Determination of the Relative Partial Single Ionization Cross Section

The raw data for the analysis o f the tim e-of-flight m ass spectra consists o f the intensities of the ion signals from the recorded mass spectra, such as Fig. 3.1. The intensities of the ion signals are determ ined by finding the areas o f the peaks and applying a suitable correction to subtract the background ion signals arising from the detection o f ions form ed outside the focused volume. The background correction is evaluated for each peak in turn, by determ ining the num ber of ion counts per channel in the region of the spectrum before the onset o f the sharp mass peaks and thus the background contribution to the peak can be calculated and subtracted.

To derive the partial ionization cross sections of the ions from the ion intensities determ ined from the m ass spectrum , it is necessary to consider the factors affecting their m agnitudes. F or a m olecule XY, the intensity of a signal 7y+ due to in the m ass spectrum after P pulses of the repeller plate can be expressed as

I ^ ^ = a n ^ , V P Eq. 3.1

w here uy+ is the num ber density o f the ion in the volum e V o f the source region that is focused onto the detector and a is the experim ental ion collection efficiency. T he constant a is assum ed to be mass independent and should therefore depend only on the channeltron efficiency and electronics. If GxY is the partial ionization cross section for form ing from the neutral m olecule XY, then by definition.

w here Ry+ is the rate o f form ation of in the ionization region and is the num ber o f electrons per second entering the ionization region that has an electron pathlength o f L

As described in C hapter 2, any ions form ed during the period betw een the extraction pulses are im m ediately accelerated tow ards the repeller plate due to the presence o f the bias field. Hence, w hen the extraction pulse is applied, ions o f two different m asses form ed w ith the sam e partial ionization cross section will have different densities in the source region, due to their differing velocities across it as a result o f the presence o f the bias field. Since the rate o f ionization is low and the residence tim e of an ion in the source region is small (< 1 |uis) in com parison to the inter-pulse period (30 ps), the fluxes o f the tw o species across the source region will be the same. That is, after a period o f less than 1 ps, which is the tim e taken for the first ions form ed to leave the interaction region, the num ber of the two species leaving the interaction region per unit tim e interval will be the same, although they leave with different velocities.

If the cross sectional area o f the focused volum e perpendicular to the bias field is A, then the flux o f Y^, the num ber o f species leaving the interaction region per unit tim e interval, across the focused volum e is J\+ w here /y+ = Ry+/A. At any point ny+ = Jy+Idy+, w here Vy+ is the velocity of Y^. Since the ions are undergoing a constant acceleration across the focused volum e under the influence of the bias electric field, Uy+ = bNmY+, w here my+ is the m ass-to-charge ratio o f Y^ and b

is a constant depending on the position of Y^ in the bias field. C om bining these expressions gives,

aVPRg n^Y^xyl^^Y^

/ = --- --- bq. 3.3

Ab

U sing a M onte Carlo sim ulation to model the ionic m otions in the source region, it is found that, under the general experim ental conditions described above, ions form ed at the sam e rate will have densities proportional to the square root o f their m asses, as predicted by Eq. 3.3.1

From the recorded tim e-of-flight m ass spectra, one w ould ideally like to determ ine absolute partial ionization cross sections of the observed ions. H ow ever, as discussed in C hapter 1, it is very difficult to m easure absolute partial ionization cross sections using a TO FM S, as an accurate determ ination of experim ental param eters such as the electron pathlength, the num ber density of the target gas and the electron flux is required. The m easurem ent o f such param eters (Eq. 3.3) is difficult and com plicated and so the relative partial ionization cross sections a / o f the observed ions are com m only determ ined. Indeed, values o f o / for reactive m olecules are determ ined from the tim e-of-flight m ass spectra recorded in these studies.

To determ ine the intensities o f the ion signals in the m ass spectrum are divided by the intensity o f the m ost abundant ion to give an intensity ratio. F or exam ple, for a spectrum of C S 2

(Fig. 3.1) w here the m ost abundant ion is the parent ion CSz^, the ion signals o f the fragm ent ions C^, S^, 82"^ and CS^ are divided by the intensity o f to give /(X'^)//(CS2^) for each fragment. H ow ever, due to the ion density effects described above, a correction factor m ust be applied to this intensity ratio to give o / , w here 0 / = a (X'^)/ct (CSz^). From Eq. 3.3, the values of a /(X V C S 2'^) will be equal to the ratio o f the intensities o f the ions m ultiplied by the ratio o f the square root of their m asses (Eq. 3.4)

I

(7 ■ = — - — = ’ - — - — Eq. 3.4

where m is the relative m olecular m ass o f the ion. U sing the above analysis procedure, mass spectra of argon from this apparatus yield a ratio of the single-to-double ionization cross sections in good agreem ent with that available in the literature.2

D ue to the small collection aperture of the channeltron detector, ions form ed with a significant translational energy perpendicular to the axis o f the TO FM S will m iss the detector (Fig. 3.2), since their transverse trajectories along the drift tube will result in a final position at the end of the drift region beyond the channeltron aperture.

— ► ►

>

₇

R epeller Plate D etector

Fig. 3.2 Diagram of the trajectory of an ion formed with significant translational energy demonstrating that it will miss the detector.

