The bipolar diffusion charging of nanoparticles: A review and development of approaches for non-spherical particles

Aerosol Science and Technology

Volumn 49, Issue 12, 2015, Pages 1181-1194

  Gopalakrishnan, Ranganathan ^a   McMurry, Peter H ^a   Hogan, Christopher J ^a  

^a University of Minnesota   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHARGE DISTRIBUTION; GOLD; IONS; NANOPARTICLES; NANORODS; REGRESSION ANALYSIS;

BROWNIAN DYNAMICS SIMULATIONS; CALCULATION APPROACHES; DISTRIBUTION CALCULATIONS; EXPERIMENTAL ANALYSIS; NANOPARTICLE SIZE DISTRIBUTION; NONSPHERICAL PARTICLE; PARTICLE MORPHOLOGIES; TANDEM DIFFERENTIAL MOBILITY ANALYSIS;

DISTRIBUTION FUNCTIONS;

GOLD NANOPARTICLE; GOLD NANOROD;

ATMOSPHERIC PRESSURE; CALCULATION; CHEMICAL COMPOSITION; COLLISIONALLY ACTIVATED DISSOCIATION; DIFFUSION; MATHEMATICAL ANALYSIS; MEASUREMENT; PARTICLE SIZE; POTENTIAL DIFFERENCE; PREDICTIVE VALUE; PRIORITY JOURNAL; REVIEW; SIMULATION; STEADY STATE; SURFACE CHARGE;

EID: 84947919903     PISSN: 02786826     EISSN: 15217388     Source Type: Journal    
DOI: 10.1080/02786826.2015.1109053     Document Type: Review

References (111)

