Download 20.3 Magnetic Field Mass Analyzers

20.3 Magnetic Field
Mass Analyzers
• magnetic sector dispersion and mass
analysis
• sector design to accommodate angular
distributions of ions from the source
• electric sector dispersion is based on
kinetic energy
• double focusing spectrometers to
accommodate kinetic energy distributions
• ion cyclotron motion and image current
• chirped excitation and the free induction
decay
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Magnetic Sector Basics
In a mass spectrometer the ions
produced in the source are extracted by
a metallic plate held at a large negative
voltage. The plate has a slit cut into it
which passes the accelerated ions.
The resultant accelerated ions are then inserted
into magnetic field. If the direction of travel is
perpendicular to the field, the ions follow a
circular trajectory with radius r. This is
because the magnetic force, F = qvB, is
counterbalanced by the centripetal force,
mv2/r.
mv 2
M+
qvB =
or mv = qBr
r
By constraining the radius with slits, ions
entering the magnetic field can be separated
on the basis of their momentum.
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e+ ++
M ++
++
VsV+
× × ×
× × × × ×
× × × × × ×
× × × × × × ×
Bout
× × × × × × ×
r
× × × × × × × ×
(mv)'
(mv)''
mv
Magnetic Sector Mass Analysis
Ion momentum is determined by its mass
and velocity. The velocity is determined
by the amount of kinetic energy obtained
in the source, mv2/2 = qVs . To obtain
the behavior of the magnetic sector with
respect to m/z, square the momentum
equation and substitute in the kinetic
energy. When using an electric potential
to accelerate ions, a mass spectrum is
obtained by fixing r and varying either Vs
or B.
( mv )2 = q 2 B 2r 2
( )
m mv 2 = m ( 2qVs ) = q 2 B 2 r 2
m B 2r 2
=
2Vs
q
For a magnetic sector the upper resolution, m/Δm, is about 5,000.
To see the precision required on scanning the magnetic field,
assume a radius of 30 cm, and an accelerating potential of 2.5 kV.
For m/z = 1,000 Th, a resolution of 5,000 requires Δm = 0.2 Th.
B1,000 = 0.75920
B1,000 − B999.8
B1,000
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B999.8 = 0.75913
= 0.0001 or
1:104
Electromagnets can be
adjusted to 1:106, so
the required precision is
not electrically difficult.
Angular Distribution of Source Ions
Ions leave the source with a distribution of angles, which will affect
the mass resolution. This problem is minimized by constructing the
magnetic field in pie-shaped sectors having angles in increments of
30° (30°, 60°, 90°, etc.), and by placing the source slit, sector apex,
and detector slit on a straight line.
60E
magnetic
sector
r
source
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detector
Kinetic Energy Distribution of Source Ions
The resolution of a single magnetic sector is limited by the ion
kinetic energy spread. The spread is due primarily to two
processes - (1) thermal energy variations due to kT; and, (2) the
spatial distributions of ion creation in the source. The spatial
distribution only matters because there is a small variation of
electric potential across the source region. Thus, ions do not have
the same potential difference with respect to the accelerating
voltage.
60E
magnetic
sector
3.0 kV
2.5 kV
source
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detector
The drawing shows ion
trajectories for a 20%
difference in kinetic energy.
This large difference was
necessary to make the
drawing! In practice the
spread in kinetic energies is
~0.02% for a spectrometer
with a resolution of 5,000.
Electric Sector Kinetic Energy Analysis
Consider an electric field which has a cylindrical geometry with all
field lines pointing out radially. An ion in this field will follow the
curved path where the centripetal force balances the electric force,
qV.
mv 2 2 Ek
qV =
=
r
r
2E
r= k
qV
In the above expression, the kinetic energy is due to acceleration in
the source, Ek = qVs = mv2/2.
+V
60E electric
sector
3.0 kV
-V
2.5 kV
source
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detector
The electric sector separates
on the basis of kinetic energy
and is independent of mass.
