PROCESAMIENTO DE LOS DATOS

The intensity of each peak /pair in the pairs spectrum is determ ined by sum m ing the num ber of ion pair ‘counts’ detected within the area o f the peak after the false coincidence subtraction procedure. As illustrated in Fig. 3.9, the relevant area o f the pairs spectrum is selected and the num ber o f counts contained within the specified region is evaluated.

Peak Intensity /pai

+

Slope b

+

Fig. 3.9 Schematic diagram of a peak in the pairs spectrum illustrating how the intensity and slope of the peak is evaluated.

This sum m ation is carried out by an analysis algorithm w ritten specifically to extract relevant data from pairs spectra. The procedure is trivial for non-identical ion pairs but for identical ion pairs, w here the peak is partially obscured by the dead time, the determ ination o f the peak intensity is m ore com plex. The com plication arises because in order to evaluate the yield o f the w hole identical pair

peak it is necessary to determ ine the area o f the peak obscured by the dead tim e and scale the intensity o f the peak accordingly.

h = h

Fig. 3.10 Schematic diagram of the peak corresponding to an identical ion pair centred on the = t i diagonal illustrating how the area obscured by the dead time can be evaluated.

As can be seen in Fig. 3.10, since the dead tim e ^dead is know n, the length o f the portion of the peak obscured by the dead tim e Xtdead can be calculated trigonom etrically. The length of the whole peak is JCpeak = %obs + %tdead, where %obs is the length o f the peak observed in the pairs spectrum. If the num ber o f counts in the observed area o f the peak is fobs, then the total num ber o f counts for the w hole peak /pair can be w orked out in the follow ing way.

■^pair

' tdead “"obs

■^obs ^ o h s Eq. 3.28

In the one-dim ensional coincidence spectra, the intensity o f the coincidence signals can give an indication of the probability of a given dissociation reaction and perhaps even the structure of the dication. Sim ilarly with the pairs spectra, a com parison o f the yield o f the dissociation reactions o f a dication, determ ined from the num ber of counts found within the area o f the peak, can give an insight into the dissociation m echanism s occurring and their probabilities. Consequently, the relative intensities /pair/Ztotai of each ion pair, relative to the total num ber o f ion pairs observed in the subtracted pairs spectrum , is calculated.

Peak Slope Determination

An inform ative w ay o f extracting data concerning the fragm entation m echanism involved with a given dissociation reaction is to consider the slope b (Fig. 3.9), and perhaps shape, of the p e a k , 6 , 2 6 T h e slopes of the peaks observed in the pairs spectra are derived from the slope of the linear regression betw een t\ and plotted w ithin the area o f a given peak (Fig. 3.9). The slope is determ ined by the least squares fit method,^^ giving t\ and t2 equal weights as they have equal

w hen perform ing the fitting procedure as this w ould result in a biased value of h. From the values of

b obtained for the peaks in the pairs spectra, it is possible to obtain inform ation concerning the dication dissociation m echanism s occurring.

As can be seen from the pairs spectrum of € 82^^ shown in Fig. 2.16, the shapes o f the peaks in the pairs spectrum are very different for the two- and three-body dissociation reactions. For the tw o-body dissociation of C S2^^ form ing CS^ + S"^, the peak is orientated diagonally in the spectrum. T his is due to the conservation of linear m om entum upon dicationic dissociation to form only a pair o f singly charged ions [Reaction (3 .IV)].^6 xf € 82^"^ dissociates to form CS^ and S^, both ions will have the sam e initial m om entum p in opposite directions.

Pi + P2 = 0 Eq. 3.29

From the general expression for the tim e-of-flight t of an ion under the W iley-M cLaren focusing c o n d i tio n s g iv e n in Eq. 2.14, it follows that the flight tim es of a pair o f ions are given by

t\ = tQ + k p cosQ Eq. 3.30

t2 = t o - k p c o s Q Eq. 3.31

Therefore, f , + f 2 = const., and the peak corresponding to C 8 ^ + 8 “^ w ill form a straight line with a slope of - 1 in the pairs s p e c t r u m . 1^46