1. Adachi, M., Kousaka Y., and, Okuyama K. (1985). Unipolar and Bipolar Diffusion Charging of Ultrafine Aerosol-Particles. J. Aerosol Sci., 16: 109-123.
2. 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.
3. Allen, J. E. (1992). Probe Theory-The Orbital Motion Approach. Phys. Scr. 45: 497-503.
4. 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.
5. 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.
6. Bricard, J. (1962). La Fixation des Petits Ions Atmosphériques Sur les Aérosols Ultra-Fins. Pure Appl. Geophys., 51: 237-242.
7. Brock, J. R. (1970). Aerosol Charging: The Role of Image Force. J. Appl. Phys., 41: 843-844.
8. Chandrasekhar, S. (1943). Stochastic Problems in Physics and Astronomy. Rev. Modern Phys., 15: 1-89.
9. 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.
10. 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.
11. 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.
12. Dahneke, B. E. (1973). Slip Correction Factors for Nonspherical Bodies-III The Form of the General Law. J. Aerosol. Sci., 4: 163-170.
13. 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.
14. 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.
15. 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.
16. Eggersdorfer, M. L., and, Pratsinis, S. E. (2014). Agglomerates and Aggregates of Nanoparticles Made in the Gas Phase. Adv. Powder Technol., 25: 71-90.
17. 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.
18. 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.
19. Ermak, D. L., and, Buckholz, H. (1980). Numerical-Integration of the Langevin Equation-Monte-Carlo Simulation. J. Comput. Phys., 35: 169-182.
20. 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.
21. Filippov, A. V. (1993). The Charging of Aerosol in the Transition Regime. J. Aerosol Sci., 24: 423-436.
22. Filippov, A. V. (1994). Charge-Distribution Among Nonspherical Particles in a Bipolar Ion Environment. J. Aerosol Sci., 25: 611-615.
23. 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.
24. Friedlander, S. K. (2000). Smoke, Dust, and Haze. Oxford University Press, New York.
25. Fuchs, N. A. (1963). On the Stationary Charge Distribution on Aerosol Particles in a Bipolar Ionic Atmosphere. Geofis. Pura Appl., 51: 185-193.
26. Fuchs, N. A. (1964). The Mechanics of Aerosols. Macmillan, New York.
27. Gatti, M., and, Kortshagen, U. (2008). Analytical Model of Particle Charging in Plasmas Over a Wide Range of Collisionality. Phys. Rev. E, 78: 046402.
28. Gopalakrishnan, R., and, Hogan, C. J. (2012). Coulomb-Influenced Collisions in Aerosols and Dusty Plasmas. Phys. Rev. E, 85: 026410.
29. 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.
30. 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.
31. 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.
32. 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.
33. Goree, J. (1992). Ion Trapping by a Charged Dust Grain in a Plasma. Phys. Rev. Lett., 69: 277-280.
34. Gunn, R. (1954). Diffusion Charging of Atmospheric Droplets by Ions, and the Resulting Combination Coefficients. J. Meteorol., 11: 339-347.
35. 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.
36. Hansen, S. (2004). Translational Friction Coefficients for Cylinders of Arbitrary Axial Ratios Estimated by Monte Carlo Simulation. J. Chem. Phys. 121: 9111-9115.
37. 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.
38. 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.
39. 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.
40. 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.
41. 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.
42. 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.
43. 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.
44. Hubbard, J. B., and, Douglas, J. F. (1993). Hydrodynamic Friction of Arbitrarily Shaped Brownian Particles. Phys. Rev. E, 47: R2983-R2986.
45. 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.
46. 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.
47. 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.
48. Khrapak, S., and, Morfill, G. (2009). Basic Processes in Complex (Dusty) Plasmas: Charging, Interactions, and Ion Drag Force. Contrib. Plasma Phys., 49: 148-168.
49. 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.
50. 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.
51. Knutson, E. O., and, Whitby, K. T. (1975). Aerosol Classification By Electric Mobility: Apparatus, Theory, and Applications. J. Aerosol Sci., 6: 443-451.
52. 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.
53. 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.
54. Langevin. (1905). Une Formule Fondamentale de Theorie Cinetique. Annales de Chimie et de Phys., 5: 245-288.
55. 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.
56. 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.
57. 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.
58. 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.
59. 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.
60. Liu, B. Y. H., and, Pui, D. Y. H. (1974). Equilibrium Bipolar Charge Distribution of Aerosols. J. Colloid Interface Sci., 49: 305-312.
61. 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.
62. 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.
63. 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.
64. Loyalka, S. K. (1973). Condensation on a Spherical Droplet. J. Chem. Physics 58: 354.
65. Lushnikov, A. A., and, Kulmala, M. (2004). Flux-Matching Theory of Particle Charging. Phys. Rev. E, 70: 046413.
66. 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.
67. 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.
68. Maricq, M. M. (2008). Bipolar Diffusion Charging of Soot Aggregates. J. Aerosol Sci., 42: 247-254.
69. Marlow, W. H., and, Brock, J. R. (1975). Calculations of Bipolar Charging of Aerosols. J. Colloid Interface Sci., 51: 23-31.
70. 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.
71. Mott-Smith, H. M., and, Langmuir, I. (1926). The Theory of Collectors in Gaseous Discharges. Phys. Rev., 28: 727-763.
72. 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.
73. 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.
74. 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.
75. 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.
76. 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.
77. 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.
78. 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.
79. 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.
80. Sahni, D. C. (1966). The Effect of a Black Sphere on the Flux Distribution in an Infinite Moderator. J. Nuclear Ener., 20: 915.
81. 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.
82. 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.
83. 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.
84. Sorensen, C. M. (2011). The Mobility of Fractal Aggregates: A Review. J. Aerosol Sci., 45: 765-779.
85. 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.
86. 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.
87. Stober, J., Schleicher, B., and, Burtscher, H. (1991). Bipolar Diffusion Charging of Particles in Noble Gases. J. Aerosol Sci., 14: 66-73.
88. Stolzenburg, M. R., and, McMurry, P. H. (1991). An Ultrafine Aerosol Condensation Nucleus Counter. J. Aerosol Sci., 14: 48-65.
89. 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.
90. 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.
91. 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.
92. 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.
93. 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.
94. 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.
95. 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.
96. 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.
97. 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.
98. 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.
99. Wagner, P. E., and, Kerker, M. (1977). Brownian Coagulation of Aerosols in Rarified Gases. J. Chem. Phys., 66: 638-646.
100. 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.
101. 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.
102. 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.
103. Wiedensohler, A. (1988). An Approximation of the Bipolar Charge-Distribution for Particles in the Sub-Micron Size Range. J. Aerosol Sci., 19: 387-389.
104. 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.
105. 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.
106. 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.
107. 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.
108. 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.
109. 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.
110. Zelenyuk, A., and, Imre, D. (2007). On the Effect of Particle Alignment in the DMA. J. Aerosol Sci., 41: 112-124.
111. 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.