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1 This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier s archiving and manuscript policies are encouraged to visit:
2 Aerosol Science 39 (2008) Morphology based particle segregation by electrostatic charge Rajan K. Chakrabarty a,b,, Hans Moosmüller b, Mark A. Garro b,c, W. Patrick Arnott d, Jay G. Slowik e, Eben S. Cross f, Jeong-Ho Han f, Paul Davidovits f, Timothy B. Onasch g, Douglas R. Worsnop g a Chemical Physics Program, University of Nevada, Reno, Nevada 89557, USA b Desert Research Institute, Nevada System of Higher Education, Reno, Nevada 89512, USA c Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA d Department of Physics, University of Nevada, Reno, Nevada 89557, USA e Department of Chemistry, University of Toronto, Ontario, Canada, M5S 3H6 f Department of Chemistry, Boston College, Chestnut Hill, MA 02467, USA g Aerodyne Research Inc., Billerica, MA 01821, USA Received 26 September 2007; received in revised form 15 April 2008; accepted 16 April 2008 Abstract A novel charge-based technique for classifying fractal-like aerosol agglomerates based on their morphology is demonstrated. The study discusses the application of this technique to flame soot aerosols where singly and doubly net-charged agglomerates of similar sizes were segregated using electrostatic classifiers and shown to have different morphologies. The flexibility and simplicity of this technique does not limit its application to aerosols, making it an attractive candidate for performing particle shape selection of different types of nano and micromaterials Elsevier Ltd. All rights reserved. Keywords: Morphology selections; Fractal; Aerosol 1. Introduction Morphology is an important control parameter in most particle-related applications. Aerosol synthesis, which is a widely used method for bulk production of nanomaterials (Aitken, Chaudhry, & Boxall, 2006; Rao, 2004), relies heavily on this parameter especially in applications involving: (1) Synthesis and processing of pharmaceuticals, where the ability to control the size and state of agglomerates determines their behavior in the human body (Stevens & George, 2005). (2) Synthesis of printer toners, tires, paints, fillers, and fiber-optics products (Industrial application of nanomaterials chances & risk, 2004; Rao, 2004), where the uniformity in the morphology of nanopowders determines the product quality. (3) Manufacture of carbon nanotubes where the ability to produce uniform sized and shaped carbon nanotubes determines the properties of the product (Ebbesen & Ajayan, 1992; Height, Howard, Tester, & Sande, 2004). Owing to their formation mechanisms (Hinds, 1999), aerosols beyond a certain length scale are often found in the form of agglomerates which have complex fractal-like morphology. Segregating agglomerate ensembles based on Corresponding author at: Chemical Physics Program, University of Nevada, Reno, Nevada 89557, USA. address: rajan@dri.edu (R.K. Chakrabarty) /$ - see front matter 2008 Elsevier Ltd. All rights reserved. doi: /j.jaerosci
3 786 R.K. Chakrabarty et al. / Aerosol Science 39 (2008) their morphology is difficult, with no well-established technique available (Waseda & Muramatsu, 2003; Zelenyuk & Imre, 2007). In this study we show that aspherical particles (in particular, fractal-like agglomerates) can be electrically charged, resulting in a strong dependence of particle morphology on particle charge. Furthermore, particles with a specific charge and associated morphology can be selected using forces that depend on the charge such as electrostatic and/or electrodynamic forces in combination with other forces such as inertial, viscous, or gravitational forces and with the use of spatial or temporal gates (Hinds, 1999). An early example of this is the Millikan oil-drop experiment (Pearson, 2005); however, our study uses a more practical charge separating instrument, the electrostatic classifier (hereafter referred to as EC). The EC utilizes a combination of a viscous and electrostatic force to select a combination of charge q and aerodynamic particle size with a spatial gate. The EC is widely used for particle sizing and for the generation of monodisperse aerosols in the size ranging from to 1.0 μm (Knutson & Whitby, 1975). An EC passes a polydisperse sample through a Kr-85 radioactive charge neutralizer where particles attain a Boltzmann charge distribution, followed by the extraction of a known size fraction of positively charged particles using a spatially varying electric field. The velocity of the extracted fraction of particles inside an EC is a function of the field