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.     

Scanning Electrical Mobility Spectrometer

The measurement of particle size distributions using electrical mobility can be accelerated significantly by an alternate mode of operating mobility instruments. Rather than changing the electric field in discrete steps to select particles in a given mobility range, the electric field can be scanned continuously. The particles are classified in a time-varying electric field, but for an exponential ramp in the field strength there remains a one-to-one correspondence between the time a particle enters the classifier and the time it leaves. By this method, complete scans of mobility with as many as 100 mobility measurements have been made in 30 seconds using a differential mobility classifier with a condensation nuclei counter as a detector.     

Radial Differential Mobility Analyzer

A differential mobility analyzer in which particles are classified in a radial flow toward the center of parallel disk electrodes, termed the Radial Differential Mobility Analyzer (RDMA), has been developed. Its classifying characteristics have been determined experimentally using both standard polystyrene latex spheres and mobility-classified aerosol particles over the size range of 3–200 nm. The idealized transfer function for the RDMA differs from that of the conventional cylindrical DMA only by a group of geometrical constants. The RDMA is designed specifically for the measurement of ultrafine aerosol particles, achieving a transmission efficiency of 0.85 to 0.90 in the 3–10-nm size range and having a short residence time to limit diffusional broadening of the transfer function. The simple design of the RDMA reduces the number of precision parts that must be fabricated below that for cylindrical DMAs, resulting in a compact, relatively lightweight, and low-cost instrument.     

On Differential Mobility Analyzer Resolution

The resolution of the differential mobility analyzer (DMA) is conveniently described as the ratio of the mobility at the peak of the column transfer function to the full width of the transfer function at 1/2 of its maximum value. The best resolution that can be achieved is that for nondiffusive particles, -nd=beta1, where beta is the flow rate ratio, beta = (Q a + Q s)/(Q sh + Q e) . Brownian diffusion causes particles to deviate from the ideal electrophoretic migration trajectories, thereby reducing the resolution. The relative importance of electrophoretic migration to diffusion can be expressed as a function of the migration Peclet number, which can be expressed either in terms of mobilities, dimensions, and flow rates or as Pe m ig = ( qV / k T ) f , where q is the charge on the particle, V is the applied voltage, and f is a geometry factor that accounts for nonuniformities in the electric field along the migration pathway. Expressed in this way, the performance of DMAs with different geometries, operating at different flow rates, are, in the absence of distortions in the flows and electric fields, shown to be nearly indistinguishable. Diffusion is shown to dominate at operating voltages below a critical value that is proportional to the square of the limiting resolution. Since the voltage range for DMA measurements is limited, the dynamic range decreases with increasing - nd . Because of the changing size dependence of the mobility, this limitation is more pronounced for free-molecular aerosols than for larger particles.     

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.     

Determination of the Mean Mobility of Aerosol Nanoparticles Classified by Differential Mobility Analyzers

MonteCarlo simulations of diffusive particle trajectories, as well as Stolzenburg's model calculations, have shown that the mean mobility of the particles classified by a differential mobility analyzer (DMA) at a given applied voltage may differ from the theoretical one inferred from the Knutson–Whitby equation if the particles are withdrawn from the tails of the particle mobility distribution. In this case, the true mean mobility, defined as the mean mobility of the particles classified at the specified voltage, can be precisely measured by a second DMA operating in series with the first one (tandem DMA). However, if particles are extracted from the central part of the distribution, their mobility can be correctly measured with a single DMA. Besides showing the importance of the usage of the tandem DMA technique for accurate measurements of mobility, this article provides an analytical expression which, if the mobility distribution of the polydisperse aerosol fed to the DMA is known, allows an accurate estimation of the true (mean) mobility of the classified particles.