The electric sector can be
combined with a magnetic
sector to create a high
resolution mass analyzer.
Double Focusing Mass Spectrometers
+V
electric
sector
-V
source
magnetic
sector
The electric sector first separates on the basis of
kinetic energy, then the magnetic sector separates
on the basis of momentum (mass). Since the ion
paths through the magnetic sector are reversible,
two ions of the same mass but different kinetic
energies will be recombined at the detector slit.
The JEOL double focusing JMS MStation
spectrometer has an upper mass of 2,400 Th and a
resolution of 60,000. Vs = 10 kV.
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detector
Ion Cyclotron Motion
When an ion is placed in a magnetic
field it travels in a circular orbit. This
has already been shown for a magnetic
sector.
mv 2
qvB =
r
v=
B is out of the plane of the figure.
q
Br
m
The time to travel one complete orbit is
given by the circumference divided by
the velocity.
t=
2π r m 2π
=
q B
v
1 q B
f = =
t m 2π
For a given m/z the cyclotron frequency is constant. With a 3 T
magnetic field, the cyclotron frequency is 1.65 MHz at 28 Th and
11.5 kHz at 4,000 Th. Because of the Boltzmann distribution of
kinetic energy, the radii will vary. Also, the phase is random. For a
large number of ions, the vector sum of the thermal cyclotron
motion is zero because of the random phase.
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Image Current
0V
r
*! V
r
0V
*+ V
r
0V
*+ V
0V
*! V
A moving ion in a vacuum will induce differential charge across two
capacitor plates.
The motion of a single, positively charged ion is shown in the figure.
As the charge travels around its orbit, it induces a negative charge
in the nearest plate, and a positive charge in the farthest plate. By
attaching a radiofrequency voltmeter to the plates, both the
magnitude and frequency of the induced current can be measured.
For a collection of thermally excited ions, the image current is zero
because of the random phase. Some method of coherent excitation
is required.
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Ion Cyclotron Resonance (ICR)
+cos(2Bft)
In order to detect cyclotron motion all
of the ions must be moving in phase.
This is accomplished by applying a
radiofrequency voltage across two
plates, as shown in the figure. The
applied radiofrequency voltage forces
all ions to move in the same phase.
r
-cos(2Bft)
Because the motion of all of ions of the
same m/z is coherent, the vector sum
is measurable as an image current.
In swept frequency ICR, each m/z is
excited sequentially and its image
current measured. This is time
consuming and is limited by noise
created by the residual thermal motion
of all ions.
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The magnetic field is perpendicular to
the excitation and detection plates.
The plates are ~ 1×1 cm.
The end plates have a +1 V potential
to trap the ions in the z-direction.
Free Induction Decay (FID)
Swept-Frequency Excitation (Chirped Excitation)
1
0.5
amplitude
In FTICR all ions are excited within a
very short time. For example, the
frequency might start at 10 kHz and
increase by 100 Hz per microsecond.
At the end of 1 ms the frequency is
then 110 kHz. This is called "chirped"
excitation.
0
0.5
1
2 .10
0
4 .10
4
4
6 .10
time
8 .10
4
4
0.001
For one frequency the image current is an exponentially damped
cosine (the FID). The decay constant is determined by the dephasing
time, which in turn is determined by the number of collisions the ions
experience (cell pressure). The Fourier transform of the FID gives the
spectrum. Resolution is determined by the decay constant. Because
the FID can last seconds, FTICR can have very high resolution.
Spectrum
Free-Induction Decay
→
0
1
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0
2 .10
4
4 .10
4
6 .10
time
4
8 .10
4
amplitude
amplitude
1
0.1
0.05
0
0.001
0
1 .10
4
4
2 .10
frequency
3 .10
4
4 .10
4
Example FID and Spectrum
Jonathan Amster, J. Mass. Spectrom., 31, 1325 (1996). As best as
I can tell from the paper this is synthetic data.
20.3 : 12/12