Trapped ion mobility spectrometry (TIMS) is a relatively new gas-phase separation method that has been coupled to quadrupole orthogonal acceleration time-of-flight mass spectrometry. The TIMS analyzer is a segmented rf ion guide wherein ions are mobility-analyzed using an electric field that holds ions stationary against a moving gas, unlike conventional drift tube ion mobility spectrometry where the gas is stationary. Ions are initially trapped, and subsequently eluted from the TIMS analyzer over time according to their mobility (K). Though TIMS has achieved a high level of performance (R > 250) in a small device (<5 cm) using modest operating potentials (<300 V), a proper theory has yet to be produced. Here, we develop a quantitative theory for TIMS via mathematical derivation and simulations. A one-dimensional analytical model, used to predict the transit time and theoretical resolving power, is described. Theoretical trends are in agreement with experimental measurements performed as a function of K, pressure, and the axial electric field scan rate. The linear dependence of the transit time with 1/K provides a fundamental basis for determination of reduced mobility or collision cross section values by calibration. The quantitative description of TIMS provides an operational understanding of the analyzer, outlines the current performance capabilities, and provides insight into future avenues for improvement.

Abstract. Trapped ion mobility spectrometry (TIMS) is a new high resolution (R up tõ 300) separation technique that utilizes an electric field to hold ions stationary against a moving gas. Recently, an analytical model for TIMS was derived and, in part, experimentally verified. A central, but not yet fully explored, component of the model involves the fluid dynamics at work. The present study characterizes the fluid dynamics in TIMS using simulations and ion mobility experiments. Results indicate that subsonic laminar flow develops in the analyzer, with pressure-dependent gas velocities between~120 and 170 m/s measured at the position of ion elution. One of the key philosophical questions addressed is: how can mobility be measured in a dynamic system wherein the gas is expanding and its velocity is changing? We noted previously that the analytically useful work is primarily done on ions as they traverse the electric field gradient plateau in the analyzer. In the present work, we show that the position-dependent change in gas velocity on the plateau is balanced by a change in pressure and temperature, ultimately resulting in near positionindependent drag force. That the drag force, and related variables, are nearly constant allows for the use of relatively simple equations to describe TIMS behavior. Nonetheless, we derive a more comprehensive model, which accounts for the spatial dependence of the flow variables. Experimental resolving power trends were found to be in close agreement with the theoretical dependence of the drag force, thus validating another principal component of TIMS theory.