values. Nor will we use activation curves for which the maximal $P$ achieved is below 30-40%, as in this case there is no assurance that the inflexion point is included in the curve. Figure 2d differs slightly from Figure 2b in that there is a finite second step to the left of the main step, which appears to also tend to zero on its left end. It may perhaps be due to a change in flow conditions above a certain $Q_{sat}$, such that two flow regions with different maximal saturation ratios are present, each resulting in a different step for each given particle. Activation curves exhibiting this double step will not be used either for the determination of $\Delta d_p$.

Activation curves similar to those shown in Figure 2 for EMI-FAP have been obtained for EMI-Im and Vinilene (not shown). $\Delta d_p$ values and corresponding $d_p$ values at which $dP/dd_p$ is maximal are collected in Table 3 for EMI-FAP and EMI-Im clusters of both polarities, and for singly charged Vinilene anions. The Table shows also the dimensionless inverse measure of resolution $\Delta d_p/d_p$. One can see that $\Delta d_p$ reaches values as small as 0.21 nm. This is about half the smallest and 1/3 the largest value inferred in Table 1 from Brilke et al. (2020), confirming that the width of
the activation curves of Brilke et al. are not representative of the actual performance of the A10 PSM. Whether the differences between our results and those of Brilke et al. are due to the use of different salts or to some other reasons is unclear. One possibility is that their instrument may not have been operating optimally, perhaps due to accumulation of residue material in the mixing piece.

The widths collected in Table 3 are also moderately smaller than those reported in Table 1 for KanomaxFMT's fast CPC.

<table><caption>Table 3: Width characteristics of activation curves obtained for the A10 PSM. $\Delta d_p$ is defined in (1). $d_p$ is the mobility diameter at the inflection point of the activation curve.</caption><tbody><tr><td rowspan="3">EMI-Im<sup>-</sup><br>T<sub>sat</sub>=70 °C</td><td>Δd<sub>p</sub> (nm)</td><td>0.29</td><td>0.291</td><td>0.285</td><td>0.234</td><td>0.217</td><td>0.238</td></tr><tr><td>d<sub>p</sub> (nm)</td><td>2.53</td><td>2.45</td><td>2.31</td><td>2.26</td><td>2.21</td><td>2.21</td></tr><tr><td>Δd<sub>p</sub>/d<sub>p</sub></td><td>0.115</td><td>0.119</td><td>0.123</td><td>0.104</td><td>0.098</td><td>0.108</td></tr><tr><td rowspan="3">EMI-FAP<sup>+</sup><br>T<sub>sat</sub>=70 °C</td><td>Δd<sub>p</sub> (nm)</td><td>0.364</td><td>0.278</td><td>0.309</td><td>0.303</td><td>0.289</td><td>0.257</td></tr><tr><td>d<sub>p</sub> (nm)</td><td>3.14</td><td>3.03</td><td>2.93</td><td>2.82</td><td>2.82</td><td>2.72</td></tr><tr><td>Δd<sub>p</sub>/d<sub>p</sub></td><td>0.116</td><td>0.092</td><td>0.105</td><td>0.107</td><td>0.102</td><td>0.094</td></tr><tr><td rowspan="3">Vinilene<sup>-a</sup><br>T<sub>sat</sub>=70 °C</td><td>Δd<sub>p</sub> (nm)</td><td>0.249</td><td>0.184</td><td>0.217</td><td>0.277</td><td></td><td></td></tr><tr><td>d<sub>p</sub> (nm)</td><td>2.145</td><td>2.02</td><td>2.08</td><td>1.92</td><td></td><td></td></tr><tr><td>Δd<sub>p</sub>/d<sub>p</sub></td><td>0.116</td><td>0.091</td><td>0.104</td><td>0.144</td><td></td><td></td></tr><tr><td rowspan="3">EMI-Im<sup>+</sup><br>T<sub>sat</sub>=82 °C</td><td>Δd<sub>p</sub> (nm)</td><td>0.294</td><td>0.319</td><td>0.239</td><td>0.327</td><td></td><td></td></tr><tr><td>d<sub>p</sub> (nm)</td><td>1.63</td><td>1.63</td><td>1.50</td><td>1.36</td><td></td><td></td></tr><tr><td>Δd<sub>p</sub>/d<sub>p</sub></td><td>0.180</td><td>0.196</td><td>0.159</td><td>0.240</td><td></td><td></td></tr><tr><td rowspan="3">EMI-FAP<sup>-</sup><br>T<sub>sat</sub>=70 °C</td><td>Δd<sub>p</sub> (nm)</td><td>0.224</td><td>0.213</td><td>0.207</td><td></td><td></td><td></td></tr><tr><td>d<sub>p</sub> (nm)</td><td>3.07</td><td>2.886</td><td>2.886</td><td></td><td></td><td></td></tr><tr><td>Δd<sub>p</sub>/d<sub>p</sub></td><td>0.073</td><td>0.074</td><td>0.072</td><td></td><td></td><td></td></tr></tbody></table>

## 4. Conclusions

We have used pre-existing data on mobility-selected clusters to evaluate the resolving power of the Airmodus A10. We find activation curves between two and three times steeper than previously inferred from the data of Brilke et al. (2020). Although these differences may be due to the different salts or the different PSM prototypes used in both studies, it is nevertheless useful to know the resolving power that may achieved in this instrument under favorable conditions. Our study also confirms that activation curves obtained with essentially monodisperse mobility-selected clusters tend to be steeper than those derived from heated wires.

**Acknowledgments:** This work has been partly funded through AFOSR grant FA9550-18-1-0165, University of Helsinki three year grant (75284132) and Academy of Finland project grant (1325656).

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