How To Calculate The Data Assisted Victory Detectors

Method of mass spectrometry

Laser ionization time-of-flight mass spectrometer where ions are accelerated and separated by mass in a field-free drift region before detection.

Bendix MA-2 Time-of-Flight Mass Spectrometer, 1960s

Time-of-flight mass spectrometry (TOFMS) is a method of mass spectrometry in which an ion'southward mass-to-charge ratio is determined by a fourth dimension of flight measurement. Ions are accelerated by an electrical field of known strength.^[one] This dispatch results in an ion having the aforementioned kinetic energy every bit any other ion that has the same accuse. The velocity of the ion depends on the mass-to-charge ratio (heavier ions of the aforementioned charge attain lower speeds, although ions with higher charge will also increase in velocity). The time that information technology subsequently takes for the ion to reach a detector at a known distance is measured. This fourth dimension volition depend on the velocity of the ion, and therefore is a measure of its mass-to-charge ratio. From this ratio and known experimental parameters, one tin can identify the ion.

Theory [edit]

Figure from William E. Stephens 1952 TOF patent.^[ii]

The potential free energy of a charged particle in an electrical field is related to the charge of the particle and to the strength of the electric field:

$E_{\mathrm {p} }=qU\,$

(1)

where E _p is potential energy, q is the charge of the particle, and U is the electric potential difference (also known every bit voltage).

When the charged particle is accelerated into fourth dimension-of-flight tube (TOF tube or flying tube) by the voltage U, its potential energy is converted to kinetic energy. The kinetic free energy of any mass is:

$E_{\mathrm {thou} }={\frac {1}{ii}}mv^{ii}$

(2)

In effect, the potential energy is converted to kinetic free energy, meaning that equations (ane) and (2) are equal

$E_{\mathrm {p} }=E_{\mathrm {k} }\,$

(3)

$qU={\frac {1}{2}}mv^{2}\,$

(4)

The velocity of the charged particle after acceleration will not change since it moves in a field-complimentary fourth dimension-of-flight tube. The velocity of the particle tin can be adamant in a fourth dimension-of-flying 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 a transient digitizer or time to digital converter.

Thus,

$v={\frac {d}{t}}\,$

(v)

and nosotros substitute the value of v in (5) into (four).

$qU={\frac {1}{two}}thousand\left({\frac {d}{t}}\correct)^{2}\,$

(6)

Rearranging (6) so that the flight fourth dimension is expressed by everything else:

$t^{ii}={\frac {d^{ii}}{2U}}{\frac {thousand}{q}}\,$

(7)

Taking the square root yields the time,

$t={\frac {d}{\sqrt {2U}}}{\sqrt {\frac {k}{q}}}\,$

(8)

These factors for the time of flight have been grouped purposely. ${\frac {d}{\sqrt {2U}}}$ contains constants that in principle practice non alter when a set of ions are analyzed in a unmarried pulse of acceleration. (8) can thus be given as:

$t=k{\sqrt {\frac {yard}{q}}}\,$

(9)

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

(9) reveals more clearly that the time of flight of the ion varies with the foursquare root of its mass-to-charge ratio (chiliad/q).

Consider a real-globe example of a MALDI fourth dimension-of-flight mass spectrometer 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 q = east in both cases. Suppose the instrument is ready to accelerate the ions in a U = 15,000 volts (15 kilovolt or 15 kV) potential. And suppose the length of the flight tube is 1.5 meters (typical). All the factors necessary to calculate the time of flying of the ions are at present known for (8), which is evaluated kickoff of the ion of mass one thousand Da:

$t={\frac {ane.v\;\mathrm {k} }{\sqrt {2(15000\;\mathrm {V} )}}}{\sqrt {\frac {(1000\;\mathrm {Da} )(i.660538921\times 10^{-27}\;\mathrm {kg\;Da} ^{-1})}{+one.602\times x^{-19}\;\mathrm {C} }}}$

(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:

t=2.788\times 10^{-5}\;\mathrm {south}

which is about 28 microseconds. If there were a singly charged tryptic peptide ion with 4000 Da mass, and it is four times larger than the yard Da mass, it would have twice the fourth dimension, or well-nigh 56 microseconds to traverse the flight tube, since time is proportional to the square root of the mass-to-charge ratio.

