Size measurements of gasborne poly(amidoamine) (PAMAM) dendrimers using a differential mobility analyzer (DMA)

Poly(amidoamine) (PAMAM) dendrimers generations 2 through 6 were aerosolized by an electrospray aerosol generator and their electrical mobility spectra observed using a differential mobility analyzer (DMA). We succeeded in measuring the electrical mobilities of the monomer and dimer ions of these dendrimers. The experimental results suggested that PAMAM dendrimers are useful as standard particles in the range of a few nanometers.     

Inversion of tandem differential mobility analyser (TDMA) measurements

The tandem differential mobility analyser (HTDMA) technique is used to detect size changes of submicron particles after a treatment such as exposure to high relative humidity (RH). Measured diameter growth factor distributions must be inverted, because they are only a skewed and smoothed integral transform of the actual growth factor probability density function (GF-PDF). We introduce a new approach, TDMAinv, representing the inverted GF-PDF as a piecewise linear function. Simulated measurements are used to prove the concept. Measurements of an aerosol with a bimodal GF-PDF show that TDMAinv provides equivalent information to TDMAfit, the most widely used inversion algorithm. The major advantage of TDMAinv is that convergence of the inversion is robust and independent of the initial guess. This makes TDMAinv a reliable tool to analyse large TDMA data sets. A methodology is also demonstrated for analysis of TDMA data in cases where the dominant fraction of selected particles is doubly or triply charged.     

Nanoparticle cross-flow differential mobility analyzer (NCDMA): Theory and design

A new instrument having a cross-flow configuration for aerosol and sheath flows is introduced for sizing of nanoparticles and referred to as nanoparticle cross-flow differential mobility analyzer (NCDMA). The flow and electrical fields in the NCDMA are analyzed theoretically, and its sizing characteristics are obtained in relation to the instrument geometry and operating conditions. The theoretical transfer functions compare well with numerical predictions for non-diffusing particles. For smaller particles, the focusing provided by the combination of the cross-flow configuration and electric field results in reduced Brownian diffusion broadening of particle position distribution in the classification region. From the analysis of instrument resolution based on the migration Peclet number, the NCDMA design is seen to provide a higher resolution than that of the TSI short column DMA (nano-DMA) for the same applied voltage. Monte Carlo simulation results of the Langevin equation confirm the theoretical prediction of improved resolution of NCDMA over conventional designs in the Brownian diffusion regime.     

Inversion to obtain aerosol size distributions from measurements with a differential mobility analyzer

To measure size distributions of submicrometer aerosols with an electrical differential mobility analyzer (DMA) requires an inversion procedure. The Knutson (1976) and the Hoppel (1978) inversion procedures were numerically investigated for the case of log-normal aerosol size distributions. It was found that the Hoppel procedure converges to the same result as that given by the Knutson procedure. The computational range for geometric mean diameter ( _g) was 0.025-0.25 μm, and for geometric standard deviation (σ_g) was 1.1–2.4. The inversion error was found to be greater than 10% in certain “forbidden zones” of _g and σ_g values. For the case of an ideal DMA having no lower mobility limit, only one forbidden zone exists, this consisting of small σ_g values. The boundary of this forbidden zone intercepts the computational range boundaries at σ_g = 1.25, and σ_g = 1.62, . These results also apply to an actual DMA when the size distribution of particles larger than the DMA singly charged mobility limit is available a priori. If such information is not available, the concentration of these larger particles is assumed to be zero in performing the inversion. This assumption adds a second forbidden zone, consisting of large σ_g values and having the intercepts σ_g = 2.44, and σ_g = 1.50, . The first forbidden zone remains nearly the same.     

A cost-effective differential mobility analyzer (cDMA) for multiple DMA column applications

In aerosol research and applications, a differential mobility analyzer (DMA) is now considered the standard tool for sizing and classifying monodisperse particles in the sub-micrometer and nanometer size ranges. However, DMA application at the pilot or industrial production scale remains infeasible because of the low mass throughput. A simple way to scale up DMA operation is to use multiple DMA columns. The manufacture and maintenance costs of existing DMAs, however, limit such a scale-up. A cost-effective DMA column (named cDMA) has thus been developed in this work to address the above issue. To reduce its manufacturing cost, the prototype was constructed using parts requiring little machining. The cDMA column was also designed for easy maintenance and easy variation of the classification length for any application-specified size range. In this study, prototypes with two particle classification lengths, 1.75 and 4.50 cm, were constructed and their performance was experimentally evaluated at sheath-to-aerosol flowrate ratios of 5:1, 10:1, and 15:1 via the tandem DMA (TDMA) technique. It was concluded that both prototype cDMAs, operated at a sheath/aerosol flowrate ratio less than 15:1 and with a polydisperse aerosol flowrate of 1.0 lpm, achieved sizing resolution comparable to that offered by Nano-DMA. The longer cDMA had comparable transmission efficiency to that of Nano-DMA, and the shorter cDMA exceeded the performance of Nano-DMA. Hence, the cDMA with the shorter (1.75 cm) classification length is better suited for the characterization of macromolecular samples.     