strength and of the particle electrical mobility, which in turn is a function of the particle net charge (q) and mobility diameter (D m ). However, if an EC is set to predominantly size-select spherical particles with a specific mobility diameter D m and q = e, it also transmits a certain percentage of particles with charge ie and mobility diameter id m, where i is an integer number. At any EC setting, depending on the polydispersivity of the particle size distribution, multiple particle size modes are being often transmitted (Manual for the Series 3080 Electrostatic Classifiers, 2006). We carried out experiments using ECs to specifically select cluster dilute agglomerates with identical D m but carrying (a) predominantly q= e, and (b) predominantly q= 2e. The cluster dilute regime is defined as the regime with a large ratio of the mean cluster nearest-neighbor separation to cluster size. (Dhaubhadel, Pierce, Chakrabarti, & Sorensen, 2006). Quantitative analysis of agglomerate morphology with the help of a scanning electron microscope (SEM) and image processing techniques showed that agglomerates with predominantly q = 2e possess very different ensemble morphology when compared to those with q = e. This phenomenon was observed for both short-chained ( 220 nm) and sub-micron-sized ( nm) agglomerates. Details regarding the experiments, analysis procedures, and the research results are discussed in the following sections. 2. Methods 2.1. Experimental setup Nanometer-scale soot aerosol agglomerates were produced using flame synthesis, which is a well-established industrial technology for producing aerosols on a large-scale (Friedlander, 1977). A schematic of the experimental setup is shown in Fig. 1. Soot agglomerates were produced by a premixed flame supported on a cooled porous frit burner (McKenna products) through combustion of ethene (C 2 H 4 )( l min 1 STP) and oxygen (O 2 )( l min 1 STP) premixed with a dilution flow of nitrogen (N 2 )( l min 1 STP) and surrounded by an N 2 sheath flow ( 25 l min 1 STP). The premixed gases were passed through a 6-cm diameter porous frit, which in turn was surrounded by a 0.5-cm wide annular sheath region through which N 2 was passed. The flame was maintained at an equivalence ratio of 2.8. Equivalence ratio is defined as the fuel to oxygen ratio divided by the stoichiometric fuel-to-oxygen ratio which can be written as φ = (n fuel /n oxygen )/((n fuel /n oxygen ) stoich ), where n stands for the number of moles of fuel or oxygen. In the present study, we chose to maintain the flame at a fuel-rich of 2.8 to obtain soot with a relatively high ratio of black-carbon to organic carbon (Slowik & Steinkan, 2004). The premixed gas and sheath flows were contained by glass housing shaped to minimize convective mixing, thereby ensuring that the flame stoichiometry was well-characterized at the point of sampling. Prior to sampling, the flatness of the flame, i.e. uniformity across a given flame cross-section was checked. A diagram of the sampling tip is shown in the inset to Fig. 1. The sampling tip consists of two concentric stainless steel tubes with particles carried up the inner tube while a separate carrier gas (N 2 )flow (14.5 l min 1 STP) is passed down the outer tube and then back up the inner tube. The gas flow around the lip of the innertube prevented soot buildup in this region and diluted the particle concentration. Particle sampling was carried out in the overfire region of the flame, where the characteristic flame residence times are roughly an order of magnitude longer than the laminar smoke point residence time. Soot particles in the long residence time regime are fully formed
4 R.K. Chakrabarty et al. / Aerosol Science 39 (2008) Fig. 1. Experimental setup. Schematic diagram of the experimental setup used for soot generation and characterization. Soot agglomerates were produced using a ethene/oxygen premixed flame system. The particle flow was directed through one of the two separate paths, A or B. Though path A (shown in bold lines) particles with D m = 220/460 nm and q = e were predominantly selected, while through path B (shown in dashed lines) particles with D m = 220/460 nm and q = 2e were selected. Particle flows exiting either of the pathways were further split into a sampling platform for scanning electron microscopy (SEM), and the scanning mobility particle sizer (SMPS) for morphology and size characterization. into agglomerates and their properties are fairly independent of position, which facilitates sampling of a steady and uniform distribution of particles. The gas flow carrying the diluted soot particles was then passed through an