•Matrix methods are used to generate stability diagrams which account for supplemental quadrupolar excitation.•The effects of mismatched frequencies and voltages are explored.•Resonance-induced unstable regions of adjustable width are described.Since their introduction, digital quadrupole mass spectrometers have described by analogy to traditional sinusoidal devices. However, digital quadrupoles exhibit unique behaviors and simplify many complex ion handling operations due to their uniquely flexible control over the frequency, duty cycle and amplitude of applied potentials. Matrix solutions to the Hill differential equation are used to explore the effects of these additional degrees of freedom on ion stability. Two parameters are explored: varying the frequency ratio of the applied potentials introduces a predictable number of bands of instability to the stability diagram. Varying the amplitude ratio of the applied potentials tunes the width of those unstable bands. Stability diagrams governing a digital mass filter employing asymmetric driving potentials to generate an arbitrary number of pass bands of adjustable width are systematically described.

Quadrupole mass filters using non-sinusoidal driving potentials present exciting opportunities for new functionality. Predicting figures of merit like resolving power and transmission efficiency helps characterize these emerging devices. To this end, matrix methods of solving the Hill equation of ion motion are employed to calculate stability diagrams and pseudopotential well depth maps in the a,q plane for arbitrary waveforms. The theoretical resolving power and well depth of digital, trapezoidal and sinusoidal mass filters are compared. Simplified expressions for digital mass filter operation are presented.

•Spreadsheet based stability diagram programs were used to produce well depth maps.•The effect of duty cycle manipulation on well depth was demonstrated.•Well depth maps were used to demonstrate duty cycle improvement of mass analysis.Previously our group developed spreadsheet based programs for facile production of stability diagrams because any change in the duty cycle of the rectangular waveforms changes their shape. In this publication, these programs have been extended to calculate the pseudopotential well depth of quadrupolar fields in each orthogonal direction for all values of the Mathieu parameter, q. These results were extended to 3D sinusoidal ion traps and the map of the pseudopotential well depth as a function of q was compared to the literature for validation. The duty cycle of digital ion trap waveforms was then varied to observe the change in the pseudopotential wells in each direction. Duty cycle was then manipulated with the goal of enhancing the capabilities and performance of the ion traps.

This publication demonstrates the use of digital waveform manipulation in linear ion guides to trap isolated ions and fragment them before mass analysis by time-of-flight mass spectrometry (TOF-MS). Ion trapping and collection was performed by waveform duty cycle manipulation to create a negative axial potential between the rods and the end-cap electrodes. Ion isolation can be performed by duty cycle manipulation to narrow the range of stable masses while continuing to axially trap the ions. Further ion isolation can then be performed by jumping the quadrupole frequency to each side of the stability zone to eliminate ions above and below the isolated ion mass. Collision-induced dissociation was demonstrated by duty cycle manipulation to either axially or radially excite the ions. The methods for performing these types of excitations are discussed and demonstrated. These techniques can be combined or used separately for MSn analysis. The use of frequency and duty cycle manipulation of the applied waveforms simplifies the hardware while greatly increasing the capabilities of linear ion guides and quadrupole time-of-flight mass spectrometers (Q-TOF-MS). Linear quadrupoles can now be used as high efficiency ion traps for collection, isolation, and tandem mass spectrometry at any value of m/z when operated digitally.

•Publicly available spreadsheet based stability diagram programs were produced.•The effect of duty cycle manipulation was systematically and visually demonstrated.•The concept of equating duty cycle changes with changes in a is erroneous.•Mapping the 50% duty cycle stability region by duty cycle change is not correct.•m/z vs frequency diagrams were shown to be more operationally useful.Spreadsheet based programs for facile production of stability diagrams have been developed to accommodate the need for rapid generation for any change in the duty cycle of rectangular waveforms. In this publication, we have used these programs to demonstrate the effects of duty cycle manipulation and visually revealed the changes in the stability diagrams for each change. The concept of equating duty cycle change with a change in the Mathieu parameter a has been reexamined and found to be incorrect with respect to matrix methods definitions. The suggestion that the 50% duty cycle stability region can be mapped by varying the duty cycle to scan along lines of constant a/q is also shown to be incorrect. These observations were possible because the spreadsheet program allowed quick alteration of the waveforms and then observation of the stability results. Finally, the needs of the operator were examined. Because the stability diagrams have to be recalculated with each change in duty cycle, it is more helpful to use the matrix methods to directly calculate the stability diagrams at a = 0 as a function of m/z and frequency. It is our intention to make these spreadsheet programs freely available to facilitate the mainstreaming of digital ion trap and guide technology.

Simulation and matrix methods were used to determine the change in the minimum trapping frequency during duty cycle base waveform manipulation to provide axial trapping. Duty cycle based axial trapping sets both rod sets of a digitally driven linear quadrupole to the same potential thereby nullifying the radial trapping field for a definable interval during the waveform cycle. Turning off the radial trapping field affects the ion motion. Consequently, the ion stability conditions and the secular frequency change with duty cycle during axial trapping. The work presented here demonstrates the change in the ion motion by simulating the ion trajectories under duty cycle base trapping conditions and determining the change in the minimum trapping frequency as a function of the change in duty cycle. The change in the stability conditions with duty cycle was determined by matrix methods. These calculations were used to determine the minimum trapping frequency change with duty cycle and validate the simulations. They were then used to discuss the duty cycle effects and propose methodology for using duty cycle waveform manipulation to perform precise ion isolation. Finally, matrix methods were used to show that ion isolation can be performed concurrently with duty cycle based axial trapping. These results were confirmed by simulation.

