The Bipolar Diffusion Charging of Nanoparticles: A Review and Development of Approaches for Non-Spherical Particles

REFERENCES

• Adachi, M., Kousaka Y., and Okuyama K. (1985). Unipolar and Bipolar Diffusion Charging of Ultrafine Aerosol-Particles. J. Aerosol Sci., 16:109–123.
   Web of Science ®Google Scholar
• Adachi, M., Okuyama, K., Kozuru, H., Kousaka, Y., and Pui, D. Y. H. (1989). Bipolar Diffusion Charging of Aerosol Particles Under High Particle/Ion Concentration Ratios. J. Aerosol Sci., 11:144–156.
   Web of Science ®Google Scholar
• Allen, J. E. (1992). Probe Theory - The Orbital Motion Approach. Phys. Scr. 45:497–503.
   Web of Science ®Google Scholar
• Alonso, M., and Alguacil, F. J. (2003). The Effect of Ion and Particle Losses in a Diffusion Charger on Reaching a Stationary Charge Distribution. J. Aerosol Sci., 34:1647–1664.
   Web of Science ®Google Scholar
• Alonso, M., Hernandez-Sierra, A., and Alguacil, F. J. (2002). Diffusion Charging of Aerosol Nanoparticles with an Excess of Bipoloar Ions. J. Phys. a-Mathemat. General, 35:6271–6280.
   Google Scholar
• Bricard, J. (1962). La Fixation des Petits Ions Atmosphériques Sur les Aérosols Ultra-Fins. Pure Appl. Geophys., 51:237–242.
   Google Scholar
• Brock, J. R. (1970). Aerosol Charging: The Role of Image Force. J. Appl. Phys., 41:843–844.
   Web of Science ®Google Scholar
• Chandrasekhar, S. (1943). Stochastic Problems in Physics and Astronomy. Rev. Modern Phys., 15:1–89.
   Google Scholar
• Chan, T. W., and Mozurkewich, M. (2001). Measurement of the Coagulation Rate Constant for Sulfuric Acid Particles as a Function of Particle Size using Tandem Differential Mobility Analysis. J. Aerosol Sci., 32:321–339.
   Web of Science ®Google Scholar
• Chaudhuri, M., Khrapak, S. A., and Morfill, G. E. (2010). Effect of Ionization/Recombination Processes on the Electrical Interactions Between Positively Charged Particles in Highly Collisional Plasmas. Phys. Plasmas, 17:034503.
   Web of Science ®Google Scholar
• Chen, D. R., Pui, D. Y. H., Hummes, D., Fissan, H., Quant, F. R., and Sem, G. J. (1998). Design and Evaluation of a Nanometer Aerosol Differential Mobility Analyzer (Nano-DMA). J. Aerosol Sci., 29:497–509.
   Web of Science ®Google Scholar
• Dahneke, B. E. (1973). Slip Correction Factors for Nonspherical Bodies—III The Form of the General Law. J. Aerosol. Sci., 4:163–170.
   Google Scholar
• Dahneke, B. E. (1983). Simple Kinetic Theory of Brownian Diffusion in Vapors and Aerosols, in Theory of Dispersed Multiphase Flow, R. E. Meyer, ed., Academic Press, New York.
   Google Scholar
• de La Verpilliere, J. L., Swanson, J. J., and Boies, A. M. (2015). Unsteady Bipolar Diffusion Charging in Aerosol Neutralisers: A Non-Dimensional Approach to Predict Charge Distribution Equilibrium Behaviour. J. Aerosol Sci., 86:55–68.
   Web of Science ®Google Scholar
• D'yachkov, L. G., Khrapak, A. G., Khrapak, S. A., and Morfill, G. E. (2007). Model of Grain Charging in Collisional Plasmas Accounting for Collisionless Layer. Phys. Plasmas, 14:042102.