Copyright 2014 American Association for Aerosol Research     

Diffusion Distortions in a Differential Mobility Analyzer: The Shape of Apparent Mobility Spectrum

The effect of molecular and or small-scale turbulent diffusion in a differential mobility analyzer (DMA) is described in terms of apparent mobility spectrum. Without restricting generality, the normalized apparent spectrum, i.e., the apparent spectrum of unimobile particles with unity charge density is introduced. An approach based on the calculation of the probabilities of the random displacements of particles around their regular trajectories enables us to derive analytical expressions for the normalized apparent spectrum. A particular derivation is carried out for the case of a second-order DMA with one collecting electrode and variable electric field strength. Explicit analytical equations of various approximation degrees have been derived. The normalized apparent spectrum of the particular DMA shows a remarkable asymmetry; its mobility mode is shifted toward lower mobilities. The derived equations serve as a basis for the estimation of the spectral resolution of the DMA. The equations can also be used for a proper design of the DMA, reducing the effect of diffusion. Once the normalized apparent spectrum is known, a possibility appears to improve the resolution of the DMA by solving a relevant equation and eliminating the effect of diffusion in such a way.     

Methodology to Estimate the Transfer Function of Individual Differential Mobility Analyzers

A method to estimate the nonideal features of the transfer function of individual differential mobility analyzers (DMA) was developed and tested experimentally. This was up to now an unsolved problem, which is important for the precision in DMA measurements. The method involves three DMAs of unknown characteristics, which are used in three rounds of experiments with two DMAs according to a fixed schedule. The width of the transfer functions of the three DMAs is obtained in a single fitting procedure where one parameter is fitted to each DMA transfer function and the particle losses in each DMA are calculated in direct relation to that parameter and parameters known from the experiment. It was shown that the proposed method could solve the apportioning problem and unambiguously estimate the transfer function width and the particle losses in each of the DMAs.     

Effect of Aerosol Volatility on the Sizing Accuracy of Differential Mobility Analyzers

Differential mobility analyzers (DMAs) are widely used for calibrating other instruments and measuring aerosol size distributions. DMAs classify aerosol particles according to their electrical mobility, which is assumed to be constant during the classification process. However, particles containing semivolatile substances can change their size in the DMA, leading to sizing errors. In this article, the effect of particle size changes during the classification process on the sizing accuracy of DMAs is discussed. It is shown that DMAs select particles whose time-of-flight-averaged electrical mobility is equal to that of stable particles that are selected under given operating conditions. For evaporating particles, this implies that DMAs select particles that are originally larger than the reported size. At the exit of the DMA, selected particles are smaller than the reported size. Particle evaporation and growth inside DMAs was modeled to study the effect of particle size changes on the sizing accuracy and the transfer function of DMAs in constant- and scanning-voltage modes of operation. Modeling predictions were found to agree well with the results of experiments with ammonium nitrate aerosol. The model was used to estimate sizing errors when measuring hygroscopic and other volatile aerosols. Errors were found to be larger at smaller sizes and low sheath flow rates. Errors, however, are fairly small when saturation concentration is below 10 μg/m³, assuming an evaporation coefficient of 0.1. Particles size changes during classification lead to distortion of the DMA transfer function. In voltage scanning mode, errors are generally larger, especially at high scan rates.

Copyright 2014 American Association for Aerosol Research     

Diffusion Distortions in a Differential Mobility Analyzer with Inclined Electric Field

An approach based on the calculation of the probabilities of the random displacements of particles around their regular trajectories enables us to derive analytical expressions for the normalized apparent mobility spectrum. A particular derivation is carried out for the case of a DMA with one collecting electrode, with inclined electric field, and variable electric field strength. Calculations show that an inclined electric field actually results in a sharper apparent spectrum, i.e., in a higher resolution than a transverse electric field does. A way to improve resolution by calculations is outlined.     

Atmospheric Size Distributions Measured by Differential Mobility Optical Particle Size Spectrometry

