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The unimolecular decomposition of excited polyatomic ions studied by time of flight mass spectrometry
Interrstional
Journal of MQSS Spectronzerry and Ion Pizysics
Elsevier Publishing Company, Amsterdam. Printed in the Netherlands
361
THE UNIMOLECULAR DECOMPOSITION OF EXCITED POLYATOMIC IONS STUDIED BY TIME OF FLIGHT MASS SPECTROMETRY
P. F. Kh~WSTUBB
Department
AN3
of Physical
N. W_ REID
Chemistry,
lenrfeld
Road, Cambridge
CB2 IEP (England)
(Received June 3rd, 1970; in final form August ISih, 1970)
ABSTRACT
The metastable transitions of the molecular ions of trimethyl phosphate and 1,3-butadiene have been studied in a specially modified time of flight mass dpectrometer, ionisation in the latter case being effected by photon impact. The results have been interpreted on the basis of the quasi-equilibrium theory of mass spectrometry, which has proved to describe them quite well.
INTRODUCTION
The study of so-called me&stable ions in mass spectrometry is one which has received considerable attention in recent years. One of the important aspects of this work is the measurement of the rate of decomposition of the parent ion, since this represents one of the purest forms of unimolecular decomposition to be found, and comparisons can often be made with unimolecular rate theory without the complications introduced by competitive and consecutive reactions. Pioneering work in this field was carried out by Hipple and co-workers1*2, who varied the residence times of the parent ions in the ion source by altering the repeller potential, and were thus able to study the progress of the reaction with time. There are many subsequent examples of the application of his technique, both to the decomposition of positive3-” and negative ions12_ A closely related method is that of Newton and Sciamanna’ 3, who produced variations in the ion residence times by altering the main accelerating voltage. The above experiments have produced rather cotiicting results, in that some workers have found that a particuiar decomposition is described by one, two, or even three discrete rate constants, while others have found that the same decomposition can best be described by a smooth distribution of rate coefficients, as is predicted by the quasi-equilibrium theory of mass spectrometry (QET). -4 drawback to this technique is the rather small range of reaction times that is accessible Inr. J. Mass Spectrom.
Ion Phys., 5 (1970) 361-380
P. F. KPU’EWSTUBB,
362
N. W.
REID
(generally from I. to 10 microseconds). It has been pointed out by Schug14 that ratht:r greater precision is required for these measurements than is generally realised (or available), and he gives an illuminating example. Ottinger, using an ele,uant apparatus’ 5s16, has been able to extend the time range by several orders of magnitude, and, in a careful study of several metastable trarrjitions, has found that all of these are best described by a distribution of rate coefiicients. The same conclusion was reached by Beckey et al.17, who were able to work down to very short times indeed using a field ionisation mass spectrometer_ Several other measurements have been carried out, e.g. by Tatarczyk and von ZIahn”, who worked at relatively long reaction times, and obtained results in agreement with the QF~, and by Benz and Brownlg, who measured half lives for metastable transitions in a cycloidal mass spectrometer by studying the peak shapes. They, in contrast, found only one case which was described by a distribution of rate coefficients, the others al1 fitting a model corresponding to decomposition via a single rate coefficient, but were unfortunately limited to a very narrow range of reaction times Thus it can be seen that there is in the literature considerabie disagreelment as to the time dependence of these decomposition reactions, and thus doubt as to whether the QET accurately reffects the behaviour of real systems. It was therefore decided to develop a new type of apparatus for the measurement of ionic lifetimes”, the experimental results to be compared with the predictions of the QET.
APPARATUS
The equipment has been described previously’*, and is, briefly: as follows. A Bendix, model 14-101 mass spectrometer has been modified by the removal of the drift tube liner, the X and Y deflection plates and the ion lens. The flight tube contains instead an assembly of field defining plates, fed from a potential divider, so that a constaut electric field of some 3000 V per metre is maintained over its length. The effect on the mass spectra is as described in ref. 20, i.e. in the absence of metastable transitions the mass spectrum looks normal, except that all flight times are doubled. If a met&able transition takes place the daughter ions will be accelerated away from the bunch of undissociated parent ions, and the result is a “smearing out” of the peaks. The time of arrival of such daughter ions is simply related to the fifetime of the corresponding parent ion. A typical trace is shown in Fig. 1. The mod&d mass spectrometer has also been provided with a photoionisation source. The light is produced by a repetitively pulsed electrical discharge in a suitable gas, constricted by a boron nitride capillary_ The repetition rate can be varied between about 5 and I5 kHz, and the duration of each flash is approximately 130 nsec- An important improveme& over the apparatus as described previously Iis_ 3- Mass Specirom. Ion Plzys., 5 (1970)
361-380
DECOMPOSITION
OF
110
EXCITED
POLYATOMIC
363
IONS
140
Fig. I_ 15 volt electron impact spectrum of trimethyl phosphate, showing the effect of the metas::ble transition (CH,O).PO+ -+ (CH30jzHPO’ +_(HCHO). Sensitivity 0.01 nA FSD; time &onstint 1 sec.
has been brought about by the instaliation of a vacuum monochromator of SeyaNamioka geometry, fitted with a Hilger and Watts type K68 grating, of 1 m radius of curvature. The inlet to the monochromator is a 0.35 mm hole and the exit slit is 4.0 by 0-i mm. The optical path is completely windowless, and, after passing through the ion source, the light beam is detected by a type lP28 photomultiplier sensitised by sodium salicyiate. The norma Bendix electron impact ion source was also retained. Typical operating pressures were 2 to 5 x IOm5tot-r in the source region, and somewhat less in the flight tube.
THEORY Of OPERATlOS
Consider the metastable transition AB+ +A’fB Ml
“2
(9 =Z3
with the notation to be used indicated in the following schematic representation of the flight tube: Ionisation Time
Velocity Distance
! 0 C Q
Becomposition --f
T Cl x
.
Multiplfer stack 1 1 T+t, T+t,+tz VZ d d:y Int. .l. Mass Spectrom. Ion H.w.,
5 (1970)
361-380
364
P. F_ KNEWSTUBS,
N_ W.
REID
If the electric field is E V/m over the first d metres of the ffight tube (field defining plates) and zero in the multiplier stack (a tube fixed to the entrance end of the Bendix electron muhipIier), and if the electronic charge is e, it can readily be shown that: u2 = (eET)/m, t, =
-?-(eEtl)/.ml
- (mJm,)Tt
[(m,/m,)‘T*
(2) +2(d-
eET2/2m,)
m,/eE]’
(3)
and t2 = y!(eET/m
I + eEr , jm2)
on the assumption that all ions are singly charged. The total flight time 2-f = Tit~-I-r*
(5)
is evahtated as above, and a conversion curve established, so that measured fiight times of daughter ions can be converted to lifetimes of the corresponding parent ion. The ion current due to daughter ions of a metastable transition arriving with flight time T, is proportional to the number of decompositions of the parent ion, yielding that charged fragment. occurring between times t and ttSt. The times t and T1 are related via equations (3): (4) and (5): as mentioned above, while 6t is the gate width of the anaIog output unit, similarly converted to a scale of decomposition time. If the decomposition is governed by a singie rate coefiicient, k, this means that 1 a [exp(-kt)-exp[-k(ti-St)]]
(5)
while if several rate coefficients are operative I CC CNiexp(-kit)-exp[-ki(tibr)l = &Nrexp(--k;t)[l i
-exp(-kist)]
where the summation may be extended to an integration to cover the case of a distribution of rate coefficients as predicted, for exampfe, by the QJZT.N, is the relative probabiiity of decomposition via ki. Two points arise from the above analysis: (1) The charged fra&ments from the metastable transition wil! strike the detector cathode with varying velocities, depending on their time offormation (SC% eqn. (2)). It is thus certain that I in eqns. (5) and (7j will not correspond exactly to the measured ion current, but rather to that quantity corrected for the above variation in velocity. . There is some disagreement in the literature as to the precise form of such a correction’l, but in this cast, where-all the particles under consideration have the Intel Mars Specfrom IonPhys.,
5 (1970)361-380
DECOMPOSITIC)N
OF
EXCITED
POLYATOMIC
365
IONS
same mass and structure, it seems most appropriate to assume that the muhipher response is directIy proportional to the velocity of the incident ion, i.e.
1 = Lsured x
velocity of daughter
(T = 0) = r x F
velocity
(T=
of daughter
T)
*
-
(2) As mentioned above, a necessary quantity in the analysis of the resuhs is &, the gate width of the analog output units on a scale of decomposition time. Since the equation relating flight time and decomposition time is quadratic it can not be assumed that 6r is constant. If the gate width is denoted by bT,, and knowing that & = T+t,ft?
(5)
we can say that 6T, = (1 -I- &,/dT; = r;; - 6t or
6t
&J dT)Et
(9)
= (I/‘&) - bT,.
(10)
The factors l/F, and Fare conveniently calculated at the same time as the conversion curve, using eqns. (3) and (4). A computer program was developed for this purpose, and typical values of l/F, are 4.7 at T = 0 and 6.6 at T = IO psec, while F varies from 1.00 to 1.36. The value of ST, was measured to be approximately 100 nsec, but trial ca!cuIations showed that varying this by a factor of ten in either direction had no observable effect on the result.
