Scanning DMA Data Analysis I. Classification Transfer Function

The scanning electrical mobility spectrometer (SEMS; also known as the scanning mobility particle sizer, SMPS) enables rapid particle size distribution measurements with a differential mobility analyzer (DMA)/condensation particle counter (CPC) combination by ramping the classifier voltage, and continuously counting particles into time bins throughout the scan. Inversion of scanning measurements poses a challenge due to the finite time response of the CPC; the distorted data can be deconvoluted to improve the fidelity of size distributions obtained with the SEMS/SMPS. Idealized models of the classification region have shown that, for rapid voltage scans that approach the particle residence time in the DMA, the nondiffusive transfer function deviates from the symmetric one seen at constant voltage. Nonetheless, most SEMS/SMPS data analyses employ the constant voltage transfer function, a result that is valid only for plug flow in the classification region. This article develops the scanning-mode transfer function for the actual geometry of the TSI Model 3081 DMA. Finite element calculations are used to determine the flow and electric fields through the entire DMA. The instantaneous scanning-DMA transfer function for diffusive particles is determined using Brownian dynamics simulations. Comparisons of the results from this simulation of a real instrument to those from the idealized models reveal the shortcomings of prior models in describing the instantaneous scanning-DMA transfer function. A companion paper (Part II) combines this scanning-mode transfer function with response functions for the other components of a SEMS/SMPS measurement system in order to derive the response function for the integrated measurement system.

Copyright © 2018 American Association for Aerosol Research     

Fast Mixing Condensation Nucleus Counter: Application to Rapid Scanning Differential Mobility Analyzer Measurements

Condensation nucleus counters (CNCs) exhibit slower time response than expected due to mixing effects within the detector.This mixing produces an exponential distribution of delay times with a characteristic mixing time m that ranges from 0.1 s to 0.9 s for commonly used instruments and limits their usefulness for measuring rapidly changing aerosols. Moreover, when used as detectors in the scanning electrical mobility spectrometer (SEMS; also known as scanning mobility particle sizer, SMPS), CNCs limit the speed with which size distribution measurements can be made. In order to overcome this limitation, a new, fast-response mixing CNC (MCNC) has been developed and characterized. The time response of this new detector and TSI Models 3025 and 3010 CNCs has been measured using a spark source to generate an aerosol pulse. The mixing induced response smearing of this new detector, m , of this instrument is 0.058 s, which is significantly shorter than either of the other instruments tested. Its lower detection limit is about 5 nm diameter. The high aerosol flow rate of the MCNC (0.65 l min -1 ), fast time response, and low detection limit make it an ideal detector for SEMS/SMPS measurements. Using this MCNC as a detector for the SEMS, size distribution measurements over the 5 nm to 140 nm range have been made in 3 s with minimal distortion. The size distribution of a coagulation aerosol was effectively recovered by deconvolution with scans as short as 1 s. Uncertainties in the 1 s scans result, in part, from electronics problems in the scanning DMA.     

Diffusional transfer function for the scanning electrical mobility spectrometer (SEMS)

Abstract

The scanning electrical mobility spectrometer (SEMS), or scanning mobility particle sizer (SMPS), uses the differential mobility analyzer (DMA) operated in scanning mode to measure particle size distribution rapidly. To obtain the actual size distribution, the real-time transfer function (transmission efficiency of particles of different mobilities) is necessary, which has previously been investigated with numerical simulations or semi-analytical calculations. We present here a rigorous derivation of the diffusional DMA transfer function for an increasing-voltage scan based on analytically resolving particle trajectories between the instrument inlet and the outlet. This requires a 2D integration in the inlet and outlet space over the contour plot of the particle mobility distribution that can successfully transmit through the scanning DMA. For the first time, we show that the up-scan DMA transfer function for non-diffusive particles is trapezoidal (instead of triangular). The key parameter that determines the shape of the scanning DMA transfer function is the ratio of the characteristic scanning time to the average residence time, which yields the same transfer function as that for the static DMA when the ratio gets sufficiently large. The effect of particle diffusion is included via an extended outlet. The dimensionless equations for the trajectories and the method presented here can be generalized to the column DMA of any geometry.