impactor to remove particles larger than about 5 μm in diameter. Sample flow exiting the impactor was directed through either path A containing a single EC, or through path B containing two ECs in series (Fig. 1). The particles were bipolarly charged using a neutralizer (model Kr-85, TSI Inc., St. Paul, MN, USA) before entering any of the identical ECs (Model 3080, TSI Inc., St. Paul, MN, USA). Two set of experiments were carried out using the setup with identical operating conditions for studying charge-related differences in agglomerate morphology corresponding to D m = 220 and 460 nm, respectively. For each set of experiments, the EC in path A was set to predominantly size select soot particles with q = e and a D m (either 220 or 460 nm). In path B the sheath flow rate of the first EC was adjusted such that the second (q = 2e) mode of particles exiting the EC corresponded to the D m in path A. In other words, the second EC size selected as its predominant (q = e) mode the q = 2e mode particles exiting the first EC. For example, in order to size select doubly charged D m = 220 nm particles in path B, the first EC was set to select singly charged particles with D m = 142 nm and doubly charged particles with D m = 220 nm. These particles were neutralized and sent to the second EC, which was set to select singly charged particles with D m =220 nm. In the present study, the D m =460 nm particles were classified using ECs at sheath flow rates of around 5 l min 1, and the D m = 220 nm particles were classified at flow rates of around 8 l min 1. A recent study (Zelenyuk & Imre, 2007) has reported the effect of varying electric fields on alignment of aspherical particles in an EC. The fact that the sheath flow rates of the ECs, during both set of our experiments, were maintained
5 788 R.K. Chakrabarty et al. / Aerosol Science 39 (2008) nearly constant has no bearing on the issue of particle alignment. Owing to a sharp decrease in particle number concentration exiting pathway B because of use of charge neutralizers before both the ECs, the aerosol to sheath flow rate ratio in the ECs for both the pathways were maintained at around 1:4 thereby assuring sufficiently high particle concentrations in path B. Under these flow conditions, the resolution of the EC in path A was approximately ±30%. The serial combination of the two ECs in path B yielded a resolution of approximately ±20%. The ECs were calibrated using National Institute of Standards and Technology (NIST) certified polystyrene sphere latex (PSL) particle size standards. The particle flow exiting each pathway was isokinetically split into a particle sampling unit for SEM, and a scanning mobility particle sizer (SMPS). The SMPS, which consists of an EC and a condensation particle counter (CPC), yields the particle number size distribution in terms of a Gaussian expression (Manual for the Series 3936 Scanning Mobility Particle Sizer (SMPS), 2003; Stolzenberg & McMurry, 1988). For each set of experiments, both the SMPS and the SEM filter sampling were operated in synchronization for one pathway at a time during each set of experiments. In this study the flow rate of the SMPS was set to measure only particles smaller than D m = 670 nm SEM sample preparation For SEM analysis, soot particles were impacted onto 10-μm thick nuclepore clear polycarbonate 13-mm diameter filters (Whatman Inc., Chicago, IL) mounted on Costar Pop-Top Membrane holders. An oil-free pump was used to draw soot particles at a flow rate of 2 l min 1 STP through copper tubing onto the nuclepore filters. The filter exposure time was adjusted to yield a moderate filter loading conducive for performing image analysis of individual agglomerates. After sampling, the filter samples were kept in refrigerated storage and later prepared for SEM analysis by coating them with a 1-nm thick layer of platinum to prevent particle charging during SEM analysis. The coated filters were analyzed using a Hitachi scanning electron microscope (Model S-4700). SEM analysis may change the shape of particles through heat damage and physical damage. Heat damage evaporates semi-volatile components from the filter due to the high accelerating voltage of the electron beam (> 20 kv) operating under vacuum conditions. Physical damage distorts the original particle shape because of particle charging by the electron beam. In this study, a relatively moderate accelerating voltage of 20 kv was used for most images. Compared with lower accelerating voltages, the use of 20 kv improves imaging of the surface and internal structure of the particles. At this operating voltage, shape distortion due to charging was observed in less than 3% of the aggregates. 