Capítulo 4: Conclusiones
4.1 Construcción de la educación popular en Chile y reflexiones sobre su rol en la
First described by Wolfgang Paul and co-workers in 1953 [26], a quadrupole mass
analyser is a tuneable m/z filter, frequently used in combination with other mass analysers, where ions of different m/z are separated by the differential stability of their trajectories as they pass through the instrument. Ions with a stable trajectory are able to pass through the length of the quadrupole and reach the detector, where ions with unstable trajectories are filtered out. The quadrupole itself is made from two pairs of parallel metal rods arranged perpendicular to one another, where opposite direct current (DC) polarities are applied to each rod pair, such that opposite rods have the same charge, and adjacent rods have opposite charge (Figure 1.5).
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Figure 1.5 Schematic diagram of a quadrupole mass analyser. Voltages applied to each rod pair are seen on the right where DC (dashed red line) and RF-AC (solid black line) potentials are superimposed, resulting in changing rod polarities which generate spiral-like trajectories for ions passing through the analyser. Separation occurs by differential stability of these ion trajectories for a given AC and DC potential.
A radio frequency (RF) alternating current (AC), with a zero-to-peak amplitude greater than that of the applied DC voltage is also applied to the rods, such that the waveforms of adjacent rods are 180° out of phase, resulting in a dynamic potential on each rod defined by:
𝛷0 = 𝑈 − 𝑉 cos(2𝜋𝑣)𝑡 (1.2)
Equation 1.2 Dynamic potential on quadrupolar rods generated by superimposed AC and DC potentials. The potential applied to the rod (Φ0) is a combination of the DC potential (U), and the AC potential
where V is the 0-to-peak amplitude, v is the frequency and t is time.
The combined effect of these potentials is to periodically change the polarity on each rod pair simultaneously, where ions are attracted to, and then repelled by, each of the four rods, resulting in a spiral-like trajectory for ions passing through the quadrupole. It is convenient to conceptualise the quadrupole as filtering ions separately in the two lateral planes of the analyser: X-Z (left to right, and along) and Y-Z (up and down, and along). In the X-Z axis, the average polarity on the rods is positive, hence
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positively charged ions will be repelled by the rods and focused into the centre of the analyser. The brief change to negative polarity in the X-Z plane will have a negligible effect on the trajectory of higher m/z ions, as they respond less significantly to the polarity change than to the average polarity on the rod, allowing these ions to pass through to the detector unhindered. Conversely, the trajectories of lower m/z ions, which respond more significantly to the polarity change, are more likely to be destabilised, and therefore less likely to reach the detector. Thus the X-Z plane of the quadrupole acts as a ‘high pass m/z filter’ allowing only high m/z ions to pass through to the analyser (Figure 1.6) [27, 28]. In the Y-Z axis, the average polarity on the electrodes
is negative, hence positively charged ions are pulled from a stable trajectory in the centre of the analyser, towards the rods. Lower m/z ions, responding more significantly to the temporary change to positive polarity, are repelled back towards the centre of the analyser and are able to pass through to the detector with stable trajectories. Higher m/z ions, being more affected by the average polarity on the rod, have unstable trajectories in this plane, and depolarise on the rods before exiting the quadrupole. The Y-Z plane, then, acts as a ‘low pass m/z filter’ (Figure 1.6).
For an ion to be able to pass through the quadrupole and reach the detector, it must lie in the overlapped stability region between the two planes of the quadrupole, where the m/z of the ion is high enough to be stable in the X-Z plane, but low enough to be stable in the Y-Z plane. The main determinants of an ion’s stability through the quadrupole are the frequency of the polarity changes (i.e. AC frequency – typically maintained constant) and the magnitude of the applied DC and AC voltages (U and V as per Equation 1.2) [29]. While a fixed value of U and V can be maintained to allow
consistently only ions of a particular m/z to have stable trajectories through the analyser, maintaining a fixed ratio of U and V while changing their absolute values, allows the quadrupole to sequentially stabilise the trajectory of different m/z ions. Thus, a quadrupole can behave as a scanning mass analyser, building up a mass spectrum by rapidly ramping up the AC and DC voltages, sequentially allowing ions of different m/z through to the detector (Figure 1.6).
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Figure 1.6 The m/z separation of ions in the two lateral planes of a quadrupole. The low pass m/z filter (Y-Z) and the high pass m/z filter (X-Z) work together to stabilise the trajectory of ions in the quadrupole (m/z values with stable trajectories in each plane are in the grey shaded area of each plot). A mass spectrum is acquired by sequentially stabilising the trajectories of different m/z ions by increasing U and V.
The effect of U and V on the stability of different m/z ions in the quadrupole can be readily visualised using stability areas calculated from a complex series of equations known as the Mathieu and Paul equations [26, 30] (Figure 1.7). The increase in DC and
AC voltage necessary for scanning m/z analysis is visualised as the scan line in Figure 1.7, where an intersection between this line and a stability area highlights conditions at which an ion will have a stable trajectory in both planes of the quadrupole, and successfully reach the detector. The green m/z value in Figure 1.7, for example, at position 1 on the scan line has an m/z too high for the applied voltages to have a stable trajectory, so is stable in the X-Z plane (high pass) but unstable in the Y-Z plane (low pass). The reverse is true for this ion at position 3 on the scan line. Only at position 2, where the scan line intersects the stability region, will the green m/z ion have a stable trajectory through the quadrupole.
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Figure 1.7 Stability diagrams for ions in a quadrupole. Each lateral plane of the quadrupole acts as an
m/z filter, allowing either low m/z ions (Y-Z), or high m/z ions (X-Z) to pass through to the detector. The combined stability area for both lateral planes as a function of DC and AC voltage for high (blue), low (purple) and intermediate (green) m/z values is shown, where an ion will have a stable trajectory in the quadrupole at voltages where the scan line intersects the stability area. The stability of the green ion is shown, in each plane of the quadrupole, at U:V ratios at positions 1,2 and 3 on the scan line.
The gradient of the scan line (i.e. the ratio of U and V) determines the m/z resolution of the quadrupole, visually represented in Figure 1.7 as the stability area above the scan line (the smaller this area, the higher the resolution). Although the resolution can be increased by adjusting to a higher U/V ratio (steeper scan line gradient), quadrupoles are inherently low resolution mass analysers, and are usually operated at unit resolution (two peaks one m/z unit apart) [29]. Similarly, quadrupoles are limited
in their detectable m/z range, which is typically no more than 3000-4000 m/z [29, 31],
although this can be increased by lowering the frequency of the AC potential, typically at the cost of sensitivity and resolution [31]. Their advantage, however, is their
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positioning on m/z separation, allowing ions to be continually infused into the analyser – a characteristic ideal for coupling to continuous ionisation sources such as ESI. Additionally, by removing the DC potential entirely, a quadrupole can function in RF-only mode (Y=0 in Figure 1.7), allowing a very wide range of m/z ions to be transmitted through the analyser simultaneously, effectively acting solely as an ion guide – a characteristic ideal for using quadrupoles in conjunction with other mass analysers.