Copyright © 2020 American Association for Aerosol Research     

Differential mobility analyser transfer functions in scanning mode

A novel method is described for the calculation of the differential mobility analyser (DMA) transfer function in scanning mode, which is based on the derivation of an analytical solution for the non-diffusive particle trajectories inside the DMA, under exponentially varying electrical field and fully developed laminar flow. The scanning mode transfer functions can substantially improve the measurement accuracy of fast scanning mobility particle sizers (SMPS) as shown by Collins, Cocker, Flagan, and Seinfeld [(2004). The scanning DMA transfer function. Aerosol Science and Technology, 38, 833–850]. Compared to the Monte Carlo simulations described by Collins et al., the method developed here is much more accurate and sufficiently fast to be employed in advanced DMA inversion algorithms.     

Local and Regional Secondary Organic Aerosol: Insights from a Year of Semi-Continuous Carbon Measurements at Pittsburgh

We present Scanning Mobility CCN Analysis (SMCA) as a novel method for obtaining rapid measurements of size-resolved cloud condensation nuclei (CCN) distributions and activation kinetics. SMCA involves sampling the monodisperse outlet stream of a Differential Mobility Analyzer (DMA) operated in scanning voltage mode concurrently with CCN and condensation particle counters. By applying the same inversion algorithm as used for obtaining size distributions with a scanning mobility particle sizer (SMPS), CCN concentration and activated droplet size are obtained as a function of mobility size over the timescale of an SMPS scan (typically 60–120 s). Methods to account for multiple charging, particle non-sphericity, and limited counting statistics are presented. SMCA is demonstrated using commercial SMPS and CFSTGC instruments with the manufacturer-provided control software. The method is evaluated for activation of both laboratory aerosol and ambient aerosol obtained during the 2004 NEAQS-ITCT2k4 field campaign. It is shown that SMCA reproduces the results obtained with a DMA operating in voltage “stepping” mode.     

Analysis of Scanning DMA Transfer Functions

A new approach to determine transfer functions of scanning differential mobility analyzers (DMAs) is introduced. An expression for non-diffusive particle trajectories in a cylindrical DMA operating in a scanning voltage mode is obtained analytically. Particle trajectory simulations are then used to determine the scanning DMA transfer functions. The results suggest that the shape of the scanning DMA transfer functions may vary with mobility for scan times smaller than a certain value, which depends on the DMA flowrates, and this provides one criteria limiting the fastest scan possible with the conventional DMAs. A simple approach to determine upscan scanning DMA transfer functions in near real-time with minimal number of simulations is described. For upscan operation, the choice of the scantime is seen to impose upper and lower limits on the particle mobility range classified by a scanning DMA. The predicted effect of voltage scanning on altering DMA transfer functions is validated with fast scan experiments.     

Differential Electrical Mobility Analysis: A Theoretical Study

ABSTRACT

The subject of this work is the theoretical investigation of slowly scanning differential mobility analyzers (DMAs) which are, e.g., utilized to determine DMA transfer functions and to measure particle mobility distributions. A model to describe such systems is introduced and applied to investigate three different regimes of input mobility distributions: 1) a mobility distribution much narrower than the DMA transfer function, 2) a mobility distribution of about the same width as the DMA transfer function, and 3) a mobility distribution much wider than the DMA transfer function. Cases 1) and 2) are relevant for DMA transfer function measurements utilizing tandem differential mobility analyzer (TDMA) systems. For either regime, it is not possible to determine DMA transfer functions directly from the concentration distributions measured at the outlet of a DMA. For these cases, a deconvolution procedure is needed. Therefore, an iterative deconvolution procedure was developed. Determining DMA transfer functions utilizing the developed deconvolution procedure, different shapes of transfer function (triangular, Gaussian) are discussed. Case 3) is relevant for particle size distribution measurements. Here, the mobility distribution upstream of the DMA can be obtained by dividing the concentration distribution measured downstream of a DMA by the DMA transfer function area. The DMA transfer function area is influenced by diffusional losses inside the DMA, and therefore is size-dependent. Neglecting this size dependence results in an underprediction of particle number concentrations in the ultrafine particle size range.     

