Ion trap 3D Quadrupole Trap -Mass spectrometer -Ion trap (Quadrupol Ion Storage, Quistor) 18. April 011 1
The trajectories of the ions can be given: They form Mathieu differential equations: with r + Ion trap: the mathematical background The potential inside the trap can be described: q mr 0 ( U U g 0 cos( ωt) )r = 0 und &z q Z= d u dξ + ( a q cos ( ( ξ ξ 0 ))u = 0 The solution in general is complex: ( ) Φ( r, z)= Φ r 0 z mr 0 18. April 011 n= n= r 0 ( U g U 0 cos( ωt) )z = 0 a z = a r = 8qU g r 0 mω = 4qU g z 0 mω und q z = q r = 4qU 0 r 0 mω = qu 0 z 0 mω.. ( ) ( ) u0( ξ)= A u c n cos ( n + βu)ξ + B u c n sin ( n + βu)ξ
Stability diagram
Ion trap: modes of operation R.E. March and J. Hughes, Quadrupol Storage Mass Spectrometry, 18. April 011 4
Conditions for the ion traping: ion trajectories There are thre equations of motion in the ion trap: z q.. x&y +.. y&x + mr 0 q mr 0 q mr 0 ( U g U 0 cos( ωt) )z = 0 ( U U g 0 cos( ωt) )y = 0 ( U U g 0 cos( ωt) )x = 0 The direction x and y have the same a and q values, but different initial conditions. With the tangential component of the velocity (x = r sinθ und y = r cosθ ) the equation of motion: and d r dξ r dθ dξ + ( a r q r cos( ( ξ ξ 0 ))r = 0 d r dθ dt dt + r d θ dt = 0 yields the conservation of the momentum L 18. April 011 5
Conditions for traping By integration we have: r dθ dt = const. = L a Moment La is constant around the z axis. Thus, there is tangential velocity component conserved and an ion will be moved in plane 18. April 011 6
Well of the traping potential generated between the caps Neglecting higher order oscylation motion in z direction can be described With qz 0.4 the frequencies can be approximate as : This gives: ω n = ( n + β) Ω β z = a z + q z d z dt = ω z z ω z = ω 0,z = β z Ω d z dt = q 0 V AC 4mz 0 Ω z and describes the ion oscillation in potential with deepness of Dz generated by the caps D z = q 0V AC 4mz 0 Ω 18. April 011 7
Traping efficiency of an ion trap With Dz = Dr the former equation can described : D r = q V 0 AC 8mz 0 Ω = q 0V AC 4mr 0 Ω The potential generated in space filled by ions is described by Poisson equation: Φ i = Ψ = 4πρ max Without DC component in potential expression one can obtain Ψ( x, y, z)= D r ( x + y )+ D z r 0 z z 0 Ψ = 3D z z 0 ρ max = 3D z 4πz 0 N max = ρ max q 0 = 3D z q 0 4πz 0 = 3 mω 64π q 0 qz = N max Ion densities are high and Coulombic repulsion will occur for larger charge densities Nmax = 10 6... 10 7 cm 3 18. April 011 8
Space charge and a parameters a z = 8q 0πρ max mω a r = 4q 0πρ max mω 18. April 011 9
3D ion trap Paul et al. ~1950 The original Paul ion trap possesses two end cap electrodes with hyperbolic surfaces and a ring electrode. The end cap electrodes are grounded whereas there is an rf voltage (1 MHz) on the ring electrode. Ions are stored together in the ion trap and are detected by changing the experimental parameters.
Operation Ions which enter through a hole in the end cap oscillate in the ion trap, whereby the stability of the oscillating ions is determined by the m/z ratio of ions, the rf (radio frequency) and voltage supplied to the ring electrode. By changing the frequency of the rf generator, which excites the ion oscillation in the ion trap, ions with different masses are destabilized step by step. They then leave the ion trap and are detected. The mass spectrum of the ions ejected from the ion trap and separated according to their m/z ratio is obtained by scanning the rf voltage (method of operation: mass selective instability mode). Another procedure for ejecting ions from the ion trap is using the mass selective instability mode by applying a second rf voltage (lower in frequency than that of the ring electrode) which is supplied to the end caps. When the rf voltage is scanned on the ring electrode, causing mass selective instability, ions are sequentially brought into resonance with the rf of the end caps. This behaviour results in an increase in translation energy of the trapped ions with defined m/z ratio and the ions are ejected from the ion trap in a well-defined manner.
