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JOURNAL OF MASS SPECTROMETRY, VOL. 3, 1519È1532 (1995) SPECIAL FEATURE: TUTORIAL Principles and Instrumentation in Time-of-ýight Mass Spectrometry Physical and Instrumental Concepts Michael Guilhaus School

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JOURNAL OF MASS SPECTROMETRY, VOL. 3, 1519È1532 (1995) SPECIAL FEATURE: TUTORIAL Principles and Instrumentation in Time-of-ýight Mass Spectrometry Physical and Instrumental Concepts Michael Guilhaus School of Chemistry, The University of New South Wales, Sydney 252, Australia The principles of time-of-ñight mass spectrometry (TOFMS) are described with a view to understanding the strengths and weaknesses of this method of mass analysis in the context of current applications of mass spectrometry and the more familiar scanning instruments. Fundamental and instrumental factors a ecting resolving power, sensitivity and speed are examined. Methods of gating ion populations and the special requirements in the detection and digitisation of the signals in the TOFMS experiment are discussed. INTRODUCTION Mass spectrometry is primarily concerned with measuring the mass-to-charge ratio (m/z) and abundance of ions moving at high speed in a vacuum. Nearly a century of research in mass spectrometry has established that it is one of the most powerful probes into the structure and composition of matter. Since J. J. ThomsonÏs invention of the magnetic deñection mass spectrometer in the Ðrst decade of this century, many descriptions of devices for determining the relative yields of ions as a function of m/z have been published. Currently there is increasing interest in mass spectrometry and this results from the advent of new ionisation methods and the wider use of compact mass spectrometers. New ionisation methods allow the characterisation of a diverse range of polar, ionic or high molecular-weight compounds which previously were not amenable to mass spectrometric analysis. Compact mass spectrometers (bench-top instruments) are increasingly used as detectors for chromatographic separations because of their capacity to identify and quantitate compounds in complex mixtures simultaneously. TOFMS, an early arrival in the mass spectrometry family, was prominent in the Ðeld during the 196s but was soon displaced by magnetic and quadrupole instruments with their higher sensitivity and mass resolving power. The most signiðcant reason for the failure of TOF to mature was the lack of technologies to facilitate the recording and processing of the mass spectrum in the microsecond time-frame. These facilitating technologies are now emerging along with methods for the ionisation of massive biological molecules and also for fast mixture separation. TOF is highly advantageous in these cases and is therefore reappearing as a prominent mass analyser. By deðnition, mass spectrometers are m/z dispersive. In this treatise it will be useful to view ion trajectories in two or more dimensions with at least one being time. TOF mass spectrometers di er fundamentally from scanning instruments in that they involve temporally discrete ion formation and mass dispersion in principally in the time domain rather than along a spatial axis. Whereas the ion optics of spatially mass dispersive instruments can readily be illustrated in a twodimensional diagram, essentially showing ion trajectories in a plane of the instrument, most TOF optics can be equally well illustrated with a diagram having one spatial dimension and one time dimension. The rays in these diagrams are space-time trajectories and the focal points show ions that are at the same place on the distance axis at the same time. It is more likely than not that ions at this focus are in fact quite defocused on the remaining spatial axes. This is illustrated in Fig. 1 which shows the principal plane of the space-time trajectory as well as one additional spatial dimension. A useful maxim in TOFMS is that it matters just as much when the ions are as where they areï. THE TOFMS EXPERIMENT The essential principle of TOFMS (Fig. 2) is that a population of ions moving in the same direction and having a distribution of masses but a (more-or-less) constant kinetic energy, will have a corresponding distribution of velocities in which velocity is inversely proportional to the square root of m/z. Consider a situation in which ions, under the inñuence of an external electric Ðeld, begin their acceleration from rest at the same time and from the same spatial plane normal to the acceleration vector. Their arrival times at a target CCC 176È5174/95/111519È14 Received 7 September 1995 ( 1995 John Wiley & Sons, Ltd. Accepted 15 September 1995 152 M. GUILHAUS Figure 1. Mass-dispersed space-time trajectories in one time (t) and two spatial (x, y) dimensions. For isobaric ions starting at t but originally spread in y, the trajectories are focusing when projected onto the y-t plane. Projections of the trajectories onto the x-y and x-t planes are diverging. plane (parallel to the plane of