Q UADRUPOLE A NALYZERS AND I ON T RAPS I. ermk, CGC Instruments, - - PowerPoint PPT Presentation

QUADRUPOLE ANALYZERS AND ION TRAPS

• I. Čermák,

CGC Instruments, Chemnitz, Germany, www.cgc-instruments.com

Presentation Outline

Physics of electrodynamic multipoles

• Focusing in 2D or 3D
• Particle trajectories
• Potentials and forces
• Effective potential and adiabaticity

Quadrupole Mass Spectrometry

• Ion motion in linear 4-poles
• Resolution and transmission
• Real devices and technical limitations

Ion Guides and Traps

• Ion-storage setups, measurement sequences
• Resulting spectra
• Study of ion-neutral reactions
• Comparison of experimental techniques
• Technical requirements

Future Developments

FOCUSING OF CHARGED PARTICLES

Electrostatic field

Electrostatic potential φ = φ(x, y, z) is time independent: ∂φ ∂t = 0 Laplace equation in vacuum: ∆φ = ∂²φ ∂x² + ∂²φ ∂y² + ∂²φ ∂z² = 0 Potential minimum in x and y directions ∂²φ ∂x² > 0, ∂²φ ∂y² > 0 ∂²φ ∂z² < 0 potential maximum in z electrostatic potential can only be saddle-shaped it cannot provide a 3D focussing

Electrodynamic field

Electrostatic potential is time variable: ∂φ ∂t ≠ 0, usually a sinusoidal signal: φ = φ(x, y, z) · sin(ωt) charged particles can gain/release kinetic energy from/to the electric field (analog to a spacecraft flyby at a planet) Principle used in electrodynamic storage devices: under certain conditions, particle gains and releases kinetic energy remains trapped Applications: ion guides, mass selectors, ion/particle traps

PARTICLE TRAJECTORIES IN MULTIPOLE TRAPS

Paul Trap 4-pole 8-pole 16-pole

POTENTIALS AND FORCES IN MULTIPOLE DEVICES

Electrostatic potential of a linear multipole: φ(r, θ) = V·

• r

r0

n

cos(nθ) 2n = electrode count (quadrupole: n = 2) ±V = voltages on electrodes r0 electrode inner radius Electrostatic field strength: E(r, θ) = –∇φ(r, θ) Er(r, θ) = dφ dr = n V r0

• r

r0

n–1

cos(nθ) Eθ(r, θ) = 1 r dφ dθ = n V r0

• r

r0

n–1

sin(nθ) E(r, θ) = Er² + Eθ² = n V r0

• r

r0

n–1

Force acting on a charged particle: F(r, θ) = q·E(r, θ) F ~ q·r n–1 quadrupole: F ~ r = harmonic force

4-pole 8-pole 22-pole Ring-Electrode Trap 4-pole 8-pole 22-pole RET

r/r0 _ _ F(r) F(r0) ___ φ(r)

φ(r0)

EFFECTIVE POTENTIAL AND ADIABATICITY

Effective Potential

Electric field strength E = E · sin(ωt) Micro-motion: motion due to the driving frequency, displacement x = q m·ω2 · E · sin(ωt), amplitude xm = q m·ω2 · E Secular motion: displacement X, adiabatic approach: secular motion is slow EOM: m·d2X dt 2 = q·E(X+x)·sin(ωt) ( x = mean value of x) Solution: approximation using Taylor series: E(X+x) = E(X) + x∇·E and considering mean values over one period of the driving frequency m·d2X dt 2 = q 2 4mω2 ·∇|E(X)|2 Effective potential Φ(X) = q 2·|E(X)|2 4mω2 is a measure for the depth of the potential well in a trap, multipole: E = n V r0

• r

r0

n–1

Φ = n2 4 q 2 mω2 V 2 r0

2

• r

r0

2n–2

, quadrupole (n = 2): Φ = q 2 mω2 V 2 r0

2

• r

r0

2

Adiabaticity

Adiabaticity η(X) = 2|xm|·|∇E(X)| |E(X)| = 2q·|∇E(X)| mω2 is a measure for the motion stability, lower values lower field variations over the micro-motion amplitude better motion stability, multipole: η = 2n (n–1) q mω2 V r0