   Web of Science ®Google Scholar
• Eggersdorfer, M. L., and Pratsinis, S. E. (2014). Agglomerates and Aggregates of Nanoparticles Made in the Gas Phase. Adv. Powder Technol., 25:71–90.
   Web of Science ®Google Scholar
• Ehn, M., Junninen, H., Schobesberger, S., Manninen, H. E., Franchin, A., Sipilä, M., Petäjä, T., Kerminen, V.-M., Tammet, H., Mirme, A., Mirme, S., Hõrrak, U., Kulmala, M., and Worsnop, D. R. (2011). An Instrumental Comparison of Mobility and Mass Measurements of Atmospheric Small Ions. J. Aerosol Sci., 45:522–532.
   Web of Science ®Google Scholar
• Eichelberger, B. R., Snow, T. P., and Bierbaum, V. M. (2003). Collision Rate Constants for Polarizable Ions. J. Amer. Soc. Mass Spectrom., 14:501–505.
   PubMed Web of Science ®Google Scholar
• Ermak, D. L., and Buckholz, H. (1980). Numerical-Integration of the Langevin Equation—Monte-Carlo Simulation. J. Comput. Phys., 35:169–182.
   Web of Science ®Google Scholar
• Fernández-García, J., and Fernández de la Mora, J. (2014). Electrical Mobilities of Multiply Charged Ionic-Liquid Nanodrops in Air and Carbon Dioxide Over a Wide Temperature Range: Influence of Ion-Induced Dipole Interactions. Phys. Chem. Chem. Phys., 16:20500–20513.
   PubMed Web of Science ®Google Scholar
• Filippov, A. V. (1993). The Charging of Aerosol in the Transition Regime. J. Aerosol Sci., 24:423–436.
   Web of Science ®Google Scholar
• Filippov, A. V. (1994). Charge-Distribution Among Nonspherical Particles in a Bipolar Ion Environment. J. Aerosol Sci., 25:611–615.
   Web of Science ®Google Scholar
• Franchin, A., Ehrhart, S., Leppä, J., Nieminen, T., Gagné, S., Schobesberger, S., Wimmer, D., Duplissy, J., Riccobono, F., Dunne, E. M., Rondo, L., Downard, A., Bianchi, F., Kupc, A., Tsagkogeorgas, G., Lehtipalo, K., Manninen, H. E., Almeida, J., Amorim, A., Wagner, P. E., Hansel, A., Kirkby, J., Kürten, A., Donahue, N. M., Makhmutov, V., Mathot, S., Metzger, A., Petäjä, T., Schnitzhofer, R., Sipilä, M., Stozhkov, Y., Tomé, A., Kerminen, V. M., Carslaw, K., Curtius, J., Baltensperger, U., and Kulmala, M. (2015). Experimental Investigation of Ion–Ion Recombination Under Atmospheric Conditions. Atmos. Chem. Phys., 15:7203–7216.
   Web of Science ®Google Scholar
• Friedlander, S. K. (2000). Smoke, Dust, and Haze. Oxford University Press, New York.
   Google Scholar
• Fuchs, N. A. (1963). On the Stationary Charge Distribution on Aerosol Particles in a Bipolar Ionic Atmosphere. Geofis. Pura Appl., 51:185–193.
   Google Scholar
• Fuchs, N. A. (1964). The Mechanics of Aerosols. Macmillan, New York.
   Google Scholar
• Gatti, M., and Kortshagen, U. (2008). Analytical Model of Particle Charging in Plasmas Over a Wide Range of Collisionality. Phys. Rev. E, 78:046402.
   Web of Science ®Google Scholar
• Gopalakrishnan, R., and Hogan, C. J. (2012). Coulomb-Influenced Collisions in Aerosols and Dusty Plasmas. Phys. Rev. E, 85:026410.
   Web of Science ®Google Scholar
• Gopalakrishnan, R., McMurry, P. H., and Hogan, C. J. (2015). The Electrical Mobilities and Scalar Friction Factors of Modest to High Aspect Ratio Particles in the Transition Regime. J. Aerosol Sci., 82:24–39.
