Quadrupolar Field and Equations for Ion Trap Φx,y,z = [U + V cos(Ωt)]
x2 + y2 – 2z2 r02 + 2z02
Quadrupolar Field and Equations for Ion Trap Φx,y,z = [U + V cos(Ωt)]
x2 + y2 – 2z2 r02 + 2z02
use cylindrical coordinate system: x = r cosθ; y = r sinθ; z = z
Φr,z = [U + V cos(Ωt)]
r2cos2θ + r2sin2θ – 2z2 r02 + 2z02
Φr,z = [U + V cos(Ωt)]
r2 – 2z2 r02 + 2z02
. . .
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Quadrupolar Field and Equations for Ion Trap d2u + [ax – 2qxcos(2ξ)]u= 0 dξ2 ξ=
Ωt 2
az =
-16eU m (r02 +2z02)Ω2
Mathieu equation
qz =
u = r, z
8eV m (r0 +2z02)Ω2 2
Regions of z motion stability – curve down Regions of r motion stability – curve up Regions of ion stability – intersection of curves
Quadrupole ion trap Mathieu Stability Diagram 0.3 0.2 0.1
q = 0.908 (when a=0)
βr = 0
0.0 -0.1
az
βz = 1
-0.2 -0.3
βz = 0
-0.4 -0.5 -0.6
βr = 1
-0.7
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
qz
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Quadrupole ion trap Ion Secular Frequency (ω)
iso β lines
qz = - 2qr =
8eV m (r02 +2z02)Ω2
ω = βΩ 2
• Ion’s secular frequency is m/z dependent and is dependent on main drive rf voltage
Quadrupole ion trap Ion Secular Frequency (ω)
2
6
2
ω = βΩ 2
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Quadrupole ion trap Ion Secular Frequency (ω)
Example
q = 0.4; a = 0 Ω = 1.1 MHz ω = 154 kHz
Quadrupole ion trap Ion Secular Frequency (ω) Ion Excitation/Ejection • Excitation or ejection of ions can be accomplished by applying single frequencies or broadband waveforms that are in resonance with an ion’s secular frequency
A single m/z is excited by the application of a single frequency
Multiple m/z’s are excited by the application of a broadband signal
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Quadrupole ion trap Mass Selective Instability Scan az
q = 0.908 qz
Scan rf
az
q = 0.908
Scan rf
qz
Quadrupole ion trap Mass Selective Instability Scan Effect of He
no helium
helium
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Quadrupole ion trap Mass Selective Instability Scan Resonance Ejection az |rf Amplitude|
qz
Scan rf
6 – 15 Vp-p frequency depends on instrument
Quadrupole ion trap Mass Selective Instability Scan Resolution 100000
40000 Ion Abundance
Ion Abundance
80000 60000 40000 20000 0
30000 20000 10000 0
646
648
650
m/z
652
Scan rate = 52,000 Da/s
654
646
648
650 m/z
652
654
Scan rate = 8,100 Da/s
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Quadrupole ion trap (2D trap) y DC 1
DC 2
DC 3
DC 1
DC 2
DC 3
z
Axial Trapping DC1, DC3 ~ 130 V DC2 ~ 3 V
y
y
RF +
x
x
RF -
y
r0
RF -
x
RF +
x rods = +V cos(Ωt) y rods = -V cos(Ωt)
Radial Quadrupolar Trapping 1.2 MHz 5 KV0-P
Quadrupole ion trap (2D trap)
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Quadrupole ion trap (2D trap) Great trapping capacity
Quadrupole ion trap (2D trap) Great trapping capacity 3D Trap
Phase Window for Successful Trapping of Injected Ions
2D Trap
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Mass Analyzers Fourier Transform Ion Cyclotron Resonance (FTICR)
Magnetic field influences ions in 2 dimensions B Ion‘s initial velocity
+
vp vo ion spirals out unimpeded
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Magnetic field influences ions in 2 dimensions TRAPPING PLATE
B
Vt
vp
+
vo
Vt TRAPPING PLATE
Magnetic field influences ions in 2 dimensions use of trapping plates introduce magnetron motion
Magnetron motion
B
Magnetic field Cyclotron motion
Trapping motion
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FTICR – Ion Detection Image Current
+ Amplifier
-
FTICR – Ion Detection Image Current
+ Amplifier
Excitation
-
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FTICR – Ion Detection Excitation
Power Spectrum
Amplitude
Amplitude
Frequency Sweep
FFT
Frequency
Time
SWIFT
FTICR – Ion Detection Fourier Transform of Image Current Transient signal
3D Quadrupole ion trap – Time-of-flight Shimadzu IT-TOF
Quadrupole – Linear (2D) Quadrupole Ion Trap Q0
Q1
Q2
Q3 LIT
SCIEX QTRAP 5500
• can act as regular quadrupole mass analyzer or linear ion trap • linear ion trap is operated with axial ejection of ions instead of radial ejection (as we talked about with the 2D quadrupole ion trap)