2

• r

r0

n–2

, quadrupole (n = 2): η = 4q mω2 V r0

2 = constant value

Adiabatic motion for η < 0.3 trapped particles do not gain energy from the field

micro-motion secular motion

QUADRUPOLE MASS SPECTROMETRY (QMS)

Electrode System

4 rods supplied by a combination of AC and DC voltages: ±VDC ± VAC sin(ωt) (patented 1956 by Wolfgang Paul and Helmut Steinwedel) DC voltage influences the adiabaticity and the effective potential in radial directions x and y

Ion motion

Stability parameters: ax,y = ± 8q mω2 VDC r0

2 , qx,y =

4q mω2 VAC r0

2 = ηx,y

ax,y ~ VDC, qx,y ~ VAC, ax,y, qx,y ~ q/m Stability diagram (stable solutions of the Mathieu equation): combination of ax,y, qx,y for stable ion trajectories

Paul Patent 2939952, Fig. 5 Ion motion in the QMS VDC + VAC sin(ωt) –VDC – VAC sin(ωt) stable ion trajectory unstable ion trajectory βx = 0 βy = 0 βx = 1 βy = 1 VDC = 0 VDC = 0.168·VAC q/m q/m unstable stable unstable unstable unstable

ax,y qx,y

QUADRUPOLE MASS SPECTROMETRY (QMS)

Resolution

Depends on the ratio VDC/VAC = ax,y/2qx,y: Values m/∆m ≈ 1000 can be reached, requirement: ions have to perform several oscillation periods in the system

Transmission

Parameter β determines the secular frequency of the harmonic oscillations in the QMS: Ω = ½βω β is given by the chosen resolution m/∆m (borders of the stability diagram: βx,y = 0 and βx,y = 1) Harmonic oscillation with Ω force field F = K·r, K = mΩ2 = β2 4 mω2 effective potential Φ = K 2 r 2 = β2 2 mω2·r 2 effective potential is deep in one direction but flat in the second one for proper ion guiding, the driving frequency ω must be high enough: Φ (0.8r0) > Ek = transversal ion energy β = a (a – 1) q2 2 (a – 1)2 – q2 (5a + 7) q4 32 (a – 1)3 (a – 4) ...

βy = 0 βx = 1 0.168 q/m unstable unstable stable VDC/VAC 0.166 0.164 q/mmax q/mmin

ax,y qx,y

QUADRUPOLE MASS SPECTROMETRY (QMS)

Real QMS Devices

Tri-Filter QMS, Extrel Pre- and Post-Filter: 4-pole w/o DC deep effective potential in all radial directions high ion transmission Entrance and Exit Lens: ion focussing from the ion source to the QMS and from the QMS to the detector

Technical Limitations

Operation pressure: collisions with residual gas modify ions mass spectrum distortion, collisions lower transmission mass discrimination, high pressure gas discharge Requirement: deep effective potential high operating frequency ω high operating voltage technical limits: several kV, several MHz Ion Source Detector

ION GUIDES AND TRAPS

Ion-Storage Setups

Ion-storage setup w/ a ring-electrode trap (RET)

Typical Measurement Sequence

1) Ion preparation, trap filling, ion cooling 2) Ion storage = time for ion-neutral reactions 3) Ion extraction, mass analysis 4) Emptying trap ensure reproducible start conditions for the next run 1 run = measurement for

• ne reaction time and
• ne product mass

many repetitions required for a complete picture

T ra p E x it T ra p R F R u n S to r a g e tim e C o u n te r G a te C a th o d e S ta r t F illin g E x tr a c tio n E m p ty in g G a s P u ls e

Ion Source Detector RET QMS Detector Optics Entrance Optics Exit Optics Trap Exit Trap Entry l-N2 (cooling) continuous gas inlet (reaction gas) pulsed gas inlet (buffer gas = He)

ION GUIDES AND TRAPS

Resulting Spectra

Example: deuteron transfer D3

+ + N2 → N2D+ + D2

Ion production: e– + D2 → D+, D2

+, D+ + D2 → D3 +

Ion reaction: D3

+ + N2 → N2D+ + D2

Delay / ms

20 40 60 80 100 120 140 160 180 200

Ion Counts per Cycle

10-3 10-2 10-1 100 101 102 103 104 105

HD+ D2

+, H2D+

HD2

+

D3

+

D2

+

H2D+ D+, H2

+

Storage Time /ms

200 400 600 800 1000 1200 1400 1600 1800 2000

Ion Counts per Filling

10-1 100 101 102 103

D3

+

HD2

+

N2H+ N2D+

15NND+

Σ

Total ion number (Σ): important quantity indicating that 1) the trap is working well and does not loose ions over the storage time 2) the mass spectrometer and detector scan all product ions 3) there is no mass discrimination in the detection system Evaluation: rate coefficient k d[N2D+] dt = d[D3

