Time-of-flight

From Wikipedia, the free encyclopedia

The Time of flight (TOF) method of measuring particle mass-to-charge ratio is done as follows. An ion of known electrical charge and unknown mass enters a mass spectrometer and is accelerated by an electrical field of known strength. This acceleration results in any given ion having the same kinetic energy as any other ion given that they all have the same charge. The velocity of the ion will depend however on the mass-to-charge ratio.

The time that it subsequently takes for the particle to reach a detector at a known distance is measured. This time will depend on the mass-to-charge ratio of the particle (heavier particles reach lower speeds). From this time and the known experimental parameters one can find the mass-to-charge ratio of the particle. This method of analysis is a powerful tool for finding the mass-to-charge ratio of charged particles, atoms and molecules.

In near infrared spectroscopy Time of Flight method is used to estimate the wavelength dependent optical pathlength.

In kinematics, TOF is the duration in which a projectile is travelling through the air. Given the initial velocity $u$ of the particle, the downward (ie., gravitational) acceleration $a$ , and the projectile's angle of projection θ (measured relative to the horizontal), then a simple rearrangement of the SUVAT equation s=ut+1/2at² results in this equation for the time of flight of a projectile: t=2 $u$ (Sin θ)/ $| a |$ .

1 Fundamental Theory
2 Time-of-flight mass spectrometers in chemistry
3 High-precision measurements in physics
4 External links
5 References

[edit] Fundamental Theory

It is well understood in physics that the potential energy of a charged particle in an electric field is related to its charge and to the strength of the electric field:

   $E p = z e V$  [1]

where E_p is potential energy, z is the absolute value of the (integral) charge of the particle (charge of ion being +1, +2, -1, -2, etc.), e is elementary charge constant ( $1.602 \times 10^{-19} C$ ), and V is the electric field charge strength.

When the charged particle is accelerated into time-of-flight tube, its potential energy is converted to kinetic energy. The kinetic energy of any mass is:

[2]

In effect, the potential energy is converted to kinetic energy, meaning that equations [1] and [2] are equal

   $E p = E k$  [3]

[4]

The velocity of the charged particle after acceleration will not change since it moves in a field-free time-of-flight tube. The velocity of the particle can be determined in a time-of-flight tube since the length of the path (d) of the flight of the ion is known and the time of the flight of the ion (t) can be measured using very sophisticated electronic stopwatch technology under the control of a crystal that oscillates at a frequency in the gigahertz range (and thus whose period is thus in the nanosecond range).

Thus,

[5]

and we substitute the value of v in Eqn [5] into Eqn [4].

[6]

Re-arranging Eqn [6] so that the flight time is expressed by everything else:

[7]

Taking the square root of the time

[8]

These factors for the time of flight have been grouped purposely. $\frac{d}{\sqrt{2eV}}$ are basically all constants that do not change when a set of ions are analyzed in a single pulse of acceleration. Eqn 8 can thus be given as:

[9]

where k is a proportionality constant representing factors related to the instrument settings and characteristics.

Eqn [9] reveals more clearly that the time of flight of the ion varies with the square root of its mass-to-charge ratio (m/z).

Consider a real world example of a MALDI ToF MS instrument which is used to produce a mass spectrum of the tryptic peptides of a protein. Suppose the mass of one tryptic peptide is 1000 daltons (Da). The kind of ionization of peptides produced by MALDI is typically +1 ions, so z = 1 is both cases. Suppose the instrument is set to accelerate the ions in a 15000 [[volt[[ (15 kilovolt, or 15 kV) field. And suppose the length of the flight tube is 1.5 meters (typical). All the factors necessary to calculate the time of flight of the ions are now known for Eqn [8], which is evaluated first of the ion of mass 1000 Da:

   [10]

Note that the mass had to be converted from daltons (Da) to kilograms (kg) to make it possible to evaluate the equation in the proper units. The final value should be in seconds:

which is about 28 microseconds. If there were a tryptic peptide +1 ion with 4000 Da mass, and it is four times larger than the 1000 Da mass, it would take twice the time, or about 56 microseconds to traverse the flight tube, since time is proportional to the square root of the mass.

[edit] Time-of-flight mass spectrometers in chemistry

A time-of-flight mass spectrometer (TOFMS), like all mass spectrometers, consists of an ion source, a mass analyzer, and a detector. TOF ion sources can be pulsed or continuous. The TOF mass analyzer can be a linear flight tube or a reflectron. The ion detector is generally a time-to-digital converter (TDC) or a fast analog-to-digital converter (ADC).