[edit]

Mass resolution tin can be improved in axial MALDI-TOF mass spectrometer where ion production takes place in vacuum by allowing the initial burst of ions and neutrals produced by the laser pulse to equilibrate and to let the ions travel some altitude perpendicularly to the sample plate before the ions can be accelerated into the flight tube. The ion equilibration in plasma plume produced during the desorption/ionization takes identify approximately 100 ns or less, after that virtually of ions irrespectively of their mass kickoff moving from the surface with some boilerplate velocity. To compensate for the spread of this average velocity and to better mass resolution, it was proposed to delay the extraction of ions from the ion source toward the flight tube past a few hundred nanoseconds to a few microseconds with respect to the beginning of short (typically, a few nanosecond) laser pulse. This technique is referred to as "time-lag focusing" ^[3] for ionization of atoms or molecules by resonance enhanced multiphoton ionization or by electron bear on ionization in a rarefied gas and "delayed extraction"^[four] ^[5] for ions produced by and large by light amplification by stimulated emission of radiation desorption/ionization of molecules adsorbed on apartment surfaces or microcrystals placed on conductive flat surface.

Delayed extraction generally refers to the operation mode of vacuum ion sources when the onset of the electric field responsible for acceleration (extraction) of the ions into the flight tube is delayed by some curt time (200–500 ns) with respect to the ionization (or desorption/ionization) event. This differs from a example of constant extraction field where the ions are accelerated instantaneously upon beingness formed. Delayed extraction is used with MALDI or laser desorption/ionization (LDI) ion sources where the ions to be analyzed are produced in an expanding feather moving from the sample plate with a loftier speed (400–1000 g/s). Since the thickness of the ion packets arriving at the detector is important to mass resolution, on first inspection it can appear counter-intuitive to allow the ion feather to farther expand before extraction. Delayed extraction is more of a compensation for the initial momentum of the ions: information technology provides the same arrival times at the detector for ions with the same mass-to-charge ratios but with different initial velocities.

In delayed extraction of ions produced in vacuum, the ions that have lower momentum in the direction of extraction kickoff to exist accelerated at higher potential due to being farther from the extraction plate when the extraction field is turned on. Conversely, those ions with greater forward momentum starting time to be accelerated at lower potential since they are closer to the extraction plate. At the get out from the acceleration region, the slower ions at the back of the plume will exist accelerated to greater velocity than the initially faster ions at the forepart of the plumage. So after delayed extraction, a grouping of ions that leaves the ion source before has lower velocity in the direction of the acceleration compared to some other group of ions that leaves the ion source later but with greater velocity. When ion source parameters are properly adjusted, the faster group of ions catches up to the slower one at some distance from the ion source, so the detector plate placed at this distance detects simultaneous arrival of these groups of ions. In its way, the delayed application of the acceleration field acts as a one-dimensional time-of-flying focusing element.

Reflectron TOF [edit]

Reflectron TOF MS schematic

A dual stage reflectron from a Shimadzu IT-TOF instrument. The 46 metallic plates acquit the voltages which fix up the potential gradient.

The kinetic energy distribution in the direction of ion flight tin be corrected by using a reflectron.^[6] ^[7] The reflectron uses a abiding electrostatic field to reflect the ion axle toward the detector. The more energetic ions penetrate deeper into the reflectron, and take a slightly longer path to the detector. Less energetic ions of the aforementioned mass-to-charge ratio penetrate a shorter altitude into the reflectron and, correspondingly, accept a shorter path to the detector. The flat surface of the ion detector (typically a microchannel plate, MCP) is placed at the plane where ions of same chiliad/z but with unlike energies arrive at the aforementioned time counted with respect to the onset of the extraction pulse in the ion source. A point of simultaneous arrival of ions of the aforementioned mass-to-charge ratio but with unlike energies is often referred equally time-of-flight focus. An boosted advantage to the re-TOF arrangement is that twice the flight path is achieved in a given length of the TOF musical instrument.

Ion gating [edit]

A Bradbury–Nielsen shutter is a type of ion gate used in TOF mass spectrometers and in ion mobility spectrometers, as well as Hadamard transform TOF mass spectrometers.^[8] The Bradbury–Nielsen shutter is ideal for fast timed ion selector (TIS)—a device used for isolating ions over narrow mass range in tandem (TOF/TOF) MALDI mass spectrometers.^[nine]

Orthogonal dispatch time-of-flight [edit]

Agilent 6210 electrospray ionization orthogonal time-of-flying mass spectrometer (right) and HPLC (left)

Orthogonal dispatch time of flying mass spectrometer schematic:^[ten] 20 – ion source; 21 – ion ship; 22 – flight tube; 23 – isolation valve; 24 – repeller plate; 25 – grids; 26 – acceleration region; 27 – reflectron; 28 – detector.

