Ion Mobilities in Diatomic Gases: Measurement versus Prediction with Non-Specular Scattering Models

Ion/electrical mobility measurements of nanoparticles and polyatomic ions are typically linked to particle/ion physical properties through either application of the Stokes-Millikan relationship or comparison to mobilities predicted from polyatomic models, which assume that gas molecules scatter specularly and elastically from rigid structural models. However, there is a discrepancy between these approaches; when specular, elastic scattering models (i.e., elastic-hard-sphere scattering, EHSS) are applied to polyatomic models of nanometer-scale ions with finite-sized impinging gas molecules, predictions are in substantial disagreement with the Stokes-Millikan equation. To rectify this discrepancy, we developed and tested a new approach for mobility calculations using polyatomic models in which non-specular (diffuse) and inelastic gas-molecule scattering is considered. Two distinct semiempirical models of gas-molecule scattering from particle surfaces were considered. In the first, which has been traditionally invoked in the study of aerosol nanoparticles, 91% of collisions are diffuse and thermally accommodating, and 9% are specular and elastic. In the second, all collisions are considered to be diffuse and accommodating, but the average speed of the gas molecules reemitted from a particle surface is 8% lower than the mean thermal speed at the particle temperature. Both scattering models attempt to mimic exchange between translational, vibrational, and rotational modes of energy during collision, as would be expected during collision between a nonmonoatomic gas molecule and a nonfrozen particle surface. The mobility calculation procedure was applied considering both hard-sphere potentials between gas molecules and the atoms within a particle and the long-range ion-induced dipole (polarization) potential. Predictions were compared to previous measurements in air near room temperature of multiply charged poly(ethylene glycol) (PEG) ions, which range in morphology from compact to highly linear, and singly charged tetraalkylammonium cations. It was found that both non-specular, inelastic scattering rules lead to excellent agreement between predictions and experimental mobility measurements (within 5% of each other) and that polarization potentials must be considered to make correct predictions for high-mobility particles/ions. Conversely, traditional specular, elastic scattering models were found to substantially overestimate the mobilities of both types of ions.