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 • 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

• 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 Detector

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

• Requires high vacuum (<10 • 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) – Large volumes of data can be generated quickly • Limited dynamic range – Often 10 2 or 10 3 at most -6 – GHz sampling digital conversion torr) • High resolution instruments can get rather large

Time-of-Flight Theory

• From Physics 1: (1)

KE = ½mv 2

• From Physics 2: (2)

KE = z*U = ½mv 2

– All ions accelerated by the same voltage, U • From Physics 1: (3)

ΔX= v 0 TOF

– ( 4 )

v

0  2 *

U m

*

z

1 / 2

+ ½aTOF

(5)

TOF = ΔX/v 0 2

– • 1,000 Th ion @ 19 kV, v ≈ 60 km/sec ( 6 )

TOF flight

_

tube

 

X

2 *

U

*

m z

– ΔX same for all ions = D (flight tube length) – No acceleration in flight tube • TOF α U -1 α (m/z) ½

Mass Scale Calibration

• TOF α (m/z) 1/2 or m/z α TOF 2 • 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 • 5 th order on some commercial instruments • Form can be (7a)

m/z = A*TOF 2 + B*TOF + C

Resolution in TOF MS

( 10 )

v



D

/

t



m

 ( 12 ) 

m

 ( 8 )

z

*

U

 1 / 2 *

m

*

v

2 2 *

z

*

U D

2 2 *

z

*

U D

2 *

t

2 * 2

t

* 

t

( 9 )

m

 2 *

z

*

U v

2 ( 11 ) 

m



t

 2 *

z D

2 *

U

* 2

t

( 13 )

m



m

  2 *

z

*

U

 *

t

2 ( 2 *

z D

2 *

U

) * 2

t

* 

dt D

2 

t

2 

t

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

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

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)

TOF obs = TOF source + TOF flight_tube

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

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

( 4 )

v



Initial Position Math

1 / 2 2 *

U

*

z m

( 15 )

U



E

*

s

( 17 )

v s

 2 *

z

*

E

*

s

 1 / 2

m

 

s



t

 ( 16 ) 

s

 2 *

z

*

E

*

s m

1 / 2 

t

( 19 ) 

s

 2 *

z

*

E

*

s m

1 / 2 

t

 ( 18 ) 

t



m

2 *

z

*

E

1 / 2 1 *

s

1 / 2 

s

( 21 ) 0

s



t



t

 0 

s m

2 *

z

*

E

1 / 2 

s s

1 / 2  ( 20 )

t s



m

2 *

z

*

E

1 / 2 * 2

s

1 / 2 ( 22 )

t s



m

2 *

z

*

E

*

s

1 / 2 * 2

s

( 23 )

t d

 ( 14 )

TOF



t s



t D

 ( 24 ) 

m

2 *

z

*

E

*

s m

2 *

z

*

E

*

s

 1 / 2 *

D

1 / 2 *  2

s



D



Starting Position Example

• Both ions are 100 m/z (1.0364*10 • Distance between plates is 1 cm – Electric field is 10,000 V/m • Detector is 1 m from 2 nd grid -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 ( 24 )

TOF



t s



t D



m

2 *

z

*

E

*

s

1 / 2 *  2

s



D

 • TOF red – E red = 94 usec TOF blue = 60 eV, E blue = 50 eV = 112 usec Detector

This effect tends to cause peaks to tail to longer TOF

Initial Kinetic Energy Spread

• If the ion has a non-zero kinetic energy along the axis of the flight tube prior to acceleration: (25)

KE total = z*U+U 0

(U 0 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 ( 26 )

m

*

v

2 2 

U

0 

z

*

E

*

s

( 27 )

v

 2

m

 1 / 2 * 

U

0 

z

*

E

*

s

 1 / 2

How long do ions spend in the source?

( 27 )

v s

 2

m

1 / 2 * (

U

0 

z

*

E

*

s

)  

s



t

 ( 28 ) 

s

 2

m

1 / 2 * (

U

0 

z

*

E

*

s

) * 

t

( 29 ) 0

s



t



t

 0 

s m

2 1 / 2 *   (

U

0 

s



z

*

E

*

s

) 1 / 2   ( 30 )

t s

   1 / 2

z

*

E

*  

U

0 *

z

*

E

*

s

 1 / 2 

U

0 1 / 2  

t

0

(initial KE and position) (initial direction) (uncertainty of ion formation)

Putting this all together

( 30 )

t s

( 31 )

t D

    1 / 2 *  

U

0 *

z

*

E

*

s

 1 / 2

z

*

E

2 * 

U

  1 0 

z

/ * 2 *

E D

*

s

 1 / 2 

U

0 1 / 2 ( 14 )

TOF

 

t

0 

t s



t D

( 32 )

TOF

   1 / 2

z

*

E

*  

U

0 *

z

*

E

*

s

 1 / 2 

U

0 1 / 2   2 * 

U

0

m



z

1 / 2 * *

D E

*

s

 1 / 2 

t

0 •

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

•

High U to minimize U 0

•

Narrow ion formation regions to minimize s

•

Pulsing ions out of source to minimize t 0

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

• There is a point in the flight tube where 2 ions starting at different positions arrive simultaneously ( 33 )

t s



t D

 ( 34 )  2 *

z m

*

E

*

s

 * 2

s

  2 *

z m

*

E

*

s

 *

D

 ( 35 )

D

 2

s

• 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) – s 0 is related to initial KE since all ions formed simultaneously Detector

Reflectrons?

• 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

Detector ( 36 )

TOF



m

2 *

z

*

E

 1 / 2 * 

D

1 

D

2  4

D ref

 ( 37 )

TO F

    2 * 

z

*

m E



U

0    1 / 2 * 

D

1 

D

2  4

D



ref

 ( 38 )

D



ref

  

z

*

E z

 *

E U

0   *

D ref

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

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

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

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