Fundamentals of travelling wave ion mobility revisited: I. Smoothly moving waves

Abstract

We give a generalised and simplified theoretical treatment of travelling wave ion mobility (TWIM), and demonstrate that it is equivalent to previously published results in the special case of symmetric waveforms. Using this result, we derive exact expressions for the trajectory and transit time of ions in a smoothly moving sinusoidal TWIM device, opening up the possibility of direct (i.e. uncalibrated) CCS measurement in such a device. We then show that two effects that would need to be considered in a realistic device, namely anharmonic components of the waveform and velocity relaxation, can be included perturbatively in our approach. We consider the effect of velocity relaxation on calibrated CCS measurement and examine the importance of including a realistic treatment of diffusion.