3. Results and discussion Two-dimensional (2-d) SEM images of about soot agglomerates corresponding to each diameter and net charge were analyzed for morphology and shape quantification using commercial image analysis software (Digital Micrograph 3, Gatan Inc.) and custom image processing routines. Since the inception of the fractal dimension concept, it has found extensive use in quantitatively describing the complex shape of agglomerates (Forrest & Witten, 1979). A simple and common empirical formula for calculating the three-dimensional (3-d) mass fractal dimension D of agglomerates is (Oh & Sorensen, 1997) ( ) D Lmax N = k, (1) d p where N is the number of monomers constituting the agglomerate, d p is the mean monomer diameter, L max is the maximum projected length of the agglomerate, and k is an empirical constant. For soot particles formed via dilute diffusion limited agglomeration processes, such as in a flame, D<2 and the projected 2-d D can be assumed to be approximately equal to the 3-d D (Jullien & Botet, 1987). However, for a finite-sized, 3-d fractal agglomerate, it has been found that parts of the agglomerate can randomly screen other parts during 2-d imaging. This is corrected through a calculation of N in Eq. (1) as (Köylü, Faeth, Farias, & Carvalho, 1995; Oh & Sorensen, 1997) ( ) κ Aagg N =, (2) A mon where κ = 1.10 takes into account of the 2-d screening effect, A agg is the agglomerate projected area, and A mon is the mean cross-sectional monomer area. Particle properties quantified using image analysis include A agg, A mon, d p, and
6 R.K. Chakrabarty et al. / Aerosol Science 39 (2008) Projected Area Diameter Mobility Diameter Projected Area Diameter Mobility Diameter dn/dlogd (Normalised) dn/dlogd (Normalised) Diameter (nm) Diameter (nm) Projected Area Diameter Mobility Diameter Projected Area Diameter Mobility Diameter dn/dlogd (Normalised) dn/dlogd (Normalised) Diameter (nm) Diameter (nm) Fig. 2. Comparison between agglomerate size distributions obtained using two techniques. The SEM projected area equivalent diameter (D eq ) and the SMPS mobility diameter (D m ) number size distribution for (a) soot particles with D m =220 nm and q = e, (b) soot particles with D m =220 nm and q = 2e, (c) soot particles with D m = 460 nm and q = e, and (d) soot particles with D m = 460 nm and q = 2e. L max as previously defined and maximum projected width W max normal to L max. Distribution of agglomerate projected area equivalent diameter D eq, defined as the diameter of a circle of the same area as the particle under consideration, was calculated for all individual agglomerates and compared to the D m distribution of the SMPS. Figs. 2a and b show the normalized number size distribution plot of D eq and D m (measured by SMPS) for q = e and 2e particles corresponding to D m = 220 nm, while Figs. 2c and d show the same for particles corresponding to D m = 460 nm. The predominant modes are comparable in each case, while comparison of higher modes could not be accomplished for 460 nm agglomerates since the SMPS was set to measure only particle diameters below 670 nm in this study. The predominant peaks of the SEM D eq number size distribution in Fig. 2 scales with the SMPS D m distribution as D eq Dm α, where α is the exponent characterizing the power law relationship. For both size distributions, α was found to be approximately 1, as expected (Chakrabarty, Moosmüller, et al., 2006; Rogak, Flagan, & Nguyen, 1993). These
7 790 R.K. Chakrabarty et al. / Aerosol Science 39 (2008) Table 1 Calculated values of agglomerate morphological properties D m and q α (D eq D α m ) β (L max D β eq) γ (D qe D γ eq) D (using Eq. (1)) D (box-counting method) Aspect ratio Roundness 220 nm, q = e 1.01 ± ± ± ± ± ± ± nm, q = 2e 1.01 ± ± ± ± ± ± ± nm, q = e 1.15 ± ± ± ± ± ± ± nm, q = 2e 1.1 ± ± ± ± ± ± ±.14 The mean values of the analyzed 2-d morphological parameters from SEM images of singly and doubly charged particles corresponding to mobility diameters 220 and 460 nm, respectively. The uncertainties reported in the table correspond to standard errors/deviations. empirical relationships helped to specifically segregate out only those particles from SEM images which were centered around 220/460 nm for morphology analysis. The larger particles corresponding to the multiply charged modes were not included for morphology analysis. Mass fractal dimension D for the agglomerates was calculated using (a) Eq. (1), and (b) the box counting technique (Kaye, 1989). The box counting technique involves calculating the number of cells required to entirely cover a