Continuous ion sources (most ordinarily electrospray ionization, ESI) are generally interfaced to the TOF mass analyzer by "orthogonal extraction" in which ions introduced into the TOF mass analyzer are accelerated forth the axis perpendicular to their initial direction of motility. Orthogonal acceleration combined with collisional ion cooling allows separating the ion production in the ion source and mass analysis. In this technique, very high resolution can be achieved for ions produced in MALDI or ESI sources. Before entering the orthogonal acceleration region or the pulser, the ions produced in continuous (ESI) or pulsed (MALDI) sources are focused (cooled) into a beam of 1–two mm diameter past collisions with a residual gas in RF multipole guides. A system of electrostatic lenses mounted in loftier-vacuum region before the pulser makes the beam parallel to minimize its divergence in the direction of dispatch. The combination of ion collisional cooling and orthogonal acceleration TOF ^[11] ^[12] has provided pregnant increment in resolution of modern TOF MS from few hundred to several tens of thousand without compromising the sensitivity.

Hadamard transform time-of-flight mass spectrometry [edit]

Hadamard transform fourth dimension-of flight mass spectrometry (HT-TOFMS) is a way of mass assay used to significantly increase the point-to-dissonance ratio of a conventional TOFMS.^[13] Whereas traditional TOFMS analyzes one packet of ions at a time, waiting for the ions to reach the detector before introducing another ion packet, HT-TOFMS can simultaneously analyze several ion packets traveling in the flight tube.^[14] The ions packets are encoded by rapidly modulating the transmission of the ion axle, so that lighter (and thus faster) ions from all initially-released packets of mass from a beam get ahead of heavier (and thus slower) ions.^[15] This process creates an overlap of many fourth dimension-of-flight distributions convoluted in form of signals. The Hadamard transform algorithm is so used to carry out the deconvolution process which helps to produce a faster mass spectral storage charge per unit than traditional TOFMS and other comparable mass separation instruments.^[xiii]

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Tandem time-of-flying [edit]

In a TOF/TOF, ions are accelerated into the beginning TOF and mass gated into a collision jail cell; fragment ions are separated in the second TOF.

Tandem time-of-flight (TOF/TOF) is a tandem mass spectrometry method where two time-of-flight mass spectrometers are used consecutively.^[xvi] ^[17] ^[18] ^[19] To record total spectrum of precursor (parent) ions TOF/TOF operates in MS manner. In this mode, the energy of the pulse laser is called slightly above the onset of MALDI for specific matrix in employ to ensure the compromise betwixt an ion yield for all the parent ions and reduced fragmentation of the same ions. When operating in a tandem (MS/MS) mode, the laser energy is increased considerably above MALDI threshold. The first TOF mass spectrometer (basically, a flying tube which ends upward with the timed ion selector) isolates forerunner ions of pick using a velocity filter, typically, of a Bradbury–Nielsen blazon, and the 2nd TOF-MS (that includes the postal service accelerator, flying tube, ion mirror, and the ion detector) analyzes the fragment ions. Fragment ions in MALDI TOF/TOF result from disuse of forerunner ions vibrationally excited above their dissociation level in MALDI source (mail source decay ^[20]). Boosted ion fragmentation implemented in a high-energy collision cell may be added to the system to increase dissociation rate of vibrationally excited precursor ions. Some designs include precursor signal quenchers as a part of 2nd TOF-MS to reduce the instant current load on the ion detector.

Detectors [edit]

A time-of-flight mass spectrometer (TOFMS) consists of a mass analyzer and a detector. An ion source (either pulsed or continuous) is used for lab-related TOF experiments, but not needed for TOF analyzers used in space, where the sun or planetary ionospheres provide the ions. The TOF mass analyzer can be a linear flight tube or a reflectron. The ion detector typically consists of microchannel plate detector or a fast secondary emission multiplier (SEM) where showtime converter plate (dynode) is flat.^[21] The electrical bespeak from the detector is recorded by means of a time to digital converter (TDC) or a fast analog-to-digital converter (ADC). TDC is more often than not used in combination with orthogonal-dispatch (oa)TOF instruments.

Time-to-digital converters register the arrival of a single ion at discrete time "bins"; a combination of threshold triggering and constant fraction discriminator (CFD) discriminates between electronic noise and ion arrival events. CFD converts nanosecond-long Gaussian-shaped electrical pulses of different amplitudes generated on the MCP's anode into common-shape pulses (e.g., pulses compatible with TTL/ESL logic circuitry) sent to TDC. Using CFD provides a time point correspondent to a position of peak maximum independent of variation in the peak amplitude caused past variation of the MCP or SEM gain. Fast CFDs of avant-garde designs have the expressionless times equal to or less than two single-hit response times of the ion detector (unmarried-hitting response time for MCP with two-five micron wide channels can be somewhere between 0.ii ns and 0.8 ns, depending on the channel angle) thus preventing repetitive triggering from the aforementioned pulse. Double-hit resolution (dead time) of mod multi-hitting TDC tin be as low as 3-5 nanosecond.