TOF requires a pulsed ion beam. Ion sources such as electron ionization and electrospray ionization that produce a continuous ion beam must be converted to a pulsed ion beam for analysis by time-of-flight. An ion gate (such as a Bradbury-Nielsen gate) that can be rapidly switched to produce a pulse of ions with a short duration is commonly used.

Matrix-assisted laser desorption ionization (MALDI) is a pulsed ionization technique that is readily compatible with TOFMS. Resolution can be improved in MALDI-TOF by allowing the initial burst of ions and neutrals produced by the laser pulse to equilibrate and dissipate before the ions are accelerated into the flight tube. This is referred to as "time-lag focusing" (Wiley and McLaren) or "delayed extraction" (Brown and Lennon).

High resolution time-of-flight mass spectrometry requires tight focusing of the ion beam in space, time, and energy. Even an efficient ion gate does not completely correct for velocity distributions originating in the ion source. Continuous ion sources (most commonly electrospray ionization) are generally interfaced to the TOF mass analyzer by "orthogonal extraction" (Dawson and Guilhaus) in which the ions are introduced into the mass analyzer in a direction perpendicular to the direction of flight. This improves duty cycle and thereby sensitivity by analyzing a "slice" of ions instead of a "packet" and removes problems arising from the initial kinetic energy distribution in the axis perpendicular to the direction of ion flight. The ion beam entering the orthogonal extraction region is focused to a small diameter by RF ion guides and electrostatic lenses to minimize the spatial distribution of the beam in the direction of ion flight.

The kinetic energy distribution in the direction of ion flight can be corrected by using a reflectron (Mamyrin and coworkers). The reflectron uses electrostatic lenses to reflect the ion beam toward the detector. The more energetic ions will penetrate deeper into the reflectron, and will take slightly longer to reach the detector. Less energetic ions only will penetrate a short distance into the reflectron and will take less time to reach the detector. The detector is placed at the focal point where ions of different energies focused by the reflectron will strike the detector at the same time.

Time-to-digital converters register the arrival of a single ion at discrete time "bins"; thresholding discriminates between noise and ion events. The mass spectrum is created by summing a large number of mass spectra. The TDC is an ion counting detector -- it is fast, but dynamic range is limited by the ability of the TDC to react to multiple ion events.

Fast analog-to-digital converters measure ion current at discrete time intervals. An ADC detector has a higher dynamic range than the TDC detector, but requires careful impedance matching to minimize "ringing".

[edit] High-precision measurements in physics

Usually the tube is praised for simplicity, but for precision measurements of charged low energy particles the electric and the magnetic field in the flight tube has to be controlled within 10 mV and 1 nT respectively.

The work function homogeneity of the tube can be controlled by a Kelvin probe. The magnetic field can be measured by a fluxgate compass. High frequencies are passively shielded and damped by radar absorbent material. To generate arbitrary low frequencies field the screen is parted into plates (overlapping and connected by capicators) with bias voltage on each plate and a bias current on coil behind plate whose flux is closed by an outer core. In this way the tube can be configured to act as a weak achromatic quadrupole lens with an aperture with a grid and a delay line detector in the diffraction plane to do angle resolved measurements. Changing the field the angle of the field of view can be changed and a deflecting bias can be superimposed to scan through all angles.

When no delay line detector is used focusing the ions onto a detector can be accomplished through the use of two or three einzel lenses placed in the vacuum tube located between the ion source and the detector.

The sample should be immersed into the tube with holes and apertures for and against stray light to do magnetic experiments and to control the electrons from their start.

[edit] External links

[edit] References

Brown, R. S.; Lennon, J. J. Mass resolution improvement by incorporation of pulsed ion extraction in a matrix-assisted laser desorption/ionization linear time-of-flight mass spectrometer. Anal. Chem., 1995, 67, 1998.
Dawson, J.H.J.; Guilhaus M. Rapid Commun. Mass Spectrom., 1989,3, 155
Mamyrin, B. A.; Karataev, V. I.; Shmikk, D. V.; Zagulin, V. A. The mass-reflectron, a new nonmagnetic time-of-flight mass spectrometer with high resolution Sov. Phys. JETP, 1973, 37, 45.
Stephens, W. E., A Pulsed Mass Spectrometer with Time Dispersion Phys. Rev., 1946, 69, 691.
Wiley, W. C.; MacLaren, I. H., Time-of-Flight Spectrometer with Improved ResolutionRev. Sci. Instr., 1955, 26, 1150.