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

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. dv 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 dv = 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.