the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 04 Aug 2026
Measurement-Model Closure of Sub-20 nm Particle Charge Fractions under Varying Trace Gas Composition
Abstract. The sizing of aerosol particles is commonly carried out by electrical techniques, requiring particles to reach a known charge distribution prior to measurement. This is typically achieved by passing the particles through bipolar diffusion chargers, where the resulting steady-state particle charge distribution depends on the properties of the ions therein. We present new measurements of the charge fractions of sub-20 nm particles after bipolar diffusion charging, along with measurements characterizing the properties of ions generated within the bipolar charger. Our results show that, under steady-state conditions, the particle charge distribution is primarily determined by charger ion properties, which can be influenced even by trace gas contamination. Specifically, the use of commonly employed conductive silicone tubing, which emits trace concentrations of volatile methyl siloxanes (VMS), changes the mean positive ion mobility by 20 %, leading to deviations of up to 25 % in the fraction of singly charged particles relative to measurements without the tubing. We further show that the use of conductive silicone tubing stabilizes the mean positive ion mobility to 1.05 ± 0.1 cm2 V−1 s−1associated with VMS. The mobility of the negative ions, on the other hand, remains highly dependent on gas composition. Building on the finding that positive ion properties can be readily stabilized to repeatable values, we show that negative ion properties can be approximated through a simple bipolar Mobility Particle Size Spectrometers (MPSS) measurement. Our measurements show good agreement with charge fractions predicted by Hoppel & Frick theory, with relative differences of up to −6.1 % and 0.6 % for positive and negative charge fractions, respectively, supporting the validity of classical charging theory for sub-20 nm particles. In contrast, significant deviations from the commonly used Wiedensohler (1988) approximation highlight the importance of accounting for environment-specific ion properties when predicting particle charge distributions.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Aerosol Research.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.- Preprint
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Status: final response (author comments only)
- RC1: 'Comment on ar-2026-29', Christof Asbach, 13 Sep 2026
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RC2: 'Comment on ar-2026-29', Anonymous Referee #2, 02 Oct 2026
Novelty of the research is rather low - prior works have already addressed the key questions being probed.
Experimental methods to quantify ion mobility using a half-mini DMA and using a mass-mobility correlation from 1971 is not arguably more accurate than resolving mass and mobility seperately. Using a DMA-MS to resolve the mobility and mass has been shown before, for example, in Gopalakrishnan et al. 2015 and Maiser et al. 2015. Authors are effectively mis-representing these two studies by saying they fit the ion mobility parameters to fit theory. I request them to kindly read the cited papers before lumping them with such sweeping statements.
Many studies since Gopalakrishnan et al. 2015 have shown that an ion population is carrier-gas composition and tubing material dependent; the novelty of the current work has been considered before. That decreases enthusiasm to recommend publication. Authors are still using a single mobility value to represent a population, without considering mass-mobility distributions. In some ways, this paper has been written a decade or two ago in time - it considers Hoppel and Frick , Weidensohler, but ignores every other contribution in the last two decades (for example, their choice of charging theories indicate that they have not considered the works of Richard Flagan (2013) or Li et al. (2020).
The use of Kilpatrick (1971) correlation to calculate mass from measured mobility is scientifically dubious. Kilpatrick was a correlation for atmospheric ions. It does not represent any causal relationship between mass and mobility of ions formed in other contexts. Authors have not provided any justification why its valid here. This is neither a new practice nor a justified one. To call this an advance is going backwards after understanding that it is correlation, not causation.
Fuchs/Hoppel and Frick theories have been pointed out to have issues in accuracy at small particle sizes that are of interest in this paper (see papers by Chris Hogan's group discussing the faulty assumptions of the flux-matching theory). Authors may or may not agree with those concerns but they do not provide any nuanced discussion of the theories used, just stating steps to compute from those theories is not adding much value.
The obtained decent agreement with simulation predictions is not a particularly strong indicator of the way ion properties are approximated - it is because, the bipolar diffusion charging process is weakly sensitive to mobility. It can be seen that to predict the neutral fraction, the theories have four degrees of freedom - ion mass and mobility for positive and negative ions - while using a mass-mobility correlation, the use of any reasonable ion mobility around 1-1.5 cm^2/s will result in a charge distribution within ~10-15%. The theories and ion mass inference chosen in this work do not provide any new insights than what has been already known from detailed mass-mobility studies.
I do not recommend publication before major revisions are made to address above concerns. The paper does not present anything that is not already known & more importantly, may be misrepresenting prior work on detailed ion population characterization to enhance their appeal. The manuscript presents an outdated approach, and a literature review that selectively ignores the developments of the last two decades to leapfrog theirs. I strongly oppose publication in the current form.
Citation: https://doi.org/10.5194/ar-2026-29-RC2
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The manuscript describes the measurement and modeling of the positively and negatively charged fraction of sub-20 nm particles in charge equilibrium in air under the influence of different trace gases. The authors studied the effect of volatile methyl siloxanes, water vapour and ethanol and found that even very low trace concentrations of these gases can have a significant influence on the ion mobility and thus the particle charge distribution. The results are of high relevance for MPSS (SMPS) measurements that rely on the knowledge of the equilibrium bipolar charge distribution of aerosol particles after they passed a bipolar charge conditioner (neutralizer). Commonly, an approximation of the charge distribution by Wiedensohler (1988) is assumed in the data deconvolution. This approximation is also included in ISO 15900 as a convention and is based on single values for the positive and negative ion mobility. The author s found that the mean ion mobilities assumed by Wiedensohler and in the convention could only approximately be reproduced by adding low concentrations of ethanol to the aerosol, whereas in all other cases, the differences in the mobilities and resulting charge fractions were significant (up to 65.1% for positive and -38.1% for negative charge fractions, respectively). In light of the new air quality directive of the EU, published in late 2024, and its obligation for all member states to measure ultrafine particle number concentrations and number size distributions, the results are of high importance to the field of atmospheric UFP monitoring. This will require a better understanding of the measurement uncertainties of MPSS measurements in the future.
The paper is very well written and merits publication. I only have a few minor comments that I suggest the authors to consider in a revision:
General:
Is there a reason, why some of the figures use a common landscape format, whereas others (Figs. 4 c&d, 5b, 6b) are in a very narrow portrait format?
What is the effect of the level of the VMS concentration on the eventual charge distribution? Is there an influence of temperature and age of the silicone tube, which both may influence the degassing of VMS?
Specific:
Line 105: You mention that for sub-20 nm particles, the fraction of doubly or higher charged particles is negligible. Could you provide an estimate of the error made by this assumption or at least provide estimates for the fraction of singly and doubly charged particles at 20 nm, e.g. from the Wiedensohler approximation?
Line 125, equation (6): What is i in the equation? Is ε the dielectric constant of the particle or air?
Line 210, Figure 1: Why does the number concentration, measured by the CPC, drop to 0 at an ESP voltage of 10 V (in the inlay on the very right of the figure)?
Line 451ff, section 4.3.1: Were these measurements carried out with or without silicone tubing? Considering that the results with the addition of ethanol agree best with the model and the widely used approximation, would it be worthwhile to consider adding ethanol as a dopant to the aerosol in MPSS measurement in order to get good agreement with the commonly used approximation and to increase the comparability among devices with different polarities?