origin) will be distributed according to the square root of m/z. In the case of subrelativistic velocities (as occurs in the kev energy regime) a good description of the TOFMS experiment requires no more than Newtonian physics as shown by the equations that follow. To avoid ambiguity, these equations are developed generally, rather than speciðcally to mass spectrometry. All fundamental quantities are in SI units as listed in Table 1. It may be useful for the reader to note that the constant for converting kg to Da is easily derived from AvogadroÏs Number (N A ): 1~3/[N A ] \ 1.66 ] 1~27 kg Da~1 and that the number of electronic charges is obtained by dividing the charge, q, by the charge of the electron ([e). Thus q appears with m in many equations rather than z. For positive ions with z charges, [ze may be substituted for q. Force and acceleration: V elocity and time to reach it: F \ Eq (1) F \ ma (2) a \ Eq/m (3) a \ du/dt (4) u \ P Eq/m dt (5) Position: t a \ u [ u E Am (7) qb s \ P u dt (8) s \ s ] u t ] 1(Eq/m)t2 2 (9) Drift V elocity and Accelerating V oltage: qv \ qes a (1) qes \ 1mu 2 a 2 D (11) u \ S2qEs a (12) D m Drift time: t \ D/u (13) D D t \ (14) D J2qEs /m a or t \ D (15) D J2qV /m Observed T OF: TOF \ t ] t ] t ] t. (16) a D d u \ u ] (Eq/m)t (6) Figure 2. Linear TOFMS instrument with a single acceleration stage. PRINCIPLES AND INSTRUMENTATION IN TOFMS 1521 Table 1. Fundamental and derived quantities, units and conversion Quantity Symbol Description Units Conversions Mass m mass in kg kg 1.66 Ã1É27 kg DaÉ1 mass in Daltons Da Charge q charge in coulombs C e charge of electron in coulombs C É1.6 Ã1É19 C z number of electron charges Éq/e Time t time-of-flight in seconds s t time after t ¼ that ion begins to accelerate s t time that ion is accelerating from u to u s a D t time that ion drifts at constant velocity s D t turn-around time (2 Ãtime of decelerate to u ¼) s É½ t response time of detection system s d s 2 variance of normal distribution of t s2 t s 2 variance of normal distribution of single ion pulse s2 p s 2 variance of time distribution attributable to jitter s2 j Distance s distance in metres m s initial position of ion m s distance in E from average s to drift region m a D drift distance m s 2 s variance of normal distribution of s m2 Energy U translational energy of ion in joules J U ¼qV, U ¼zeV translational energy in ev ev 1.6 Ã1É19 J (ev)é1 U initial translational energy of ion (at t,s ) J U drift energy of ion J D U* translational energy of fragment ion formed by J decomposition of parent ion having energy U D Velocity u velocity in metres per second msé1 u initial velocity msé1 u drift velocity msé1 D s 2 variance of normal distribution of initial velocity m2 sé2 u Electric field E electric-field strength V mé1 MASS RESOLVING POWER In most experimental arrangements ions are brought to kev translational energies over a distance of a few millimeters and the time that the ions drift in a Ðeld-free region of about 1mismuch larger than the time of acceleration. Equation (15) therefore serves as a useful approximation to determine the approximate Ñight time of an ion (in the 1 ls time frame for typical conditions). In mass spectrometry it is conventional to measure resolving power by the ratio of m/*m where *m is a discernable mass di erence. In TOFMS it is convenient to work in the time domain. Thus the resolving power m/*m can be measured in terms of t/*t as follows: Since m P t2, m \ At2 and dm/dt \ 2At where A is a constant; dm/m \ 2dt/t thus: m *m \ t 2*t. (17) The Ðnite time interval, *t, is usually the full-width at half-maximum (height) of the peak (FWHM). This deðnition of resolving power gives values which are approximately double those deðned by the 1% valley deðnition which is perhaps more familiar to users of sector mass spectrometers. Mass resolving power is limited by small di erence in measured Ñight-times for ions of the same mass (typically in the 1 ns time frame). These have their origins in the distributions in initial energy (i.e., molecular speed), position and time of formation of the ions prior to acceleration. Non-ideal acceleration Ðelds and, in some important applications of TOF, collisions, impart additional energy spread. The response time of the detection system as well as instrumental uncertainties in the timing/duration of the gating and detection events contribute additional temporal spread. In most cases these are uncorrelated distributions. Each maps to a contributing arrival-time distribution which can be calculated but not observed separately. The sum of the e ects can be obtained by convolution of the individual uncorrelated arrival-time distributions and this can be compared with the observed peak-shape. An understanding of the dependence of the width of the resultant temporal-distributions on key experimental factors such as ion acceleration voltage and drift length allows the best choice of instrumental parameters. In order to realise useful resolving powers for most applications, however, ion optical methods must