Towards measuring ion mobilities in non-stationary gases and non-uniform and dynamic electric fields (I). Transport equation

• Equation of motion for ions in non-uniform and dynamic electric fields under the influence of non-stationary buffer gases.
• Direct determination of ion mobilities from measurements conducted in trapping ion mobility spectrometry (TIMS).
• Results show that relative ion mobilities are currently directly amenable from TIMS experiments.

The feasibility of determining ion mobilities from measurements conducted in non-stationary buffer gases and in the presence of dynamic and non-uniform electric fields is examined theoretically and experimentally. First, an equation of motion of an ion ensemble is derived on the basis of a solution to the Boltzmann transport equation. Subsequently, this equation of motion is applied to derive the relationship between ion mobility and arrival time for the conditions present in an ion mobility drift tube and a trapped ion mobility spectrometry (TIMS) apparatus. Finally, the theoretical analysis is tested by determining the ion mobility of compounds present in an ESI tune mix directly from experimental TIMS data. Comparison to ion mobilities measured on a drift tube shows that relative ion mobilities are currently directly amenable from TIMS experiments. The analysis further suggests that absolute ion mobilities are, in principle, directly amenable from ion mobility measurements performed with non-stationary buffer gases and non-uniform and dynamic electric fields.

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