Fundamentals of traveling wave ion mobility spectrometry

Abstract

Traveling wave ion mobility spectrometry (TW IMS) is a new IMS method implemented in the Synapt IMS/mass spectrometry system (Waters). Despite its wide adoption, the foundations of TW IMS were only qualitatively understood and factors governing the ion transit time (the separation parameter) and resolution remained murky. Here we develop the theory of TW IMS using derivations and ion dynamics simulations. The key parameter is the ratio (c) of ion drift velocity at the steepest wave slope to wave speed. At low c, the ion transit velocity is proportional to the squares of mobility (K) and electric field intensity (E), as opposed to linear scaling in drift tube (DT) IMS and differential mobility analyzers. At higher c, the scaling deviates from quadratic in a way controlled by the waveform profile, becoming more gradual with the ideal triangular profile but first steeper and then more gradual for realistic profiles with variable E. At highest c, the transit velocity asymptotically approaches the wave speed. Unlike with DT IMS, the resolving power of TW IMS depends on mobility, scaling as K(1/2) in the low-c limit and less at higher c. A nonlinear dependence of the transit time on mobility means that the true resolving power of TW IMS differs from that indicated by the spectrum. A near-optimum resolution is achievable over an approximately 300-400% range of mobilities. The major predicted trends are in agreement with TW IMS measurements for peptide ions as a function of mobility, wave amplitude, and gas pressure. The issues of proper TW IMS calibration and ion distortion by field heating are also discussed. The new quantitative understanding of TW IMS separations allows rational optimization of instrument design and operation and improved spectral calibration.

Fig. 1

Traveling wave propelling ions in the Synapt system. Adapted from (K. Giles al., Applications of a travelling wave-based radio-frequency-only stacked ring ion guide, Rapid Commun. Mass Spectrom. 18, 2401), © 2004, with permission from John Wiley & Sons.

Fig. 2

Model traveling wave profiles: triangular (a), bitriangular (b), and half-sinusoidal (c). Characteristic parameters are labeled.

Fig. 3

Ion transit velocities in TW IMS calculated for the triangular profile (dotted line), bitriangular waveforms (dashed lines) with {b₂/b₁; E₂/E₁} ratios of {0.5; 2} (a); {0.25; 4} (b); {0.5; 4} (c), and {2; 4} (d), and half-sinusoidal profile (solid line). Note the horizontal scale in terms of c².

Fig. 4

Simulated arrival time distributions in TW IMS using a half-sinusoidal waveform for ions with c = 1.173 (a), 0.922 (b), and 0.126 (c). The spectra with triangular profile are similar.

Fig. 5

Ion transit velocities calculated with diffusion ignored (lines) and included (symbols) for the triangular waveform (dashed line and empty symbols) and half-sinusoidal profile (solid line and filled symbols). We show the velocity relative to the wave speed (a) and relative velocities with and without diffusion (b). The horizontal scale is in terms of ${\stackrel{‒}{c}}^2$.

Fig. 6

Calculated characteristics of TW IMS resolution: (a) apparent resolving power, (b) logarithmic derivative of $\stackrel{‒}{v}\left(K\right)$, and (c) effective resolving power. The resolving power in (a, c) is on the logarithmic scale, other nomenclature follows Fig. 5.

Fig. 7

Ion mobility spectra for (H⁺Bradykinin)_n ions obtained using DT IMS in He gas (a) and TW IMS in Ar gas as a function of wave amplitude U (b). The values of n for all peaks are labeled. Panel (a) is reprinted with adaptation from (A. E. Counterman et al., High-order structure and dissociation of gaseous peptide aggregates that are hidden in mass spectra, J. Am. Soc. Mass Spectrom. 9, 743), © 1998, with permission from Elsevier. Panel (b) is adapted from (K. Giles al., Applications of a travelling wave-based radio-frequency-only stacked ring ion guide, Rapid Commun. Mass Spectrom. 18, 2401), © 2004, with permission from John Wiley & Sons.

Fig. 8

Analysis of TW IMS data in Fig. 7b: (a) mean transit velocities for n = 1 (triangles), 2 (squares), and 3 (circles) as a function of wave amplitude, with linear regressions for each curve; (b, c) deviations of functions in (a) from linear regressions; (d) logarithmic derivatives of the functions in (a), with linear regressions for each (dashed lines) and for all data (solid line). The horizontal scales are quadratic, in terms of U² in (a, b) and (KU)² in (c, d). In (a) for n = 2, solid squares and the regression are for the data at U ≤ 8.5 V, blank squares are for U ≥ 9.5 V.

Fig. 9

Resolving power of TW IMS: (a) spectra for gramicidin S 2+ (left peak) and leucine enkephalin 1+ (right peak) obtained using the wave amplitudes and Ar gas pressures of 1 V and 0.025 mbar (panel A), 2.6 V and 0.075 mbar (B), and 7 V and 0.2 mbar (C); (b) resolving power in panels B and C relative to the values in panel A — measured (solid circles for gramicidin S, blank circles for leucine enkephalin) and calculated (line). Panels in (a) are adapted from (K. Giles al., Applications of a travelling wave-based radio-frequency-only stacked ring ion guide, Rapid Commun. Mass Spectrom. 18, 2401), © 2004, with permission from John Wiley & Sons.