It has proved possible to operate the instrument using ionisation by both eIectron and photon impact, and an example of each is presented below. A. Electron impact ionisation The metastable
peak due to the transition
(CH30),PO’ --, (CH30)2HPOf
i
(HCHO)
occu.rring in the mass spectrum of trimethyl phosphate, has been observed by Dugger and Kiser’“. This process is very well suited to study in the present apparatus because of the relatively large mass ions, and the lack of interfering peaks this decomposition have been measured and daughter peaks was shown in Fig.
difference between the parent and daughter in the intervening region. The kinetics of aiready’ ‘, and a typicaI trace of the parent 1, Int. J_ Mass Spectmm. Ion Phys., 6 (1970) 361-380
366
P. F. KNEWSTUBB,
N. W.
REID
Fig. 2 shows the decay curve obtained from the average of several traces simiiar to that of Fig. l_ The iwo sets of points were obtained from sets of experiments at two different values of the scan rate of the analog output unit, and are
0s2
20
3.0
4.0
5.0
60
7.0
8.0
9.0
Lifetime (psec.)
Fig. 2. Unimolecular decay curve for the decomposition of the molecular ion of trimethyl phosphate. Ion&&on by 50 eV ekctrons. (0) at scan rate 2: (0) at scan rate I.
plotted separately in this instance, rather than taking the combined average as was done previously, to illustrate the scatter inherent in the reslults. The error bars give the estimated uncertainty, which is the same for both sets of points. Ionisation was by impact of 50 eV electrons. As Fig. 2 is a smooth curve, it is probable that the results are in agreement wjth the Q?Zr, although it must be pointed out that decay via a single rate coefficient wouid not give a straight line on the above plot because 6t is not constant. It was decided to carry out a complete QJX calculation to give a quantitaiive check on the validity of the theory- On the basis of the QET the rate coeEcient for the decomposition of an ion having internal energy E is23: _,
where N’(E) is the number of states of the activated complex up to energy E, p(E) is the density of states of the parlznt ion at energy E, E, is the activation energy of the decomposition reaction and h is Plan&s constant. Before this equation can be applied the following quantities must be known: Vi, the vibrational frequencies of the parent ion, Vsi, the vibraticnal frequencies of the activated complex, P(E), th e relative probability that the parent ion has internal energy E, and E,, BS above. The approxiznation is made in this work, as in many other cases, that the vibrational frequencies of %he parent ion are the same as those of the neutral Int. J. Mass Spectrom. Ion Phys., 5 (1970) 361-380
DECO_MPOSfTlON
OF
EXCITED
POLYATOMIC
367
IONS
species. It is further assumed that the parent ion and the activated complex can be considered as a collection of Ioosely coupled harmonic osciliators, as this ,oreatIy simplifies the computation of N’(E-E,) and p(E). N’(E-~5~) was evaluated by direct count up to an energy correspording to 15000 states, and thereafter the approximation of Whitten and Rabinovitch’* was used. The latter equation (digerentiated) was used for al1 calculations of (E)_ It appears that no complete vibrational frequency assignrnent is avaifable for trimethyl phosphate, so some frequencies had to be estimated by comparison with analogous compounds_ Two slight& different sets of freq!lencies were proposed to allow an estimate of the importance of errors in this assignment. These are shown in Table 1, and the two modek are designated PI and Pu. TABLE
I
VIBRATIONAL
FREQUENCIES
OF THE TRIMETHI’L
Desfgrrarion
Descrip fion
PHOSPHATE
stretch C-H bend CH3 rock CH 3 torsion” P-O stretch P-O bend’ P-O stretch P-O stretch P-O bend’ P-O bend* C-O stretch C-O-P bend”
PSI
t’29.30
3000 1500 1250 250 1250 250
1’31.32
iOO0
~.I-9 ~v10--18 “19-24 f’ 25-27 =‘tS
l’33 t’3.z F35.36 p37-39 I’d0
ION
Frequency (cm - ’ ) PX
C-H
MOLECULAR
-45
759 1000 1000 1250 750
is00
1250 250 1250 250 1000 750 1000 750 1250 500
-1 These frequencies were estimated. All others were rounded off to the nearest 250 cm-l values given by CoIthup et aI.25 and Bellamy’s.
The activated
The possibility
compIex is assumed to have the four membered
of the five membered
ring transition
from the
ring structure
state
H CH,O
o-c/ \p/
/‘H
ht. J. Mass Spectrum. Icn Phys., 5 (1970) 361-380
368
P. F. KNEWSTUBB,
N. W.
REILi
has much to commend it, but it was not adopted in this case as elimination of HCHO -would leave (CH,O),POH, requiring migration of the hydrogen from the oxygen atom to the phosphorus before the next HCHO group could be eliminated. The successive elimination of HCHO is described by Bafus et aL2’. The frequency changes made in attaining the activated complex configuration were analogous to those used by earlier workers (e.g. ref. 28). In fact, it was again felt safer tn postulate two slightIy different sets of frequency changes in going to the activated complex, to check on the importance of errors. There are thus two models of the activated complex for each model of the parert ion, and these are designated AC:, AC:, SC,‘, and AC; respectively, where the subscript gives the relevant parent model. The necessary frequency changes are given in Table 2, and the Aculations were carried out for all four possible reaction paths. TABLE
2
FREQUENCY
CHXSGES
MADE TO THE TR:MmYL
PHOSPHATE
MOLECULtrR
ION TO GIVE THE ACTIVATED
COMPJmEX CONFIGLXATiOX
Frequency changed
VI VIO.
11
VIZ
New
cake
(cm-‘)
AC,:
ACI’
1500
500
750
unchanged
v19
500
925
500
933 937 =40
1500
500
1500
750
750
750
unchanged
250
500
500 750
750 250
unchanged 500 unchanged reatiion coordinate 15%
1000
1500
1590
500
1030
Earlier workers have approximated E, by the difference in appearance poten-
tials of the parent and daughter ions, but this is unsatisfactory, particularly in the case of decomposition of the molecular ion, because the appearance potential of a daughter ion is not just the threshold energy for its production, but is rather the minimum energy at which it is produced rapidly enough to be detected as such. As
is well known, this minimum
rate is of the order of 10” set-’
if the measurement
is
made in a magnetic sector instrument, and the internal ener,T of the parent ion required to give this rate of decomposition (i.e. the difFerence in appearance potentiais) is equal to the activation energy plus a certain excess, known as the kinetic shift- The correct procedure for estimating E, is to carry out the rate calculatioti for values ofE, less than the: difference in appearance potentials (denoted as A?‘---I;P), until one is foundwhich gives k(AP-IP) s 10’ set-‘. This is then the correct value.
lirf. J.
Mass Sgectrom. Ion Ptiys_, 5 (1970) 361-380
DECOMPOSITION
OF
EXCITED
For the case of trimethyl
POLYATOMIC
phosphate
369
Bafus et aL2’ give
IP[(CH30)3PO]
= 10.77+_0.3
AP[(CH,O),HPO+]
= 11.9
kO.2 eV
.- .(AP-IP)
=
+0.35
1.1
IONS
eV
eV.
A trial calculation showed that the kinetic shift was less than 0.3 eV, so the calculations were carried out for E, equal to 0.9, 1.0, 1.1, 1.2 and I.3 eV. Chnpka and Kaminskyz9 have shown that P(E) can be obtained experimentally. Forionisation by electron impact it is the second derivat.ive of the total ionisation as a function of ener,7. Unfortunately, this has not been measured for trimethyl phosphate, but the general form is common to many compounds, so a curve similar to theirs for n-butane was assumed as a first approximation. A portion of this curve is reproduced in Fig. 3.
I
150
I
I
2
1
I
3
Errergy (e!ectron volts)
Fig. 3. Assumed internal energy distribution for (CHaO)xPO*. imation which proved adequate for computational purposes.
The straight line gives the approx-
A theoretical decay curve to be compared with the experimental results may be obtained by putting the function for P(E) into eqn. (6) together with the values of k(E) calculated using eqn. (10). A s was pointed out earlier, the summation of eqn. (6) should be replaced by integration, but it proved suficiently accurate to sum with steps of E equal to 0.01 eV. This sum converges within 100 steps, i.e. 1.0 eV, so P(E) may be approximated by the straight line drawn in Fig. 3, which is described by P(E)
= 42.4-
18.4E.
This is referred to as distribution C. Trimethyl phosphate has 45 vibrations, as compared with 36 for n-butane, so it is highly likely that the true form for P(E) will peak at a higher value ofE than Int. J. Muss
Spectrom.
Ion Phys.,
5 (1970)
361-380
370
P. F. KNEWSTUBB,
N. W.
REID
is predicted by the internal energy distribution assumed above. To allow for this possibility two further distributions were postulated: (ij distribution B; P(E) (ii> distribution A; P(E)
= constant =
42.4+ 18.4 E_
Distribution B described, approximately, the case where the maximum is in the aiddie of the region of interest, and distribution A that where it is at higher energy. The results of these calculations, for all assumed values of E3+ and all three internal energy distributions, lie on or between the lines shown in Fig. 4, which
0
1
2
3 4 5 6 tifetkf? (p KC.)
