Relation between Electrical Mobility, Mass, and Size for Nanodrops 1–6.5 nm in Diameter in Air

A large number of data on mobility and mass have been newly obtained or reanalyzed for clusters of a diversity of materials, with the aim of determining the relation between electrical mobility (Z) and mass diameter d m = (6m/ π ρ ) 1/3 (m is the particle mass and ρ the bulk density of the material forming the cluster) for nanoparticles with d m ranging from 1 nm to 6.5 nm. The clusters were generated by electrospraying solutions of ionic liquids, tetra-alkyl ammonium salts, cyclodextrin, bradykinin, etc., in acetonitrile, ethanol, water, or formamide. Their electrical mobilities Z in air were measured directly by a differential mobility analyzer (DMA) of high resolution. Their masses m were determined either directly via mass spectrometry, or assigned indirectly by first distinguishing singly (z = 1) and doubly (z = 2) charged clusters, and then identifying monomers, dimers, … n-mers, etc., from their ordering in the mobility spectrum. Provided that d m > 1.3 nm, data of the form d m vs. [z(1+m g /m) 1/2 /Z)] 1/2 fall in a single curve for nanodrops of ionic liquids (ILs) for which ρ is known (m g is the mass of the molecules of suspending gas). Using an effective particle diameter d p = d m + d g and a gas molecule diameter d g = 0.300 nm, this curve is also in excellent agreement with the Stokes-Millikan law for spheres. Particles of solid materials fit similarly well the same Stokes-Millikan law when their (unknown) bulk density is assigned appropriately.