The electrical mobilities and scalar friction factors of modest-to-high aspect ratio particles in the transition regime

Abstract

In this work, we compared measured electrical mobilities of spherical and non-spherical nanoparticles to the predictions of both transition regime and free molecular theories. Mobility measurements were performed using a differential mobility analyzer (DMA) with both air and carbon dioxide as background gases, at atmospheric pressure and room temperature. For all measurements, DMA operational settings were selected in an attempt to minimize particle alignment with the electric field or flow direction, such that particles traversed the DMA rotating close to randomly. The particles included gold nanospheres (diameters of 50nm and 70nm), polystyrene latex dimers (primary particle diameter of 116nm), gold nanorods (mobility equivalent diameters of 40–70nm; aspect ratio 1.8–14) and carbon nanotubes (mobility equivalent diameters of 48.3nm –60.3nm; aspect ratios 9.5–243). Our primary objective was to test the accuracy of a transition regime theory (Dahneke’s adjusted sphere model) for non-spherical particles; this theory suggests that electrical mobilities are dependent upon a particle Knudsen number, specifically defined as Kn=λπRH/PA, where λ is the background gas mean free path, RH is the particle’s hydrodynamic radius, and PA is its projected area. For this test, electrical mobilities were calculated from the dimensions of particles collected downstream of a DMA and observed via TEM, with the DMA operated with fixed voltage and sheath flowrate. Mobility calculations for each particle were used to reconstruct electrical mobility histograms, which we show are directly comparable to the DMA transfer function for the operating conditions selected. We further compared the mean electrical mobilities of electrical mobility ranked sub-populations to the transfer function weighted mean mobilities of “windows” smaller in width than the DMA transfer function. Through analysis we find that in the 0.7<Kn<6 range, measurements are explained well by the proposed transition regime expression (the adjusted sphere model), with transfer function weighted and sub-population mean electrical mobilities typically within 10% of one another. Electrical mobilities calculated using solely free molecular models were in reasonable agreement with observations (±20%) for Kn>3, but were systematically lower (by up to 50%) than measurements for 1<Kn<3. Based upon the presented measurements and analysis, we propose that (1) an appropriate Knudsen number-dependent friction factor/electrical mobility expression needs to be used in interpreting DMA measurements not only for spheres (as is common practice), but also non-spherical nanorods and nanotubes, and (2) the expression tested here is suitable for such measurement interpretation.