   Web of Science ®Google Scholar
• Gopalakrishnan, R., Meredith, M. R., Larriba-Andaluz, C., and Hogan, C. J. (2013a). Brownian Dynamics Determination of the Bipolar Steady State Charge Distribution on Spheres and Non-Spheres in the Transition Regime. J. Aerosol Sci., 63:126–145.
   Web of Science ®Google Scholar
• Gopalakrishnan, R., Thajudeen, T., and Hogan, C. J. (2011). Collision Limited Reaction Rates for Arbitrarily Shaped Particles across the Entire Diffusive Knudsen Number Range. J. Chem. Phys., 135:054302.
   PubMed Web of Science ®Google Scholar
• Gopalakrishnan, R., Thajudeen, T., Ouyang, H., and Hogan, C. J. (2013b). The Unipolar Diffusion Charging of Arbitrary Shaped Aerosol Particles. J. Aerosol Sci., 64:60–80.
   Web of Science ®Google Scholar
• Goree, J. (1992). Ion Trapping by a Charged Dust Grain in a Plasma. Phys. Rev. Lett., 69:277–280.
   PubMed Web of Science ®Google Scholar
• Gunn, R. (1954). Diffusion Charging of Atmospheric Droplets by Ions, and the Resulting Combination Coefficients. J. Meteorol., 11:339–347.
   Google Scholar
• Hagen, D., E., and Alofs, D. J. (1983). Linear Inversion Method to Obtain Aerosol Size Distributions from Measurements with a Differential Mobility Analyzer. J. Aerosol Sci., 2:465–475.
   Web of Science ®Google Scholar
• Hansen, S. (2004). Translational Friction Coefficients for Cylinders of Arbitrary Axial Ratios Estimated by Monte Carlo Simulation. J. Chem. Phys. 121:9111–9115.
   PubMed Web of Science ®Google Scholar
• He, M., and Dhaniyala, S. (2014). Experimental Characterization of Flowrate-Dependent Bipolar Diffusion Charging Efficiencies of Sub-50nm Particles. J. Aerosol Sci., 76:175–187.
   Web of Science ®Google Scholar
• Hogan, C. J., and Fernandez de la Mora, J. (2010). Ion-Pair Evaporation from Ionic Liquid Clusters. J. Amer. Soc. Mass Spectrom., 21:1382–1386.
   PubMed Web of Science ®Google Scholar
• Hogan, C. J., Li, L., Chen, D. R., and Biswas, P. (2009). Estimating Aerosol Particle Charging Parameters using a Bayesian Inversion Technique. J. Aerosol Sci., 40:295–306.
   Web of Science ®Google Scholar
• Hogan, C. J., and Fernandez de la Mora, J. (2009). Tandem Ion Mobility-Mass Spectrometry (IMS-MS) Study of Ion Evaporation from Ionic Liquid-Acetonitrile Nanodrops. Phys. Chem. Chem. Phys., 11:8079–8090.
   PubMed Web of Science ®Google Scholar
• Hoppel, W. A., and Frick, G. M. (1986). Ion-Aerosol Attachment Coefficients and the Steady-State Charge Distribution on Aerosols in a Bipolar Ion Environment. J. Aerosol Sci., 5:1–21.
   Web of Science ®Google Scholar
• Hoppel, W. A., and Frick, G. M. (1990). The Nonequilibrium Character of the Aerosol Charge-Distributions Produced by Neutralizers. J. Aerosol Sci., 12:471–496.
   Web of Science ®Google Scholar
• Hsieh, E. T.-Y., and Castleman, A. W. Jr (1981). A Reconsideration of the Theory of Capture Cross-Sections for Ion/Molecule Reactions and a Total Energy and Angular Momentum Conserved Average Charge—Dipole Interaction Theory (teams). Int. J. Mass Spectrom. Ion Phys., 40:295–329.