be used to control and/or compensate for the initial distributions. Initial Energy (velocity) of Ions Ions Formed in the Gas-Phase. Ions generated or sampled from the gas-phase1,2 are subject to a Boltzmann distributions of initial velocity (u ). The ions initially 1522 M. GUILHAUS moving towards the detector arrive there before the ions which are initially moving away from it. Indeed, the latter ions are Ðrst decelerated to zero velocity before being re-accelerated and passing through their original position. The time for this to happen is often referred to as the turn-around timeï t. Assuming ions are all formed at the same time and ~` at the same distance from the detector and setting u \[uin Eqn (7) gives: t 2ou om (18) ~`\ Eq Substituting u \ J2U /m allows the equality to be expressed in terms of the initial translational energy U : t \ 2J2mU (19) ~` Eq Two ions with the same speed but moving in opposite directions will reach the same Ðnal velocity after acceleration. They remain separated by the turnaround time until the detector is reached. This is depicted by the parallel rays in the drift region of Fig. 3. If the drift region is lengthened, this separation in time becomes smaller relative to the total Ñight time. As is also apparent from Eqn (19), the turn-around time can be decreased by increasing the strength of the accelerating Ðeld. As an example consider the turn-around time for an m/z 1 ion in a source of about 5 K where the mean initial energy of ions is about 6.4 ] 1~21 J (4 mev). In a weak accelerating Ðeld of 3 ] 1~4 Vm~1 Eqn (19) calculates t \ 19 ns. The ~` resulting peak broadening would signiðcantly limit resolving power. Increasing E by a factor of 1 reduces the turn-around time to 1.9 ns, which is about the same temporal contribution as made by a good detection system. The time for an ion to travel a distance s from initial position s can be obtained from the quadratic Eqn (9). Obtaining the roots of this equation and, once again using J2U /m for u gives: t\ [J2mU ^ J2m[U ] Eqs] (2) Eq Eq The physical meaning of Eqn (2) is evident in Fig. 3 which shows the space-time trajectory of an ion passing through t \ t with an initial velocity u. Along this trajectory the ion is accelerating at the distance s \ s (after t ) and could be imagined to have been travelling t in the opposite direction (decelerating) at s, before t. The trajectory of the ion before t is in most t cases only imaginary but, usefully, when reñected about t, it gives the trajectory of a corresponding ion at the original position (t, s ) with an initial velocity of [u. This gives the equation for the time t to reach the drift velocity: a t \ J2m[U ] qes] ^ J2mU (21) a Eq Eq Here the turn-around time is apparent in the second term. Setting the distance from s to the beginning of the drift region as s, the drift energy is (U ]qes ) from which the drift velocity a is: a u \ S2(U ] qes a ) D m The drift time is thus: (22) S t \ D 2m (23) D 2 (U ] qes ) a Adding Eqns (21) and (23) and taking out a common factor of J2m gives the familiar equation published in 1955 by Wiley and McLaren1 and reproduced by many authors since then: t \ ] qes a ^ U qe ] (24) 2(U ] qes a As stated above, the e ect of the turn-around time can be decreased by increasing D. However the spread of arrival times due to di erences in the magnitude of initial velocity will increase with drift length. Long driftlengths also introduce technical difficulties such as the need to increase the size of the detector and the vacuum system. Generally the approach taken to reduce velocity e ects in linear TOFMS is to increase E. Figure 3. Parabolic space-time trajectories showing turn-around effect due to ions having initial velocity both away from and towards the drift region. PRINCIPLES AND INSTRUMENTATION IN TOFMS 1523 Ions Formed from Surface. Simpler conditions usually prevail for acceleration of ions from a surface. All the ions in the populations travel the same distance in the acceleration Ðeld from an equipotential surface to an equipotential grid. If V is the di erence in the potentials the drift energy is: U \ U ] qv (25) D and S t \ D 2m (26) D 2 (U ] qv ) In most conðgurations D? s, t? t and the ion arrival time spread from U is mostly D accounted a for by the spread in drift time (i.e., *t? *t ). Thus, assuming t B t, di erentiating with respect D to a U and multi- plying D by du gives: D Sm 2 2 dt \ (U ] qv )JU ] qv du (27) Dividing by: S t B t \ D 2m (28) D 2 (U ] qv ) and multiplying by 2 gives: 2dt \ dm t m \ du (29) U ]qv or in terms of resolving power: m *m \ U ] qv (3) *U Normally qv? *U which leads to the simple result that m *m B qv. (31) *U Thus, when the drift region is much longer than the acceleration region, the resolving power does not depend on the length of the drift region. In practice the time resolution of the detector and digitiser combination places a lower limit on the length of the Ñight tube in the range.5è1. m with V (typically 3È3 kv) adjusted to give a t of about 1È2 ls for the upper limit of