7
8
Fig. 4. Computed decay curves for (CH,O)JPO+, tal points are included.
showing the maximum
spread. The experimen-
shows, for PI decomposing via AC:, rhe maximum spread in the calculated decay curves_ The calculated curves were shifted vertically to coincide with the experimental results at a time of 2 WC, and the experimental points are included in the figure to allow a comparison. The calculated decay curves for the other thret: assumed reaction paths (i.e. PI + AC:, etc.) are not inc1ildc.d here, since they are practically indistinguishable from those of Fig. 4. thus
B. Photoionisation The metastable tr.ansition studied using photcioaisation C4H6-f
--, C&Is+
f
Ini. J_ M& SFecrrom. Ion P&s.,
(CH,). 5 (1970)
361-380
was
DECOMPOSITION
OF
EXCITED
POLYATOMIC
371
IONS
Unfortunately, sufficient intensity for quantitative measurements was only availabie if the grating was set to its zero orger position, giving no waveiength selection. Even so, the detection system had to be operated at its mtimum sensitivity, and the recorded signal was rather noisy. In an attempt to obtain a smooth result, and yet avoid the subjective procedure known as “drawing a smooth curve through the trace” the following approach was adopted. The length of the recorded chart was divided into 0.5 cm divisions, and the integrator count read off for each of these. This was repeated for several scans of the required portion of the mass spectrum and the count in each “channel” summed, giving, in a crude sort of way, the effect of multichannel analysis. The histogram obtained in this way is shown in Fig_ 5, and the decay curve of Fig. 6 was calculated from &is as before. Since 36 32
2
24
e 20 t a = 16 zz v 12 8 4
I
L
mfez39 * I 5 IO
20
Ckmel
25
30
. 53. I54 1 40 35
1I 45
Nmlxr
Fig. 5. Histogram presentation of the photoionisation mass spectrum the effect of the metastable transition CaH6* + CBH9++(CH3).
Fig. 6. Ur.imotecufar
decay curve for the decomposition
of 1,3-butadiene,
of the molecular
showing
ion of_ 1,3-butadiene.
Inr. J. Mass Spectrorn. Ion Phys., 5 (1970)
361-380
372
P.
F. KNEWSTUBB,
N. W.
REID
the signal strength was so much lower than that given by electron impact ionisation, the estimated uncertainty is correspondingly greater, as shown by the error bars. The rheorztical situation is considerably happier than for the previous example, though, and a complete vibrational frequency assignment is available3’. This is reproduced in 7kbIe 3, with the excepiion of vg, the symmetric C=C stretching frequency, which is given the value of 1400 cm-‘, as measured by Elandj’ for the molecular ion_ TABLE
3
VIEK.ATIONAL
FREQLEXCIES
OF THE ACTIVATED
TJOS!S
Description
OF THE 1,3-BUTADIESE MOLECULAR ION, AXD TWO POSSIBLE CONFXGURACOMPLEX
Desi~mnation Parezt
Frequency (cm-‘) AC1
C-H C-H
C-H
stretch stretch
C-H C-K C-H GH C-H
stretch stretch stretch stretch bend bend
C-C C-C
stretch stretch
c- C
stretch
C-C-C bend C-C-C bend CH, scissor CH+ scissor CH, CHt
rock rock
3014
3014
3014
3056
3056
3056
3101 3102 3014
3101 3102 1400
3101 3102 1400
2985
2985
2985
1379 1285
1279 1285
1279 1285
1400 1599 1205 513 301 l&2
reaction
1355
890 987 686 520
CH wag CH
wag torsion CHt twist CH2 twist
AC2
coordinate
1599
1599
1400 5i3 301 1-2
1205 513 301 I&Q
1385
1385
890 987 686 520
s90 987 686 520
C-C
153
900
900
C&
967 1013 910
967 1013 910
700 1013 700
909
909
909
=g
CH,wag
Two forms of the activated complex are suggested for this decomposition. The first is based on the idea 32 that at energies below the threshold of the above process the sk.e!etal hydrogen atoms become mobile, so that the I,Zbutadiene configuration is accessible, and can decompose by simple C-C cleavage. [C&=C==CH+CHJ
+_
@CO
The second form, ACZ, allows for decomposition via a transition state.containing Int. 3. .Mu.vSprct~om_ Ion Phys_, 5 (1970) 361-380
DECOMPOSITION
OF
a four membered
EXCITED
i-
1
-_..---; c = c ---/ Lc -;,/”
[
3?3
IONS
ring.
K \ H
POLYATOhfiC
H
/
lH
-
1
The four membered ring transition state is preferred to that having five members because of the rarity of the latter3 3, and also because the C3HJ’ ion is believed to have the propargyi structure’”
The proposed vibrational frequencies of AC1 and AC2 are included in Table 3. The ener,o data were taken from the work of Brehm35, who gives: WC.&) AP(C,Hs’) giving AP-IP
=
9.075*0.005
= 11.35 =
2.27
eV
kO.05 eV kO.05
eV.
Trial calculations gave a value of the kinetic shift of about 0.47 eV, which compares very well with 0.45 eV given by Vesta136, so the activation energy was taken to be 1.80 eV. The internal energy distribution of C,HGi, P(E), was taken from the photoelectron spectrum of tra~zs-1,3-butadiene measured by Eland3’. The relevant portion of the curve is cIosely approximated by P(E)
= -11.111 = O-6 =
-23
EZ;
56.001 E-69.564
2.22 < E < 2.72 2.72 =$ E < 2.92
EZ t 16.60 E-26.556
2.92 < E
which is plotted in Fig_ 7. For E !ess than 2.22 eV P(E) is very small, and this value was treated as a paramet,r in th: final calculation. It turns out that the best fit is found for P(E) = 0.02 tL 0.03 (t’ < 2.22). . It must be remembered, however, that this curve corresponds to ionization by helium resonance radiation (21.21 eV), so account must be taken of the range of wavelengths emitted by the present photon source. If one assumes that the internal energy distribution of the molecular ion only depends on the photon energy insofar as it cuts off at hv-I.., the true distribution to be used in these calculations is given by P,(E) = P(E)j;=+‘)
dE’
where R(F) is the relative probability that the photon reIative to the ionisation potential of the molecule).
energy is E’ (measured
Inr. J. Mass Spectrom.
Jon Phys.. 5 (1970) 361-380
P. F. KNEWSTUBB,
FL W. B.EID
Ionization Energy [eV)
J
0 I.8
22
I
1
I
26 X0 Intemai Energy (eV)
I
I
3.4
I
Fig_ 7. internal energy distribution of &?&I, +_ (a) Photoekctron spectrum measured by Eland3’; (b) form assumed for computation.
The form of R(E’) was obtained by srudyin,0 the variation of the height of the parent ion peak from 1,3-butadiene as a f’unction of the wavelength transmitted by the monochromator, and comparing this with the photoionisation cross section given by Brehm 35. The result is shown in Fig. 8, where the uncertainty is rather
Fig. 8. Spectral distribution of tie Iamp output. The points are experimental result-s, and the strai&t line gives the approximation med _for the calculations. ht. I. +7SS SpC*Um.
zG?lP&S., 5 (1370) 361-380
DECOMPOSITION
OF EXCITED
POLYATOMIC
375
IONS
large because of the very low ion currents obtained with dispersed radiation. This indirect procedure had to be adopted because the photon intensity was too low to be distinguished from the background noise on the photomultiplier. For the purposes of computation R(E’) was approximated by the straight line shown in Fig. 8, so that R(E’)
= 3.4-E’
and EL,
= 3.4 eV.
This means that P,(E)
= P(E)(5.78-33.4
E-l-O.5 E’).
The results of the computation are compared with the experimental results in Fig. 9, the theoretical curves again bein, = shifted vertically to agree with the experimental results at a time of 2 ,~sec. Two theoretical curves are given to iilus-
0
1
2
3 4 5 Lifetime(p SK)
6
7
8
Fig. 9. Calculated decay curves for C4H6*, showing the effect of altering the internal energy distribution in the region beIow E = 2.22 eV. (a) P(E) = 0.02; (b) P(E) = 0.03.
trate the effect of varying P(E) in the region below E = 2.22 eV. The curves for decomposition via AC2 only are shown, as the results for AC1 are virtually indistinguishable.
DISCUSSION
I. Experimental
merhod
The validity of the experiments described here depends on the assurance that the ion current measured as being due to daughter ions fro.m a metastaMe Int. J. Mass
Spectmm.
Ion Phys.,
5 (1970)
361-350
P. F. KNEWSTUBB,
376
N. W. REID
transition is just that, and does not contain any contributioneitherfrom other peaks in the mass spxtrum of the sample, or arising from Amy impurity. This is relatively easy to check in a mass spectrometric instrument such as that described here, but, as an additional safeguard, the sample of trimethyl pho.iphate was checked in an anaiytical mass spectrometer (A93 MS9) at 50 eV ionising energy> and the region between the parent and daughter peaks was found to be free of interfering ions. -4nother point to be considered is the effect on the shape of the peaks of the initial thermal energy of the parer3 ions, and any kinetic energy reieased in the decomposition reaction. This was checked by means of a model calcuIation on the decomposition of the n-butane molecular ion GH10 -+ + C3H6+ +- (cM,j which was assumed to proceed with a rate coefficient equal to 2 jc lo5 set-‘. The expected peak .&ape is iliustrated in Fig. 10, the solid line being for the decomposif7 5 I-a6L
..