Characterization of a Herrmann-type high-resolution differential mobility analyzer

Aerosol instrument characterization and verification for nanometer-sized particles requires well-established generation and classification instruments. A precise size selection of sub-3-nm charged aerosol particles requires a differential mobility analyzer (DMA), specially designed for the sub-3-nm size range. In this study, a Herrmann-type high-resolution DMA developed at Yale University was characterized in various operation conditions. A relation between sheath flow rate and tetraheptylammonium ion (C₂₈H₆₀N⁺, THA⁺, 1.47 nm, mobility equivalent diameter) was established. The maximum particle size that the DMA was able to classify was 2.9 nm with the highest sheath flow rate of 1427 liters per minute (Lpm), and 6.5 nm with the lowest stable sheath flow rate of 215 Lpm, restricted by the maximum and minimum flow rates provided by our blower. Resolution and transmission of DMA are reported for tetrapropylammonium (C₁₂H₂₈N⁺, TPA⁺, 1.16 nm), THA⁺, and THA₂Br⁺ (1.78 nm) ions measured with two different central electrodes and five different sheath flow rates. The transmission varied between 0.01 and 0.22, and the resolution varied between 10.8 and 51.9, depending on the operation conditions.

Copyright © 2016 American Association for Aerosol Research     

Miniature differential mobility analyzer for compact field-portable spectrometers

A low-flow miniature differential mobility analyzer (mDMA) has been developed for compact field-portable mobility spectrometers to classify the submicrometer aerosol. The mDMA was designed for an ultra-low aerosol flow rate of 0.05 L/min. At a sheath flow rate of 0.2 L/min, the mDMA's upper size limit was estimated to be about 921 nm. The mDMA has a classification zone of 2.54 cm long, an outer diameter of 2.54 cm, and an inner diameter of 1.778 cm. The design allows low-cost fabrication and easy assembly. Tandem DMA measurements were carried out to evaluate the performance of the mDMA. Its transfer function was described using Stolzenburg's model. The experimentally measured transfer function shows close agreement with the theory. The transmission efficiency was comparable to that of the Knutson–Whitby DMA for particles in the range of 10–1000 nm. The mobility resolution was comparable to that of the TSI 3085 nanoDMA at the same aerosol flow rate. The design features and performance of the mDMA make it suitable for compact field portable mobility size spectrometers for measurement of nanoparticles and submicrometer aerosol.     

Development of a toroidal-shaped differential mobility analyzer for effective measurements of airborne particles: Experiment and modeling

Abstract

A toroidal-shaped differential mobility analyzer (DMA), called toroidal Hanyang-DMA (toroidal Hy-DMA), was developed for particle characterization. The height, width, and weight of the newly developed toroidal Hy-DMA are 8?cm, 14?cm, and 1.2?kg, respectively, indicating that it is much more compact and lighter than the TSI long-DMA; nevertheless, the classifiable particle size range is up to 400?nm. Therefore, the toroidal Hy-DMA can be useful for many applications in a limited space owing to its small size. The performance of the Hy-DMA was evaluated using tandem differential mobility analyzer (TDMA) experiments with two identical Hy-DMAs and numerical simulations using a single-particle tracking analysis in a Lagrangian framework. To simulate particle behaviors, a flow-rate-weighted particle injection method, which is more realistic, was employed, and the proposed particle tracking method can be widely applied to any non-plug flow conditions. The obtained experimental data and numerical results of central particle sizes are consistent with each other. Empirical and numerical transfer functions of the toroidal Hy-DMA were obtained and compared with those of other types of well-known DMAs. It is concluded that the toroidal Hy-DMA has an empirical transmission probability ranging from 0.5 to 0.9 and a sizing resolution ranging from 5.5 to 9.0, which indicates acceptable performance in classifying monodisperse particles within the test size range of 20 to 400?nm.