A ssum ing a point ion source, the m axim um translational energy E an ion can possess perpendicular to the axis o f the TO FM S and still be detected can be calculated in the follow ing way,

E = — m Vj Eq. 3.5

where v t is the transverse velocity of the ion, aw ay from the axis o f the TO FM S. The transverse velocity of the ion can be calculated from v t = /hou w here is the radius o f the detector. F or a N 2"^ ion with a flight time in the apparatus o f 2.2 ps,

0.3

Vj = — = 0.14 cm ps'^ Eq. 3.6

2.2 ^

and thus from Eq. 3.5, E = 0.28 eV. Therefore, for the one-dim ensional apparatus set-up, ions with a translational energy greater than -0 .3 eV will be inefficiently detected. H ence, the above analysis procedure used to determ ine values of üt is only valid if an insignificant proportion of the fragm ent

ions are produced with kinetic energies above 0.3 eV, although the ratio o f the cross section for the different fragm ent ions will be consistent if there are no m arked differences in the high energy parts o f the kinetic energy release distributions for the form ation o f the different fragm ents. ^ Studies of the fragm entation of triatom ic parent ions, such as CSz^, and form ed by electron impact, indicate that only a small percentage o f the fragm ent ions from these species have kinetic energies greater than 0.3 eV,k3 D ue to the increased num ber of available internal m odes o f vibration, one w ould expect a similar, if not smaller, proportion o f high kinetic energy fragm ents to result from the dissociation of polyatom ic ions. Therefore, one w ould conclude that the analysis procedure described above should yield accurate values o f the partial ionization cross sections, a conclusion supported by previous w ork on the ionization o f O 3.1

It is im portant to realise that the small aperture detector discrim inates strongly against the detection o f energetic fragm ents produced by the dissociation o f m ultiply charged ions, as such fragm ents are usually form ed with kinetic energies in excess o f 2 eV."^ H ence, energetic ions are not efficiently detected in the one-dim ensional experim ents and as a result, the fragm ent ions observed in the m ass spectrum are “low ” energy ions arising from the dissociation of singly charged parent ions. Thus the values o f derived using the apparatus set-up em ployed in the one-dim ensional investigations should perhaps be correctly described as relative partial single ionization cross sections a / ‘. H owever, if a fragm ent ion form ed from dissociative double ionization receives an im pulse from the dissociation event along the axis of the TO M FS then this ion, although highly energetic, will be detected in the tim e-of-flight m ass spectrum since it has no translational energy perpendicular to the axis o f the TO FM S. But, the double ionization cross section is generally small com pared to the single ionization cross section^. H ence, any neglected contribution from m ultiple ionization to the values of the partial ionization cross sections determ ined in this study will for the m ost part be insignificant in com parison with the statistical sources o f uncertainty.

3.2.2 Double Ionization

In order to investigate the form ation and fragm entation o f doubly charged m olecular ions, ion-ion coincidence techniques^»^’^ are used. The experim ental procedure em ployed is described in C hapter 2. Ion-ion coincidence experim ents involve m easuring the tim e-of-flight difference A w betw een a pair o f ions produced by dissociative double ionization,

-4. X T" + Y * (3.1)

and a plot of ion signal intensity as a function of A w is a coincidence spectrum . As discussed in Chapter 2 (Eq. 2.6), A^t^f ’ w here mi and m2 are the m asses of the pair of ions. A fter

coincidence spectrum can be identified (Eq. 2.13). The relative intensities o f the peaks in the coincidence spectrum may, perhaps, be interpreted to give an indication o f the structure o f the dication as it may be possible to infer the connectivity within the dication from the pairs o f ions produced upon dicationic dissociation.

In a TO FM S under the W iley-M cLaren focusing conditionsi®, the tim e-of-flight o f an ion ^tof is given by

^ o f = ^ o Eq. 3.7

a

w here fo is the flight tim e for a therm al ion, v/a is the braking tim e w hich is the change in the flight tim e o f the ion caused by its initial velocity , v is the initial velocity com ponent o f the ion along the axis o f the TO FM S and a is its acceleration in the source region."*

From the tem poral w idth of the coincidence peak, the K ER associated with dicationic dissociation resulting in the form ation of an ion pair can be determ ined. F or a tw o-body dissociation reaction, form ing the pair o f product ions,

—> m\^ + (3.II)

conservation of linear m om entum requires that m\V\ + mivj = 0 and, since the acceleration o f the ions is inversely proportional to the ion mass, the braking times for the tw o fragm ents are equal in m agnitude but opposite in sign. Therefore, Aftof is given by

2 v ,

= A^o + --- Eq. 3.8

a

Since, v% ranges from +vo to -vq, where vo is the initial speed of m\^ and vi = vq cos 0 (w here 0 is the angle betw een the axis o f the TO FM S and the initial ion trajectory), the total peak width w (ns) will be 4vo/a. Thus, from the conservation of m om entum and N ew tonian m echanics, the K ER upon dissociation Uo (eV) can be obtained directly from the w idth o f the coincidence peak using the follow ing equation,

UQin^m^ 4vo 5766 w = --- = --- m -r Eq. 3.9 w here E (V cm ' ) is the source field voltage and m, m\ and m2 are relative m olecular masses."*

However, for a three-body dissociation reaction, w here neutral products are form ed in conjunction with the pair o f fragm ent ions, there is no unique relationship betw een the total KER and the w idth o f the coincidence peak. Therefore, deductions about the overall K ER can only be m ade with the help o f assum ptions about the dissociation m echanism and dynam ics. F or exam ple, if the reaction m echanism is sequential, following

m^^ —> mi"^ +

. . (3 .m )

and it is further assum ed that the K ER o f the m onocation dissociation is negligible, the observed peak width can be related to the total energy release in the follow ing w ay,4

2882

w = Eq. 3.10