Performance Comparison of Scanning Electrical Mobility Spectrometers

Scanning electrical mobility spectrometers (SEMS) are commonly used for near real-time ultrafine particle size distribution measurements. Analysis of SEMS measurements to calculate particle size distributions requires detailed understanding of instrument characteristics and operation. Varying instrument designs are used in the different commercial SEMS systems, and data analysis with these instruments requires accurate knowledge of their relative performance. In this study, an experimental approach to evaluate and reconcile differences between different SEMS instruments is established. This approach is used to characterize the relative performance of two SEMS systems—TSI's SMPS 3936-L22 and MSP's WPS XP1000—for particle sizes in the range of 20 to 300 nm. In these tests, the instruments were operated under a low flowrate condition with aerosol and sheath air flows of 0.3 and 3 LPM, respectively. Measurements show that the particle sizing characteristics of the instruments are very consistent with each other over the entire range of particle sizes studied. Particle number characteristics are dependent on the treatment of particle losses in the system and accounting of non-idealities of transfer function. The number concentrations reported by two instruments are generally consistent with each other and with an upstream reference counter for particle sizes larger than ～ 90 nm. For smaller particles, the low flowrate operation of the two systems results in significant penetration losses. A net particle detection efficiency (NPDE) factor for the two systems was determined from experiments with monodisperse aerosol. This factor is seen to be effective in characterizing and reconciling measurements made with these two SEMS instruments.     

Evaluation of DMA Size Selection of Dry Dispersed Mineral Dust Particles

Mineral dust particles play a significant role in the Earth's radiative balance via direct interaction with solar radiation and indirectly through their ability to initiate cloud formation. Many field and laboratory studies utilize a differential mobility analyzer (DMA) for particle size selection. Here we evaluate the use of a DMA to size-segregate dry dispersed mineral dust particles. We examine the post-DMA size distribution using four different techniques: a scanning mobility particle sizer (SMPS) for mobility sizing, an optical particle sizer (OPS) for optical sizing, the Particle Analysis by Laser Mass Spectrometry (PALMS) instrument for vacuum aerodynamic sizing, and electron microscopy (EM) for geometric sizing. While the SMPS measured a narrow mobility size distribution at the DMA-selected diameter, the OPS, PALMS, and EM in most cases showed broader distributions and a smaller mode size than that selected by the DMA. These techniques also observed super-micrometer particles, often extending beyond the upper size limit of a typical SMPS scan. Complicating analysis, particle shape factor (χ) was observed to be a function of mobility size, ranging from 1.3 at 500 nm to 3.1 at 1000 nm. We conclude that mobility size selection of mineral dust particles using a DMA most often does not yield particles of the desired physical size or surface area. We suggest that attempts to size-select from a broad distribution of non-spherical particles require an independent measurement downstream of the DMA to verify the actual selected size.

Copyright 2015 American Association for Aerosol Research     

Measuring aerosol size distributions with the fast integrated mobility spectrometer

A fast integrated mobility spectrometer (FIMS) has been developed for rapid aerosol size distribution measurements including those aerosols with low particle number concentrations. In this work, an inversion routine has been developed for the FIMS and it is demonstrated that the FIMS can accurately measure aerosol size distributions. The inversion routine includes corrections for the particle residence time in the FIMS and other factors related to the width of the response (or transfer) function and multiple charging of particles. Steady-state size distributions measured with the FIMS compared well with those measured by a scanning mobility particle sizer (SMPS). Experiments also show that the FIMS is able to capture the size distribution of rapidly changing aerosol populations. The total particle concentration integrated from distributions measured by the FIMS agrees well with simultaneous measurements by a condensation particle counter (CPC).     

Relaxed step functions for evaluation of CCN counter data on size-separated aerosol particles

Atmospherically important data are gained from cloud condensation nucleus counter (CCNC) analysis of aerosols that are particle mobility separated using differential mobility analysers (DMA). We present relaxed step functions that can be fitted to these data to obtain critical diameters or critical supersaturations. The step functions are based on the DMA transfer function. We treat the case with fixed supersaturation and varied particle diameter as well as fixed particle size and varied supersaturation. Comparison with experimental data shows that the width of the DMA transfer function controls the steepness of the relaxed step function. The less steep slope in the activation curve caused by the presence of a slightly soluble compound in the particle is discussed. Also in this case, the DMA transfer function width influences the steepness of the activation curve. Finally we demonstrate the errors made if doubly charged particles are not accounted for and a wide DMA transfer function is used.     