F or a three-body dissociation reaction, e.g. + 8 ^ from € 82^'*' in Fig. 2.16, the dynam ics upon dissociation may be far m ore com plicated. As discussed above, a three-body dissociation reaction can occur via a variety of different m echanism s, a direct m echanism or a sequential m echanism involving either a deferred charge separation or an initial tw o-body charge separation follow ed by further dissociation to give the detected ion pair and n e u t r a l s . I f the three-body dissociation o f the dication involves a direct m echanism then the dissociation is considered to occur

via an instantaneous explosion [Reaction (3.VI)], breaking all the bonds sim ultaneously. Thus the two ions are form ed with equal and opposite initial m om enta w hile the neutral fragm ent receives no im pulse and therefore, providing there are no collisions between any o f the fragm ents, as with the tw o-body m echanism b = -1.15.16 p o r a deferred charge separation m echanism [Reaction (3 .V ni)], the dom inant energy release occurs on the second dissociation step, m i m j ^ —> m\^ + m2 , which

again is com parable to the tw o-body dissociation and therefore Z? = -1.15,16

If the dissociation m echanism is a sequential m echanism involving an initial charge separation [Reaction (3.Ill)], for the initial charge separation, m^^ m\^ -f m2m3^, from the

conservation o f m om entum , m\Vi + m2m3V23= 0 and therefore

Pi = -p23 Eq. 3.32

F or the secondary dissociation, m2m3^ m2^ + m3.

P i = /M2V23 = — — : P23 Eq. 3.33

and from Eq. 3.32,

P i = —~(m2 + m3 )—---~ P i Eq. 3.34

m2

H ence, b = -(m 2+m3)/m2,^^46 when the flight tim e o f the heavier ion is plotted on the %-axis. H ow ever, this is a lim iting case where m2ms^ has tim e to rotate freely and leave the Coulom b field of

m\^ before the secondary dissociation occurs. If 17121713^ dissociates w ithin the Coulom b field of the

other fragm ent ion, m2 ' w ill gain increased m om entum and therefore b will increase towards - 1.

C onsequently the value o f b will lie betw een -1 and the m ass ratio - (m 2+m3)/m2. This is an indication o f a fast dissociation as it occurs before the fragm ents form ed in the initial charge separation have tim e to leave each other’s Coulom b field (~ 1 p s).i^d 6

In PEPIPICO experim ents, 1^*20,26 further details concerning the dication dissociation m echanism s can be obtained from the peak shapes as for a three-body dissociation reaction the resulting peak shapes are characteristic of directional correlations betw een the fragm ents. However, the resolution in a PEPIPICO spectrum is better than in the pairs spectra presented here because the detection o f the photoelectron in PEPIPICO as a tim e zero precisely defines the instant of dissociation. As a result, extrem ely w ell-resolved peaks are observed in the PEPIPICO spectrum from which inform ation concerning the dissociation dynam ics can be derived. H owever, in the 2D experim ents discussed in this thesis, there is a finite tim e during w hich dications can be form ed in the electron pulse and hence an inherent uncertainty ( - 1 0 ns) o f w hen the dissociation event occurred. This is apparent as an increased perpendicular width o f the peaks.

Kinetic Energy Release Determination

It is difficult to directly obtain data about the energetics associated with a given dissociation reaction ju st by looking at the peaks in the pairs spectrum .I6 in order to extract inform ation about the KER upon dicationic dissociation to form a particular ion pair it is convenient to convert the pairs peak into an ion-ion coincidence peak.

To transform a pairs spectrum into an ion-ion coincidence spectrum , the tim e-of-flight difference A/tof betw een the two ions of a pair is determ ined for all the pairs recorded,

^txof=t2- t \ Eq. 3.35

As with the one-dim ensional ion-ion coincidence spectrum , a plot of A w against intensity is constructed, with the num ber o f ion pairs in each channel being a m easure o f the num ber of ion pairs with that particular A?tof-

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

Aftof/HS

Fig. 3.11 Ion-ion coincidence peak of the CS^ + S"^ ion pair from CS2^^ transformed from the pairs spectrum. The error bars shown are derived from the counting statistics and represent two standard deviations.

A M onte Carlo sim ulation of this coincidence peak can be perform ed using the same procedure described in Section 3.2.2.1, in order to obtain values o f the K ER and F k e r d for the given

dissociation reaction for com parison with the values o f these param eters obtained from the one­ dim ensional coincidence spectra.

For the peak corresponding to CS^ 4- S"^ shown in Fig. 3.11, a value o f the K ER as 4.4 ± 0.2 eV is determ ined, a value w hich is in good agreem ent both with the literature"^ and the one­ dim ensional study of CSi^^.