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The principle of the time-of-flight (TOF) mass analyser was first introduced by Stephens in 1946 and was further designed into the first commercial instrument (linear TOF mass analyser) in 1955 by Wiley and McLaren.59, 60

In TOF-MS, ions generated from an ion source are accelerated through the flight tube by an electric field which is caused by the potential difference between the electrode and extraction grid. To a first-order approximation, all ions obtain same kinetic energy in the acceleration region, and drift in a flight tube which is a free-field region according to their m/z, and reach the detector at different times, allowing separation of ions by m/z ratios (see Figure 1.12). The process of ion drifting in TOF mass analyser can be represented by the following equations: Kinetic energy obtained by the ion:

E = 1₂𝑚𝜐2 = qV [Eq. 8]

Velocity of the ion (rearranged from Eq. 8):

υ = √2𝑞𝑉_𝑚 [Eq. 9]

where E is the kinetic energy obtained by the ion, m is the ion mass, υ is the ion velocity, q is the ion charge, and V is the electric potential generated from the

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potential difference between electrode and extraction grid.

Figure 1.12. The outline of a linear TOF (Reproduced from Opsal et al. 1985).61 Ions (black dot) are accelerated in the yellow region by the electric potential, drift through the green region (flight tube), and reach the detector (right).

Eq. 9, it shows the velocity of ion is inversely proportional to the mass1/2 which indicates heavier ions have a lower velocity, thus they require a longer time to drift through a flight tube and vice versa. The time for ion to reach a detector can be calculated by the following equation:

t = 𝐿

𝜐 [Eq. 10]

where t is the ion drift time across the flight tube and L is the length of flight tube. The time for ions to reach a detector can be presented in terms of ion mass by combining Eq. 9 and Eq. 10 as follows:

t = √𝑚𝐿_2𝑞𝑉2 = √𝑚_𝑧 √_2𝑒𝑉𝐿2 [Eq. 11] where z is the number of charge on the ion and e is the charge constant.

Previous results showed that a linear TOF mass analyser could detect protein samples in 100 – 200 attomole amounts.62, 63 _{In a linear TOF mass analyser, there} is, in theory, no upper mass limit which makes it suitable for the detection of large biomolecules and polymers.64, 65 Furthermore, the analysis speed of TOF is very

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fast, in which a spectrum can be obtained in ~100 micro-seconds.8

In reality, the kinetic energies obtained by each ion are slightly different, which results in the spreading of ions (with same m/z) drift times and causes peak broadening and decreases mass resolution. In order to minimise the spreading of ion’s (same m/z) drift time, delayed pulsed extraction and reflectron are the two common techniques that applied to correct the kinetic energy differentiation between ions (see Figure 1.13). In delayed pulsed extraction, a delayed pulse is applied to all ions and ions with lower kinetic energy stay in the acceleration region longer than higher kinetic energy ions which results in lower kinetic energy ions obtain more energy before entering the flight tube. Since the initial lower kinetic energy ions receive more energy in the acceleration region, the velocities of these ions increase and catch up with the initial higher kinetic energy ions in the flight tube, both ions reach the detector at the same time.

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Figure 1.13. The implication of a delayed pulsed extraction in a TOF mass analyser which improves the mass resolution (Reproduced from De Hoffmann et al. 2007).8 _{The black dot represents an ion with higher kinetic energy, while the} white dot represent an ion with lower kinetic energy. The white dot (low kinetic energy ion) stays longer in the acceleration region which gains more energy before entering the flight tube, as a result the velocity of white dot is higher than the black dot and both dots reach the detector at the same time.

The reflectron is also used to correct the kinetic energy spreading between ions. This idea was first introduced by Mamyrin in 1973.66 The reflectron, placed opposite to the source and detector, acts like a mirror which reflects the ions coming from the source to the detector which is placed next to the ion source (see

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Figure 1.14). The ions with higher kinetic energy penetrate the reflectron more deeply than the ions with lower kinetic energy, the higher kinetic energy ions, therefore, stay in the reflectron longer than the lower kinetic energy ions which results in both ions reach the detector at the same time. With the applications of delayed pulse extraction and reflectron, the accuracy of the TOF mass analyser can be improved from 200 ppm to 10 ppm and the FWHM resolution is enhanced from 5,000 to 20,000 (at m/z 1,000).8

Figure 1.14. The application of a reflectron in a TOF mass analyser which helps to improve the mass resolution (Reproduced from De Hoffmann et al. 2007).8 The black dot represents an ion with higher kinetic energy, while the white dot represents an ion with lower kinetic energy. Since the black dot contains higher kinetic energy, it penetrates the reflectron deeper than the white dot, which results in arriving the detector at the same time.