Effects of exponentially decaying and growing concentrations on particle size distribution from a scanning mobility particle sizer

Abstract

A scanning mobility particle sizer (SMPS) is one of the most widely used instruments to obtain size distribution for atmospheric particles. In an SMPS measurement, a voltage scanning process on a differential mobility analyzer is required, and it typically takes 30?s to 120?s to obtain one entire size distribution. A size distribution obtained by an SMPS measurement might have significant deviations from actual values due to the scanning process when the measured particle concentrations change over time. In this study, we introduce an analytical approach for estimating particle size distribution under exponentially decaying and growing particle concentrations. The analytical SMPS results are validated by performing experiments using exponentially decaying particle concentrations under the same conditions. Furthermore, the effects of a decay parameter, initial size distribution, and scan time are evaluated, and the deviations from actual (real or true) size distributions obtained by an exact solution are analyzed. Geometric mean diameters and standard deviations of the size distributions from SMPS results increase or decrease with exponentially decaying or growing concentrations, respectively, and total concentrations estimated by the analytical SMPS approach are significantly underestimated or overestimated compared to real total concentrations. While SMPS measurements have been widely employed in various applications such as atmospheric particle characterization in highly variable particle concentrations versus time, very few studies on the influence of changing concentrations on SMPS measurements have been conducted. Therefore, the introduced analytical approach and findings provide valuable insight into the importance of accurate SMPS measurements with changing particle concentrations.

Copyright © 2020 American Association for Aerosol Research     

Online Nanoparticle Mass Measurement by Combined Aerosol Particle Mass Analyzer and Differential Mobility Analyzer: Comparison of Theory and Measurements

A combination of a differential mobility analyzer (DMA) and aerosol particle mass analyzer (APM) is used to measure the mass of NIST Standard Reference Materials (SRM®) PSL spheres with 60 and 100 nm nominal diameter, and NIST traceable 300 nm PSL spheres. The calibration PSL spheres were previously characterized by modal diameter and spread in particle size. We used the DMA to separate the particles with modal diameter in a narrow mobility diameter range. The mass of the separated particles is measured using the APM. The measured mass is converted to diameter using a specific density of 1.05. We found that there was good agreement between our measurements and calibration modal diameter. The measured average modal diameters are 59.23 and 101.2 nm for nominal diameters of 60 and 100 nm (calibration modal diameter: 60.39 and 100.7 nm) PSL spheres, respectively. The repeatability uncertainty of these measurements is reported. For 300 nm, the measured diameter was 305.5 nm, which is an agreement with calibration diameter within 1.8%.

The effect of spread in particle size on the APM transfer function is investigated. Two sources of the spread in “mono-dispersed” particle size distributions are discussed: (a) spread due to the triangular DMA transfer function, and (b) spread in the calibration particle size. The APM response function is calculated numerically with parabolic flow through the APM and diffusion broadening. As expected from theory, the calculated APM response function and measured data followed a similar trend with respect to APM voltage. However, the theoretical APM transfer function is narrower than the measured APM response.     

Size Distributions of Motor Vehicle Exhaust PM: A Comparison Between ELPI and SMPS Measurements

Particle size measurements using the electrical low pressure impactor (ELPI) and scanning mobility particle sizer (SMPS) are compared from the perspective of characterizing the particulate matter in motor vehicle exhaust. Both steady state vehicle operation and transient drive cycles are considered, and both gasoline and diesel fueled vehicle emissions are compared. Although the ELPI and SMPS measure different physical properties, respectively, the aerodynamic diameter and mobility diameter, the steady state particle size distributions are in close agreement, except for the 37 nm impactor stage of the ELPI which may overestimate particle number by up to a factor of two relative to the SMPS. This has little effect on the volume, or mass, weighted distribution. These, too, are generally in good agreement, though discrepancies appear at large particle size due to multiple charging effects in the SMPS and to electrometer offsets and the small particle loss correction in the ELPI. Selecting particles based on their electrical mobility with the SMPS, and then measuring their aerodynamic diameter with the ELPI, reveals that diesel particulate matter with well-specified mobility diameter exhibits a wide range in aerodynamic diameter and, therefore, also in effective density. Over transient drive cycles, the ELPI provides second by second particle distributions, whereas the SMPS must be run in a fixed particle size mode and size distributions constructed from repeated tests. The ELPI registers higher instantaneous PM emission rates during transients than the SMPS due to the faster time responses of the ELPI. The time integrated ELPI and SMPS size distributions, however, remain in good agreement. The relative merits of the two instruments for steady state and transient tests are discussed.     

