A little something on the Quadrupole

This post will cover the working principle of a quadrupole mass analyzer (or mass filter), wich will eventually be the "heart" of my DIY mass spectrometer.

A Quadrupole (short Quad) is a quadratic arrangement of four linear rod-shaped electrodes, wich - under high vacuum - can filter ions for their m/z ratio, when certain voltages are applied. Ions enter the quad on one side, through the symmetry center of the arrangement (green dot in the center of the drawing), and resonant ions roughly move along the symmetry-axis, parallel to the rods (normally indicated as the z-axis). Opposite electrodes are always equally charged, whereas juxtaposed electrodes are of opposite charge (red formula in the drawing).  Furthermore, electrode (rod) voltages are a composition of a constant offset voltage U and a radio-frequency RF-voltage V.

Owing to the charge of the rods, ions entering will be either attracted or repelled by their nearest rod, resulting in oscillating flight curves through the mass analyzer. If no constant voltage is applied to the rods (U=0), all ion flight curves are stable (for a broad range of RF-voltages), meaning that all ions entering the quad will leave it on the other side, even though they might perform oscillations when flying through. This however is not a mass filter, because all ions are passed through, regardless of their m/z. But if now a constant offset voltage is also applied, suddenly not all ion-oscillations are stable anymore. Depending on their m/z, ions on unstable flight-curves will eventually hit one of the electrodes. Ideally, the quad can be configured in a way, that only one ion m/z is stable by adjusting U and V. You now have a mass filter, allowing for selectively passing through ions of defined m/z!

It turns out that an ideal Quad can achieve unlimited resolution when 2U/V equals 0,336 (green dotted lines above). In reality however, U is lowered so that a broader m/z area is passed. Note that every mass has its own stability-region on the diagram. With a quad it is therefore possible to scan for all expected m/z by lowering U and V respectively while keeping the ratio 2U/V constant.

There is a lot of practical experience for the construction of these mass filters available and it turns out that quads show their best performance when ions of 10eV energy perform about 100 oscillations when passing through. This performance is - by default - reached with quads of 15 to 25 cm length and rod diameters of 10 to 20 mm. The ideal inner radius of the quad (r0) turns out to be a function of its rod-diameter (r) with r0=r/1,1468. DC and RF voltages range between 100 and 2000 volts and RF-frequency lays between 1-4 MHz.

For further reading I suggest Mass Spectrometry: A Textbook by Jürgen H Gross. All information contained in this post is taken out of that book.