ABSTRACT

A differential mobility and optical particle size spectrometer (DMOPSS) was developed to measure ambient size distributions based on geometric particle diameter in the size range of 0.1 to 1.0 μm diameter. The DMOPSS consists of a high-flow differential mobility analyzer (HF-DMA) followed by an optical particle counter (OPC) and condensation nucleus counter (CNC) operating in parallel. The OPC and CNC sample monodisperse aerosol of known geometric diameter from the HF-DMA output or, alternatively, polydisperse aerosol with known dilution directly from the ambient air. The monodisperse samples are used to create time-dependent calibrations of the OPC, providing optical response versus geometric size for the ambient aerosol under study. The direct ambient measurements are then reduced, using this ambient-based calibration. A field test of the DMOPSS system was performed in the summer of 1992 at Meadview, Arizona, where more than 12,000 size spectra were collected; they consisted of roughly one-third direct ambient samples and two-thirds HF-DMA sized samples. Measured aerosol volumes and calculated particle scattering coefficients were strongly correlated with nephelometer measurements, with a mean scattering-to-volume ratio of 5 m²/cm³. With the ambient aerosol calibration, the measured aerosol volumes were 47% larger, and volume geometric mean diameters were 12% larger, than would have been obtained using a polystyrene latex calibration.     

An Effective Antifreeze Protein Predictor with Ensemble Classifiers and Comprehensive Sequence Descriptors

Antifreeze proteins (AFPs) play a pivotal role in the antifreeze effect of overwintering organisms. They have a wide range of applications in numerous fields, such as improving the production of crops and the quality of frozen foods. Accurate identification of AFPs may provide important clues to decipher the underlying mechanisms of AFPs in ice-binding and to facilitate the selection of the most appropriate AFPs for several applications. Based on an ensemble learning technique, this study proposes an AFP identification system called AFP-Ensemble. In this system, random forest classifiers are trained by different training subsets and then aggregated into a consensus classifier by majority voting. The resulting predictor yields a sensitivity of 0.892, a specificity of 0.940, an accuracy of 0.938 and a balanced accuracy of 0.916 on an independent dataset, which are far better than the results obtained by previous methods. These results reveal that AFP-Ensemble is an effective and promising predictor for large-scale determination of AFPs. The detailed feature analysis in this study may give useful insights into the molecular mechanisms of AFP-ice interactions and provide guidance for the related experimental validation. A web server has been designed to implement the proposed method.     

Determination of Particle Size Distribution of Ultra-Fine Aerosols Using a Differential Mobility Analyzer

The size analysis of ultrafine aerosol particles using a differential mobility analyzer combined with a CNC is discussed from two standpoints: (1) particle loss caused by Brownian diffusion in the analyzer, and (2) data reduction procedure where Fuchs' charging theory is applied. As a result, it has been found that (1) particle loss becomes significant when particle size is smaller than about 15 nm, and (2) a simple and practical data reduction procedure may be used, where the stationary bipolar charge distribution given by Boltzmann's law is modified by using Fuchs' charge distribution in the smaller size range.     

Electrospraying Large Sparingly Soluble Tetraalkylammonium Ions as Monomobile Standards of Moderately Low Electrical Mobility

A procedure is described to electrospray the relatively large ions tetrahexadecylammonium (C₁₆H₃₃)₄N⁺ and tetraoctadecylammonium (C₁₈H₃₇)₄N⁺ from their commercially available bromide salts. Their low solubility and the corresponding low conductivity of their alcohol solutions complicates their electrospraying by the convenient method of applying the high voltage to the solution reservoir (rather than to the electrospraying tip). If the capillary bore is widened to reduce the reservoir-tip electrical resistance, the solvent evaporates at its tip, leading to solute precipitation and spray destabilization. These difficulties are overcome via conventional nanospray: we use a wide (～100 μm ID) capillary whose tip is pulled in a flame down to <20 μm OD. Mobility spectra result where the dominant and most mobile peaks are (C₁₆H₃₃)₄N⁺ or (C₁₈H₃₇)₄N⁺. Their electrical mobilities in air at room temperature and pressure are 0.63 and 0.60 cm²/V/s (±1%).

Copyright 2015 American Association for Aerosol Research     

Comparison and Combination of Aerosol Size Distributions Measured with a Low Pressure Impactor,Differential Mobility Particle Sizer,Electrical Aerosol Analyzer,and Aerodynamic Particle Sizer

Data from a different mobility particle sizer (DMPS) or an electrical aerosol analyzer (EAA) has been combined with data from an aerodynamic particle sizer (APS) and converted to obtain aerosol mass distribution parameters on a near real-time basis. A low pressure impactor (LPI), a direct and independent measure of this mass distribution, provided information for comparison.

