Fundamental Studies of Particle Growth and Structure During Powder Synthesis

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Richard C Flagan Steven N Rogak
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United States


The primary objective of the Caltech program supported by IFPRI is to understand the dynamics of particles which do not coalesce immediately upon coagulation and, through that understanding, to guide the development of processes for production of particles with particular properties. Theoretical and experimental investigations of the dynamics of aggregate aerosols have been undertaken. The factors that must be taken into account in such models were first explored theoretically. Particles are represented as fractal agglomerates. The mobilities and cross sections of such aggregates were examined, and upper and lower bound estimates of the collision frequency function are developed. Predictions of the dynamics of a coagulating aerosol indicate that aggregates coagulate more rapidly than do dense spheres.

In the initial year of the program we have focussed our experimental program on describing the mobility of agglomerates. Agglomerate particles were classified using electrical mobility techniques. The classified particles were collected on electron microscope grids for image analysis of the photographs taken from those samples to estimate fractal structure parameters. The particles studied include titanium dioxide particles produced by pyrolysis of titanium tetraisopropoxide and elemental silicon particles produced by pyrolysis of silane. The former particles are representative of particles of considerable industrial interest. The latter particles are a convenient model system that has been used for initial studies of coalescence of agglomerate particles.

The mobility equivalent size of the free molecular and transition regime aggregates studied to date has been found to correlate well with the projected area of the particles. During the past year we also had an opportunity to study the mass transfer to agglomerate particles using an instrument which was brought to Caltech by Urs Baltensperger, a visitor from ETH in Zurich. The instrument, called an epiphaniometer, is a device for measuring the mass transfer to particles by attachment of radioactive lead atoms. The experiments have been performed using mobility classified particles and, as expected, we find that the mass transfer rate scales directly with the mobility for drag equivalent diameter of the particles. That is, spherical particles and agglomerate particles with the same migration velocity in an electric field exhibit the same mass transfer rates.

Because electrical mobility measurements play a key role in our studies of the dynamics of agglomerate particles, we have also conducted a series of experiments aimed at measuring the charge uptake by these agglomerate particles. These experiments have been conducted using bipolar chargers, that is, radioactive sources that generate both positive and negative ions in the gas that then attach to the particles. The experiments involve taking a neutral aerosol from which all charge particles have been removed with an electrostatic precipitator and exposing it to bipolar ions. The number of neutral particles remaining after exposure to a fixed ion concentration is measured. The neutral fraction scales, once again, directly with the mobility equivalent diameter.

Thus, from each of our studies to date, we find that the mobility equivalent diameter is a very convenient quantity for characterizing the agglomerate particles. During the past year we have also advanced our efforts somewhat in the modeling of the agglomeration process itself. This requires an understanding not only of the mobility or diffusivities of the particles, but also of their collision cross sections. To date, we do not have direct measurements of the collision cross section, so we have been forced to make estimates to provide upper and lower bounds on those cross sections and, hence, on the coagulation rates. Still, the estimates that we have made do provide some insights into the differences between the agglomeration process and coagulation of rapidly coalescing particles.