   Web of Science ®Google Scholar
• Hubbard, J. B., and Douglas, J. F. (1993). Hydrodynamic Friction of Arbitrarily Shaped Brownian Particles. Phys. Rev. E, 47:R2983–R2986.
   PubMed Web of Science ®Google Scholar
• Hussin, A., Scheibel, H. G., Becker, K. H., and Porstendörfer, J. (1983). Bipolar Diffusion Charging of Aerosol Particles—I: Experimental Results within the Diameter Range 4–30 nm. J. Aerosol Sci., 14:671–677.
   Web of Science ®Google Scholar
• Jiang, J., Kim, C., Wang, X., Stolzenburg, M. R., Kaufman, S. L., Qi, C., Sem, G. J., Sakurai, H., Hama, N., and McMurry, P. H. (2014). Aerosol Charge Fractions Downstream of Six Bipolar Chargers: Effects of Ion Source, Source Activity, and Flowrate. J. Aerosol Sci., 48:1207–1216.
   Web of Science ®Google Scholar
• Kaufman, S. L. (1998). Analysis of Biomolecules using Electrospray and Nanoparticle Methods: The Gas-Phase Electrophoretic Mobility Molecular Analyzer (GEMMA). J. Aerosol Sci., 29:537–552.
   Web of Science ®Google Scholar
• Khrapak, S., and Morfill, G. (2009). Basic Processes in Complex (Dusty) Plasmas: Charging, Interactions, and Ion Drag Force. Contrib. Plasma Phys., 49:148–168.
   Web of Science ®Google Scholar
• Khrapak, S. A., Ratynskaia, S. V., Zobnin, A. V., Usachev, A. D., Yaroshenko, V. V., Thoma, M. H., Kretschmer, M., Höfner, H., Morfill, G. E., Petrov, O. F., and Fortov, V. E. (2005). Particle Charge in the Bulk of Gas Discharges. Phys. Rev. E, 72:016406.
   Web of Science ®Google Scholar
• Kilpatrick, W. D. (1971). An Experimental Mass-Mobility Relation for Ions in Air at Atmospheric Pressure, in Proceedings of the 1s9th Annual Conference on Mass Spectroscopy.
   Google Scholar
• Knutson, E. O., and Whitby, K. T. (1975). Aerosol Classification By Electric Mobility: Apparatus, Theory, and Applications. J. Aerosol Sci., 6:443–451.
   Google Scholar
• Ku, B. K., Deye, G. J., Kulkarni, P., and Baron, P. A. (2011). Bipolar Diffusion Charging of High-Aspect Ratio Aerosols. J. Electrostat., 69:641–647.
   Web of Science ®Google Scholar
• Kulkarni, P., Deye, G. J., and Baron, P. A. (2009). Bipolar Diffusion Charging Characteristics of Single-Wall Carbon Nanotube Aerosol Particles. J. Aerosol Sci., 40:164–179.
   Web of Science ®Google Scholar
• Langevin (1905). Une Formule Fondamentale de Theorie Cinetique. Annales de Chimie et de Phys., 5:245–288.
   Google Scholar
• Larriba, C., Hogan, C. J., Attoui, M., Borrajo, R., Fernandez-Garcia, J., and Fernandez de la Mora, J. (2011). The Mobility-Volume Relationship below 3.0 nm examined by Tandem Mobility-Mass Measurement. J. Aerosol Sci., 45:453–467.
   Web of Science ®Google Scholar
• Larriba, C., Fernandez de la Mora, J., and Clemmer, D. E. (2014). Electrospray Ionization Mechanisms for Large Polyethylene Glycol Chains Studied Through Tandem Ion Mobility Spectrometry. J. Amer. Soc. Mass Spectrom., 25:1332–1345.
