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Time-of-Flight Mass Analyzers. Jonathan Karty C613 lecture 21 March 26, 2008. (Section 4.2 in Gross, pages 115-128). TOF Overview. Time-of-flight (TOF) is the least complex mass analyzer in terms of its theory

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Time of flight mass analyzers l.jpg

Time-of-Flight Mass Analyzers

Jonathan Karty

C613 lecture 21

March 26, 2008

(Section 4.2 in Gross, pages 115-128)

Tof overview l.jpg
TOF Overview

  • Time-of-flight (TOF) is the least complex mass analyzer in terms of its theory

  • Ions are given a defined kinetic energy and allowed to drift through a field-free region (0.5 to several meters)

  • The time ions arrive at the detector is measured and related to the m/z ratio

Tof concept l.jpg
TOF Concept

  • A packet of stationary ions is accelerated to a defined kinetic energy and the time required to move through a fixed distance is measured

    • First TOF design published in 1946 by W.E. Stephens


Tof advantages l.jpg
TOF advantages

  • Theoretically unlimited mass range

    • Ions are not trapped (quad, IT, FTICR) nor are their flight paths curved (BE sectors)

    • Detection efficiencies induce practical limits of a few hundred kDa (M+H)+

  • Instrument is not scanning (it is dispersive)

    • Analysis is very rapid (40+ kHz acquisition possible)

    • Wide range of m/z’s can be measured with good sensitivity

  • Moderate to high resolving powers (5,000-20,000+)

  • Moderate cost ($100k to $500k)

  • Relatively high duty cycle

  • Couples extremely well with pulsed ion sources (e.g. MALDI)

Tof disadvantages l.jpg
TOF Disadvantages

  • Requires high vacuum (<10-6 torr)

  • Coupling to continuous ion sources (e.g. ESI or EI) not straight forward

  • Requires complex and high speed electronics

    • High acceleration voltages (5-30 kV)

    • Fast detectors (ns or faster)

    • GHz sampling digital conversion

    • Large volumes of data can be generated quickly

  • Limited dynamic range

    • Often 102 or 103 at most

  • High resolution instruments can get rather large

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Time-of-Flight Theory

  • From Physics 1: (1) KE = ½mv2

  • From Physics 2: (2) KE = z*U = ½mv2

    • All ions accelerated by the same voltage, U

  • From Physics 1: (3) ΔX= v0TOF + ½aTOF2

    • (5) TOF = ΔX/v0

      • 1,000 Th ion @ 19 kV, v ≈ 60 km/sec

    • ΔX same for all ions = D (flight tube length)

    • No acceleration in flight tube

  • TOF α U-1α (m/z)½

Mass scale calibration l.jpg
Mass Scale Calibration

  • TOF α (m/z)1/2 or m/z α TOF2

  • Mass scale is calibrated measuring flight times known m/z ions and fitting them to a polynomial equation

  • (7) TOF = a*(m/z)1/2 + b also

    • Higher order calibrations are often used

      • 5th order on some commercial instruments

      • Form can be (7a) m/z = A*TOF2 + B*TOF + C

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Resolution in TOF MS

Easy way to improve resolution is to increase flight tube length (assuming excellent vacuum)

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Real-world TOF MS

  • Previous examples all assumed ions formed at rest, at the same time, and all at the same position in the source

  • In reality, ions are formed throughout the source at various times, in various locations, with a range of initial kinetic energies

  • Practical TOF instrument design relies on minimizing the contributions of each of these realities

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Influence of Initial Position

  • In EI, CI, and ESI sources, ions are NOT formed all in the exact same position

    • These differences in initial position have profound effects on the mass spectrum

  • Ions spend some time in the source prior to crusing through the flight tube

    • (14) TOFobs = TOFsource + TOFflight_tube

  • A more complete treatment of the TOF requires that we consider how the ions get accelerated

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A brief discussion of acceleration

  • Ions are usually accelerated by using parallel plates at different potentials to create electric fields

  • Ions in an electric field gain energy according to the equation: (15) KE = z*(E*s) or U = z*(E*s)

    • z is charge, E is electric field strength in V/m, and s is distance the ion travels in the field (Lorentz force equation)

