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/pi rho)(1/3) (m is the particle mass and rho the bulk density of the material forming the cluster) for nanoparticles with dm 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 dm vs. [z(1+ m(g)/m)(1/2)/Z)](1/2) fall in a single curve for nanodrops of ionic liquids (ILs) for which. 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.