Feasibility of higher-order differential ion mobility separations using new asymmetric waveforms

Abstract

Technologies for separating and characterizing ions based on their transport properties in gases have been around for three decades. The early method of ion mobility spectrometry (IMS) distinguished ions by absolute mobility that depends on the collision cross section with buffer gas atoms. The more recent technique of field asymmetric waveform IMS (FAIMS) measures the difference between mobilities at high and low electric fields. Coupling IMS and FAIMS to soft ionization sources and mass spectrometry (MS) has greatly expanded their utility, enabling new applications in biomedical and nanomaterials research. Here, we show that time-dependent electric fields comprising more than two intensity levels could, in principle, effect an infinite number of distinct differential separations based on the higher-order terms of expression for ion mobility. These analyses could employ the hardware and operational procedures similar to those utilized in FAIMS. Methods up to the 4th or 5th order (where conventional IMS is 1st order and FAIMS is 2nd order) should be practical at field intensities accessible in ambient air, with still higher orders potentially achievable in insulating gases. Available experimental data suggest that higher-order separations should be largely orthogonal to each other and to FAIMS, IMS, and MS.

Fig. 1

Optimized time-dependent electric fields for FAIMS (solid lines, left axis) and the ideal ion trajectories in those fields (dashed lines, right axis). There are two possible polarities: (a) and (b).

Fig. 2

Same as Fig. 1 for 3^rd order differential IMS separating ions by coefficient b (only one polarity is shown for each waveform). Maximum ion oscillation amplitudes Δr are calculated for each E(t).

Fig. 3

Same as Fig. 3 for n = 4, with ions separated by coefficient c.

Fig. 4

Same as Fig. 3 for n = 5, with ions separated by coefficient d. Twelve out of 24 total waveforms are shown, the other 12 could be obtained via time inversion.

Fig. 5

Compensation field for representative ions in FAIMS and HODIMS computed as a function of dispersion field. Lines in both panels are for a hypothetical “average” amino acid described in the text, for separation orders of n = 2 in FAIMS (solid), n = 3 (dashed), n = 4 (dash-dot), and n = 5 (dotted). In (a), filled symbols are for FAIMS and empty ones are for 3^rd -order HODIMS: circles for H⁺ lysine and triangles for an “average“ ketone.

Fig. 6

Pairwise correlations between ion mass, low-field mobility, and coefficients a and b for amino acid cations (filled circles) and anions (empty circles). Values are from IMS and FAIMS measurements (in N₂ gas). Slightly different K₀(0) values were reported in (Beegle, L.W.; Kanik, I.; Matz, L.; Hill Jr., H.H. Anal. Chem. 2001, 73, 3028), but the effect on r² is negligible. Absolute mobilities for anions have not been measured.

Fig. 7

Pairwise correlations between ion mass and coefficients a, b, and c for 9 small organic cations, from FAIMS measurements (in air at 20 °C).