Resolution of the radial differential mobility analyzer for ultrafine particles

The resolution of the radial differential mobility analyzer (radial DMA) for particles in 3–60 nm diameter range is probed through tandem radial DMA measurements employing identical radial DMAs. The observed broadening of the range of transmitted particles with decreasing particle Peclet number was shown to be consistent with Stolzenburg's (1988, Ph.D. Thesis, University of Minnesota) model of diffusion broadening of the transfer function, although the broadening was somewhat greater than predicted. A similar, but smaller, deviation is seen in Stolzenburg's data obtained using a cylindrical DMA. The enhanced broadening is thought to result from flow disturbances within the DMA. Diffusional deposition of particles in the radial DMA for two different sheath flow rates correlated well with Pe^−2/3, while electrophoretic particle losses in the transition from high voltage at the outlet of the DMA to grounded tubing are shown to be independent of the particle Peclet number. The latter effect is, however, small for the radial DMA. Consistent with observations previously made using cylindrical DMAs, the voltage corresponding to the peak in the number concentration is slightly higher for the second DMA than for the first one. This apparent decrease in mobility correlates with Pe⁻¹.     

Direct Transfer of Gas-Borne Nanoparticles into Liquid Suspensions by Means of a Wet Electrostatic Precipitator

The direct transfer of flame-synthesized aerosols of silica nanoparticles into aqueous suspensions is investigated. Silica nanoparticle aerosols with production rates of 0.5 g/h and different mean diameters and degrees of agglomeration are transferred into liquid suspensions by means of a novel wet electrostatic precipitator. Particle collection efficiencies above 99.999% were measured. The influence of the transfer on the particle size distribution was investigated by comparison of aerosol and suspensions size measurements. Aerosol sizes were measured with the scanning mobility particle sizer (SMPS), and suspension size measurements were conducted by dynamic light scattering (DLS) and by SMPS measurements of the aerosolized suspension employing a novel nebulizer. Depending on the aerosol and stabilization conditions, particle transfer with nearly no influence on the particle size distribution is possible. Suspensions generated from the same particle aerosol by direct transfer and by sonication of the respective powder were compared. In contrast to the direct transfer, the aerosol particle size distribution could not be restored by ultrasonication.

Copyright © 2015 American Association for Aerosol Research     

Retrieval of high time resolution growth factor probability density function from a humidity-controlled fast integrated mobility spectrometer

Hygroscopicity describes the tendency of aerosol particle to uptake water and is among the key parameters in determining the impact of atmospheric aerosols on global radiation and climate. A hygroscopicity tandem differential mobility analyzer (HTDMA) system is the most widely used instrument for determining the aerosol hygroscopic growth. Because of the time needed to scan the classifying voltage of the DMA, HTDMA measurement often requires a minimum of 30?min to characterize the particle hygroscopic growth at a single relative humidity for five to six different sizes. This slow speed is often inadequate for measurements onboard mobile platforms or when aerosols evolve rapidly. Recently, a humidity-controlled fast integrated mobility spectrometer (HFIMS) was developed for measuring the hygroscopic growth of particles. The measurement speed of the HFIMS is about one order of magnitude faster than that of the conventional HTDMA. In this work, a data inversion routine is developed to retrieve the growth factor probability density function (GF-PDF) of particles measured by the HFIMS. The inversion routine considers the transfer functions of the upstream DMA and the downstream water-based fast integrated mobility spectrometer (FIMS), and derives the GF-PDF that reproduces the measured responses of the HFIMS. The performance of the inversion routine is examined using ambient measurements with different assumptions for the spectral shape of the particle GF-PDF (multimodal lognormal or piecewise linear). The influences of the data inversion parameters and counting statistics on the inverted GF-PDFs were further investigated, and an approach to determine the optimized inversion parameters is presented.

