Electrodynamic balance

The development of the electrodynamic balance and other particle traps has made it possible to perform precise measurements of the properties of small particles by focusing on the single particle. The variety of processes and phenomena that can be investigated with particle traps is quite extensive and includes gas/liquid and gas/solid chemical reactions, chemical spectroscopies, heat and mass transfer processes, interfacial phenomena, thermodynamic properties, phoretic forces, and other topics of interest to chemical engineers. 

The Wyatt and Phillips instrument has the features of primary importance for subsequent electrical levitators—specifically, feedback control for vertical positioning and scattered light detection. However, the restoring forces exerted on the particle were not adequate for a number of applications. Slight convective currents in the chamber would cause the particle to be lost, so it was not possible to provide flow through the device. The electrodynamic balance does not have this difficulty. 

The electrodynamic balance or quadrupole began with the electric mass filter of Paul and Raether (1955), who demonstrated that a charged mass can be stably levitated by means of a quadrupole arrangement of electrodes, one of the simplest configurations being that shown in Fig. 3. An ac potential is applied to the rods in the horizontal plane, and a dc potential is applied to the upper and lower rods as in the Millikan condenser. The ac field has horizontal and vertical components that are 180° out of phase, thereby... 

Fig. 4. The electrodynamic balance of Fulton (1985) with the bihyperboloidal configuration of Wuerker et al. (1959).

Fig. 5. The first two marginal stability envelopes for VJV = 0 for the bihyperboloidal electrodynamic balance. Also shown as open circles are the experimental stability data of Taflin et a/. (1989). Reprinted, in part, with permission from Taflin, D. C, Ward, T. L., and Davis, E. J., Langmuir 5, 376-384, Copyright 1989 American Chemical Society.

The stability characteristics of electrodynamic balances with electrode configurations other than bihyperboloidal are affected by the different electrode geometry. Once the electrical fields are determined for the geometry in question, the stability characteristics can be established quantitatively. Muller (1960) developed expressions for the electrical fields for several configurations, including Straubel s disk and torus system, and Davis et al. (1990) analyzed the double-ring which is discussed below. 

Fig. 7. Droplet charge and levitation voltage for radioactivity detection in a C-con-taminated electrodynamic balance, from Davis et al. (1988).

Measurements of the photophoretic force on crystalline ammonium sulfate particles were made by Lin and Campillo (1985) using an electrodynamic balance. The measurement procedure is identical to that for any such force, that is, the levitation voltage is measured in the absence of the photophoretic force and then when the force is exerted. A force balance yields an equation for the photophoretic force similar to Eq. (31) ... 

A force that is as large as the gravitational force can be used to suspend a particle against gravity, provided that it can be controlled and directed upward to balance gravity. One such force is the radiation pressure force or radiometric force. Ashkin and Dziedzic (1977), whose work is discussed in the next section, were the first to use the radiation pressure to levitate a microsphere stably. It was demonstrated by Allen et ai (1991) that the radiometric force can be measured with the electrodynamic balance, and they used the technique to determine the absolute intensity of the laser beam illuminating a suspended particle. This was accomplished in the apparatus displayed in Fig. 13. The laser illuminated the microparticle from below, and... 

Fig. 12, Photophoretic force data of Lin and Campillo (1985) for crystalline ammonium sulfate particles levitated in an electrodynamic balance. Reprinted with permission from Lin, H.-B., and Campillo, A. J., Applied Optics 24, 244, Copyright 1985, The Optical Society of America.

Fig. 13. The double-ring electrodynamic balance used by Allen et al. (1991) to measure the radiation pressure force on a microparticle.

Fig. 29. Evaporation rate data for several low-volatility species in Nj measured by Tallin et al. (1988) by levitating microdroplets in an electrodynamic balance. From Measurement of Droplet Interfacial Phenomena by Light-Scattering Techniques, by Daniel C. TafBin, S. FI. Zhang, Theresa Allen and E. James Davis, A/CIiE Journo/, 34, No. 8, pp. 1310-1320, reproduced by permission of the American Institute of Chemical Engineers 1988 AIChE.

Fig. 46. An overhead view of the electrodynamic balance and Raman spectrometer developed by Buehler (1991) for gas/microparticle chemical reaction studies.

This review of the chemistry and physics of microparticles and their characterization is by no means comprehensive, for the very large range of masses that can be studied with the electrodynamic balance makes it possible to explore the spectroscopy of atomic ions. This field is a large one, and Nobel laureates Hans Dehmelt and Wolfgang Paul have labored long in that fruitful scientific garden. The application of particle levitation to atmospheric aerosols, to studies of Knudsen aerosol phenomena, and to heat and mass transfer in the free-molecule regime would require as much space as this survey. 

Although this overview of the electrodynamic balance and its applications has been directed to chemical engineers, it is hoped that physicists, chemists, atmospheric scientists, aerosol researchers, and environmental engineers will find something here to interest them. 

The electrodynamic balance (EDB) is a modern version of the Millikan oil drop apparatus in which a charged particle is levitated in an electric field [20]. By using quadrupole focusing, it is possible to suspend a single particle in a controlled environment virtually indefinitely. The size of a levitated particle can be measured by a variety of methods, the most precise of which uses the information contained in the resonant structure of light... 

For strongly paramagnetic substances Aw may be several hundred mg when the cylindrical sample has a diameter of 5 to 10 mm, and an ordinary balance is sufficient. For measurements on weakly paramagnetic materials a microbalance or electrodynamic balancing (Hilal and Fredericks, 1954) may be substituted. 

Cohen, M. D., Flagan, R. C., and Seinfeld, J. H. (1987) Studies of concentrated electrolyte solutions using the electrodynamic balance. 2. Water activities for mixed-electrolyte solutions, /. Phys. Chem. 91, 4575-4582. 

Peng C, Chow AHL, Chan CK (2001) Hygroscopic study of glucose, citric acid, and sorbitol using an electrodynamic balance. Comparison with UNIEAC predictions. Aerosol Sci Technol 35 753-758... 

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