particle, with grids of cells of varying size. The logarithm of the number of occupied cells versus the logarithm of the size of one cell gives a line whose gradient corresponds to the fractal dimension of the particle. Two shape descriptors namely aspect ratio and roundness, which are sensitive to particle elongation, were calculated from the projected particle properties (Chakrabarty, Moosmüller, et al., 2006). The scaling exponent β of the power-law relationship between L max D β eq, another parameter indicative of particle elongation, was also calculated for each of the agglomerates. In the case of charging of spherical particles in a bipolar ionic environment, the Boltzmann distribution is a good approximation for calculating the fraction of particles carrying charge ie, where i is an integer 1(Rogak & Flagan, 1992). For D<2 agglomerates the same approximation, after a slight modification in its formulation, was also found to hold good within ±10% (Wen, Reischl, & Kasper, 1984a, 1984b). The modification involved replacing of the physical diameter term in the Boltzmann distribution expression with a parameter called the charging equivalent diameter D qe for fractal-like agglomerates. We calculated the D qe of the individual agglomerates, which in turn is a direct representative of the average net-charge residing on the agglomerates, and scaled it with their respective D eq (which is approximately equal to their D m ) as D qe D γ eq, where γ is the power law relationship exponent. Table 1 lists the mean values of all the analyzed 2-d morphological parameters from SEM images of particles with q = e and 2e, and corresponding to D m = 220 and 460 nm, respectively. The analysis results summarized in Table 1 imply that for soot agglomerates produced under similar flame conditions and possessing the same mobility diameter, the morphology of doubly charged (q = 2e) particles is distinctly different from that of singly charged (q = e) particles. The lower values of fractal dimensions and shape descriptors suggest more elongated and open morphology for q = 2e particles in comparison with q = e particles, which possess more compact and rounded morphology. Typical morphology of singly and doubly charged agglomerates corresponding to both mobility diameters of 220 and 460 nm, respectively are shown in Fig. 3. The values of D observed in this study for the singly charged particles, of D m = 220 and 460 nm, correspond with previously reported values of D for soot agglomerates grown via diffusion-limited-agglomeration process in pre-mixed flames (Cai, Lu, & Sorensen, 1993; Köylü, Faeth, et al., 1995). The higher value of the charging equivalent diameters for q = 2e agglomerates suggest more over-equilibrium charge deposited on them than their counterpart agglomerates with q = e. This observation is in accordance with the qualitative reasoning that the likelihood of a particle acquiring a certain number of charges in the charging process depends on its morphology. For example, more elongated particles are more likely to acquire a second charge than spherical particles as, for the same particle mass, the second charge can be located at a larger distance from the first charge thereby requiring less energy for the charging process and significantly changing the charging probability at room temperature. In conclusion, our novel morphology classification technique of charging aspherical particles in order to obtain different morphologies as function of charge, and separating these morphologies based on their charge should find applications in a variety of nano and microparticle-related procedures as a simple and inexpensive morphology-classification technique. Future research work needs to characterize and optimize the application of this technique to different types of particles and at different operating conditions (e.g., temperature) and to identify limitations of this technique.
8 R.K. Chakrabarty et al. / Aerosol Science 39 (2008) Fig. 3. Electron microscopy images of singly and doubly charged agglomerates. Typical agglomerate morphology of (a) soot particles with D m = 220 nm and q = e, (b) soot particles with D m = 220 nm and q = 2e, (c) soot particles with D m = 460 nm and q = e, and (d) soot particles with D m = 460 nm and q = 2e. The elongated morphology of doubly charged particles is apparent. Acknowledgments This research was partially supported by the U.S. Department of Energy Atmospheric Science Program through Grants DE-FG02-05ER64008, DE-FG02-98ER62581, and DE-FG02-05ER63995, by the National Air and Space Administration (NASA) through the Upper Atmosphere Research Program Contract NAG