4.2.6.1 Magnetic sector mass filter
It has been known for some time that the trajectory of a point charge, in our case a positively charged ion, can be altered by an electrical or magnetic field. Thus, the first MS systems employed permanent magnets or electromagnets to bend the packets of ions in a semi-circular path and separated ions based on their momentum and kinetic energy. Common angles of deflection are 60, 90, and 180 degrees. The change in trajectory of the ions is caused by the external force of the magnetic field. The magnitude of the centripetal force, which is directly related to the ions velocity, resists the magnetic field’s force. Since each mass to charge ratio has a distinct kinetic energy, a given magnetic field strength will separate individual mass to charge ratios through space. A slit is placed in front of the detector to aid in the selection of a single mass to charge ratio at a time.
A relatively simple mathematical description will allow for a better understanding of the magnetic field and the ions centripetal force. First, it is necessary to compute the kinetic energy (KE) of an ion with mass m possessing a charge z as it moves through the accelerator plates. This relationship can be described by
KE = ½ mv2 = zeV
where e is the charge of an electron (1.60 x 10-19 C), v is the ion velocity, and V is the voltage between the two accelerator plates (shown in the Animation 1.5 below). Fortunately for the ionizations occurring in the plasma, most ions have a charge of +1. As a result, an ions’ kinetic energy will be inversely proportional to its mass. The two forces that determine the ion's path, the magnetic force (FM) and the centripetal force (FC), are described by
FM = Bzev
and
FC = (mv2)/r
where B is the magnetic field strength and r is the radius of curvature of the magnetic path. In order for an ion of particular mass and charge to make it to the detector, the forces FM and FC must be equal. This obtains
BzeV = (mv2)/r
which upon rearrangement yields
v = (Bzer)/m .
Substituting this last equation into our first KE equation yields
m/z = (B2r2e)/2V
Since e (the charge of an electron) is constant and r (the radius of curvature) is not altered during the run, altering the magnetic field (B) or the voltage between the accelerator plates (V) will vary the mass to charge ratio that can pass through the slit and reach the detector. By holding one constant and varying the other throughout the range of m/z values, the various mass to charge ratios can be separated. One option is to vary the magnetic field strength while keeping the voltage on the accelerator plates constant.
In general, it is difficult to quickly vary the magnetic field strength, and while this is problematic in chromatography it is of little consequence with ICP instruments. Generally, several complete mass to charge scans are desired for accurate analyte identification and this can be completed ICP analysis by simply sampling longer. This entire problem can be overcome in modern magnetic sector instruments by rapidly sweeping the voltage between the accelerator plates, in order to impart different momentums on the ions, as opposed to sweeping the field strength. Due to the operational advantages of this technique, most electromagnets hold the magnetic field strength (B) and vary the voltage (V) on the accelerator plates.
The magnetic sector mass filter is illustrated in Animation 4.3 below. As noted above, although B and r are normally held constant, this modern design is difficult to animate, so we will illustrate a magnetic sector MS where B, the magnetic field, is varied to select for different ions. After ions pass the cones at the ICP MS interface, they are uniformly accelerated by the constant voltage between the two accelerator plates/slits on the left side of the figure. As the different ions travel through the electromagnet, the magnetic field is varied to select for different m/z ratios. Ions with the same momentum or kinetic energy (and therefore mass) pass through the exit slit together and are measured by the detector, followed by the next ion, and so on.
Animation 4.3. Illustration of a Magnetic Sector MS.
While magnetic sector mass filters were once the only tool used to create a mass spectrum, they are becoming less common today. This is due to the size of the instrument and its weight. As a result, many magnetic sector instruments have been replaced by quadrupole systems that are much smaller, lighter, and able to perform extremely fast scans. Magnetic sector instruments are still used in cases where extremely high-resolution is required such as with double-focusing instruments (discussed later in this section).
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