b
p
i
.-
L
Fig. 10. Computer simu!ation illustrating the expected effect on the peak shapes of initial thermal energy and kioetic energy of decompositior?. * simpie decomposition; - - - - - -, added energies-
tion of ions with zero initial energy, and the release of no kinetic energy of decomposition. The dotted line is for the decomposition of ions having initial thermal energy correspnding to average room temperature, and 18 kcal/mole kinetic energy of decomposition. It can be seen that the effect of these added energies is only appreciabie at the extremes of the trace, where no experimental measurements are made, b--use of interference from the wings of the cormal peaks. It shouId be noted, though, that the curve of Fig. 10 w-as cafculated on the assumption of a constant gate width. This is not actuaiiy the case, as was discussed earlier (eqn. lo), and, since the effective gate width increases as the flight time approaches that of the parent ion, the coliected ion current can show an increase Ieading to curvature of the parent peak to the Iow mass side. This effect can be seen in Fig. 5. Znt. J_ M-S
Spectrum, ion Phys.,
5 (1970) 361--380
DECO.+ZPOSXTION
OF
EXCITED
POLYATOMIC
iONS
377
it is further necessary to be sure that the ion current of daughters is due only to thr effects of unimolecular decompositions of the parent ion. The results on 1,3-butaciiene illustrate this very well, since there is appreciable “smearingout” of the parent peak to its high m&s side, which is not to be expected in the light of the operation of the instrument as given above. If this curvat-ure is due to some other effect, so too could be the curvature of the daughter peak, interpreted above as being due to unimoiecular decompositions of the parent ion. There are four possible expianations of the shape of the parent peak reproduced in Fig. 5: 1. It could be caused by some sort of instrumental defocussing effect; in this case one would expect ail -peaks to be broadened to the high mass side, which has not been observed in practice. In fact there are many more sharp peaks than curved ones in the mass spectra measured in this instrument, in line with the observation in conventional instruments that there are many more ncrmal than metastable pea&s. 2. Elastic scattering of ions by background gas molecules in the flight tube would slow down any ions which suffered collisions, and thus cause tailing of ail peaks to the high mass side. This is unlikely, because of the many sharp peaks to be found, as described above, and is confirmed by measurements of the pressure dependence of the high mass tail. It was found that the intensity at any point in the tail depends on the first power of the pressure, while collision-dependent effects would vary as the square of the pressure. 3. Ion-molecule reactions could be responsible. These could explain ali features of the observed mass spectrum if both lighter and heavier ions than the molecular ion were formed. This is known to be the case for 1,3-butadiene3’, but this explanation is unlike!y for the reason given above, i-e_ the first order pressure dependence of the ion current. 4. It appears most probable, from the above, that the “smearing out” of the peaks is due only to unimolecular decompositions of the parent ions, in which case the tail to high mass of the peak at nz/e = 54 must be due to the detection of neutral species from the decomposition. These will always have flight times ionger than that of the parent ion, and it can readily be shown that the veiocity with which they reach the detector cathode varies linearly as (Z-,-T), where Tp is the flight time of the undissociated parent ion, and ‘1’is the lifetime of the parent ion decomposing to give the particular neutral under consideration. This means that the velocity dependence of the multiplier response is not unduly important in determining whether neutral spzzcies will give a significant output current. Of course, it is necessary to explain why the methyl radical from the decomposition of I,3-butadiene gives a much larger signal than formaldehyde, which appears likely to be the neutral fragment from the dissociation of (CH30)3POt. There are two possible explanations: I. It is possible to derive an equation, analogous to eqn. (IO), relating St,, In?. f. Masz S~~erfronr.Ion Phys., 5 (1970) 361-380
378 the
P_ Fe RNEWSTUBB,
sampling St, =
width for neutrals,
N. W.
REID
to the gate width of the analog output unit, i.e.
1/F,., x Gate width.
Note that F, is not the same as Fl, since eqns. (3), (4) and (5) do not hold for neutrals. In fact, it can be shown that F, depends linearly on the mass of the ion which is decomposing, so that in the case of the trimethyl phosphate molecuiar ion decomposition, l]r;h (and thus St,) will be considerably smaller than for the decomposition of C,H, +. This means that the multiplier output current for a given flux of neutral is smaher in the former case. 2- It is po.ssibIe that the decomposition of (CH,O),PO+ involves the release of some kinetic ener,oy. Most of this will be carried away by the lighter neutral fragment, which will not benefit from the focussing effect of the electric field, and will bave a Xgh probabibty of striking one ofthe field defining plates, thus reducing the flux of neutrals reaching the detector. It must be assumed that IittIe, or no, kinetic ener,ay is released in the decomposition of C,H6+.
A. Trinrerhyl phosphate From Fig. 4 it can be seen that, within the uncertzinty in the various parameters required in the calculation, it is possibie to get very good agreement between theory and experiment for the decomposition of the trimethyl phosphate molecular ion. Since the compuied curves were virtually unaltered by changes in the vibrational frequency patterns of the parent ion and the activated complex, it appears that uncertainties in the activation energy and the internal ener,7 distribution are most important in determining the uncertainty in the computed result. Thus, for a more rigcrous test of the theory, a more accurate knowledge of these quantities is required. Nevertheless, it is interesting that a relatively iarge uncertainty in all these parameters only results in a small spread in the computed curves. in other words, if the experimentai ree;ults had been more than about 20 % different from their actual vaiues it would have been impossibie to reconcile them with the predictions of the QET. It can thus be said that these results represent further support for the theory. The convolution routine given by eqn. (7) reveals an important property of the instrument. The point of convergence of the sum taken there gives the maxi12um vaI*z? af the rate coeEcient which contributes to the “smearing out” of the peaks, i.e. the maximum rate coefficient measurable here. With the field strength normally used (3000 V/m) this maximum rate is about 2 x IO5 set-‘. This ensures that the daughter ic-ns detected from the metastable transition are incapab!e of further decomposition, which would have rendered the analysis of the results considerably more complicated. Any parent ion which decomposes ht.
J- Mess Spectrom_Ion Ph,-s, 5 (1970)
361-380
DECOMPOSITION
OF
EXCITED
POLYATO_MIC
379
IONS
with a rate coefficient less than 2 x lo6 set-’ has insufficient internal energy to cause further decomposition of the dau&ter ion, as is illustrated by a particular example. Consider decomposition of P,, via activated complex AC:, assuming that the activation energ is 2,-l eV. To decompose with a rate coegiicient equal to 2 x 106 see-’ this model of the parent ion requires 1.55 eV of internal ener,y. The further decomposition of the io:l ~C~YI,O)~HPO 4 is known, and gives rise to a metastable peak, but the appearance poten:iai of the next daughter ion, (CH@)HaPO’ is given as 13_9C_O.4eV2’, which corresponds to the molecular ion having 3.1 eV of internal ener_ey,so clearly this further decomposition is unlikeiy to upset the measured decay curve_ 3.
i,3-Butadierze
Here, too, the calculated curves show excellent agreement with the experimental results. This agreement is more satisfactory than that of the previdus exampIe, because the parameters required in the ealculaticn are known to a greater degree of precision, although it must be remembered that the uncertainty in the experimental results is larger, as a consequence of the use of photoionisation Nevertheless, the extent of the agreement is most gratifying_ In this case, too, the possibility of further decompositions of the daughter ion can be excluded. For example, decomposition via AC2 requires an internal energy of 2.29 eV for the parent ion to give a rate coefficient equal to 2 x LG6set- r. The appearance potential oi the next daughter ion (C,H,+) is 12.4-1-0.1 eV3’, corresponding to an internal energy of the molecular ion of 3.37 eV.
We wish to acknowledge with thanks the suppc~%of one of us (N. W. R.) by an Elsie Ballot Scholarship, and also by a maintenance grant from the South African Council for Scientific and Industrial Research. Thanks are also due to the Royai Society fOi a grant for apparatus.
REFERENCES
1 2 3 4 5 6 7 8 9
J. A-HIPPLE, R-E. Fox AND E. U.CONDON, Phys. RG., 68 (!945)54. 3. A. HwP~_E, Phys- Rec., 71 (1947)594. J. k~OMIGXY, Buli.Sot_ ChimBelges,70 (1961) 291. N. D.COGGESHALL,J. Chem. Phys., 37 (1962)X67. G. A_ Muccm~, W- H. HAZUXLLAND R. A, BXRKER,.J.Phys- Chem., 68 (1964) 261. G. M. BEGUN &ND L. LMDAU, 1. Chem. Phys., 35 (1961) 547. L. FRIEDSWN MD A. P. IXSA, J. Chem. Phys., 36 (1962) lil82. G. ht. BEGUN XND L. LANDAU, J. Chem. Phys., 36 (1962) lC83. A. S. Nmox AXD A. F. SCI_UNSA, J. Cfzem. Phys., 4% (1966) 4327. Inr. J_ Mass
Spectrom.
Ion Ph_vs., 5 (1970) 361-380
380
P. F. KNEWSTUBB,
N. W. REID
3. S- DELDERFIEW xzcm 3. G. REUBEX, Inr.J. L%ZassSpeczrom. 10~ P&s., 2 (1969)25. II 3. C. SCHUG,]_ Chenr_ Ph,-s.,40 (1964) 1283. 12 5. L. DOYX~LY AYD H- E. CARR. Phys. Ret-, 93 (L954) 111. 13 A. S. Xm-rox am A. F. Scr~suxx~. J. Chem_ Phys_, 40 (1964) 718. 14 J. C_ SCHUG, J_ Chem. Phys., N (1964) 1283. 15 C. OITNGER, 2. h’arm-firs&, 22a (1967) 20_ 16 I. H~TELXXD C. OITXXGER, Z. Narurforsch., 22s (1967) 1141. 17 H. D. BECKEY, H. KEY, K_ LEVSEN ohm G. TEXSCHERT, ht. .i_ Ma Specrrom. Ion Phys., 2 (1969) 101. 18 H. TATARCZYK AXD U. vex ZAHN, 2. Narurfirsch., 2Ga (1965) 1708. L 19 H. BENZ AE~C X-I.W. BRO\\X. J_ Chem. Phys_, 48 (1968) 4308. 20 P. F. KFZTW~I-UEIBXND N. W_ RJZID, in D. PRICE AJ. WILLIAMS (Editors), L?yzm.vic Mum Specrrometry, Vol. 1, Heyden-Sadtler, London, pp_ 59-70. 21 (a) H_ S. W_ M~EY ASI E. I-LS. BURHOP, Ekcrronic and roorric Impact Phenomena, Clarendon Press, o.xf-orci, 1952. (b) P. MA~DEVAX, G. D_ MAGS~;SOS, J. K. LEYTOX XSD C. E. CARLSON, Phys Rec., 130 <1965) AIS07; (c)E-L. SCHR~V,A.J. H.EOERBOO~,W.KLEI~~AABDJ.KISTE~URER, PhJsica, 32(1966)749. 22 D. L. DUGGER am R. W. KISER, 1. Chenr. P&-L, 47 (1967) 5054. 23 H. M_ Ros~~sroce, M. B. W.~LLESSTEZS, A. L. %‘AHRHFGTI G AXP H. EYRISG, Proc. _?'a& i0 R. J. GDLE?MX,
Acad. Scf. U.S., 38 (1952) 667. (!3ee also ref. 36 fix- a review of the current status of the QET-) 21 G. Z. WHITTEN A>D B. S. ~XXSISOVITCH, 3. Chem. Ph_vs_,58 (1963) 2466.
