Factors Contributing to the Collision Cross Section of Polyatomic Ions in the Kilodalton to Gigadalton Range: Application to Ion Mobility Measurements

The projected superposition approximation (PSA) method was used to theoretically evaluate the factors contributing to the cross section measured in ion mobility experiments and to study how the significance of these factors varies with ion size from diglycine to a 1 mu m oil droplet. Thousands of PSA calculations for similar to 400 different molecules in the temperature range from 80 to 700 K revealed that the molecular framework made up of atomic hard spheres is, as expected, a major component of the cross section. However, the ion-buffer gas interaction is almost equally important for very small peptides, and although its significance decreases with increasing ion size, interaction is still a factor for megadalton ions. An additional major factor is the ion shape: Fully convex ions drifting in a buffer gas have a minimal frictional resisting force, whereas the resisting force increases with degree of ion surface concaveness. This added resistance is small for peptides and larger for proteins and increases the ion mobility cross section from 0 to greater than 40%. The proteins with the highest degree of concaveness reach a shape-effected friction similar to, and sometimes larger than that of, macroscopic particles such as oil droplets. In summary, our results suggest that the transition from nanoparticle (with Lennard-Jones-like interaction with the buffer gas) to macroscopic particle (with hard sphere-like interaction) occurs at similar to 1 GDa.