Download - Octopole Technology ---Sha Joshua Ye Department of Chemistry, University of Utah Nov 6th, 2002
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Octopole Technology
---Sha Joshua Ye
Department of Chemistry, University of Utah
Nov 6th, 2002
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Outline
• Theory behind the octopole
• Some experimental applications
• Gerlich, D. Inhomogeneous rf Fields: A Versatile Tool for the Study of Processes with Slow Ions. In State-Selected and Sate-to State Ion-Molecule Reaction Dynamics, Part I: Experiment, Ng, D.-Y.; Baer, M., Eds.; 1992; pp 1-176
• Ervin, K. M.; Armentrout, P. B. Translational Energy Dependence of Ar+ + XY ArX+ + Y (XY = H2, D2, HD) from Thermal to 30 eV cm. J. Chem. Phys. 1985, 83, 166-189.
• Armentrout, P. B. Mass Spectrometry—Not Just a Structural Tool: The Use of Guided Ion Beam Tandem Mass Spectrometry to Determine Thermochemistry. J. Am. Soc. Mass Spectrom. 2002, 13, 419-434.
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Development of the theory
• Thomson’s (1903) determination of the X-ray scattering cross section.
• Electron motion eq:
• If include a static field, the above eq can be:
• If E0 is homogeneous, we get the special solution:
where
E is the electronic field; is the angular freq;
m2trd
d
2 q E0 cos t
m2trd
d
2 qE0 r( ) cos t qEs r( )
r t( ) r 0( ) a cos t m
2trd
d
2 qE0 r( ) cos t qEs r( )
r t( ) r 0( ) a cos t a qE0
m 2
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• If E0 is inhomogeneous, using the 1st order approxation:
• Few steps later:
= q2·E02/4m2
• Also Es= Φs
• If we define an effective potential:
r t( ) R0 t( ) Rl t( )
m2tR0
d
d
2
V R0 q2 E0 2
4m 2 q s
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• We get a simple expression: = -V(R0)
• The first integral of that is:
• Because
• Motion through an inhomogeneous field leads to an exchange between kinetic energies and electrostatic potential energy
m2tR0
d
d
2
1
2m
tR0
d
d
2
q2 E0 2
4m 2 q s Em
1
2m
tRl
d
d
2
q2 E0 2
4m 2
Rt t( ) q E0R0
m 2cos t
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• Under adiabaticity approximations, we obtain the so-call adiabaticity parameter :
=2q| E0|/m2 • The empirical safe operation value of is
<0.3, derived from that the (r/r0)max<0.8
• How to obtain the effective potential for the 2D multipole device?
v 8
1
2 n 1( )v
r0
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• By solving the Laplace’s Equation Ф(r)=0 assuming the equipotential surfaces of electrodes, we obtain the potential for long cylindrical conductors:
• For the 2D multipole, we adopt the following form for the applied potential:
• So
by setting Ф(r=r0,φ)=Ф0cosnφ, Ф(r=0,φ)=0
q2 E0rm 2
4m 2 q s rm Em
r Ar n Br n C sin n D cos n
0 U0 V0 cos t
r 0r
r0
cos n
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• A couple of steps later,
where 2n is the number of poles, r0 is the inner radius to the poles,and
the rf potential applied to alternate rods is V0cos(t)
• The r2n-2 term tells us why octopole is mainly used for confining ion(guiding ion beam).
• How is the trapping field of octopole looks like compared to that of quatrupole?
Vn2
4
q2
m 2
V0 2
r0 2
r
r0
2n 2
q U0r
r0
n
cos n
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• Collect more scattered reactant and product ions.• Bring the usable energy region down to
0.04eV(lab).• The relatively flat well renders much less
pertubation in ions’ radial momentum.
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• Cross views of the effective potential:
Total E
Ideal hyperbolic electrodes Some deformation of electrodes
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The total instaneous kinetic energy of an ion during one reflection from an rf wall.
E t( ) kin1
2m
tr0
d
d trl
d
d
2
1
2m
trl
d
d
2
2 V sin t 2
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• The average kinetic energy distribution
The most probable average Ekin The fluctuations of the mean Ekin
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Some applications
• The first octopole technique was used to by Gerlich in 1971 to make the first version of the guided-ion-beam apparatus.
• The improved one by Gerlich in 1984 extend the energy range to below 0.01eV(lab).
• Commercially, it has also been widely used.
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Guided-ion-beam apparatus
26cm 14cm
46cm
Crossed-beam arrangement
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Agilent 7500c octopole reaction system in Inductively Coupled Plasma MS
The octopole is mounted off-axis to prevent photons reaching the detector
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The coulombic interactin of ions in the octople ion trap casue a strong non-linearity trapping efficiency in the octopole
200cm
3.5cm 14cm
FT-ICR
• New concept of ion traps having field of octopole or hexopole components.
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The Trick About Life is Too Make It Look Easy
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q n 2n n 1( )qV0
m2r0 2
2n 1( )
n
qV0
an 4n n 1( )qU0
m2r0 2
2n 1( )
n
qU0
2n n 1( )qV0
m 2 r0 2
r
r0
n 2
• In reality, the inscribed circle radius
r0=(n-1)d/2
• This figure shows the potential disturbtion from the cylinder surrounding an octopole.
where a = qE0/m2