About the underlying principle of the quadrupole?

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Introduction

Quadrupole mass analysers, also known as quadrupole mass filters, are among the most widely used analysers. A quadrupole mass analyser is considered as a mass filter because of its ability to select for analysis ions of a specific mass-to-charge ratio, which are essentially separated by applying DC and AC voltages. As the name suggests, it consists of four cylindrical rods parallel to each other, and the separation of ions is based on: the ability of the ions to maintain a stable trajectory on the quadrupole in an oscillating electric field (a combination of DC and AC voltages).

Physical Principle

Quadrupoles are charged by DC and AC voltages to affect the motion of ions in such a way that two quadrupoles diagonally opposite to each other have the same voltage, while two quadrupoles perpendicular to each other have voltages of opposite sign.

The ions must enter the quadrupole field slowly (with only a few eV of kinetic energy) in order to interact with the oscillating electric field located between the rods. In direct current, the voltage (U) is constant, whereas in alternating current (Vcosωt), the direction of the voltage changes. If an AC voltage is applied, the chance of hitting the metal rod depends on the mass and charge of the ions, as well as on the electric field strength and frequency of oscillation. The operator can adjust the electric field strength and oscillation frequency.

If the frequency applied is very high, then the ion will not have time to react at all and nothing will happen; but if the frequency is too low, then the ion will be attracted to the rod before the potential changes. In the case of a positive ion, a rod with a positive potential will repel the ion, while a rod with a negative potential will attract the ion and capture it.

If the DC and AC fields are combined, then the positive ions are forced into the middle of the two positive poles, and the AC field destabilises them. If the ions have a large mass or a small charge, they are virtually unaffected by the AC field, and their trajectories are largely determined by the DC field. However, the trajectories of ions with too small a mass-to-charge ratio are strongly disrupted by the AC field, causing them to strike the rod. A rod with a negative potential attracts positive ions, which can be prevented from striking the rod by applying an appropriate AC voltage.

Simply put, the potential of the two opposing rods is positive except for a brief period of time when the negative AC voltage exceeds the positive DC voltage. During this time, the rods will only cause the positively charged lighter ions to scatter, because the lighter ions are faster and therefore will hit the rods without being detected.

In addition, this also means that these rods can be considered as high mass-to-charge ratio filters because they can only detect positively charged ions with high mass-to-charge ratios. Similarly, when the AC voltage is positive on the rods, the other two rods can only focus on lighter ions for a short period of time, so they can be considered low mass-to-charge ratio filters. If the voltage is chosen correctly, then ions with a narrower range of mass-to-charge ratios can pass through the rods and with reach the detector.

The stability of ions can be detected by simply calculating the force associated with the electric field in a quadrupole field. potential at any point in the hyperbolic field.

The electric field along each plane is the partial derivative with respect to the x, y or z axis.

where ω = angular frequency and r0 = quadrupole radius

According to Newton's second law, the

Simplifying the above equation, the

DC voltage: AC voltage:

When plotting AC voltage versus DC voltage on a two-dimensional coordinate axis, we find the stability trajectory to be.

Practical Working Principle

A quadrupole mass analyser consists of four parallel cylindrical metal rods arranged equidistant from the central axis. To ensure that only the desired mass-to-charge ratio of ions passes through the quadrupole and reaches the detector, the quadrupole is subjected to both direct and alternating current, and the number of ions entering the detector is signalled and displayed on a computer.

Firstly, the ions are ionised using ionisation techniques such as electrospray ionisation, chemical ionisation and matrix assisted laser desorption ionisation (MALDI). The ions are then fed into a quadrupole mass analyser, where ions with stable trajectories are detected in the detector and ions with unstable trajectories are not detected. The likelihood of ions being detected can be controlled by adjusting the electric field strength and oscillation frequency.

Initially, only a relatively small voltage of a few hundred volts was used to accelerate a continuous source of ions generated in the ionisation unit in the Z-direction. These ions entered the quadrupole through a small inlet. Voltages of opposite polarity were applied to two adjacent poles, while voltages of the same polarity were applied to two poles of opposite diagonal. When AC and DC voltages are applied to each rod simultaneously, the quadrupole produces an electric field with a rapidly changing phase.

Therefore, ions moving through this electric field will oscillate in the x and y directions, and ions with a specific mass-to-charge ratio will produce stable oscillations and reach the detector through the quadrupole at a specific parameter setting. On the other hand, the oscillations of ions with different charge ratios become unstable, causing them to hit the rod and leave the system, thus not being detected.

How do we separate gaseous ions?

The separation of gaseous ions in a quadrupole is: based on the stability of the path or trajectory in an oscillating electric field applied to the rod. A combination of AC and DC applied to the rods will determine the trajectory. This electric field is created if AC is applied to one of two pairs of rods opposite each other in the quadrupole. The operator can improve the chances of the ions being detected by adjusting the strength of the electric field and the frequency of the oscillations, and the frequency required to stabilise the oscillations can be determined by equations.

How do we make quality choices?

The quadrupole mass analyser performs mass selection by varying the AC and DC voltages. Let us consider that if only one alternating voltage is applied, then in this case, when the voltage is positive, the positive ions will be repelled and stay in the centre of the two rods. Similarly, when the potential is negative, the positive ions will accelerate towards the two rods and will not be detected.

If an AC voltage and a positive DC voltage are supplied to the pair of rods at the same time, ions of different masses will respond differently to the applied voltage. Heavy ions are unaffected by the AC voltage and will therefore be detected by the detector because they will be concentrated in the centre of the rods, even when the AC voltage is applied, as heavy ions are much slower than lighter ions.

Similarly, the other pair of rods will be subjected to a reverse AC/DC voltage, so it will have a negative DC voltage, and because it is negative, the heavy ions will hit the electrodes without being detected, but the lighter ions will respond to the AC potential and will be concentrated in the centre of the quadrupole. Therefore, in this case, the lighter ions will have a stable trajectory and act as a low mass filter.

A single mass-to-charge ratio can be selected by combining two electrodes into the same system with a stabilised trajectory. If the amplitudes of AC and DC are changed, the stabilisation trajectory is also changed. Ions of different magnitudes have different stabilisation trajectories and reach the detector at different times. Therefore, the desired mass range can be selected by simply changing the AC and DC voltages.