Quadrupole Ion Trap

1
Quadrupole Ion Trap
end cap electrodes
ring electrode
2
Quadrupole Ion Trap Mass Spectrometer
end cap electrodes
z
x
min pot
ring electrode
y
z

• as they deviate from the centre ions feel a
  restoring force.
• the Mathieu equation describes ion motion in an
  oscillating rf quadrupole field
• the mathematics of this device is similar to
  that describing a vibrating skin
• Mathieu described the solutions to vibrations of
  stretched skins in terms of stability and
  instability regions.

potential felt by ions
potential felt by ions
x
3
In order to use the solutions to the Mathieu
equation, we must first verify that the equation
of motion of an ion confined in a quadrupole
device can be described by the Mathieu equation.
In other words we must obtain an expression for a
force in Mathieus equation and compare it to
that for an ion in a quadrupole field. In order
to do this we will follow closely the derivations
presented by March in R.E. March, J. Mass
Spectrom. 1997, 32, 351. The numbers of the
equations presented here are, for the most part
the same as those in this paper.
The Mathieu equation where u represents the
coordinates, x, y and z, and Since t is time
and x is dimensionless, W is a frequency which
will later be seen to be the radial frequency of
an rf potential on the ring electrode. au and
qu are dimensionless parameters known as trapping
parameters.
(2)
4
In equation 2, we want to sub for x Wt/2 so,
and,
(3)
therefore,
or,
Substituting this into equation 2 along with x
Wt/2 yields,
5
multiplying through by m and rearranging yields,
(4)
Force (ie. mass multiplied acceleration in x, y
or z.)
The field in quadrupole devices is uncoupled so
that the forces in the x, y, or z directions can
be determined separately. The force in the x
direction, experienced by an ion of mass, m, and
charge e (rather than q, although they are the
same) is,
(5)
Where f is the potential at any point.
Equation 5 relates the force on an ion at any
point in the trap to the electric field
(derivative of potential with respect to
distance) in the trap.
6
The quadrupole potential within the trap is given
by, where fo is the applied electric potential
(rf alone or in combination with a dc potential),
l, s, and g are weighting constants and ro is a
constant defined separately depending on whether
the device is 2-D or 3-D (filter or trap).
(6)
z
end cap electrodes
x
min pot
ring electrode
y
z
potential felt by ions
potential felt by ions
x
7
x
z
y
y
V contour plotted as a function of x and y at z0.
V contour plotted as a function of z and y.
8
In any electric field, it is essential that the
Laplace condition,
where be met. The Laplace condition ensures
that the electric field is uniform. Therefore,
(7)
For the ion trap, ls1 and g-2 and for the mass
filter, l1 s-1 and g0. Substituting the
values for the ion trap into equation 6 yields,
(8)
9
which we convert to the cylindrical coordinate
system. (x rcosq, y rsinq, z z) yielding
(9)
But, since sin2q cos2q 1
(10)
The applied potential is of the
form, where the angular frequency, and f is
the frequency in Hz.
(11)
When equation 11 is substituted into equation 10,
10
and differentiating with respect to r
yields,
(12)
Substituting eq. 12 into eq. 5 yields
(13)
This is an expression for the force in the r
dimension on an ion.
Now we can compare directly equations 4 and 13
and find that for an ion trap,
(14)
(realize that for a trap, axay ar and qxqy
qr, and for a mass filter ax-ay and qx-qy).
11
Similarly one obtains for the z direction, since
g-2 For a typical commercial trap, U0 so
az 0. The expression for qz contains the m/z
ratio, the trap dimensions, ro, the amplitude of
the rf, V, and the angular frequency of the rf, W.
(15)
12
Quadrupole Ion Trap (QIT) or 3-D quadrupole
13
As was shown previously,
Thus the region of stability is not symmetric
about qu, as was the case for the quadrupole mass
filter QMF since az and qz are different than ar
and qr, respectivelyby a factor of 2.
14
qz 0.908
15
Mass analysis by ion ejection at the stability
limit. Most commercial ion traps operate with
U0, or on the qz axis. This enables one to
