Single-Molecule Pycnometry and Shape Analysis of Ions in the Gas Phase

The analysis of ions and clusters by mobility-classified mass spectrometry provides information on the mobility of analytes in the drift gas and the analyte mass. Mass equivalent and mobility equivalent diameters of globular analytes, such as ions, poly(ethylene glycol) (PEG), and ionic liquid nanodroplets, can be correlated with good accuracy by the Stokes–Millikan mobility model. A prerequisite to such an analysis is, however, the assumption of a globular analyte shape, which then allows determination of material density for globular ions. We show that the analyte density can be evaluated with high precision, independent of any assumptions on the analyte shape, by careful analysis of analyte-PEG-cluster ions following the concept of classical pycnometry. In particular, the analyte is entrapped in a globular PEG-analyte droplet. Based on the now independently derived mobility diameter and volume equivalent diameter, it is possible to attribute two parameters, size and shape, to the analyte molecule. We demonstrate the approach for lysozyme, cyano-cobalamin (vitamin B12), and glucose, which cover two orders of magnitude in analyte mass (180···14 300 Da). The derived densities for these analytes are highly accurate, i.e., they deviate less than 1% from literature values. Our method can be applied to newly synthesized molecules, supramolecular assemblies, isolated biomolecules, and molecular clusters, where only minor amounts of materials are available. The obtained shape parameters of lysozyme and cyano-cobalamin agree well with the expected molecular shapes. Data evaluation relies only on locations of the species in the mass–mobility plane and is in principle independent of any mobility theory. Our approach is thus robust with respect to experimental uncertainties and produces identical results irrespective of the type of mobility classification and drift gas.