Copyright © 2019 American Association for Aerosol Research     

Design and optimization of a medium flow differential mobility analyzer (MF-DMA) for classification of high-density particles

A new design of a Differential Mobility Analyzer (DMA) was tested with medium aerosol flow rates ranging from 1.5 to 10 slm and high-density particles. The vacuum-tight construction makes it possible to classify pure metal nanoparticles from production processes. The selectable electrical mobility range is comparable to the TSI Long and Nano DMA and covers the full nanometer scale from 15–600?nm. The Medium Flow-DMA (MF-DMA) is characterized by its transfer function, which was determined by a tandem DMA setup using a SMPS with Long DMA downstream. Silver nanoparticles with a density of 10.49?g cm^?3 were used to demonstrate the size-selecting performance of high-density particles. The transfer function was calculated for aerosol to sheath gas flow ratios of 1/10, 1/5, and 1/3 directly from the SMPS data by a new method using modeling approach and comparison to the theory. Sufficiently high resolution was reached by increasing the SMPS scan time of the classified size distribution to 300?s. During the investigation, a broadened transfer function could be attributed to an inhomogeneous flow field resulting from the aerosol inlet design. The aerosol inlet of the MF-DMA was optimized by the number of inlet drillings and the opening of the inlet slit to achieve a more homogeneous flow field. CFD simulations of the MF-DMA also confirmed this. The modification improved the transfer function especially for medium aerosol flow rates above 5 slm.

Copyright © 2019 American Association for Aerosol Research     

Characterization of the TSI model 3086 differential mobility analyzer for classifying aerosols down to 1 nm

Measurement systems for particle sizing starting at 1 nm are used to bridge the gap between mass spectrometer measurements and traditional aerosol sizing methods, and thus to enable measurement of the complete size distribution from molecules and clusters to large particles. Such a measurement can be made using a scanning mobility particle sizer equipped with a diethylene glycol growth engine (e.g., TSI Model 3777 Nano Enhancer) along with a condensation particle counter, and a differential mobility analyzer (DMA) appropriate for such small sizes. Previous researchers have used high-resolution DMA (HRDMA) and also the TSI Nano-DMA (Model 3085) in such a scanning mobility particle sizer system. In this study, we evaluate the performance of the recently introduced TSI 1 nm-DMA (Model 3086). The transfer function was characterized using 1–2 nm monomobile molecular ion standards. The same measurements were repeated on a TSI Nano-DMA, with good agreement to previously published values. From the measured transfer function, the resolution of each DMA model was determined as a function of particle size and sheath flow rate. Resolution of the TSI 3086 in the 1–2 nm range was 10–25% higher than the TSI 3085. Measured resolutions of the TSI 3086 were 10–20% lower than theoretically predicted values, whereas those of the Model 3085 were 0–10% lower.

Copyright © 2018 TSI Inc.     

A language to simplify computation of differential mobility analyzer response functions

A language for computation of differential mobility analyzer (DMA) response functions is introduced. The language consists of short programming language expressions that evaluate to the size distribution of particles exiting a DMA. The language permits application of the same framework to single and tandem DMA setups. Expressions are derived for calculation of the convolution matrix used in inversion of size distribution data, calculation of the convolution matrix for transit through tandem DMA systems, and calculation of the size and mobility distribution through DMA systems that involve one or multiple DMAs. The contribution of multiply charged particles to the total response distributions can be explicitly resolved. The derived convolution matrix is suitable for inverting scanning mobility particle sizer response functions using standard regularization techniques. Users can modify and substitute any of the convolution terms—comprising the DMA transfer function, detector efficiency, loss rate, and charging efficiencies—to express response functions of nonstandard DMA configurations. Example applications are presented, including classification of particle size, measurement of size-resolved cloud condensation nuclei activity, characterization of hygroscopicity and volatility tandem DMA response functions, and characterization of the dual tandem DMA system for dimer preparation. The source code and examples are shared as free software and are hosted on an online collaborative software development platform that allows for version tracking and crediting contributors. Adoption of the language may facilitate the design and optimization of custom-built systems that involve unique arrangements of DMAs and detectors.

Copyright © 2018 The Author(s). Published with license by Taylor & Francis Group, LLC.