Copyright © 2019 American Association for Aerosol Research     

Atmospheric particle composition-hygroscopic growth measurements using an in-series hybrid tandem differential mobility analyzer and aerosol mass spectrometer

The ability of atmospheric particles to absorb water has extensive climate, atmospheric chemistry, and health implications, and considerable effort has gone into determining relationships between particle composition and hygroscopicity. Parallel techniques, in which co-located composition and hygroscopicity measurements are combined to infer composition-hygroscopicity relationships, may not detect the influence of external mixtures. Previous in-line measurements have been limited to single-particle composition or a limited analyte range, and are often non-quantitative and/or offline. Here, we present for the first time in-series, online, quantitative hygroscopicity-composition measurements using a Brechtel Manufacturing, Inc. Hybrid Tandem Differential Mobility Analyzer and an Aerodyne High-Resolution Time-of-Flight Aerosol Mass Spectrometer. This technique is first verified using laboratory-generated external particle mixtures, then extended to ambient measurements at a seaside sampling side at the Hong Kong University of Science and Technology. The technique successfully separated laboratory-generated particles of differing hygroscopicities and showed promise for atmospheric particles, though high mass attenuation endemic to the HTDMA dual size selection limits application to environments with at least ～14–41 μg/m³ of particulate mass, depending on composition.

Copyright © 2017 American Association for Aerosol Research     

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.     

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     

The Spider DMA: A miniature radial differential mobility analyzer

Abstract

The Spider differential mobility analyzer (DMA) is a novel, miniaturized radial DMA developed to provide size classification in the 10–500?nm range for applications requiring high portability and time resolution. Its external dimensions are ～12?cm in diameter by 6?cm in height (excluding tubing); it weighs ～350?g, and is designed to operate at 0.6–1.5?L/min sheath and 0.3?L/min sample flowrates. It features a new sample inlet geometry that is designed to produce a uniform azimuthal particle distribution at the entrance of the classifier, optimized sample/sheath flow streams introduction in the classifier to minimize particle delays, and extension of the electric field interaction volume for ～30% enhanced dynamic range. Based on three-dimensional finite element simulations of flows, electric fields, and particle trajectories, we demonstrate that the Spider DMA transfer functions can be predicted with high fidelity using a parameterized fit based on the Stolzenburg semi-analytical model. Experimental characterization of the instrument response with size-selected particles confirmed close agreement with model prediction; mobility size response is linear over three orders of magnitude in mobility span. Electrical ground shielding of the external surfaces of the DMA has been found to be necessary to avoid particle losses associated with field effects as the high voltage operating limit is approached. The mean deviation between the reference size of polystyrene latex spheres and the Spider DMA measurement is less than 2%, corroborating its high sizing precision and potential for high quality size distribution measurements.

Copyright © 2019 American Association for Aerosol Research     

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.     

Characterization of a high-resolution supercritical differential mobility analyzer at reduced flow rates

Classifying sub-3?nm particles effectively with relatively high penetration efficiencies and sizing resolutions is important for atmospheric new particle formation studies. A high-resolution supercritical differential mobility analyzer (half-mini DMA) was recently improved to classify aerosols at a sheath flow rate less than 100?L/min. In this study, we characterized the transfer functions, the penetration efficiencies, and the sizing resolution of the new half-mini DMA at the aerosol flow rate of 2.5–10?L/min and the sheath flow rate of 25–250?L/min using tetra-alkyl ammonium ions and tungsten oxide particles. The transfer functions of the new half-mini DMA at an aerosol flow rate lower than 5?L/min and a sheath flow rate lower than 150?L/min agree well with predictions using a theoretical diffusing transfer function. The penetration efficiencies can be approximated using an empirical formula. When classifying 1.48?nm molecular ions at an aerosol-to-sheath flow ratio of 5/50?L/min, the penetration efficiency, the sizing resolution, and the multiplicative broadening factor of the new half-mini DMA are 0.18, 6.8, and 1.11, respectively. Compared to other sub-3?nm DMAs applied in atmospheric measurements (e.g. the mini-cyDMA, the TSI DMA 3086, the TSI nanoDMA 3085, and the Grimm S-DMA), the new half-mini DMA characterized in this study is able to classify particles at higher aerosol and sheath flow rates, leading to a higher sizing resolution at the same aerosol-to-sheath flow ratio. Accordingly, the new half-mini DMA can reduce the uncertainties in atmospheric new particle formation measurement if coupled with an aerosol detector that could work at the corresponding high aerosol flow rate.

© 2018 American Association for Aerosol Research     

Mobility shift in the differential mobility analyzer due to Brownian diffusion and space-charge effects

The space-charge field is usually ignored when performing aerosol size measurements with the differential mobility analyzer (DMA). In the case of extremely fine particles requiring low electric fields for their classification, the space-charge field developed within the DMA can even be larger than the applied field and, hence, the mobility of the particles exiting through the sampling port may be very different from that expected. On the other hand, the trajectories of different-sized diffusing particles mix up with each other, resulting also in a shift of the average mobility of the classified particles. When non-uniform electric fields are present, the variance of the particle position probability distribution is larger than in the case of a pure Brownian process. Both phenomena, space charge and diffusion, are thus interrelated and cannot be treated separately. A very simplified theoretical treatment is presented which enables estimation of the order of magnitude of the mobility shift. Experiments with a tandem DMA system have shown that, at very low classification voltages, the measured mobility of the classified particles can be as high as three times the actual mobility. The experimental trends are qualitatively well reproduced by the model calculations.     