25 N. B. COLTHUP, L. H. DALY AND S. E. WIBERLY, Introduction to Infrared and Raman Spectroscopy, Academic Tress, New York, I964 26 L. J. BELU.\~Y, Adcances ir,Infared Group Frequencies, Methen, London, 1968. 27 D. A. Btius, E. 3. GXLEGOS AXD R_ W. KLSER, -r_ P&x. Chem., 7C (i.966) 2614. 28 J. C. Tou, L. P. Hess AND A_ L. WAHRHXFTIG, J. Chem. Phys-, 45 (I 966) 2129. 29 W. A. CHVPICA A&D M. K.+MISSKY, J. Chem. Phys., 35 (1961) 1991. 30 R. K. HARRIS, Spcctrochim. Acta, 20 (1964) 1129. 3 I J. H. D. ELAND, hr. J_ &fus Spectrom. Zen Phys., 2 (1969) 47132 A. C. PARR xm F_ A_ EIDER. J_ Chem. P.+s., 49 (1968) 2659. 33 F. W. MC~FFERTY, in F. W. l&'kL&FFERTY (Editor), Mass Spectrometry of Organic Ions, Academic Press, New York, 1963, pp. 331-40. 34 J. COLLIN XSD F. P. bSSI?iG, J_ Am. Chem. SOC.. 79 (1957) 584% 35 B. BREHM, 2. Xaturforsch., 21a (1966) 196. 36 M. L. VEST=, in P. Amroos (Editor), Fundamental Processes in Radiation Chemistr_v, Interscience, New Yor!c, 1965, pp_ 59-1 IS. 37 I_ Kov~so. I_ OMUUR~L ,GZZ I_ Trlx~x.*, J. Cltem. Whys_, 44 (1966) 3850. ht. J. Mass Spectrom. Ion Phw., 5 (1970) 36X-380
Journal of MQSS Spectronzerry and Ion Pizysics
Elsevier Publishing Company, Amsterdam. Printed in the Netherlands
361
THE UNIMOLECULAR DECOMPOSITION OF EXCITED POLYATOMIC IONS STUDIED BY TIME OF FLIGHT MASS SPECTROMETRY
P. F. Kh~WSTUBB
Department
AN3
of Physical
N. W_ REID
Chemistry,
lenrfeld
Road, Cambridge
CB2 IEP (England)
(Received June 3rd, 1970; in final form August ISih, 1970)
ABSTRACT
The metastable transitions of the molecular ions of trimethyl phosphate and 1,3-butadiene have been studied in a specially modified time of flight mass dpectrometer, ionisation in the latter case being effected by photon impact. The results have been interpreted on the basis of the quasi-equilibrium theory of mass spectrometry, which has proved to describe them quite well.
INTRODUCTION
The study of so-called me&stable ions in mass spectrometry is one which has received considerable attention in recent years. One of the important aspects of this work is the measurement of the rate of decomposition of the parent ion, since this represents one of the purest forms of unimolecular decomposition to be found, and comparisons can often be made with unimolecular rate theory without the complications introduced by competitive and consecutive reactions. Pioneering work in this field was carried out by Hipple and co-workers1*2, who varied the residence times of the parent ions in the ion source by altering the repeller potential, and were thus able to study the progress of the reaction with time. There are many subsequent examples of the application of his technique, both to the decomposition of positive3-” and negative ions12_ A closely related method is that of Newton and Sciamanna’ 3, who produced variations in the ion residence times by altering the main accelerating voltage. The above experiments have produced rather cotiicting results, in that some workers have found that a particuiar decomposition is described by one, two, or even three discrete rate constants, while others have found that the same decomposition can best be described by a smooth distribution of rate coefficients, as is predicted by the quasi-equilibrium theory of mass spectrometry (QET). -4 drawback to this technique is the rather small range of reaction times that is accessible Inr. J. Mass Spectrom.
Ion Phys., 5 (1970) 361-380
P. F. KPU’EWSTUBB,
362
N. W.
REID
(generally from I. to 10 microseconds). It has been pointed out by Schug14 that ratht:r greater precision is required for these measurements than is generally realised (or available), and he gives an illuminating example. Ottinger, using an ele,uant apparatus’ 5s16, has been able to extend the time range by several orders of magnitude, and, in a careful study of several metastable trarrjitions, has found that all of these are best described by a distribution of rate coefiicients. The same conclusion was reached by Beckey et al.17, who were able to work down to very short times indeed using a field ionisation mass spectrometer_ Several other measurements have been carried out, e.g. by Tatarczyk and von ZIahn”, who worked at relatively long reaction times, and obtained results in agreement with the QF~, and by Benz and Brownlg, who measured half lives for metastable transitions in a cycloidal mass spectrometer by studying the peak shapes. They, in contrast, found only one case which was described by a distribution of rate coefficients, the others al1 fitting a model corresponding to decomposition via a single rate coefficient, but were unfortunately limited to a very narrow range of reaction times Thus it can be seen that there is in the literature considerabie disagreelment as to the time dependence of these decomposition reactions, and thus doubt as to whether the QET accurately reffects the behaviour of real systems. It was therefore decided to develop a new type of apparatus for the measurement of ionic lifetimes”, the experimental results to be compared with the predictions of the QET.
APPARATUS
The equipment has been described previously’*, and is, briefly: as follows. A Bendix, model 14-101 mass spectrometer has been modified by the removal of the drift tube liner, the X and Y deflection plates and the ion lens. The flight tube contains instead an assembly of field defining plates, fed from a potential divider, so that a constaut electric field of some 3000 V per metre is maintained over its length. The effect on the mass spectra is as described in ref. 20, i.e. in the absence of metastable transitions the mass spectrum looks normal, except that all flight times are doubled. If a met&able transition takes place the daughter ions will be accelerated away from the bunch of undissociated parent ions, and the result is a “smearing out” of the peaks. The time of arrival of such daughter ions is simply related to the fifetime of the corresponding parent ion. A typical trace is shown in Fig. 1. The mod&d mass spectrometer has also been provided with a photoionisation source. The light is produced by a repetitively pulsed electrical discharge in a suitable gas, constricted by a boron nitride capillary_ The repetition rate can be varied between about 5 and I5 kHz, and the duration of each flash is approximately 130 nsec- An important improveme& over the apparatus as described previously Iis_ 3- Mass Specirom. Ion Plzys., 5 (1970)
361-380
DECOMPOSITION
OF
110
EXCITED
POLYATOMIC
363
IONS
140
Fig. I_ 15 volt electron impact spectrum of trimethyl phosphate, showing the effect of the metas::ble transition (CH,O).PO+ -+ (CH30jzHPO’ +_(HCHO). Sensitivity 0.01 nA FSD; time &onstint 1 sec.
has been brought about by the instaliation of a vacuum monochromator of SeyaNamioka geometry, fitted with a Hilger and Watts type K68 grating, of 1 m radius of curvature. The inlet to the monochromator is a 0.35 mm hole and the exit slit is 4.0 by 0-i mm. The optical path is completely windowless, and, after passing through the ion source, the light beam is detected by a type lP28 photomultiplier sensitised by sodium salicyiate. The norma Bendix electron impact ion source was also retained. Typical operating pressures were 2 to 5 x IOm5tot-r in the source region, and somewhat less in the flight tube.
THEORY Of OPERATlOS
Consider the metastable transition AB+ +A’fB Ml
“2
(9 =Z3
with the notation to be used indicated in the following schematic representation of the flight tube: Ionisation Time
Velocity Distance
! 0 C Q
Becomposition --f
T Cl x
.
Multiplfer stack 1 1 T+t, T+t,+tz VZ d d:y Int. .l. Mass Spectrom. Ion H.w.,
5 (1970)
361-380
364
P. F_ KNEWSTUBS,
N_ W.