This work demonstrates sampling of singly charged particles up to 200 nm in diameter at atmospheric pressure into vacuum and trapping large numbers (>106) at a point in front of the end cap electrode of a linear quadrupole ion guide/trap for on-demand injection into the acceleration region of a time-of-flight mass spectrometer in a well-collimated ion packet. This procedure was shown to yield trapping efficiencies that ranged from 4 to 5% for 10 nm diameter urea particles (∼400 kDa) to 1% for 200 nm urea particles (∼3 × 109 Da). Analysis of the inlet optimization procedure suggests that the inlet can be adapted to sample and trap beyond the 200 nm range. Review of the most likely places for ion loss in the sampling process suggests that the sampling and trapping efficiencies can be improved well beyond the 4–5% shown. Moreover, it suggests that sampling of smaller than 10 nm ions could achieve efficiencies in the 10s of percent range thereby suggesting new levels of sensitivity can be achieved for small ions (<200 kDa). Finally, demonstration of trapping large numbers of 200 nm (3 × 109 Da) ions for on-demand ejection in well collimated temporally discrete ion packets is a prelude to resolved mass analysis in that range.Graphical abstractHighlights► Atmospheric sampling and trapping of singly charged particulates is demonstrated. ► Sampling and trapping was demonstrated up to m/z = 3 × 109 with an efficiency of 1%. ► Trapping larger ions is possible. ► Trapping millions of ions is a prelude to resolved mass analysis in this range.

The proof of principle for high-resolution analysis of intact singly charged proteins of any size is presented. Singly charged protein ions were produced by electrospray ionization followed by surface-induced charge reduction at atmospheric pressure. The inlet and trapping system “stops” the forward momentum of the protein ions over a very broad range to be captured by the digitally produced electric fields of a large radius linear ion trap whereupon they are moved into a smaller radius linear ion trap and collected and concentrated in front of its exit end-cap electrode using digital waveform manipulation. The protein ions are then ejected on demand from the end of the small radius linear quadrupole in a tightly collimated ion beam with an instrumentally defined kinetic energy into the acceleration region of an orthogonal acceleration reflectron time-of-flight mass analyzer where their flight times were measured and detected with a Photonis BiPolar TOF detector. We present results that clearly prove that massive singly charged ions can yield high-resolution mass spectra with very low chemical noise and without loss of sensitivity with increasing mass across the entire spectrum. Analysis of noncovalently bound protein complexes was demonstrated with streptavidin-Cy5 bound with a biotinylated peptide mimic. Our results suggest proteins across the entire range can be directly quantified using our mass analysis technique. We present evidence that solvent molecules noncovalently adduct onto the proteins while yielding consistent flight time distributions. Finally, we provide a look into future that will result from the ability to rapidly measure and quantify protein distributions.

In this work, we have examined the reason for the deterioration of resolution and mass accuracy of time-of-flight mass analyzers with increasing mass after the expansion-induced kinetic energy has been eliminated by collisional cooling in an ion guide. Theoretically, removing the expansion-induced kinetic energy by collisional cooling permits the ions to travel along the ion guide axes without significant deviation so that they can be injected into the analyzer in a well-collimated ion beam with well-defined kinetic energy. If the ions can be injected into an orthogonal acceleration time-of-flight mass analyzer (oa-TOF) in this manner, high-resolution mass analysis can be obtained regardless of mass or m/z. Unfortunately, high resolution did not result. It is our contention that the effusive expansion out of the first ion guide yields dispersive axial ejection that reduces TOF resolving power with increasing mass not m/z.

Duty cycle-based trapping and extraction processes have been investigated for linear digitally driven multipoles by simulating ion trajectories. The duty cycles of the applied waveforms were adjusted so that an effective trapping or ejection electric field was created between the rods and the grounded end cap electrodes. By manipulating the duty cycles of the waveforms, the potentials of the multipole rods can be set equal for part of the waveform cycle. When all rods are negative for this period, the device traps positive ions and when all are positive, it ejects them in focused trajectories. Four Linac II electrodes [1] have been added between the quadrupole rods along the asymptotes to create an electric field along the symmetry axis for collecting the ions near the exit end cap electrode and prompt ejection. This method permits the ions to be collected and then ejected in a concentrated and collimated plug into the acceleration region of a time-of-flight mass spectrometer (TOFMS). Our method has been shown to be independent of mass. Because the resolution of orthogonal acceleration TOFMS depends primarily on the dispersion of the ions injected into the acceleration region and not on the ion mass, this technology will enable high resolution in the ultrahigh mass range (m/z > 20,000).Graphical abstractHighlights► The duty cycle of the waveforms applied to a digital ion guide can be used to trap and eject ions. ► Adding Linac electrodes to the guide permits ion to be trapped and collected in front of the exit end cap electrode. ► Collected ions can be ejected in plug with well-collimated trajectories into the acceleration region of an oa-TOFMS. ► Trapping, collecting and ejection by this method permits ions of ANY mass-to-charge ratio to be injected into a oa-TOFMS in collimated trajectories with controlled kinetic energy distributions. ► This technology will enable high resolution TOFMS in the ultra high mass range (m/z > 20 kDa).