Bipolar charging

To simplify the calculations, it is assumed that the concentrations, mobilities, and other properties of the positive and negative ions are equal and that the concentrations of the tons and charged particles have reached a steady slate. We consider a group of particles of uniform size no coagulation occurs,. so a polydisperse aerosol can be treated as a set of uncoupled monodisperse particles. The rates at which ions of both signs attach to particles are assumed to be independent ol each other. In the steady state, ions are generated and destroyed at the same rate by attachment to particles. Calculations indicate that ion recombination is not an important mechanism for ion loss in the atmosphere (Bricard and Pradel, Ii966). 

In the continuum regime dp 0.1 /xm), the ion fluxes ft and ft can be estimated from steady-state solutions to the ion diffusion equation (2.43) in the presence of a Coulomb force field. surrounding the particles image forces are neglected (Fuchs and Sutugin, 1971)  

the particle charge distribution is approximated by the Boltzmann equation. This expression holds best for particles larger than about 1 /.tm. For smaller particles, the flux terms (2,49) based on continuum transport theory must be modified semiempirically. The results of calculations of the fraction of charged particles are given in Table 2.2. The fraction refers to particles of charge of a given sign. 

Steady-Slate Particle Charge Distribution m a Bipolar Ionized Atmosphere. (Fuchs and Sutugin, 1971, p. 45  

The steady-state distribution is independent of the ionic concentration. However, the rate of approach to the steady state depends on the ionic concentrations and other properties of the system. The net result can be summarized as follows for the atmosphere. Ions are steadily generated by cosmic rays and radioactive decay processes. These attach to particle surfaces where they are neutralized at a rate equal to their rate of formation. The particle charge distribution is determined by the steady state relationship between particles separated by one charge. In the atmosphere, the equilibration process takes about 30 min. The rate of equilibration can be increased by increasing the ion concentration using a bipolar ion generator. Radioactive ion sources such as are often used in electrical aerosol instrumentation (Chapter 6). 

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There are a series of papers that focus on the behavior of the radon decay products and their interactions with the indoor atmosphere. Previous studies (Goldstein and Hopke, 1983) have elucidated the mechanisms of neutralization of the Po-218 ionic species in air. Wilkening (1987) reviews the physics of small ions in the air. It now appears that the initially formed polonium ion is rapidly neutralized, but can become associated with other ions present. Reports by Jonassen (1984) and Jonassen and McLaughlin (1985) suggest that only 5 to 10% of the decay products are associated with highly mobile ions and that much of the activity is on large particles that have a bipolar charge distribution. 

Mobility data on bipolar charge-transport materials are still rare. Some bipolar molecules with balanced mobilities have been developed [267], but the mobilities are low (10 6—10 8 cm2/Vs). Up to now, no low molecular material is known that exhibits both high electron and hole conductivity in the amorphous state, but it is believed that it will be only a matter of time. One alternative approach, however, is to use blends of hole and electron transporting materials [268]. 

A theoretical approach defining bipolar charge equilibrium has been developed by Keefe et al. (1959), and comparison with experimental data suggests that it provides a reasonable model for particle sizes from about 0.05 to at least 2 pm. Keefe et al. applied Boltzmann s law to the distribution of particle charges in dynamic electrical equilibrium. The usual statement of this law is that the number of particles per unit volume having an energy E, denoted c E), is given by... 

Oligofluorenes are exceptional in their charge transport properties, exhibiting relatively high bipolar charge-carrier mobilities in comparison to other non-crystalline organic materials. An interesting study of the dependence... 

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