obtain a mass spectrum by simply ramping the rf
voltage (V), and ions will exit the endcap
electrodes at the stability limit, qz0.908,
bz
bz
16
The Dehmelt potential in the axial coordinate is
given by,
17
Mass analysis by resonant ejection The motion of
an ion in the ion trap is composed of two
fundamental frequency components, wr,0 and wz,0.
There are are higher-order frequencies described
by wu,n (secular frequencies) but these higher
order frequencies are of little practical
significance. However, it is possible to utilize
the fundamental axial secular frequency, wz,0, by
applying a small supplementary voltage (few
hundred mV) across the end-cap electrodes at the
same frequency as wz,0 to excite the ions
motion, thereby resonantly ejecting the ion at a
qz value lower than 0.908.
18
The fundamental axial secular frequency, wz,0 (in
rad s-1, not Hz), is given by, where By
resonantly ejecting, one can extend the mass
range of the quadrupole ion trap. Note See
the March paper in order to be able to do
calculations based on the quadrupole ion trap.
19
MS/MS in the quadrupole ion trap. It is possible
to do tandem mass spectrometry with the
quadrupole ion trap. One can resonantly eject
unwanted ions from the mass spectrometer by
applying a small rf potential at each of the
unwanted ions secular frequency. Then the
isolated ion can be excited using a very small
amplitude rf excitation in order to cause
collisions with the bath gas (usually He). These
collisions provide internal excitation and cause
fragmentation. Any fragments which have masses
which correspond to stable regions will be
trapped. The collision induced dissociation
(CID) spectrum can then be acquired.
20
Quadrupole Mass Filter(QMF) or 2-D quadrupole
Ideally the rods of the quadrupole mass filter
would be hyperbolic (see right), however, in
practice they are cylindrical which gives the
appropriate potential at the centre of the filter.
21
Stability Diagram for QMF
22
working point a0.237 q0.706
Any ion of mass m with a and q values within the
stability region will be transmitted by the
device. For ions outside the stability range,
the trajectories will be unstable with time and
the ions will collide with the electrodes or the
vacuum chamber walls.
Stability region for a quadrupole mass filter is
symmetric (unlike the ion trap).
The device is typically used such that the values
of U and V are adjusted so that an ion of mass m
has a and q values of 0.237 and 0.706,
respectively. For higher throughput, lower
values of a and q can be used at the cost of
resolution.
23
operating line
Above is a plot of the stability areas as a
function of U and V for ions with different
masses. Changing U linearly as a function of V,
we obtain a straight operating line that allows
us to observe each of these lines in succession.
A line with a higher slope would give higher
resolution. If U is zero, there is no
resolution, all ions pass through the filter (rf
only mode).
24
A QMF can not be used for MSn (tandem mass
spectrometry) unless you have more than one. For
example a triple quad. Typically q1 is a
mass selection process, to select an ion of a
particular m/z ratio. q2, then, is operated in
rf only mode and has a high pressure of collision
gas to collide the q1-mass selected ions. q3
operates as a mass analyzer in order to scan and
obtain a mass spectrum. This is called a
fragment ion or product ion scan.
Precursor selection
Fragmentation
Mass Scan
CID
MS1
MS2
q1
q2
q3
25
For a parent ion or precursor ion scan, q1 is
scanned, q2 is, again simply a collision cell
operated in rf only mode while q3 is set to pass
a fragment of a particular mass. This will give
a plot of all the precursor ions which fragment
to give a particular mass ion.
Fragment selection
Precursor scan
Fragmentation
CID
MS1
MS2
q1
q2
q3
26
In the third common scan mode, both q1 and q2 are
scanned but with a constant mass offset.
Therefore, for a mass difference, a, when an ion
of mass m goes through q1 detection of the ion
occurs only if it has yielded a fragment with a
mass m-a when it leaves q2. This is called a
neutral loss scan.
Fragment m-a scan
Precursor m scan
Fragmentation
CID
MS1
MS2
q1
q2
q3