+]

dt = k · [D3

+] · [N2] k

[X] = number density (concentration) of X knowledge of [N2] required, evaluation by 1) test reaction or 2) precise pressure measurement (e.g. viscovac) D2 gas pulse

ION GUIDES AND TRAPS

Study of Ion-Neutral Reactions

Bimolecular reactions A+ + B → C+ + D d[C+] dt = d[A+] dt = kAB · [A+] · [B] reaction time τAB = [A+] d[A+] dt = 1 kAB · [B] reaction rate 1 τAB = kAB · [B] typical Langevin reaction rate k = 10–9cm3/s 1 reaction per ion per second at [B] = 109cm–3 (~4·10–8mbar) Pressure dependence of the rate coefficient k distinguishing between radiative and ternary association reactions radiative association: only two collision partners (A+ and B), rate coefficient is independent on the pressure ternary association: third collision partner (A+, B and B/C), rate coefficient is proportional to the pressure Radiative association may be very inefficient rate coefficient k is low low reaction yield, long reaction time, long storage time possible detection limit: < 1 reaction / 10 ions / 100 sec. = 1/103 sec. very inefficient reaction can be investigated Temperature dependence temperature of stored ions can be controlled by the buffer gas and trap temperature ion temperature well defined from the experiment beginning population of rotational, vibrational and transitional energy levels is controllable down to several K (astrophysical relevance)

reaction rate / s–1

number density / cm–3 10–9 cm3/s 10–10 cm3/s 10–11 cm3/s 10–12 cm3/s

ION GUIDES AND TRAPS

Comparison of Experimental Techniques

Studies of

• bimolecular ion-molecule reactions
• ionization
• neutralization

Method Temperature Range Density Range Drift Tube 20 – 80 K 1015 – 1017 cm-3 Free Jet 0.1 – 20 K 1013 – 1015 cm-3 Axis-Symmetric Jet 8 – 80 K 1015 – 1017 cm-3 Merged Beam 3 – 300 K 1012 – 1014 cm-3 Penning Trap 10 – 80 K 107 – 108 cm-3 RF Trap 10 – 300 K 109 – 1015 cm-3

• nly ion traps can observe binary association processes

ION GUIDES AND TRAPS

Technical Requirements

Ion temperature (transversal kinetic temperature) and mass range operating parameters of the trap: effective potential: Φ (0.8r0) > Ek = transversal ion energy adiabaticity: η < 0.3 Multipole: Φ = n2 4 q 2 mω2 V 2 r0

2

• r

r0

2n–2

> Ek, η = 2n (n–1) q mω2 V r0

2

• r

r0

n–2

< 0.3 requirements on operating frequency and voltage Example: 16-pole, electrode inner radius r0 = 10 mm

limit: 100meV (~300K) limit: 0.3 300V, 1.5MHz 500V, 1MHz 750V, 10MHz 500V, 3MHz 300V, 1.5MHz 500V, 1MHz 750V, 10MHz 500V, 3MHz effective potential / eV

ion mass / amu ion mass / amu

adiabaticity

FUTURE DEVELOPMENTS

Mass Analysis

Combination of traps and TOF advantages: analysis of the complete trap content difficulties: usual multipole trap does not provide radial and axial focussing bad TOF resolution Mass analysis via image charge advantages: non-destructive ion detection, analysis of the complete trap content difficulties: image charge obscured by the RF drive

Ion Preparation and Manipulation

Traps with switchable geometry switching between a higher multipole and quadrupole ion focussing - e.g. for TOF detection switching between 2D and 3D multipoles smooth switching between an ion guide and ion trap simpler ion capture and extraction Difficulties: complex electronics for switching the RF drive

Ion Traps for Defining the Mass Unit

Mass unit still not well defined (weight of the International Prototype of the Kilogram = IPK) Proposed future definitions: Watt balance Ampere-based force Atom-counting: Ion trap can accumulate large molecules up to a macroscopic grain that can be weighted