The mobilities of flame synthesized aggregates/agglomerates in the transition regime

Mobility analysis is frequently used to evaluate the size distribution of nanoparticle aggregates synthesized in high temperature, gas phase environments, such as flames. Theoretically, the scalar mobilities of such non-spherical entities, whose characteristic sizes are similar to the mean free path of their background gas (λ), are dependent on two size descriptors, the hydrodynamic radius (R_H) and the orientationally averaged projected area (PA) (as well as λ). Unfortunately, the theoretical relationship linking the mobility to R_H and PA for aggregates has not been experimentally tested, and has often been discarded in lieu of simpler yet theoretically invalid expressions. Here, we examine the mobilities of flame synthesized titanium dioxide (TiO₂) aggregates to directly test the link between the mobility, R_H, PA, and λ. Flame synthesized aggregates with mobility equivalent diameters in air in the 45-80nm range were classified with a differential mobility analyzer (DMA) and deposited on a transmission electron microscope (TEM) grid for subsequent imaging. Probable 3-dimensional structures for each imaged aggregate were constructed, based on the assumption that aggregates were quasifractal in nature and by comparing four 2-dimensional size descriptors calculated for images to those of computationally generated projections of quasifractal aggregates (of prescribed pre-exponential factor, fractal dimension, and number of primary particles). The calculated mobilities for the 3-dimensional structures inverted for each image are found to be in excellent agreement with their mobilities inferred from DMA classification, supporting the theoretically proposed relationship between the mobility and R_H, PA, and λ in the Kn=πλR_H/PA=1.27-4.11 range. Although a wide range of fractal dimensions and pre-exponential factors are inferred for the observed aggregates, the volumes of the reconstructed aggregates are still found to scale with the mobility diameters.