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Time-of-Flight Mass Spectrometry

Linear Time-of-Flight Mass Analysers

Time-of-flight mass spectrometers are based on a simple mass separation principle. Consider ionised species starting from the same position at the same time, being accelerated by means of a constant homogeneous electrostatic field. Their velocities are unambiguously related to their mass-to-charge ratio and times of arrival at a detector directly indicate their masses:

Equation 1

where m = mass of particle, e = electronic charge, E = electrostatic field applied in source, d = length of accelerating region, L = length of field-free region, and Vo = accelerating potential.

The principle of time-of-flight has been known since Thomson carried out his experiments on ionised particles. The first proposal, however, for a mass spectrometer based on the time-of-flight principle was made by Stephens.[1]

The time-of-flight instrument possesses a number of extraordinary advantages over most other types of mass analyser:

* Theoretically unlimited mass range.
* Ideal where ionisation is pulsed or spatially confined.
* Complete mass spectrum for each ionisation event.
* High transmission.
* No need for scanning the ion beam (the Fellgett advantage[2] ).
* Spectra can be obtained for extremely small sample amounts ( <10-18 mole in the most modern instruments).
* Relatively low cost.

Wiley and McLaren observed that ions of a particular mass-to-charge ratio would reach the detector with a spread in arrival times, due to the effects of uncertainty in the time of ion formation, location in the extraction field and initial kinetic energy, resulting in reduced resolution. Wiley and McLaren devised an instrument, incorporating a pulsed two-grid ion source, to compensate for temporal, spatial and initial kinetic energy distributions.[3] The basic geometry of the Wiley-McLaren design is shown in the figure below.

TEMPORAL DISTRIBUTION.
Two ions of the same mass that are formed at different times with the same kinetic energy will traverse the field-free region maintaining a constant difference in time and space.

Equation 2

As the time interval (dt) is constant, the mass resolution (dm/m) in a linear time-of-flight instrument can be improved by increasing the flight time (t) by using either a low accelerating potential or a long field-free region. In the Wiley and McLaren instrument the electron beam pulses used for ionisation were of the order of 0.5 to 5.0 microseconds, necessitating a reduction in the effective value of dt. This was achieved by using pulsed extraction. Whilst the ions are being formed, they do not experience a potential gradient as the backing plate is held at the same voltage as the first grid. After a certain time, which is longer than the time for ion formation to occur, a positive pulse is applied to the backing plate such that a potential gradient is formed, accelerating the ions toward the detector. This reduces in the effective value of dt as all the ions experience the potential gradient at approximately the same time.

SPATIAL DISTRIBUTION.
When ions of the same mass are formed at the same time with the same initial kinetic energy, but are formed at different locations in the extraction field, the ions near the back of the source will experience a larger potential gradient and be accelerated to higher kinetic energy, than those formed close to the extraction grid. The ions formed at the back of the source will enter the field-free region later, but will eventually pass the ions formed closer to the extraction grid due to having larger velocities.
By adjusting the extraction field it is possible to achieve a space focus plane, where ions of any given mass arrive at the space focus plane at the same time. The location of the space focus plane is independent of mass, but ions of different masses will arrive at the space focus plane at different times.

KINETIC ENERGY DISTRIBUTION.
Ions formed with different initial kinetic energies will have different final velocities after acceleration and arrive at the detector at different times. The initial kinetic energy distribution also includes ions with the same kinetic energy, but velocities in different directions. Ions of the same kinetic energy but with velocities in different directions will arrive at the detector at different times corresponding to their turn around time in the source. This effect can be minimised by utilising longer field-free regions:

Equation 3

ts = time in the source and tD = time in the drift region.

Equation 4

The quantity (U0+eEso) is the final kinetic energy of an ion having initial kinetic energy (U0) and accelerated from position so.
Thus the longer the drift length (D), the greater the magnitude of tD. This reduces the effect of turn-around time on resolution, as well as uncertainties in the time of ion formation (tD ).

The first commercial time-of-flight instrument was produced in the late 1950’s by the Bendix Corporation. This was a linear instrument, with mass resolution of around 200-300 for organic species, and with a very high recording speed (20 kHz), giving the potential to monitor very fast reactions.


The Ion Reflectron in Time-of-Flight Mass Spectometry

In 1966 Mamyrin and co-workers proposed a way to correct for the temporal spread due to the initial velocity of the ions.[5] This technique utilises a device called a ‘reflectron’ consisting of a decelerating and reflecting field. For ions of the same m/z entering such a field, those with higher kinetic energy (and velocity) will penetrate the decelerating field further than ions with lower kinetic energy. Therefore the faster ions will spend more time within the reflecting field, and ‘catch up’ with lower energy ions further down the flight path. By adjusting the reflectron voltages it is possible to achieve a time-focusing plane. In this ideal case, the resolution of the peaks in the mass spectrum will only be dependent on the time-width of ion formation.

