Mass Spectrometry
Fundamentals of Vacuum Technology
D00.91
LEYBOLD VACUUM PRODUCTS AND REFERENCE BOOK 2001/2002
4.3.1.2 The quadrupole separation
system
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 trajec-
tory 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 cylin-
drical metal rods, set up in parallel and iso-
lated one from the other; the two opposing
rods are charged with identical potential.
Fig. 4.2 shows schematically the arrange-
ment 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 volta-
ge:
Φ = (U + V ⋅ cos ωt) · (x
2
– y
2
) / r
0
2
r
0
= radius of the cylinder which can be
inscribed inside the system of rods
Exerting an effect on a single charged ion
moving near and parallel to the center line
inside the separation system and perpen-
dicular to its movement are the forces
The mathematical treatment of these equa-
tions 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 r
o
(passage condition).
With unstable paths, the distance from the
axis will grow until the ion ultimately colli-
des with a rod surface. The ion will be
discharged (neutralized), thus becoming
unavailable to the detector (blocking con-
dition).
Even without solving the differential equa-
tion, it is possible to arrive at a purely phe-
nomenological explanation which leads to
an understanding of the most important
characteristics of the quadrupole sepa-
ration system.
If we imagine that we cut open the se-
F
e
r
x t
x
= − ⋅ ⋅ ⋅
2
0
2
cos ( )ω
F
e
r
y t
y
= − ⋅ ⋅ ⋅
2
0
2
cos ( )ω
F
z
= 0
paration system and observe the deflec-
tion 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):
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
voltage 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 execute transverse
oscillations with ever greater amplitu-
des 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 oscilla-
tions 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 < V
1
the
deflection which leads to an escalation
of the oscillations is smaller than V
1
, i.e.
still in the “pass” range. Where V > V
1
the deflection will be sufficient to
induce escalation and thus blockage.
yz plane (right): For voltages of V < V
1
the deflection which leads to the dam-
ping of the oscillations is smaller than
V
1
, i.e. still in the “block” range. Where
V > V
1
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 oppo-
site 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 < M
1
the
deflection which results in escalation of
the oscillations is greater than at M
1
,
which means that the ions will be
blocked. At M > M
1
the deflection is no
longer sufficient for escalation, so that
the ion can pass.
yz plane: For masses of M < M
1
the
deflection which results in damping of
the oscillations is greater than at M
1
,
which means that the ion will pass. At
M > M
1
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 (corre-
sponding to high sensitivity) is bought
at the price of low selectivity (= resolu-
tion, see Section 4.5). Ideal adjustment
of the separation system thus requires
a compromise between these two prop-
D00
xz plane yz plane
+
+
+
+
+
+
-
-
+
-
-
+
Superimposition of the xy and yz planes
Rod:
+U
Transmission:
full
Rod:
+U+V, cos ω
Transmission:
low-pass
i
+
i
+
i
+
VV
1
V
1
V
M
i
+
MM
1
M
1
i
+
M
I III
II
yz
xz
Rod:
–U
Transmission:
none
Rod:
–U–V · cos ω
Transmission:
high-pass
( )
U
V
fixed
U
V
.. Selectivity (resolution) Sensitivity
1
2
3
4
5
Fig. 4.5 Phenomenological explanation of the
separation system
D00 E 19.06.2001 21:39 Uhr Seite 91