m/z. Note D that these approximate parameters place the upper limit of m/z at 6. Energy Focusing. Wiley and McLaren1 introduced a technique called time-lag focusing to overcome the energy problem. By conðning ionisation to a small distance and allowing a delay between ionisation and ion extraction, the velocity dispersion causes the ion packet to become spread-out. The resulting large spatial distribution (correlated to the initial velocity distribution) is refocused by a spatial focusing technique as described in the next section and shown in Fig. 4. Unfortunately this correction is mass dependent and enhanced resolving power is attainable only over a limited mass range. More recently, the most common solution to the energy problem has been to make the more energetic ions follow a longer trajectory. This is achieved with some form of retarding Ðeld. An early implementation of this approach was to use an electric sector. As shown in Fig. 5(a), the more energetic ions have a larger radius of curvature in this device and therefore taken longer to travel through it. The optics are adjusted to minimise the dt/du function. More recent versions of this approach have used a number of electric sectors in a clover-leaf conðguration [Fig. 5(b)]. The most successful energy focusing method to date has been the reñectionï.3 Essentially an electrostatic ion mirror, this device creates one or more retarding Ðelds after a drift region. These are orientated to oppose the acceleration Ðeld. Ions re-emerge from the device with their velocities reversed. More energetic ions penetrate more deeply and hence take longer to be reñected. Thus the optics can be adjusted to bring ions of di erent energies to a space-time focus as shown in Fig. 6. Usually the angle of ion entry into the mirror is adjusted slightly away form 9 so that the ions follow a different path after being turned around. This allows the detector to positioned where it will not interfere with Figure 4. Time-lag focusing: Ions initially at A have a small distribution. During a delay after ionisation, this is converted into a larger spatial spread which is correlated with initial velocity at B prior to ion acceleration. The delay is chosen so that the ions of a particular m/z focuses sharply at the space-time point C. 1524 M. GUILHAUS Figure 6. Space-time trajectory for a reflecting TOFMS. Ions initially have simultaneous spatial and velocity spreads at A. Spatial focus is produced along B B with m/z separated by small intervals in time. Final focus is on the detector plane along C C after passing through an ion mirror. Figure 5. (a) Energy focusing effect of electric sector-trajectories are defocusing in space dimension but focusing in time as shown by the ion fronts which make time contours on the trajectories. (b) Configuration of four electric sectors to achieve energy focusing in TOFMS ÍFrom Sakurai et al., Int. J. Mass Spectrom. Ion Proc. 66, 283 (1985) ( 1985 by the American Chemical SocietyË. the axis of the ions from the ion source. Alternatively an annular detector allows the accelerator and mirror to be coaxial. The mirror has an added advantage in that it increases the drift-length without increasing the size of the instrument. The problem of the turn-around of the ions in the source, being e ectively temporal, cannot be corrected by the ion mirror. Thus, strong extraction Ðeld is often used with a gaseous ion source. In this case the ions are brought to a sharp spatial focus (see below) located at a short distance along the drift region. Di erent masses will focus there at di erent times but, at the respective times, the ion packets will be sharply focused in the direction of the drift velocity. There will be a large energy spread resulting from the energy and spatial spreads in the source but as the temporal and spatial spreads are very small for each m/z, the ion mirror can substantially correct for the large velocity spread. The mirro is positioned so that the Ðrst spatial focus acts as a pseudo ion source. This is illustrated with the space-time trajectories of Fig. 6. Due to the lack of the ion turn-around problem, the ion mirror works very well with TOFMS sources which generate ions from surfaces. Initial Position of Ions and Spatial Focusing An initial spatial distribution of ions maps to an arrivaltime distribution due to two opposing factors: (i) ions initially more distant from the detector spend more time in the accelerator, and (ii) ion initially more distant from the detector have a shorter drift-time because, as they spend more time under the inñuence of E, they reach a higher drift velocity. Setting U \ in Eqn (24) and dif- ferentiating with respect to s gives: a S A dt B (U \ ) \ m ] 1 [ D. (32) ds 2qEs 2s a a a This function reaches a minimum (zero) when D \ 2s. a Thus a spatial focus is achieved at a plane located at a distance of 2s along the drift region. Figure 7 shows the spatial focus a principle on a space-time diagram. In a uniform accelerating Ðeld

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