The TDC is a counting detector – information technology tin exist extremely fast (downwardly to a few picosecond resolution), but its dynamic range is express due to its disability to properly count the events when more than one ion simultaneously (i.e., within the TDC dead time) hit the detector. The result of limited dynamic range is that the number of ions (events) recorded in one mass spectrum is smaller compared to existent number. The problem of limited dynamic range tin exist alleviated using multichannel detector design: an array of mini-anodes attached to a common MCP stack and multiple CFD/TDC, where each CFD/TDC records signals from private mini-anode. To obtain peaks with statistically acceptable intensities, ion counting is accompanied by summing of hundreds of individual mass spectra (so-called hystograming). To reach a very high counting rate (limited only past duration of individual TOF spectrum which can exist equally high equally few milliseconds in multipath TOF setups), a very high repetition rate of ion extractions to the TOF tube is used. Commercial orthogonal acceleration TOF mass analyzers typically operate at 5–twenty kHz repetition rates. In combined mass spectra obtained past summing a big number of individual ion detection events, each top is a histogram obtained past adding upwardly counts in each individual bin. Because the recording of the individual ion arrival with TDC yields merely a single time point, the TDC eliminates the fraction of height width determined by a limited response time of both the MCP detector and preamplifier. This propagates into ameliorate mass resolution.

Modern ultra-fast 10 GSample/sec analog-to-digital converters digitize the pulsed ion current from the MCP detector at detached fourth dimension intervals (100 picoseconds). Modern 8-bit or 10-bit 10 GHz ADC has much higher dynamic range than the TDC, which allows its usage in MALDI-TOF instruments with its high elevation currents. To tape fast analog signals from MCP detectors one is required to carefully match the impedance of the detector anode with the input circuitry of the ADC (preamplifier) to minimize the "ringing" upshot. Mass resolution in mass spectra recorded with ultra-fast ADC can be improved by using small-pore (2-5 micron) MCP detectors with shorter response times.

Applications [edit]

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Matrix-assisted laser desorption ionization (MALDI) is a pulsed ionization technique that is readily uniform with TOF MS.

Atom probe tomography also takes advantage of TOF mass spectrometry.

Photoelectron photoion coincidence spectroscopy uses soft photoionization for ion internal energy selection and TOF mass spectrometry for mass analysis.

Secondary ion mass spectrometry unremarkably utilizes TOF mass spectrometers to let parallel detection of different ions with a loftier mass resolving power.

History of the field [edit]

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An early time-of-flying mass spectrometer, named the Velocitron, was reported by A. East. Cameron and D. F. Eggers Jr, working at the Y-12 National Security Complex, in 1948. The idea had been proposed 2 years before, in 1946, past Due west. E. Stephens of the University of Pennsylvania in a Fri afternoon session of a meeting, at the Massachusetts Constitute of Technology, of the American Concrete Society.^[22] ^[23]

References [edit]