  • Time of flight in the source must be computed with a differential equation

Initial position math l.jpg

0 V

+100 V

Initial Position Math

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Starting Position Example

  • Both ions are 100 m/z (1.0364*10-6 kg/C)

  • Red ion is 6 mm from 0 V plate, blue ion is 5 mm from 0 V plate

    • s for red is 0.006 m; s for blue is 0.005 m

  • Distance between plates is 1 cm

    • Electric field is 10,000 V/m

  • Detector is 1 m from 2nd grid

  • TOFred = 94 usec TOFblue = 112 usec

    • Ered = 60 eV, Eblue = 50 eV


0 V

This effect tends to cause peaks to tail to longer TOF

+100 V

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Initial Kinetic Energy Spread

  • If the ion has a non-zero kinetic energy along the axis of the flight tube prior to acceleration: (25) KEtotal = z*U+U0(U0 is initial KE)

    • At 500 K, kT = 0.043 eV

  • Kinetic energies perpendicular to this axis can cause the ions to miss the detector entirely

  • The initial kinetic energy spread and initial position can be accounted for mathematically

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How long do ions spend in the source?

(initial KE and position)

(initial direction)

(uncertainty of ion formation)

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Putting this all together

  • Source design is used to minimize the variables that contribute to peak broadening

    • High U to minimize U0

    • Narrow ion formation regions to minimize s

    • Pulsing ions out of source to minimize t0

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TOF designs to maximize resolving power

  • High acceleration voltages can reduce impact of initial KE distribution

  • Initial position effects are harder to minimize

  • Additional ion optical elements can be introduced to compensate for these two effects

  • Set flight tube axis perpendicular to major vector of KE distribution

    • orthogonal extraction

Time lag focusing l.jpg
Time-lag focusing

  • There is a point in the flight tube where 2 ions starting at different positions arrive simultaneously

  • Adding a third grid allows the analyst to move this “focus plane” to the detector

    • 1955, Wiley and McLaren

    • 1994, Colby, King, and Reilly @ IU (special case for MALDI)

      • s0 is related to initial KE since all ions formed simultaneously

+100 V

+90 V


0 V

+100 V

Reflectrons l.jpg

  • In 1966, B. Mamyrin patented an ion mirror device for energy focusing and resolution improvement

  • A reflectron is a long series of electrodes that create an electric field to reverse the direction the ions travel

  • Higher energy ions spend more time in reflectron than lower energy ions

  • By adjusting parameters, ions with same m/z but slightly different KE’s can be made to arrive at a detector simultaneously

Reflectron drawing l.jpg
Reflectron drawing

0 V

+110 V

0 V

+100 V


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Reflectron Pros and Cons

  • Advantages

    • Focuses kinetic energies

      • Better resolution

    • Allows one to use same flight tube twice

      • Remember, res power increases with D

  • Cons

    • Only a narrow range of KE can be focused

      • Usually 85%-105% of E

    • Metastable ions are not focused by reflectron

      • If ion fragments in flight tube, products have same velocity as precursors (but KE is proportional to mass of product)

      • Reflectron focuses by energy

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Measuring TOF Signals

  • Oscilloscope (aka multi-channel scaler)

    • Analog recorder (ion current vs. time)

    • Great for intense signals

    • Generates large data files (all times recorded)

    • Noise recorded as well as signal

  • Time to Digital Converter

    • Records only when an event occurred

      • Threshold is set so an event is arrival of 1 ion

    • Excellent for low signals (single ion counting)

    • Does NOT take into account intensity

      • 2 ions arriving simultaneously counts as 1 event

      • Limited dynamic range

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Factors that Influence Resolution

  • Laser pulse width in MALDI

  • Detector response profile

  • Digitization rate and amplifier bandwidths

  • Kinetic energy distribution of ions

  • Initial position of ions in source

  • Power supply stability

  • Response profiles of pulsing electronics

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Waters LCT Drawing

Mass range: 60-20,000 m/z

Resolving power: ~5,000

254 psec resolution TDC

ESI or APCI source

MS recorded at ~20 kHz

Table-top MS (1.5x1x1 m)

Cost ~$200,000