REID
If the electric field is E V/m over the first d metres of the ffight tube (field defining plates) and zero in the multiplier stack (a tube fixed to the entrance end of the Bendix electron muhipIier), and if the electronic charge is e, it can readily be shown that: u2 = (eET)/m, t, =
-?-(eEtl)/.ml
- (mJm,)Tt
[(m,/m,)‘T*
(2) +2(d-
eET2/2m,)
m,/eE]’
(3)
and t2 = y!(eET/m
I + eEr , jm2)
on the assumption that all ions are singly charged. The total flight time 2-f = Tit~-I-r*
(5)
is evahtated as above, and a conversion curve established, so that measured fiight times of daughter ions can be converted to lifetimes of the corresponding parent ion. The ion current due to daughter ions of a metastable transition arriving with flight time T, is proportional to the number of decompositions of the parent ion, yielding that charged fragment. occurring between times t and ttSt. The times t and T1 are related via equations (3): (4) and (5): as mentioned above, while 6t is the gate width of the anaIog output unit, similarly converted to a scale of decomposition time. If the decomposition is governed by a singie rate coefiicient, k, this means that 1 a [exp(-kt)-exp[-k(ti-St)]]
(5)
while if several rate coefficients are operative I CC CNiexp(-kit)-exp[-ki(tibr)l = &Nrexp(--k;t)[l i
-exp(-kist)]
where the summation may be extended to an integration to cover the case of a distribution of rate coefficients as predicted, for exampfe, by the QJZT.N, is the relative probabiiity of decomposition via ki. Two points arise from the above analysis: (1) The charged fra&ments from the metastable transition wil! strike the detector cathode with varying velocities, depending on their time offormation (SC% eqn. (2)). It is thus certain that I in eqns. (5) and (7j will not correspond exactly to the measured ion current, but rather to that quantity corrected for the above variation in velocity. . There is some disagreement in the literature as to the precise form of such a correction’l, but in this cast, where-all the particles under consideration have the Intel Mars Specfrom IonPhys.,
5 (1970)361-380
DECOMPOSITIC)N
OF
EXCITED
POLYATOMIC
365
IONS
same mass and structure, it seems most appropriate to assume that the muhipher response is directIy proportional to the velocity of the incident ion, i.e.
1 = Lsured x
velocity of daughter
(T = 0) = r x F
velocity
(T=
of daughter
T)
*
-
(2) As mentioned above, a necessary quantity in the analysis of the resuhs is &, the gate width of the analog output units on a scale of decomposition time. Since the equation relating flight time and decomposition time is quadratic it can not be assumed that 6r is constant. If the gate width is denoted by bT,, and knowing that & = T+t,ft?
(5)
we can say that 6T, = (1 -I- &,/dT; = r;; - 6t or
6t
&J dT)Et
(9)
= (I/‘&) - bT,.
(10)
The factors l/F, and Fare conveniently calculated at the same time as the conversion curve, using eqns. (3) and (4). A computer program was developed for this purpose, and typical values of l/F, are 4.7 at T = 0 and 6.6 at T = IO psec, while F varies from 1.00 to 1.36. The value of ST, was measured to be approximately 100 nsec, but trial ca!cuIations showed that varying this by a factor of ten in either direction had no observable effect on the result.
It has proved possible to operate the instrument using ionisation by both eIectron and photon impact, and an example of each is presented below. A. Electron impact ionisation The metastable
peak due to the transition
(CH30),PO’ --, (CH30)2HPOf
i
(HCHO)
occu.rring in the mass spectrum of trimethyl phosphate, has been observed by Dugger and Kiser’“. This process is very well suited to study in the present apparatus because of the relatively large mass ions, and the lack of interfering peaks this decomposition have been measured and daughter peaks was shown in Fig.
difference between the parent and daughter in the intervening region. The kinetics of aiready’ ‘, and a typicaI trace of the parent 1, Int. J_ Mass Spectmm. Ion Phys., 6 (1970) 361-380
366
P. F. KNEWSTUBB,
N. W.
REID
Fig. 2 shows the decay curve obtained from the average of several traces simiiar to that of Fig. l_ The iwo sets of points were obtained from sets of experiments at two different values of the scan rate of the analog output unit, and are
0s2
20
3.0
4.0
5.0
60
7.0
8.0
9.0
Lifetime (psec.)
Fig. 2. Unimolecular decay curve for the decomposition of the molecular ion of trimethyl phosphate. Ion&&on by 50 eV ekctrons. (0) at scan rate 2: (0) at scan rate I.
plotted separately in this instance, rather than taking the combined average as was done previously, to illustrate the scatter inherent in the reslults. The error bars give the estimated uncertainty, which is the same for both sets of points. Ionisation was by impact of 50 eV electrons. As Fig. 2 is a smooth curve, it is probable that the results are in agreement wjth the Q?Zr, although it must be pointed out that decay via a single rate coefficient wouid not give a straight line on the above plot because 6t is not constant. It was decided to carry out a complete QJX calculation to give a quantitaiive check on the validity of the theory- On the basis of the QET the rate coeEcient for the decomposition of an ion having internal energy E is23: _,
where N’(E) is the number of states of the activated complex up to energy E, p(E) is the density of states of the parlznt ion at energy E, E, is the activation energy of the decomposition reaction and h is Plan&s constant. Before this equation can be applied the following quantities must be known: Vi, the vibrational frequencies of the parent ion, Vsi, the vibraticnal frequencies of the activated complex, P(E), th e relative probability that the parent ion has internal energy E, and E,, BS above. The approxiznation is made in this work, as in many other cases, that the vibrational frequencies of %he parent ion are the same as those of the neutral Int. J. Mass Spectrom. Ion Phys., 5 (1970) 361-380
DECO_MPOSfTlON
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EXCITED
POLYATOMIC
367
IONS
species. It is further assumed that the parent ion and the activated complex can be considered as a collection of Ioosely coupled harmonic osciliators, as this ,oreatIy simplifies the computation of N’(E-E,) and p(E). N’(E-~5~) was evaluated by direct count up to an energy correspording to 15000 states, and thereafter the approximation of Whitten and Rabinovitch’* was used. The latter equation (digerentiated) was used for al1 calculations of (E)_ It appears that no complete vibrational frequency assignrnent is avaifable for trimethyl phosphate, so some frequencies had to be estimated by comparison with analogous compounds_ Two slight& different sets of freq!lencies were proposed to allow an estimate of the importance of errors in this assignment. These are shown in Table 1, and the two modek are designated PI and Pu. TABLE
I
VIBRATIONAL
FREQUENCIES
OF THE TRIMETHI’L
Desfgrrarion
Descrip fion
PHOSPHATE
stretch C-H bend CH3 rock CH 3 torsion” P-O stretch P-O bend’ P-O stretch P-O stretch P-O bend’ P-O bend* C-O stretch C-O-P bend”
PSI
t’29.30
3000 1500 1250 250 1250 250
1’31.32
iOO0
~.I-9 ~v10--18 “19-24 f’ 25-27 =‘tS
l’33 t’3.z F35.36 p37-39 I’d0
ION
Frequency (cm - ’ ) PX
C-H
MOLECULAR
-45
759 1000 1000 1250 750
is00
1250 250 1250 250 1000 750 1000 750 1250 500
-1 These frequencies were estimated. All others were rounded off to the nearest 250 cm-l values given by CoIthup et aI.25 and Bellamy’s.
The activated
The possibility
compIex is assumed to have the four membered
of the five membered
ring transition
from the
ring structure
state
H CH,O
o-c/ \p/
/‘H
ht. J. Mass Spectrum. Icn Phys., 5 (1970) 361-380
368
P. F. KNEWSTUBB,
N. W.
REILi
has much to commend it, but it was not adopted in this case as elimination of HCHO -would leave (CH,O),POH, requiring migration of the hydrogen from the oxygen atom to the phosphorus before the next HCHO group could be eliminated. The successive elimination of HCHO is described by Bafus et aL2’. The frequency changes made in attaining the activated complex configuration were analogous to those used by earlier workers (e.g. ref. 28). In fact, it was again felt safer tn postulate two slightIy different sets of frequency changes in going to the activated complex, to check on the importance of errors. There are thus two models of the activated complex for each model of the parert ion, and these are designated AC:, AC:, SC,‘, and AC; respectively, where the subscript gives the relevant parent model. The necessary frequency changes are given in Table 2, and the Aculations were carried out for all four possible reaction paths. TABLE
2
FREQUENCY
CHXSGES
MADE TO THE TR:MmYL
PHOSPHATE
MOLECULtrR
ION TO GIVE THE ACTIVATED
COMPJmEX CONFIGLXATiOX
Frequency changed
VI VIO.
11
VIZ
New
cake
(cm-‘)
AC,:
ACI’
1500
500
750
unchanged
v19
500
925
500
933 937 =40
1500
500
1500
750
750
750
unchanged
250
500
500 750
750 250
unchanged 500 unchanged reatiion coordinate 15%
1000
1500
1590
500
1030
Earlier workers have approximated E, by the difference in appearance poten-
tials of the parent and daughter ions, but this is unsatisfactory, particularly in the case of decomposition of the molecular ion, because the appearance potential of a daughter ion is not just the threshold energy for its production, but is rather the minimum energy at which it is produced rapidly enough to be detected as such. As
is well known, this minimum
rate is of the order of 10” set-’
if the measurement
is
made in a magnetic sector instrument, and the internal ener,T of the parent ion required to give this rate of decomposition (i.e. the difFerence in appearance potentiais) is equal to the activation energy plus a certain excess, known as the kinetic shift- The correct procedure for estimating E, is to carry out the rate calculatioti for values ofE, less than the: difference in appearance potentials (denoted as A?‘---I;P), until one is foundwhich gives k(AP-IP) s 10’ set-‘. This is then the correct value.
lirf. J.
Mass Sgectrom. Ion Ptiys_, 5 (1970) 361-380
DECOMPOSITION
OF
EXCITED
For the case of trimethyl
POLYATOMIC
phosphate
369
Bafus et aL2’ give
IP[(CH30)3PO]
= 10.77+_0.3
AP[(CH,O),HPO+]
= 11.9
kO.2 eV
.- .(AP-IP)
=
+0.35
1.1
IONS
eV
eV.