   PubMed Web of Science ®Google Scholar
• Lawless, P. A. (1996). Particle Charging Bounds, Symmetry Relations, and an Analytic Charging Rate Model for the Continuum Regime. J. Aerosol Sci., 27:191–215.
   Web of Science ®Google Scholar
• Lee, H. M., Kim, C. S., Shimada, M., and Okuyama, K. (2005). Effects of Mobility Changes and Distribution of Bipolar Ions on Aerosol Nanoparticle Diffusion Charging. J. Chem. Eng. Jpn., 38:486–496.
   Web of Science ®Google Scholar
• Lenggoro, I. W., Widiyandari, H., Hogan, C. J., Biswas, P., and Okuyama, K. (2007). Colloidal Nanoparticle Analysis by Nanoelectrospray Size Spectrometry with a Heated Flow. Anal. Chimica Acta, 585:193–201.
   PubMed Web of Science ®Google Scholar
• Liu, B. Y. H., and Pui, D. Y. H. (1974). Equilibrium Bipolar Charge Distribution of Aerosols. J. Colloid Interface Sci., 49:305–312.
   Web of Science ®Google Scholar
• Li, M., You, R., Mulholland, G. W., and Zachariah, M. R. (2013). Evaluating the Mobility of Nanorods in Electric Fields. J. Aerosol Sci., 47:1101–1107.
   Web of Science ®Google Scholar
• López-Yglesias, X., and Flagan, R. C. (2013). Ion–Aerosol Flux Coefficients and the Steady-State Charge Distribution of Aerosols in a Bipolar Ion Environment. J. Aerosol Sci., 47:688–704.
   Web of Science ®Google Scholar
• Lòpez-Yglesias, X., and Flagan, R. C. (2013). Population Balances of Micron-Sized Aerosols in a Bipolar Ion Environment. J. Aerosol Sci., 47:681–687.
   Web of Science ®Google Scholar
• Loyalka, S. K. (1973). Condensation on a Spherical Droplet. J. Chem. Physics 58:354.
   Web of Science ®Google Scholar
• Lushnikov, A. A., and Kulmala, M. (2004). Flux-Matching Theory of Particle Charging. Phys. Rev. E, 70:046413.
   Web of Science ®Google Scholar
• Maisser, A., Thomas, J. M., Larriba-Andaluz, C., He, S., and Hogan, C. J. (2015). The Mass-Mobility Distributions of Ions Produced by a Po-210 Source in Air. J. Aerosol Sci., 90:36–50.
   Web of Science ®Google Scholar
• Manirakiza, E., Seto, T., Osone, S., Fukumori, K., and Otani, Y. (2013). High-Efficiency Unipolar Charger for Sub-10 nm Aerosol Particles Using Surface-Discharge Microplasma with a Voltage of Sinc Function. J. Aerosol Sci., 47:60–68.
   Web of Science ®Google Scholar
• Maricq, M. M. (2008). Bipolar Diffusion Charging of Soot Aggregates. J. Aerosol Sci., 42:247–254.
   Web of Science ®Google Scholar
• Marlow, W. H., and Brock, J. R. (1975). Calculations of Bipolar Charging of Aerosols. J. Colloid Interface Sci., 51:23–31.
   Web of Science ®Google Scholar
• Mohnen, V. A. (1976). Formation, Nature, and Mobility of Ions of Atmospheric Importance, in Electrical Processes in Atmospheres, H. Dolezalek, R. Reiter, and H. Landsberg, eds., Steinkopff, Darmstadt, Germany, pp. 1–17.
   Google Scholar
• Mott-Smith, H. M., and Langmuir, I. (1926). The Theory of Collectors in Gaseous Discharges. Phys. Rev., 28:727–763.
   Google Scholar
• Northrup, S. H., Allison, S. A., and McCammon, J. A. (1984). Brownian Dynamics Simulation of Diffusion-Influenced Bimolecular Reactions. J. Chem. Phys., 80:1517–1526.