State of application Ion trap mass analyzers ca permit mass spectrometric measurements of large organic compounds such as proteins and biomolecules (with masses 100 000 Da) at high mass resolution and low detection limit down to10 15 g. Over the last few decades, quadrupole ion trap mass analyzers (now known as the 3D QIT), together with soft ionization techniques, such as electrospray ionization (ESI) or MALDI, have developed into a sensitive and versatile analytical tool for identifying organic molecules (especially for biomolecular analysis) in order to look at intact ions with masses into the kda range. The use of low cost quadrupole ion traps as high efficient mass analyzers is well known from their application in tandem mass spectrometers (MS/MS) also coupled together with liquid and gas chromatography (LC-MS and GC-MS, respectively) in organic mass spectrometry.
A linear quadrupole ion trap for use as a mass spectrometer by applying a radial ion ejection. The schematic of the trap shows the ejection slot along the length of one of the x-rods. An overall view of the complete instrument shows a typical potentials and pressures. The first (square) quadrupole is an ion guide to transport ions from the ESI source into the higher vacuum region and the function of the small octapole is similar but to facilitate ion transfer into the trap. Schwartz, et al., J. Am. Soc. for Mass Spectr., 13, p. 659 669, 00,.
Other systems used: hexapole, octopole, -pole ion trap The key point for understanding the principle of operation of ion guides, traps etc. is the treatment of the equation of motion within an adiabatic approximation which leads to the introduction of the so called effective potential (also called quasi-, pseudo- or ponderomotive potential). In the case of a particle with charge q and mass m, moving in an oscillatory electrical field E, cos (Qt), the trajectory r(t) can be approximated by superimposing a smooth drift term R,(t) secular motion a rapidly oscillating motion R,(t) micro motion
Ion motion in octopole and 3 pole fields
Slowly varying term R 0 (t) is derived from the V* potential: Adiabaticity approximation is valid at a sufficiently high frequency and for η<0.3 where Adiabaticity parameter
Stability parameter vs. velocity
Potential used in calculation of a smooth trajectory in n-poles, 0 0 4 Ω = n eff m q r V n V ρ At sufficiently high frequency the smooth trajectory can be calculated from the effective potential which is time independent: The adiabatic conservation of energy ensures that transmission and confinement of the ions do not depend on the individual initial conditions but only on the transverse energy. 0 0 1) ( Ω = n m q r V n n ρ η
The total energy of an ion, E T (transverse), is conserved within narrow limits (better than for η < 0.3). E T can be determined by averaging the energy of an ion over a sufficient large number of rf periods or by calculating (or measuring) the ion energy in a region where the rf field is sufficiently small. The conservation of energy holds only in average and that, in reality, the energy of an ion is modulated repeatedly, especially if it enters strong electric field regions, i.e. if it approaches an electrode.
Field-free potentials The ion energy never exceeds 3E T - a very general result and independent on the field geometry, provided that η remains smaller than 0.3. The probability to find the ion with an energy close to its nominal value E T depends quite strongly on the trap structure. The influence of the rf field can also be estimated from the effective potential V* One can see that for the large n potentials field free volume is large and trajectories of ions are affected only in vicinity of electrodes.
Quadrupole -Octupole fields
Cooling in high-order rf poles Numerical calculations and experimental tests have proven that, in traps with wide field free regions, the energy distribution of the ions can be narrow down by using cold buffer gas (few K or lower). In quadrupole for example, ions can be heated to rather high energies. An interesting aspect of collisional relaxation of stored ions is to use a cloud of laser cooled atoms (sympathetic cooling) as buffer gas. This effect becomes especially efficient if the atom cloud is localized in the central part of the -pole, i.e. in the near field free region.
Typical operation parameters m = 1-100u η = 0,16 8 pole: n = 4; r 0 =3 mm; V 0 = 105 V; f 7,8 MHz Electrode dia. ~10 mm pole: n = 11; r 0 = 5 mm; Vo = 50 V; f 16 MHz Electrode dia. ~1 mm
Real -Pole Trap
Example of possible experimental setup for ion trapping and cooling in the trap
Effect of the buffer gas on the signal intensity
Spectroscopic studies of cold rare species trapped in pole trap e.g., Jochnowitz & Maier, Mol. Phys.(008), 106, 093
Future trends Sub-K cooling Quantum effects Super hot conditions 1000 K Chemical reactions Coupling with ESI (electro-spray ionization source); biorelated applications (Rizzo group, Lausanne) Spectroscopy and reaction dynamics of large intermediates in chemical reactions