A trial calculation showed that the kinetic shift was less than 0.3 eV, so the calculations were carried out for E, equal to 0.9, 1.0, 1.1, 1.2 and I.3 eV. Chnpka and Kaminskyz9 have shown that P(E) can be obtained experimentally. Forionisation by electron impact it is the second derivat.ive of the total ionisation as a function of ener,7. Unfortunately, this has not been measured for trimethyl phosphate, but the general form is common to many compounds, so a curve similar to theirs for n-butane was assumed as a first approximation. A portion of this curve is reproduced in Fig. 3.
I
150
I
I
2
1
I
3
Errergy (e!ectron volts)
Fig. 3. Assumed internal energy distribution for (CHaO)xPO*. imation which proved adequate for computational purposes.
The straight line gives the approx-
A theoretical decay curve to be compared with the experimental results may be obtained by putting the function for P(E) into eqn. (6) together with the values of k(E) calculated using eqn. (10). A s was pointed out earlier, the summation of eqn. (6) should be replaced by integration, but it proved suficiently accurate to sum with steps of E equal to 0.01 eV. This sum converges within 100 steps, i.e. 1.0 eV, so P(E) may be approximated by the straight line drawn in Fig. 3, which is described by P(E)
= 42.4-
18.4E.
This is referred to as distribution C. Trimethyl phosphate has 45 vibrations, as compared with 36 for n-butane, so it is highly likely that the true form for P(E) will peak at a higher value ofE than Int. J. Muss
Spectrom.
Ion Phys.,
5 (1970)
361-380
370
P. F. KNEWSTUBB,
N. W.
REID
is predicted by the internal energy distribution assumed above. To allow for this possibility two further distributions were postulated: (ij distribution B; P(E) (ii> distribution A; P(E)
= constant =
42.4+ 18.4 E_
Distribution B described, approximately, the case where the maximum is in the aiddie of the region of interest, and distribution A that where it is at higher energy. The results of these calculations, for all assumed values of E3+ and all three internal energy distributions, lie on or between the lines shown in Fig. 4, which
0
1
2
3 4 5 6 tifetkf? (p KC.)
7
8
Fig. 4. Computed decay curves for (CH,O)JPO+, tal points are included.
showing the maximum
spread. The experimen-
shows, for PI decomposing via AC:, rhe maximum spread in the calculated decay curves_ The calculated curves were shifted vertically to coincide with the experimental results at a time of 2 WC, and the experimental points are included in the figure to allow a comparison. The calculated decay curves for the other thret: assumed reaction paths (i.e. PI + AC:, etc.) are not inc1ildc.d here, since they are practically indistinguishable from those of Fig. 4. thus
B. Photoionisation The metastable tr.ansition studied using photcioaisation C4H6-f
--, C&Is+
f
Ini. J_ M& SFecrrom. Ion P&s.,
(CH,). 5 (1970)
361-380
was
DECOMPOSITION
OF
EXCITED
POLYATOMIC
371
IONS
Unfortunately, sufficient intensity for quantitative measurements was only availabie if the grating was set to its zero orger position, giving no waveiength selection. Even so, the detection system had to be operated at its mtimum sensitivity, and the recorded signal was rather noisy. In an attempt to obtain a smooth result, and yet avoid the subjective procedure known as “drawing a smooth curve through the trace” the following approach was adopted. The length of the recorded chart was divided into 0.5 cm divisions, and the integrator count read off for each of these. This was repeated for several scans of the required portion of the mass spectrum and the count in each “channel” summed, giving, in a crude sort of way, the effect of multichannel analysis. The histogram obtained in this way is shown in Fig_ 5, and the decay curve of Fig. 6 was calculated from &is as before. Since 36 32
2
24
e 20 t a = 16 zz v 12 8 4
I
L
mfez39 * I 5 IO
20
Ckmel
25
30
. 53. I54 1 40 35
1I 45
Nmlxr
Fig. 5. Histogram presentation of the photoionisation mass spectrum the effect of the metastable transition CaH6* + CBH9++(CH3).
Fig. 6. Ur.imotecufar
decay curve for the decomposition
of 1,3-butadiene,
of the molecular
showing
ion of_ 1,3-butadiene.
Inr. J. Mass Spectrorn. Ion Phys., 5 (1970)
361-380
372
P.
F. KNEWSTUBB,
N. W.
REID
the signal strength was so much lower than that given by electron impact ionisation, the estimated uncertainty is correspondingly greater, as shown by the error bars. The rheorztical situation is considerably happier than for the previous example, though, and a complete vibrational frequency assignment is available3’. This is reproduced in 7kbIe 3, with the excepiion of vg, the symmetric C=C stretching frequency, which is given the value of 1400 cm-‘, as measured by Elandj’ for the molecular ion_ TABLE
3
VIEK.ATIONAL
FREQLEXCIES
OF THE ACTIVATED
TJOS!S
Description
OF THE 1,3-BUTADIESE MOLECULAR ION, AXD TWO POSSIBLE CONFXGURACOMPLEX
Desi~mnation Parezt
Frequency (cm-‘) AC1
C-H C-H
C-H
stretch stretch
C-H C-K C-H GH C-H
stretch stretch stretch stretch bend bend
C-C C-C
stretch stretch
c- C
stretch
C-C-C bend C-C-C bend CH, scissor CH+ scissor CH, CHt
rock rock
3014
3014
3014
3056
3056
3056
3101 3102 3014
3101 3102 1400
3101 3102 1400
2985
2985
2985
1379 1285
1279 1285
1279 1285
1400 1599 1205 513 301 l&2
reaction
1355
890 987 686 520
CH wag CH
wag torsion CHt twist CH2 twist
AC2
coordinate
1599
1599
1400 5i3 301 1-2
1205 513 301 I&Q
1385
1385
890 987 686 520
s90 987 686 520
C-C
153
900
900
C&
967 1013 910
967 1013 910
700 1013 700
909
909
909
=g
CH,wag
Two forms of the activated complex are suggested for this decomposition. The first is based on the idea 32 that at energies below the threshold of the above process the sk.e!etal hydrogen atoms become mobile, so that the I,Zbutadiene configuration is accessible, and can decompose by simple C-C cleavage. [C&=C==CH+CHJ
+_
@CO
The second form, ACZ, allows for decomposition via a transition state.containing Int. 3. .Mu.vSprct~om_ Ion Phys_, 5 (1970) 361-380
DECOMPOSITION
OF
a four membered
EXCITED
i-
1
-_..---; c = c ---/ Lc -;,/”
[
3?3
IONS
ring.
K \ H
POLYATOhfiC
H
/
lH
-
1
The four membered ring transition state is preferred to that having five members because of the rarity of the latter3 3, and also because the C3HJ’ ion is believed to have the propargyi structure’”
The proposed vibrational frequencies of AC1 and AC2 are included in Table 3. The ener,o data were taken from the work of Brehm35, who gives: WC.&) AP(C,Hs’) giving AP-IP
=
9.075*0.005
= 11.35 =
2.27
eV
kO.05 eV kO.05
eV.
Trial calculations gave a value of the kinetic shift of about 0.47 eV, which compares very well with 0.45 eV given by Vesta136, so the activation energy was taken to be 1.80 eV. The internal energy distribution of C,HGi, P(E), was taken from the photoelectron spectrum of tra~zs-1,3-butadiene measured by Eland3’. The relevant portion of the curve is cIosely approximated by P(E)
= -11.111 = O-6 =
-23
EZ;
56.001 E-69.564
2.22 < E < 2.72 2.72 =$ E < 2.92
EZ t 16.60 E-26.556
2.92 < E
which is plotted in Fig_ 7. For E !ess than 2.22 eV P(E) is very small, and this value was treated as a paramet,r in th: final calculation. It turns out that the best fit is found for P(E) = 0.02 tL 0.03 (t’ < 2.22). . It must be remembered, however, that this curve corresponds to ionization by helium resonance radiation (21.21 eV), so account must be taken of the range of wavelengths emitted by the present photon source. If one assumes that the internal energy distribution of the molecular ion only depends on the photon energy insofar as it cuts off at hv-I.., the true distribution to be used in these calculations is given by P,(E) = P(E)j;=+‘)
dE’
where R(F) is the relative probability that the photon reIative to the ionisation potential of the molecule).
energy is E’ (measured
Inr. J. Mass Spectrom.
Jon Phys.. 5 (1970) 361-380
P. F. KNEWSTUBB,
FL W. B.EID
Ionization Energy [eV)
J
0 I.8
22
I
1
I
26 X0 Intemai Energy (eV)
I
I
3.4
I
Fig_ 7. internal energy distribution of &?&I, +_ (a) Photoekctron spectrum measured by Eland3’; (b) form assumed for computation.
The form of R(E’) was obtained by srudyin,0 the variation of the height of the parent ion peak from 1,3-butadiene as a f’unction of the wavelength transmitted by the monochromator, and comparing this with the photoionisation cross section given by Brehm 35. The result is shown in Fig. 8, where the uncertainty is rather
Fig. 8. Spectral distribution of tie Iamp output. The points are experimental result-s, and the strai&t line gives the approximation med _for the calculations. ht. I. +7SS SpC*Um.
zG?lP&S., 5 (1370) 361-380
DECOMPOSITION
OF EXCITED
POLYATOMIC
375
IONS
large because of the very low ion currents obtained with dispersed radiation. This indirect procedure had to be adopted because the photon intensity was too low to be distinguished from the background noise on the photomultiplier. For the purposes of computation R(E’) was approximated by the straight line shown in Fig. 8, so that R(E’)
= 3.4-E’
and EL,
= 3.4 eV.
This means that P,(E)
= P(E)(5.78-33.4
E-l-O.5 E’).
