The Beauty of the Quadrupole Mass Analyzer

The quadrupole mass analyzer is now available to many analytical chemists as a detector for high performance liquid chromatography (HPLC) and gas chromatography (GC), thanks to its increasingly accessible price point. Although it’s not vital to understand the working details of these detectors, insight into their design and operation can help enormously when planning, optimizing, or troubleshooting analytical methods.

Quadrupole mass analyzers are composed of four parallel poles or rods, situated between the ion source on one end and the detector at the other. As ions travel through the central axis of the device, strong electric fields separate them according to their mass-to-charge (m/z) ratio.

Opposing rods are connected in pairs, and two combined voltages are applied to each pair: a fixed direct current (DC, or U) voltage, and an alternating current (AC, or V). The latter is often called the radio frequency (RF) voltage. DC and RF voltages are adjusted so that only ions of a specific m/z ratio follow a stable path to the detector. All other ions are deflected onto unstable trajectories, forcing them to collide with the rods or be ejected from the analyzer.

A common misconception is that the quadrupole consists of a pair of positive and negative rods. This misconception arises because one pair has a positive (+U), and the other a negative (-U), DC voltage. Rod polarity alternates with RF voltage; however, as they are offset by +U or -U, the time-averaged voltage of one pair of rods is positive, while the other is negative.

Thus, ions traversing the central space of the quadrupole are forced into complex trajectories as they are alternately attracted and repelled by the rods. The combined voltages create a hyperbolic field that has been described as a “saddle”: Imagine a tennis ball at rest on a horse saddle. Nudging the ball will cause it to fall down the side, but quickly rotating the saddle pushes the ball back to the original position, becoming unstable, falling, and returning repeatedly.

Light ions respond readily to alternating electrical fields, describing erratic trajectories that quickly eject them from the quadrupole. Heavy ions, having greater linear momentum, are less affected and eventually reach the detector. By increasing RF voltages, eventually heavier ions also become destabilized. RF voltage therefore functions as a high-mass filter.

Heavy ions are weakly deflected by RF fields, but their movement is influenced by the overall positive–or negative–DC offset, which deflects them into increasingly divergent trajectories. Eventually, they either collide with a rod, or are ejected from the analyzer. Higher DC voltages deflect heavier ions while having a minor effect on light ions trapped in the RF field. The DC voltage thus provides a tunable low-mass filter.

The motion of all those ions is ultimately dictated by the geometry of the quadrupole, the DC, and RF voltages being applied. A specific combination of voltages allows only ions within a narrow mass range to be detected, whereas all other ions are filtered out. The remaining question is, how do we set the voltages to detect specific masses?

Simply put, the voltages are optimized by “tuning” the device with a mixture of accurately known ions. Here’s the theory: U and V voltages, and m/z ratios, are related by Mathieu’s differential equation, the solutions of which can be visualized in Mathieu stability diagrams. Combinations of U and V that lie within the stability region of a given m/z ratio will result in stable trajectories for those ions. Combinations of U and V outside the region will filter those ions out. We can also describe this in reverse: only those ions whose stability region contains the current U and V voltages will be detected, all other ions will be filtered out.

Which finally takes us into known territory: This is the working principle of a single ion monitoring (SIM) mode experiment, where U and V are fixed to just detect ions of a specific m/z ratio. It is also possible to vary U and V voltages over time, which allows the quadrupole to sweep a range of masses, each sequentially becoming stable and reaching the detector. We do this in scan experiments, where a range of m/z values are detected by varying U and V along the so-called "scan line."

The scan line of a quadrupole is determined by two parameters, offset and slope, or gain. These can be adjusted to optimize sensitivity and mass resolution of the analyzer. Decreasing either offset or gain increases sensitivity, at the expense of poorer resolution. Increasing these parameters improves resolution, but decreases sensitivity.

It is not necessary to understand the complex physics behind the quadrupole to produce data, but a brief peek into the underlying principles can truly reveal the sheer beauty of these devices!

Tony Taylor is the Chief Science Officer of Arch Sciences Group and the Technical Director of CHROMacademy. Direct correspondence to: LCGCedit@mmhgroup.com.