Effect of ion-neutral collision mechanism on the trapped-ion equation of motion: a new mass spectral line shape for high-mass trapped ions

Abstract

The decay amplitude envelope of an ICR time-domain signal determines its corresponding Fourier transform mass spectral line shape. The commonly accepted FT-ICR frequency-domain unapodized Lorentzian spectral line shape originates from the Langevin ion-neutral collision model, in which an ion is treated as a point charge that induces an electric dipole moment in a neutral collision partner. The Langevin model provides a good description of reactions of low-energy collisions of low-mass positive ions with neutrals. However, the Langevin model is inappropriate for collisions of high-mass gas-phase biopolymer ions with low-mass neutrals. Here, we examine ion trajectories for both Langevin and hard-sphere ion-neutral collision models. For the Langevin model, collision frequency is independent of ion speed, leading to a linear differential equation of ion motion with a frictional damping term linearly proportional to ion velocity. For the hard-sphere model, collision frequency is proportional to ion speed and the frictional damping term is proportional to the square of ion velocity. We show that the resulting (non-linear) equation of ion motion leads to a non-exponential time-domain ICR signal whose amplitude envelope has the form, 1 (1 + σt) , in which σ is a constant. Dispersion-vs-absorption (DISPA) line shape analysis reveals that the ‘hard-sphere’ spectral line shape resembles that of overlaid narrow and broad Lorentzians. We discuss several important implications of the new ‘hard-sphere’ line shape for ICR spectral analysis, ICR signal processing, collision-based ion activation, and ion axialization. Finally, in the hard-sphere limit, a non-linear frictional damping term will also apply to ions in a Paul trap.