Instant acquisition of high resolution mobility spectra in a differential mobility analyzer with 100 independent ion collectors: Instrument calibration

Abstract

A parallel plate differential mobility analyzer (DMA) having 100 independent current collectors is calibrated to relate the axial distances L_n between the inlet slit and the detector position to the particle mobility Z at given voltage difference V and sheath gas flow rate Q. Calibrating species are tetraheptylammonium bromide clusters (THABr) and polyethylene glycol (PEG35k, 5?nm in diameter), generated by a bipolar electrospray source, and purified in a cylindrical DMA. Gaussian fitting of the raw discrete mobility spectra in the form of ion current I_n versus collector position L_n , I_n (L_n ), yield the mean value L_o of the collector position maximizing the signal for a given ion. The many (Z,V,L_o ) triads obtained at given Q from many different DMA voltages and standard mobilities collapse into a single 1/(Z_iV_j ) vs L_o curve when slight adjustments are made to the Z_i . For different flow rates, Q/(Z_iV_j ) vs. L_o curves collapse also, as long as the peaks are moderately narrow. However, for sufficiently small Q/Z, the THABr cluster peaks become broad, and the curves Q/(Z_iV_j ) vs. L_o cease to collapse precisely. In contrast, the data for PEG show that this behavior is not a low-Q (Reynolds number) effect from the growth of the two lateral boundary layers, but is rather due to the broad and non-Gaussian peak shapes obtained at low Q or high Z. The calibration is accordingly unaffected by the Reynolds number. This simplicity was unexpected, given the three-dimensional flow in this DMA with growing lateral boundary layers.

Copyright © 2020 American Association for Aerosol Research     

Particle charge-size distribution measurement using a differential mobility analyzer and an electrical low pressure impactor

We introduce a particle charge-size distribution measurement method using a differential mobility analyzer and an electrical low pressure impactor in tandem configuration. The main advantage of this type of measurement is that it is suitable for a wide range of particle sizes, from approximately 30 nm up to a micrometer, and for high charge levels, which have been problematic for previously used methods. The developed charge measurement method requires information on the particle effective density, and the accuracy of the measurement is dependent on how well the particle effective density is known or estimated. We introduce the measurement and calculation procedures and test these in laboratory conditions. The developed method has been tested using narrow and wide particle size distributions of a known density and well-defined particle charging states. The particles have been produced by the Singly Charged Aerosol Reference (SCAR) and an atomizer and charged with the previously well-characterized unipolar diffusion chargers used in the Nanoparticle Surface Area Monitor (NSAM) and in the Electrical Low Pressure Impactor (ELPI+). The acquired charge-size distributions are in good agreement with the reference values in terms of the median charge levels and widths of the charge distributions.

Copyright © 2017 American Association for Aerosol Research     

Conceptual possibilities for extending the particle size range of a differential mobility analyzer using longitudinal and transversal electrodes

A new type of differential mobility analyzer (DMA) is proposed which is, in theory, applicable to the measurement of particle size distributions of aerosols over the full range of particle size. The basic concept of the full-range DMA can be best realized using a parallel-plate geometry. It contains two arrays of detectors, e.g. thin metal strips connected to electrometers. One array of detectors is placed longitudinally along one of the plates, and the other one is placed transversally downstream of the aerosol entrance. With this arrangement, too low mobility particles which escape undetected in a conventional DMA settle onto the transversal detectors and can thus be measured. For small particles collected along the longitudinal array of detectors, the resolution of the instrument is the same as for a conventional multi-channel DMA. For the largest particles, which are collected on the transversal detectors, the resolution deteriorates as the particle size increases.     

A differential mobility analyzer and a Faraday cup electrometer for operation at 200–930 Pa pressure

We have developed a differential mobility analyzer (DMA) based on the DMA devised by Seto et al. (1997) and a Faraday cup electrometer for measurement of nanometer-sized particles at a few hundred Pa and examined the operating characteristics of the DMA using the tandem DMA technique. The tandem DMA calibration establishes that the DMA successfully classifies particles in the 200–930 Pa pressure range. It was also found that the transfer function of the DMA follows the triangular transfer function and the resolution of the DMA is close to that given for an ideal case. As a standard of a minimum pressure that may be probed with the present DMA system, 400 Pa is estimated when the DMA operates with a 3 nlmin⁻¹ sheath flow and a 1 nlmin⁻¹ aerosol flow rate.