   Web of Science ®Google Scholar
• Ouyang, H., Gopalakrishnan, R., and Hogan, C. J. (2012). Nanoparticle Collisions in the Gas Phase in the Presence of Singular Contact Potentials. J. Chem. Phys., 137:064316.
   PubMed Web of Science ®Google Scholar
• Ouyang, H., Larriba-Andaluz, C., Oberreit, D. R., and Hogan, C. J. (2013). The Collision Cross Sections of Iodide Salt Cluster Ions in Air via Differential Mobility Analysis-Mass Spectrometry. J. Amer. Soc. Mass Spectrom., 24:1833–1847.
   PubMed Web of Science ®Google Scholar
• Park, M., Li, M., Shin, W. G., Moon, H. J., and Ko, S. H. (2014). Electrical Mobility of Silver Nanowires in Transition and Continuum Regimes. J. Aerosol Sci., 72:21–31.
   Web of Science ®Google Scholar
• Porstendörfer, J., Hussin, A., Scheibel, H. G., and Becker, K. H. (1984). Bipolar Diffusion Charging of Aerosol Particles—II. Influence of the Concentration Ratio of Positive and Negative Ions on the Charge Distribution. J. Aerosol Sci., 15:47–56.
   Web of Science ®Google Scholar
• Reischl, G. P., Mäkelä, J. M., Karch, R., and Necid, J. (1996). Bipolar Charging of Ultrafine Particles in the Size Range Below 10 nm. J. Aerosol Sci., 27:931–949.
   Web of Science ®Google Scholar
• Reischl, G. P., Scheibel, H. G., and Porstendörfer, J. (1983). The Bipolar Charging of Aerosols: Experimental Results in the Size Range Below 20-nm Particle Diameter. J. Colloid Interface Sci., 91:272–275.
   Web of Science ®Google Scholar
• Rus, J., Moro, D., Sillero, J. A., Royuela, J., Casado, A., Estevez-Molinero, F., and Fernandez de la Mora, J. (2010). IMS–MS Studies Based on Coupling a Differential Mobility Analyzer (DMA) to Commercial API–MS Systems. Int. J. Mass Spectrom., 298:30–40.
   Web of Science ®Google Scholar
• Sahni, D. C. (1966). The Effect of a Black Sphere on the Flux Distribution in an Infinite Moderator. J. Nuclear Ener., 20:915.
   Web of Science ®Google Scholar
• Sahni, D. C. (1983). An Exact Solution of Fokker-Planck Equation and Brownian Coagulation in the Transition Regime. J. Colloid Interface Sci., 91:418–429.
   Web of Science ®Google Scholar
• Shimada, M., Han, B. W., Okuyama, K., and Otani, Y. (2002). Bipolar Charging of Aerosol Nanoparticles by a Soft X-Ray Photoionizer. J. Chem. Eng. Jpn., 35:786–793.
   Web of Science ®Google Scholar
• Shin, W. G., Mulholland, G. W., and Pui, D. Y. H. (2010). Determination of Volume, Scaling Exponents, and Particle Alignment of Nanoparticle Agglomerates using Tandem Differential Mobility Analyzers. J. Aerosol Sci., 41:665–681.
   Web of Science ®Google Scholar
• Sorensen, C. M. (2011). The Mobility of Fractal Aggregates: A Review. J. Aerosol Sci., 45:765–779.
   Web of Science ®Google Scholar
• Steiner, G., Jokinen, T., Junninen, H., Sipila, M., Petaja, T., Worsnop, D., Reischl, G. P., and Kulmala, M. (2014). High-Resolution Mobility and Mass Spectrometry of Negative Ions Produced in a Am-241 Aerosol Charger. J. Aerosol Sci., 48:261–270.
   Web of Science ®Google Scholar
• Steiner, G., and Reischl, G. P. (2012). The Effect of Carrier Gas Contaminants on the Charging Probability of Aerosols Under Bipolar Charging Conditions. J. Aerosol Sci., 54:21–31.