In practical cases, there are a number of time-widening parameters that can degrade resolution. These include, spatial and initial-energy distributions, and metastable ion formation.


Single-stage Reflectrons

The single-stage reflectron is the simplest type of ion reflectron. A homogeneous reflecting electrostatic field is created between two parallel flat grids. The first grid constitutes the entrance of the ion mirror, and the second the end. A detector is usually places behind the reflectron for linear time-of-flight experiments when the reflectron is grounded. In order to improve the homogeneity of the field in the reflectron a number of equally spaced ring electrodes are usually placed between the end electrodes, connected by a chain of equal value resistors.

Mass measurement in a single-stage ion reflectron is obtained by applying the following equation:

Equation 5

where t is the time-of-flight, m and q are the mass and charge of the ion respectively, and a and b are calibration constants that depend on instrument dimensions. In practice a and b are determined experimentally, calculated from the flight times and masses of known peaks in a particular mass spectrum.
The mass resolution that can be obtained using this type of mass spectrometer is limited by the temporal width of the initial ion pulse from the ion source, and the initial kinetic energy distribution of the ions, as it only corrects to the first order of approximation for the initial velocity spread:

Equation 6

where t is the time-of-flight, vo is the initial velocity of the ions and d is a deviation in the initial velocity.


Double-stage Reflectrons

In a double-stage reflectron, two separate homogeneous field regions, of different potential gradient, are utilised. A schematic diagram demonstrating the use of double-stage ion reflectron is shown below. Mamyrin has shown that, by choosing mirror voltages and dimensions to match the lengths of the field-free region, that it is possible to solve Equation 6 to the second order of approximation.[4, 5, 6] The result is a large enhancement in resolution, in particular for ion beams with broad kinetic energy distributions.



V0 - The accelerating potential
V1 - Applied potential to create first homogeneous field region
V2 - Applied potential to create second homogeneous field region (V2 does not equal V1)
d0 - Length of accelerating potential gradient
d1 - Length of first field-free region
d2 - Length of second field-free region
L1 - Length of first potential gradient of ion mirror
L2 - Length of second potential gradient of ion mirror


Quadratic-field Reflectrons

By introducing a second finite region of different potential gradient it is possible to make the second-order term in Equation 6 vanish. Extending this reasoning, if a field with an infinite number of changes in field gradient were introduced, all terms of time-aberration could be made to vanish. This would mean that the time-of-flight in an ion reflectron would be independent of the initial velocity of the ion, and depend only upon the specific charge qe/m (ideal time-focusing).[7] An ion mirror with this characteristic can be thought of in the same way as a pendulum, where the frequency of the body is dependent only on its mass and the length of the pendulum.
There are a variety of fields that can be utilised to provide ideal time-focusing. It has been shown that when demands of high transmission and simplicity of construction are taken into account, that only a few fields can be practicably useful:[8]

1) axially-symmetrical hyperbolic potential:

Equation 7

r, z are cylindrical co-ordinates. k, a and C are constants.


2) axially symmetrical hyper-logarithmic potential:

Equation 8

d>0 and b>0 are constants.


3) planar hyperbolic potential:[9]

Equation 9

a, b and d are constants.



References

1) Stephens, W. E., Phys. Rev., 1946, 69, 691
2) Skoog , D. A.; Holler, F. J.; Nieman, T. A., 'Principles of Instrumental Analysis', fifth edition, Saunders College Publishing, Orlando, USA, 1992, 184
3) Wiley, W. C.; MacLaren, I. H., Rev. Sci. Instr., 1955, 26, 1150
4) Mamyrin, B. A. USSR Patent No. 198,034, 1996
5) Mamyrin, B. A.; Karataev, V. I.; Shmikk, D. V.; Zagulin, V. A. Sov. Phys. JETP, 1973, 37, 45
6) Karataev, V. I.; Mamyrin, B. A.; Shmikk, D. V. J. Tech. Phys., 1971, 16, 1498
7) Gall, L. N.; Golikov, M. L.; Alexsandrov, M. L.; Pechalina, Y. E.; Holin, N. R., USSR Inventor’s Certificate No. 1,247,973, 1986
8) Makarov, A. A., J. Phys. D; Appl. Phys., 1991, 24, 533
9) Derrick, P. J.; Colburn, A. W.; Giannakopulos, A. E.; Raptakis, E. N.; Reynolds, D. J.; Davis, S. C.; Hoffmann, A. D.; Wright, B., Proceedings of 42nd ASMS Conference on Mass Spectrometry and Allied Topics, Chicago, 1994, 1152

All of the above text is an excerpt from:

Bottrill, A.R., Ph.D. Thesis, University of Warwick, 2000.
'High-energy Collision-induced Dissociation of Macromolecules using Tandem Double-focusing/Time-of-flight Mass Spectrometry.'



maintained by:
Dr. Gerhard Saalbach