# How does a mass spectrometer separate ions?

Here the ions are separated on the basis of their mass-to-charge ratio. We know from physics that the deflection of electrically charged particles (ions) from their trajectory is possible only in accordance with their ratio of mass to charge, since the attraction of the particles is proportional to the charge while the inertia (which resists change) is proportional to its mass. The separation system comprises four cylindrical metal rods, set up in parallel and isolated one from the other; the two opposing rods are charged with identical potential. Fig. 4.2 shows schematically the arrangement of the rods and their power supply. The electrical field Φ inside the separation system is generated by superimposing a DC voltage and a high-frequency AC voltage:

r0 = radius of the cylinder which can be inscribed inside the system of rods.

Fig 4.2 Schematic for quadrupole mass spectrometer

Exerting an effect on a single charged ion moving near and parallel to the center line inside the separation system and perpendicular to its movement are the forces:

The mathematical treatment of these equations of motion uses Mathieu’s differential equations. It is demonstrated that there are stable and unstable ion paths. With the stable paths, the distance of the ions from the separation system center line always remains less than ro (passage condition). With unstable paths, the distance from the axis will grow until the ion ultimately collides with a rod surface. The ion will be discharged (neutralized), thus becoming unavailable to the detector (blocking condition).

Even without solving the differential equation, it is possible to arrive at a purely phenomenological explanation which leads to an understanding of the most important characteristics of the quadrupole separation system.

If we imagine that we cut open the separation system and observe the deflection of a singly ionized, positive ion with atomic number M, moving in two planes, which are perpendicular one to the other and each passing through the centers of two opposing rods. We proceed step-by-step and first observe the xz plane (Fig. 4.5, left) and then the yz plane (Fig.4.5, right):

Fig 4.5 Phenomenological explanation of the separation system

### 1. Only DC potential U at the rods:

xz plane (left): Positive potential of +U at the rod, with a repellant effect on the ion, keeping it centered; it reaches the collector (→ passage).

yz plane (right): Negative potential on the rod -U, meaning that at even the tiniest deviations from the center axis the ion will be drawn toward the nearest rod and neutralized there; it does not reach the collector (→ blocking).

### 2. Superimposition of high-frequency volt age V · cos ω t:

xz plane (left): Rod potential +U + V · cos ω t. With rising AC voltage amplitude V the ion will be excited to exe cute transverse oscillations with ever greater amplitudes until it makes contact with a rod and is neutralized. The separation system remains blocked for very large values of V.

yz plane (right): Rod potential -U -V · cos ω t. Here again superimposition induces an additional force so that as of a certain value for V the amplitude of the transverse oscillations will be smaller than the clearance between the rods and the ion can pass to the collector at very large V.

### 3. Ion emission i+ = i+ (V) for a fixed mass of M:

xz plane (left): For voltages of V < Vthe deflection which leads to an escalation of the oscillations is smaller than V1, i.e. still in the “pass” range. Where V > V1 the deflection will be sufficient to in duce escalation and thus blockage.

yz plane (right): For voltages of V < Vthe deflection which leads to the damping of the oscillations is smaller than V1, i.e. still in the “block” range. Where V > V1 the damping will be sufficient to settle oscillations, allowing passage.

### 4. Ion flow i+ = i+ (M) for a fixed ratio of U / V:

Here the relationships are exactly opposite to those for i+ = i+ (V) since the influence of V on light masses is great er than on heavy masses.

xz plane: For masses of M < M1 the deflection which results in escalation of the oscillations is greater than at M1, which means that the ions will be blocked. At M > M1 the deflection is no longer sufficient for escalation, so that the ion can pass.

yz plane: For masses of M < M1 the deflection which results in damping of the oscillations is greater than at M1, which means that the ion will pass. At M > M1 the damping is not sufficient to calm the system and so the ion is blocked.

### 5. Combination of the xz and yz planes.

In the superimposition of the ion currents i+ = i+ (M) for both pairs of rods (U / V being fixed) there are three important ranges:

Range I: No passage for M due to the blocking behavior of the xz pair of rods.

Range II: The pass factor of the rod systems for mass M is determined by the U/V ratio (other ions will not pass). We see that great permeability (corresponding to high sensitivity) is bought at the price of low selectivity (= resolution, see Specifications in mass spectrometry). Ideal adjustment of the separation system thus requires a compromise between these two properties. To achieve constant resolution, the U/V ratio will remain constant over the entire measurement range. The “atomic number” M (see page on Ionization) of the ions which can pass through the separation system must satisfy this condition:

V = High-frequency amplitude,
f = High-frequency

As a result of this linear dependency there results a mass spectrum with li near mass scale due to simultaneous, proportional modification of U and V.

Range III: M cannot pass, due to the blocking characteristics of the yz pair of rods.

## The measurement system (detector)

Once they have left the separation system the ions will meet the ion trap or detector which, in the simplest instance, will be in the form of a Faraday cage (Faraday cup). In any case the ions which impinge on the detector will be neutralized by electrons from the ion trap. Shown, after electrical amplification, as the measurement signal itself is the corresponding “ion emission stream”. To achieve greater sensitivity, a secondary electron multiplier pickup (SEMP) can be employed in place of the Faraday cup.

Channeltrons or Channelplates can be used as SEMPs. SEMPs are virtually inertia-free amplifiers with gain of about 10+6 at the outset; this will indeed drop off during the initial use phase but will then become virtually constant over a long period of time. Fig. 4.6 shows at the left the basic configuration of a Faraday ion trap and, on the right, a section through a Channeltron. When recording spectra the scanning period per mass line t0 and the time constants of the amplifier t should satisfy the condition that t0 = 10 τ. In modern devices such as the TRANSPECTOR the otherwise unlimited selection of the scanning period and the amplifier time constants will be restricted by microprocessor control to logical pairs of values.

Fig 4.6 Left: principle of the Faraday cup. Right: Configuration of the Channeltron

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## References

Vacuum symbols

### Vacuum symbols

A glossary of symbols commonly used in vacuum technology diagrams as a visual representation of pump types and parts in pumping systems

Glossary of units

### Glossary of units

An overview of measurement units used in vacuum technology and what the symbols stand for, as well as the modern equivalents of historical units

References and sources

### References and sources

References, sources and further reading related to the fundamental knowledge of vacuum technology

### Vacuum symbols

A glossary of symbols commonly used in vacuum technology diagrams as a visual representation of pump types and parts in pumping systems

### Glossary of units

An overview of measurement units used in vacuum technology and what the symbols stand for, as well as the modern equivalents of historical units