^ Stephens W. East. (1946). "A Pulsed Mass Spectrometer with Fourth dimension Dispersion". Phys. Rev. 69 (11–12): 691. Bibcode:1946PhRv...69R.674.. doi:10.1103/PhysRev.69.674.2.
^ US 2847576, Lawrence, Ernest O., "Calutron arrangement", published 1958-08-12, assigned to USA, Diminutive Free energy Commission
^ Wiley, W. C.; McLaren, I. H. (1955). "Time-of-Flight Mass Spectrometer with Improved Resolution". Review of Scientific Instruments. 26 (12): 1150. Bibcode:1955RScI...26.1150W. doi:10.1063/i.1715212.
^ V. S. Antonov; V. Southward. Letokhov & A. Due north. Shibanov (1980). "Germination of molecular ions as a result of irradiation of the surface of molecular crystals". Pis'ma Zh. Eksp. Teor. Fiz. 31: 471. JETP Lett. 31: 441.
^ Dark-brown, R. South.; Lennon, J. J. (1995). "Mass resolution improvement by incorporation of pulsed ion extraction in a matrix-assisted laser desorption/ionization linear time-of-flying mass spectrometer". Anal. Chem. 67 (thirteen): 1998–2003. doi:10.1021/ac00109a015. PMID 8694246.
^ Mamyrin, B. A.; Karataev, 5. I.; Shmikk, D. V.; Zagulin, 5. A. (1973). "The mass-reflectron, a new nonmagnetic fourth dimension-of-flight mass spectrometer with high resolution". Sov. Phys. JETP. 37: 45. Bibcode:1973JETP...37...45M.
^ US 4072862, Mamyrin, Boris A.; Karataev, Valery I. & Shmikk, Dmitry V., "Time-of-flying mass spectrometer", published 1978-02-07
^ U.Due south. Patent 6,664,545
^ U.S. Patent 6,489,610
^ U.Southward. Patent seven,230,234
^ Dodonov, A. F., Chernushevich, I. V., Dodonova, T. F., Raznikov, V. Five., Tal'rose, Five. L. Inventor'due south Document No. 1681340A1, USSR, Feb 25, 1987.
^ A.F. Dodonov, I.V. Chernushevich and 5.V. Laiko, Time-of-Flight Mass Spectrometry (1994) ACS Symposium Series 549, Chap. 7.
^ ^a ^b Richard N., Zare (2003). "Hadamard Transform Time-of-Flight Mass Spectrometry: More Betoken, More than of the Time" (PDF). Angewandte Chemie International Edition. 42 (ane): 30–35. doi:10.1002/anie.200390047. PMID 19757587 – via Wiley-VCH.
^ Ansgar, Brock (1999). "Label of a Hadamard transform fourth dimension-of-flight mass spectrometer" (PDF). Review of Scientific Instruments. 71 (3): 1306–1318. Bibcode:2000RScI...71.1306B. doi:10.1063/1.1150456 – via American Constitute of Physics.
^ Ansgar, Brock; Rodriguez, Nestor; Zare, Richard Due north. (1998). "Hadamard Transform Time-of-Flight Mass Spectrometry". Analytical Chemical science. seventy (eighteen): 3735–3741. doi:10.1021/ac9804036.
^ U.S. Patent five,206,508
^ U.S. Patent 7,196,324
^ Medzihradszky KF, Campbell JM, Baldwin MA, Falick AM, Juhasz P, Vestal ML, Burlingame AL (2000). "The characteristics of peptide collision-induced dissociation using a high-performance MALDI-TOF/TOF tandem mass spectrometer". Anal. Chem. 72 (iii): 552–8. doi:10.1021/ac990809y. PMID 10695141.
^ Vestal ML, Campbell JM (2005). "Tandem Time‐of‐Flying Mass Spectrometry". Tandem time-of-flight mass spectrometry. Meth. Enzymol. Methods in Enzymology. Vol. 402. pp. 79–108. doi:10.1016/S0076-6879(05)02003-3. ISBN9780121828073. PMID 16401507.
^ Spengler B.; Kirsch D.; Kaufmann R. (1991). "Metastable decay of peptides and proteins in matrix-assisted laser-desorption mass spectrometry". Rapid Communications in Mass Spectrometry. 5 (4): 198–202. Bibcode:1991RCMS....v..198S. doi:10.1002/rcm.1290050412.
^ U.Due south. Patent 7,446,327
^ Campana, Joseph E. (1987). "Time-of-Flight Mass Spectrometry: a Historical Overview". Instrumentation Science & Technology. sixteen (1): ane–14. Bibcode:1987IS&T...sixteen....1C. doi:10.1080/10739148708543625. ISSN 1073-9149.
^ Mirsaleh-Kohan, Nasrin; Robertson, Wesley D.; Compton, Robert N. (2008). "Electron ionization time-of-flying mass spectrometry: Historical review and current applications". Mass Spectrometry Reviews. 27 (3): 237–285. Bibcode:2008MSRv...27..237M. doi:10.1002/mas.20162. ISSN 0277-7037. PMID 18320595.

Bibliography [edit]

Cotter, Robert J. (1994). Fourth dimension-of-flight mass spectrometry. Columbus, OH: American Chemical Society. ISBN978-0-8412-3474-1.
Ferrer, Imma; Thurman, E. Chiliad. (2009). Liquid chromatography-Time of Flight Mass Spectrometry: Principles, Tools and Applications for Authentic Mass Analysis. New York, NJ: Wiley. ISBN978-0-470-13797-0.
Ferrer, Imma; Thurman, E. M. (2005). "Measuring the Mass of an Electron past LC/TOF-MS: A Written report of "Twin Ions"". Anal Chem. 77 (10): 3394–3400. doi:10.1021/ac0485942. PMID 15889935.
A. E. Cameron & D. F. Eggers Jr (1948). "An ion "velocitron"". Rev Sci Instrum. 19 (nine): 605–607. Bibcode:1948RScI...19..605C. doi:x.1063/1.1741336.
W. E. Stephens (1946). "A pulsed mass spectrometer with time dispersion". Bull Am Phys Soc. 21 (2): 22.