   PubMed Web of Science ®Google Scholar
• Stober, J., Schleicher, B., and Burtscher, H. (1991). Bipolar Diffusion Charging of Particles in Noble Gases. J. Aerosol Sci., 14:66–73.
   Web of Science ®Google Scholar
• Stolzenburg, M. R., and McMurry, P. H. (1991). An Ultrafine Aerosol Condensation Nucleus Counter. J. Aerosol Sci., 14:48–65.
   Web of Science ®Google Scholar
• Stolzenburg, M. R., and McMurry, P. H. (2008). Equations Governing Single and Tandem DMA Configurations and a New Lognormal Approximation to the Transfer Function. J. Aerosol Sci., 42:421–432.
   Web of Science ®Google Scholar
• Stommel, Y. G., and Riebel, U. (2005). A Corona-Discharge-Based Aerosol Neutralizer Designed for use with the SMPS-System. J. Electrostat., 63:917–921.
   Web of Science ®Google Scholar
• Stommel, Y. G., and Riebel, U. (2007). Comment on the Calculation of the Steady-State Charge Distribution on aerosols <100 nm by Three Body Trapping Method in a Bipolar Ion Environment. J. Aerosol Sci., 41:840–847.
   Web of Science ®Google Scholar
• Su, T., and Bowers, M. T. (1973). Ion-Polar Molecule Collisions - Effect of Molecular-Size on Ion-Polar Molecule Rate Constants. J. Amer. Chem. Soc., 95:7609–7610.
   Web of Science ®Google Scholar
• Talukdar, S. S., and Swihart, M. T. (2003). An Improved Data Inversion Program for Obtaining Aerosol Size Distributions from Scanning Differential Mobility Analyzer Data. J. Aerosol Sci., 37:145–161.
   Web of Science ®Google Scholar
• Tanaka, Y., Higashi, H., Manirakiza, E., Seto, T., Otani, Y., and Hirasawa, M. (2014). Charge Neutralization of Aerosol Carbon Nanofibers. J. Chem. Eng. Jpn. 47:644–650.
   Web of Science ®Google Scholar
• Thajudeen, T., Jeon, S., and Hogan, C. J. (2015). The Mobility of Flame Synthesized Aggregates/Agglomerates in the Transition Regime. J. Aerosol Sci., 80:45–57.
   Web of Science ®Google Scholar
• Tigges, L., Jain, A., and Schmid, H. J. (2015). On the Bipolar Charge Distribution used for Mobility Particle Sizing: Theoretical Considerations. J. Aerosol Sci., 88:119–134.
   Web of Science ®Google Scholar
• Timko, M. T., Yu, Z., Kroll, J., Jayne, J. T., Worsnop, D. R., Miake-Lye, R. C., Onasch, T. B., Liscinsky, D., Kirchstetter, T. W., Destaillats, H., Holder, A. L., Smith, J. D., and Wilson, K. R. (2009). Sampling Artifacts from Conductive Silicone Tubing. J. Aerosol Sci., 43:855–865.
   Web of Science ®Google Scholar
• Ude, S., and Fernandez de la Mora, J. (2005). Molecular Monodisperse Mobility and Mass Standards from Electrosprays of Tetra-alkyl Ammonium Halides. J. Aerosol Sci., 36:1224–1237.
   Web of Science ®Google Scholar
• Wagner, P. E., and Kerker, M. (1977). Brownian Coagulation of Aerosols in Rarified Gases. J. Chem. Phys., 66:638–646.
   Web of Science ®Google Scholar
• Wellisch, E. M. (1909). The Mobilities of the Ions Produced by Rontgen Rays in Gases and Vapours. Philosophic Transac Royal Soci London. Series A, Containing Papers of a Mathematical or Physical Character 209:249–279.
   Google Scholar
• Wen, H. Y., Reischl, G. P., and Kasper, G. (1984a). Bipolar Diffusion Charging of Fibrous Aerosol-Particles. 1. Charging Theory. J. Aerosol Sci., 15:89–101.