and the Atmospheric Chemistry Program Contract NNH04CC09C, and by the Atmospheric Chemistry Program of the National Science Foundation (NSF) Grant nos. ATM and ATM Rajan K. Chakrabarty and Mark A. Garro acknowledge the support received from the National Science Foundation (Grant no ) for carrying out this research work. Jay G. Slowik and Eben S. Cross were funded by the NASA Earth System Science Fellowship Program. References Aitken, R. J., Chaudhry, M. Q., & Boxall, A. B. A (2006). Manufacture and use of nanomaterials: Current status in the UK and global trends. Occupational Medicine Oxford, 56, Cai, J., Lu, N., & Sorensen, C. M. (1993). Comparison of size and morphology of soot aggregates as determined by light-scattering and electronmicroscope analysis. Langmuir, 9, Chakrabarty, R. K., Moosmüller, H., Garro, M. A., Arnott, W. P., Walker, J. W., Susott, R. A., et al. (2006). Emissions from the laboratory combustion of wildland fuels: Particle morphology and size. Journal of Geophysical Research, 111(D07204), doi: /2005jd
9 792 R.K. Chakrabarty et al. / Aerosol Science 39 (2008) Dhaubhadel, R., Pierce, F., Chakrabarti, A., & Sorensen, C. M. (2006). Hybrid superaggregate morphology as a result of aggregation in a cluster-dense aerosol. Physical Review E, 73(1). Ebbesen, T. W., & Ajayan, P. M. (1992). Large-scale synthesis of carbon nanotubes. Nature, 358(6383), Forrest, S. R., & Witten, T. A. (1979). Long-range correlations in smoke-particle aggregates. Journal of Physics A Mathematical and General, 12(5), L109 L117. Friedlander, S. K. (1977). Smoke, dust, and haze. New York: Wiley-Interscience. Height, M. J., Howard, J. B., Tester, J. W., & Sande, J. B. V. (2004). Flame synthesis of single-walled carbon nanotubes. Carbon, 42(11), Hinds, W. C. (1999). Aerosol technology (Vol. xx, 483pp). New York: Wiley Interscience. Industrial application of nanomaterials Chances and risk (2004). Future Technologies Division of VDI Technologiezentrum GmbH, (Vol. 54, 111pp.). Dusseldorf. Jullien, R., & Botet, R. (1987). Aggregation and fractal aggregates (Vol. ix, 120pp.). Singapore: World Scientific. Kaye, B. H. (1989). A random walk through fractal dimensions (Vol. xxv, 421pp.). New York, NY: VCH Publishers. Knutson, E. O., & Whitby, K. T. (1975). Aerosol classification by electric mobility: Apparatus, theory, and applications. Journal of Aerosol Science, 6(6), Köylü, Ü. Ö., Faeth, G. M., Farias, T. L., & Carvalho, M. G. (1995). Fractal and projected structure properties of soot aggregates. Combustion and Flame, 100(4), Manual for the Series 3080 Electrostatic Classifiers. (2006). Minnesota, TSI. Manual for the Series 3936 Scanning Mobility Particle Sizer (SMPS). (2003). Minnesota, TSI. Oh, C., & Sorensen, C. M. (1997). The effect of overlap between monomers on the determination of fractal cluster morphology. Journal of Colloid and Interface Science, 193(1), Pearson, E. F. (2005). Revisiting Millikan s oil-drop experiment. Journal of Chemical Education, 82(6), Rao, C. N. R. (2004). New developments in nanomaterials. Journal of Materials Chemistry, 14(4), E4. Rogak, S. N., & Flagan, R. C. (1992). Bipolar diffusion charging of spheres and agglomerate aerosol particles. Journal of Aerosol Science, 23(7), Rogak, S. N., Flagan, R. C., & Nguyen, H. V. (1993). The mobility and structure of aerosol agglomerates. Aerosol Science and Technology, 18(1), Slowik, J. G., Steinkan, K., et al. (2004). Particle morphology and density characterization by combined mobility and aerodynamic diameter measurements. Part 2: Application to combustion-generated soot aerosol as a function of fuel equivalence ratio. Aerosol Science and Technology, 38, Stevens, M. M., & George, J. H. (2005). Exploring and engineering the cell surface interface. Science, 310(5751), Stolzenberg, M. R., & McMurry, P. H. (1988). TDMAFIT user s manual (Vol. 653). PTL, University of Minnesota. Waseda, Y., & Muramatsu, A. (2003). Morphology control of materials and nanoparticles: Advanced materials processing and characterization, Springer series in materials science (Vol. 64, 284pp.). New York: Springer. Wen, H. Y., Reischl, G. P., & Kasper, G. (1984a). Bipolar diffusion charging of fibrous aerosol particles I. Charge and electrical mobility, measurements on linear chain aggregates. Journal of Aerosol Science, 15(2), Wen, H. Y., Reischl, G. P., & Kasper, G. (1984b). Bipolar diffusion charging of fibrous aerosol particles I. Charging theory. Journal of Aerosol Science, 15(2), Zelenyuk, A., & Imre, D. (2007). On the effect of particle alignment in the DMA. Aerosol Science and Technology, 41(2),
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