Measuring the effect of ion-induced drift-gas polarization on the electrical mobilities of multiply-charged ionic liquid nanodrops in air.

The electrical mobilities of multiply-charged nanodrops of the ionic liquid 1-ethyl, 3-methylimidazolium dicyanamide (EMI-N[CN]2) were accurately measured in air at 20 °C for mass-selected clusters of composition [EMI-N[CN]2] n [EMI(+)] z , with 2 ≤ n ≤ 369 and 1 ≤ z ≤ 10. We confirm prior reports that the mobility Z of a globular ion of mass m is given approximately by the modified Stokes-Millikan law for spheres, Z  =  Z SM,mod (d m   +  d g , z, m), where d m   =  (6m/πρ)(1/3) is the nanodrop mass-diameter based on the density ρ of the liquid (corrected for the capillary compression and electrostatic deformation of the nanodrop), and d g is an effective air molecule diameter. There is however a measurable (up to 7%) and systematic z-dependent departure of Z from Z SM,mod . As theoretically expected at small ε (*) , this effect is accurately described by a simple correction factor of the form Z/Z SM,mod   =  δ(1  -  βε (*)), where kTε (*) is the potential energy due to the ion-induced dipole (polarization) attraction between a perfectly-conducting charged nanodrop and a polarized neutral gas-molecule at a distance (d m   +  d g )/2 from its center. An excellent fit of this model to hundreds of data points is found for d g ≈ 0.26 nm, β ≈ 0.36, and δ ≈ 0.954. Accounting for the effect of polarization decreases d g considerably with respect to values inferred from earlier nanodrop measurements that ignored this effect. In addition, and in spite of ambiguities in the mobility calibration scale, the measured constant δ smaller than unity increases Millikan's drag enhancement factor from the accepted value ξ m ≈ 1.36 to the new value ξ ≈ ξ m /δ ≈ 1.42  ± 0.03.