   Web of Science ®Google Scholar
• Wen, H. Y., Reischl, G. P., and Kasper, G. (1984b). Bipolar Diffusion Charging of Fibrous Aerosol-Particles. 2. Charge and Electrical Mobility Measurements on Linear-Chain Aggregates. J. Aerosol Sci., 15:103–122.
   Web of Science ®Google Scholar
• Wiedensohler, A. (1988). An Approximation of the Bipolar Charge-Distribution for Particles in the Sub-Micron Size Range. J. Aerosol Sci., 19:387–389.
   Web of Science ®Google Scholar
• Wiedensohler, A., Birmili, W., Nowak, A., Sonntag, A., Weinhold, K., Merkel, M., Wehner, B., Tuch, T., Pfeifer, S., Fiebig, M., Fjäraa, A. M., Asmi, E., Sellegri, K., Depuy, R., Venzac, H., Villani, P., Laj, P., Aalto, P., Ogren, J. A., Swietlicki, E., Williams, P., Roldin, P., Quincey, P., Hüglin, C., Fierz-Schmidhauser, R., Gysel, M., Weingartner, E., Riccobono, F., Santos, S., Grüning, C., Faloon, K., Beddows, D., Harrison, R., Monahan, C., Jennings, S. G., O'Dowd, C. D., Marinoni, A., Horn, H.-G., Keck, L., Jiang, J., Scheckman, J., Mcmurry, P. H., Deng, Z., Zhao, C. S., Moerman, M., Henzing, B., De Leeuw, G., Löschau, G., and Bastian, S. (2012). Mobility Particle Size Spectrometers: Harmonization of Technical Standards and Data Structure to Facilitate High Quality Long-Term Observations of Atmospheric Particle Number Size Distributions. Atmos. Measurement Tech., 5:657–685.
   Web of Science ®Google Scholar
• Wiedensohler, A., and Fissan, H. J. (1991). Bipolar Charge-Distributions of Aerosol-Particles in High-Purity Argon and Nitrogen. J. Aerosol Sci., 14:358–364.
   Web of Science ®Google Scholar
• Wiedensohler, A., Lutkemeier, E., Feldpausch, M., and Helsper, C. (1986). Investigation of the Bipolar Charge-Distribution at Various Gas Conditions. J. Aerosol Sci., 17:413–416.
   Web of Science ®Google Scholar
• Wild, M., Meyer, J., and Kasper, G. (2012). A fast and Accurate Method of using Electrical Mobility Scans for the Direct Measurement of Aerosol Charge Distributions. J. Aerosol Sci., 52:69–79.
   Web of Science ®Google Scholar
• Xiao, K., Swanson, J. J., Pui, D. Y. H., and Kittelson, D. B. (2012). Bipolar Diffusion Charging of Aggregates. J. Aerosol Sci., 46:794–803.
   Web of Science ®Google Scholar
• Yu, Y., Alexander, M. L., Perraud, V., Bruns, E. A., Johnson, S. N., Ezell, M. J., and Finlayson-Pitts, B. J. (2009). Contamination from Electrically Conductive Silicone Tubing during Aerosol Chemical Analysis. Atmos. Environ., 43:2836–2839.
   Web of Science ®Google Scholar
• Zelenyuk, A., and Imre, D. (2007). On the Effect of Particle Alignment in the DMA. J. Aerosol Sci., 41:112–124.
   Web of Science ®Google Scholar
• Zhang, C., Thajudeen, T., Larriba, C., Schwartzentruber, T. E., and Hogan, C. J. (2012). Determination of the Scalar Friction Factor for Non-spherical Particles and Aggregates Across the Entire Knudsen Number Range by Direct Simulation Monte Carlo (DSMC). J. Aerosol Sci., 46:1065–1078.
   Web of Science ®Google Scholar