The results of the computation are compared with the experimental results in Fig. 9, the theoretical curves again bein, = shifted vertically to agree with the experimental results at a time of 2 ,~sec. Two theoretical curves are given to iilus-
0
1
2
3 4 5 Lifetime(p SK)
6
7
8
Fig. 9. Calculated decay curves for C4H6*, showing the effect of altering the internal energy distribution in the region beIow E = 2.22 eV. (a) P(E) = 0.02; (b) P(E) = 0.03.
trate the effect of varying P(E) in the region below E = 2.22 eV. The curves for decomposition via AC2 only are shown, as the results for AC1 are virtually indistinguishable.
DISCUSSION
I. Experimental
merhod
The validity of the experiments described here depends on the assurance that the ion current measured as being due to daughter ions fro.m a metastaMe Int. J. Mass
Spectmm.
Ion Phys.,
5 (1970)
361-350
P. F. KNEWSTUBB,
376
N. W. REID
transition is just that, and does not contain any contributioneitherfrom other peaks in the mass spxtrum of the sample, or arising from Amy impurity. This is relatively easy to check in a mass spectrometric instrument such as that described here, but, as an additional safeguard, the sample of trimethyl pho.iphate was checked in an anaiytical mass spectrometer (A93 MS9) at 50 eV ionising energy> and the region between the parent and daughter peaks was found to be free of interfering ions. -4nother point to be considered is the effect on the shape of the peaks of the initial thermal energy of the parer3 ions, and any kinetic energy reieased in the decomposition reaction. This was checked by means of a model calcuIation on the decomposition of the n-butane molecular ion GH10 -+ + C3H6+ +- (cM,j which was assumed to proceed with a rate coefficient equal to 2 jc lo5 set-‘. The expected peak .&ape is iliustrated in Fig. 10, the solid line being for the decomposif7 5 I-a6L
..
b
p
i
.-
L
Fig. 10. Computer simu!ation illustrating the expected effect on the peak shapes of initial thermal energy and kioetic energy of decompositior?. * simpie decomposition; - - - - - -, added energies-
tion of ions with zero initial energy, and the release of no kinetic energy of decomposition. The dotted line is for the decomposition of ions having initial thermal energy correspnding to average room temperature, and 18 kcal/mole kinetic energy of decomposition. It can be seen that the effect of these added energies is only appreciabie at the extremes of the trace, where no experimental measurements are made, b--use of interference from the wings of the cormal peaks. It shouId be noted, though, that the curve of Fig. 10 w-as cafculated on the assumption of a constant gate width. This is not actuaiiy the case, as was discussed earlier (eqn. lo), and, since the effective gate width increases as the flight time approaches that of the parent ion, the coliected ion current can show an increase Ieading to curvature of the parent peak to the Iow mass side. This effect can be seen in Fig. 5. Znt. J_ M-S
Spectrum, ion Phys.,
5 (1970) 361--380
DECO.+ZPOSXTION
OF
EXCITED
POLYATOMIC
iONS
377
it is further necessary to be sure that the ion current of daughters is due only to thr effects of unimolecular decompositions of the parent ion. The results on 1,3-butaciiene illustrate this very well, since there is appreciable “smearingout” of the parent peak to its high m&s side, which is not to be expected in the light of the operation of the instrument as given above. If this curvat-ure is due to some other effect, so too could be the curvature of the daughter peak, interpreted above as being due to unimoiecular decompositions of the parent ion. There are four possible expianations of the shape of the parent peak reproduced in Fig. 5: 1. It could be caused by some sort of instrumental defocussing effect; in this case one would expect ail -peaks to be broadened to the high mass side, which has not been observed in practice. In fact there are many more sharp peaks than curved ones in the mass spectra measured in this instrument, in line with the observation in conventional instruments that there are many more ncrmal than metastable pea&s. 2. Elastic scattering of ions by background gas molecules in the flight tube would slow down any ions which suffered collisions, and thus cause tailing of ail peaks to the high mass side. This is unlikely, because of the many sharp peaks to be found, as described above, and is confirmed by measurements of the pressure dependence of the high mass tail. It was found that the intensity at any point in the tail depends on the first power of the pressure, while collision-dependent effects would vary as the square of the pressure. 3. Ion-molecule reactions could be responsible. These could explain ali features of the observed mass spectrum if both lighter and heavier ions than the molecular ion were formed. This is known to be the case for 1,3-butadiene3’, but this explanation is unlike!y for the reason given above, i-e_ the first order pressure dependence of the ion current. 4. It appears most probable, from the above, that the “smearing out” of the peaks is due only to unimolecular decompositions of the parent ions, in which case the tail to high mass of the peak at nz/e = 54 must be due to the detection of neutral species from the decomposition. These will always have flight times ionger than that of the parent ion, and it can readily be shown that the veiocity with which they reach the detector cathode varies linearly as (Z-,-T), where Tp is the flight time of the undissociated parent ion, and ‘1’is the lifetime of the parent ion decomposing to give the particular neutral under consideration. This means that the velocity dependence of the multiplier response is not unduly important in determining whether neutral spzzcies will give a significant output current. Of course, it is necessary to explain why the methyl radical from the decomposition of I,3-butadiene gives a much larger signal than formaldehyde, which appears likely to be the neutral fragment from the dissociation of (CH30)3POt. There are two possible explanations: I. It is possible to derive an equation, analogous to eqn. (IO), relating St,, In?. f. Masz S~~erfronr.Ion Phys., 5 (1970) 361-380
378 the
P_ Fe RNEWSTUBB,
sampling St, =
width for neutrals,
N. W.
REID
to the gate width of the analog output unit, i.e.
1/F,., x Gate width.
Note that F, is not the same as Fl, since eqns. (3), (4) and (5) do not hold for neutrals. In fact, it can be shown that F, depends linearly on the mass of the ion which is decomposing, so that in the case of the trimethyl phosphate molecuiar ion decomposition, l]r;h (and thus St,) will be considerably smaller than for the decomposition of C,H, +. This means that the multiplier output current for a given flux of neutral is smaher in the former case. 2- It is po.ssibIe that the decomposition of (CH,O),PO+ involves the release of some kinetic ener,oy. Most of this will be carried away by the lighter neutral fragment, which will not benefit from the focussing effect of the electric field, and will bave a Xgh probabibty of striking one ofthe field defining plates, thus reducing the flux of neutrals reaching the detector. It must be assumed that IittIe, or no, kinetic ener,ay is released in the decomposition of C,H6+.
A. Trinrerhyl phosphate From Fig. 4 it can be seen that, within the uncertzinty in the various parameters required in the calculation, it is possibie to get very good agreement between theory and experiment for the decomposition of the trimethyl phosphate molecular ion. Since the compuied curves were virtually unaltered by changes in the vibrational frequency patterns of the parent ion and the activated complex, it appears that uncertainties in the activation energy and the internal ener,7 distribution are most important in determining the uncertainty in the computed result. Thus, for a more rigcrous test of the theory, a more accurate knowledge of these quantities is required. Nevertheless, it is interesting that a relatively iarge uncertainty in all these parameters only results in a small spread in the computed curves. in other words, if the experimentai ree;ults had been more than about 20 % different from their actual vaiues it would have been impossibie to reconcile them with the predictions of the QET. It can thus be said that these results represent further support for the theory. The convolution routine given by eqn. (7) reveals an important property of the instrument. The point of convergence of the sum taken there gives the maxi12um vaI*z? af the rate coeEcient which contributes to the “smearing out” of the peaks, i.e. the maximum rate coefficient measurable here. With the field strength normally used (3000 V/m) this maximum rate is about 2 x IO5 set-‘. This ensures that the daughter ic-ns detected from the metastable transition are incapab!e of further decomposition, which would have rendered the analysis of the results considerably more complicated. Any parent ion which decomposes ht.
J- Mess Spectrom_Ion Ph,-s, 5 (1970)
361-380
DECOMPOSITION
OF
EXCITED
POLYATO_MIC
379
IONS
with a rate coefficient less than 2 x lo6 set-’ has insufficient internal energy to cause further decomposition of the dau&ter ion, as is illustrated by a particular example. Consider decomposition of P,, via activated complex AC:, assuming that the activation energ is 2,-l eV. To decompose with a rate coegiicient equal to 2 x 106 see-’ this model of the parent ion requires 1.55 eV of internal ener,y. The further decomposition of the io:l ~C~YI,O)~HPO 4 is known, and gives rise to a metastable peak, but the appearance poten:iai of the next daughter ion, (CH@)HaPO’ is given as 13_9C_O.4eV2’, which corresponds to the molecular ion having 3.1 eV of internal ener_ey,so clearly this further decomposition is unlikeiy to upset the measured decay curve_ 3.
i,3-Butadierze
Here, too, the calculated curves show excellent agreement with the experimental results. This agreement is more satisfactory than that of the previdus exampIe, because the parameters required in the ealculaticn are known to a greater degree of precision, although it must be remembered that the uncertainty in the experimental results is larger, as a consequence of the use of photoionisation Nevertheless, the extent of the agreement is most gratifying_ In this case, too, the possibility of further decompositions of the daughter ion can be excluded. For example, decomposition via AC2 requires an internal energy of 2.29 eV for the parent ion to give a rate coefficient equal to 2 x LG6set- r. The appearance potential oi the next daughter ion (C,H,+) is 12.4-1-0.1 eV3’, corresponding to an internal energy of the molecular ion of 3.37 eV.
We wish to acknowledge with thanks the suppc~%of one of us (N. W. R.) by an Elsie Ballot Scholarship, and also by a maintenance grant from the South African Council for Scientific and Industrial Research. Thanks are also due to the Royai Society fOi a grant for apparatus.
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1 2 3 4 5 6 7 8 9
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