The number distribution of particles within the electrical measurement range was obtained with the DMPS and EAA. Data from the APS for particles greater than that size were used to complete the number distribution. Two methods of obtaining mass distribution parameters from this number data were attempted. The first was to convert the number data, channel by channel, to mass data and then fit a log-normal function to this new mass distribution. The second method was to fit a log-normal function to the combined number distribution and then use the Hatch-Choate equations to obtain mass parameters.

Both the DMPS / APS and the EAA / APS systems were shown to successfully measure aerosol mass distribution as a function of aerodynamic diameter. Careful operation of the measurement equipment and proper data manipulation are necessary to achieve reliable results. A channel-by-channel conversion from number to mass distribution provided the best comparison to the LPI measurement. The DMPS / APS combination furnishes higher-size resolution and accuracy than the EAA / APS system. A small gap was observed in the EAA / APS combined data; however, this did not seem to adversely affect the determination of mass distribution parameters.     

Sizing of Aerosol in Gases Other Than Air Using a Differential Mobility Analyzer

The differential mobility analyzer (DMA) is a device that sizes aerosol particles based on their electrical mobility. The relationship between particle size and mobility depends, among other factors, on three gas specific parameters, namely, dynamic viscosity, mean free path, and Cunningham slip correction factor C c . Provided these parameters are known, DMA theory is expected to be valid independent of gas type. The present study demonstrates the sizing accuracy of DMAs for gases other than air using monodisperse polystyrene latex (PSL) spheres with nominal diameters of 60 nm, 149 nm, and 343 nm in He, Ar, H 2 , CO 2 , and N 2 O. Eliminating possible systematic errors due to uncertainties in DMA geometry and nominal PSL diameter by normalizing the measured PSL diameters to their respective diameters measured in air, the sheath flow rate Q sh and C c are expected to be the main sources for measurement errors. Since C c data are lacking for PSL spheres in gases other than air, an expression given by Allen and Raabe (1985b) was used to approximate C c . The experimental results of the present study are consistent with a 2% accuracy of this expression for C c , which is considerably better than the 5% accuracy estimated by Rader (1990) for a similar expression for oil drops. Finally, we discuss other aspects of operating a DMA with gases other than air, namely, flow meter calibration and dependence of electrical breakdown voltage on gas type. In the present study a thermal mass flow meter (MFM) was used to measure Q sh . Calibration of this MFM revealed that the gas specific MFM correction factors ( K factors) provided by the technical literature can be highly inaccurate (here between -12% and +31%). More accurate K factors are presented.     

An Analysis of Nucleation-Rate Type of Curves in Glass as Determined by Differential Thermal Analysis

The nucleation rate ( I ) versus temperature type of curves for a Na₂O2·CaO·3SiO₂ (NC₂S₃) glass doped with 0.1 wt% platinum, 0.5 wt% Ag₂O, and 2.0 wt% P₂O₅ were determined using a previously developed differential thermal analysis (DTA) technique. In this DTA technique, a constant amount of glass sample was nucleated at selected temperatures for a specific time, followed by a DTA scan at a fixed heating rate. The functional dependence of the maximum intensity of the exothermic DTA crystallization peak ((delta T )_p) or the inverse temperature at the DTA peak maximum ( T _p⁻¹) on the nucleation temperature ( T _n) was used to determine the nucleation rate versus temperature type of curves. Calculations for qualitatively assessing the dependence of (delta T )_p on T _n were performed using I and crystal growth rate ( U ) curves for a hypothetical system. Values of (delta T )_p calculated for different degrees of overlap between the I and U curves were compared with those measured experimentally. The (delta T )_p vs T _n curves depended strongly on the overlap of I and U , whereas the T _p⁻¹ vs T _n curves were unaffected by the overlap.     

一种液压差速电气控制方法在离心机上的应用

控制系统采用该液压差速电气控制方法,可以时时把转接板管路中的液体压力变化信号及时反馈给控制器,根据压力的变化,实时地、成比例地调节液压系统的流量,且结构简单,使用方便。同时大大降低了卧螺离心机的液压差速控制系统的生产成本。