The Mobility–Volume Relationship below 3.0 nm Examined by Tandem Mobility–Mass Measurement

Abstract

The validity of the Stokes-Millikan equation is examined in light of mass and mobility measurements of clusters of the ionic liquid 1-ethyl-3-methyl-imidazolium tetrafluoroborate (EMI-BF₄) in ambient air. The mobility diameter d_Z based on the measured mobility and the Stokes-Millikan law is compared with the volume diameter d_v , which generalizes the mass diameter for binary substances such as salts. d_v is based on the sum of anion and cation volumes in the cluster corrected for the void fraction of the bulk ionic liquid. For d_v > 1.5 nm, d _Z is within 1.4% of d_v + 0.3 nm. For smaller clusters 3.84 and 14.3% deviations are observed at d_v = 1.21 nm and 0.68 nm, respectively. These differences are smaller than expected due to a cancellation of competing effects. The increasing difference seen for d_v < 1.5 nm is due primarily to the interaction between the cluster and the dipole it induces in the gas molecules. Other potential sources of disagreement are non-globular cluster geometries, and departures of the cluster void fraction from the bulk value. These two effects are examined via molecular dynamics simulations, which confirm that the volume diameter concept is accurate for EMI-BF₄ nanodrops with d_v as small as 1.6 nm.

Acknowledgments

We thank Alejandro Casado of SEADM and Bruce Thomson of MDS Sciex for the advice on the DMA-MS graphic software and the operation of the QStar. We are grateful to Dr. Dominic Goshtik of Applied Biosystems, and Gonzalo Fernandez de la Mora of SEADM for the loan of the MS and the DMA, respectively, and to the Yale Keck Biotechnology Center for hosting the tandem instrument.