Effective collisional cross-section of small ions in the gas phase: Application to ion mobility spectrometry

The observed drift times of monoatomic ions, including alkali metal ions and halide anions, are not fully consistent with their size. When the effect of mass is included through the Mason-Schamp equation, the deviation gets worse so that the trend of the experimental collisional cross-sections becomes completely opposite to what is expected. This is attributed to the stronger local electric field around smaller ions. The strong electric field in the vicinity of a small ion leads to strong ion-neutral interactions and creates a drag force against ion motion. The smaller the ions, the stronger the interaction, because of the higher charge density.

In view of this, a modified equation is introduced to describe the relationship between the observed drift times or ion mobilities and the cross-sections of small ions. Here, for small ions with high charge density, the experimental collision cross-section is expressed as the effective collision cross-section, Ω_eff = σ_i (1 + α/r_i ³ ), that takes into account both intrinsic ion size, σ_i , and the ion-molecule interactions through a correction term of α/r_i ³ , which is proportional to the charge density.

A linear fit of the drift times of alkali metal ions and halide anions to the proposed equation showed relative deviations of <8.2%. The model successfully predicted the drift time of other small diatomic ions with reasonable error.

The proposed model can be used as a simple and efficient relationship in predicting the effective cross-section of small ions.