Electrical mobilities of multiply charged ionic-liquid nanodrops in air and carbon dioxide over a wide temperature range: influence of ion-induced dipole interactions

Abstract

The electrical mobilities of hundreds of mass-selected, multiply charged nanodrops (2–6 nm in diameter) of the ionic liquid EMI-BF₄ have been measured in air and CO₂ at temperatures, T, ranging from 20 to 100 °C, extending previous studies, based on EMI-N(CN)₂ nanodrops in air at 20 °C, to other temperatures and drift gases. The known compressibility of EMI-BF₄ removes prior slight ambiguities in the mass-based determination of nanodrop diameters. We confirm the previous finding that the collision cross-sections Ω of these nanodrops, inferred from their electrical mobilities, are related to their diameters d via a relation of the form , where ε* is the ratio between the polarization and thermal energies of the ion–gas molecule system at contact, f(Kn) is a continuum-correction that vanishes in the free-molecule limit, and the coefficients d_g, β, and ξ are inferred experimentally as functions of temperature and drift gas. This expression for Ω(d,z) enables determining true (geometric) cross-sections of globular ions from their measured electrical mobilities in molecular gases. We also corroborate prior reports that the drag-enhancement factor ξ, which remains nearly constant with temperature and drift-gas, exceeds slightly the value ξ_m ≈ 1.36 established by Millikan's oil drop measurements. Unexpectedly, the coefficient β shows a significant temperature dependence, suggesting that the ion–gas molecule scattering process is affected by T. The effective gas-molecule collision diameter d_g is seen to decrease with T, and takes a value in excess of 0.45 nm in CO₂ at 20 °C, considerably larger than in room-temperature air.