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Studies of gas-phase ion/molecule reacations in relation to a proposed ionic mechanism of soot formation

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Studies of gas-phase ion/molecule reacations in relation to a proposed ionic mechanism of soot formation
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Öztürk, Feza
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English
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viii, 196 leaves : ill. ; 28 cm.

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Subjects / Keywords:
Alkynes ( jstor )
Charge transfer ( jstor )
Iodides ( jstor )
Ionization ( jstor )
Ions ( jstor )
Isomers ( jstor )
Kinetics ( jstor )
Reactants ( jstor )
Reaction mechanisms ( jstor )
Soot ( jstor )
Combustion deposits in engines ( lcsh )
Hydrocarbons -- Combustion ( lcsh )
Ionization of gases ( lcsh )
Soot -- Environmental aspects ( lcsh )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

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Thesis:
Thesis (Ph. D.)--University of Florida, 1988.
Bibliography:
Includes bibliographical references.
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Typescript.
General Note:
Vita.
Statement of Responsibility:
by Feza Öztürk.

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STUDIES OF GAS-PHASE ION/MOLECULE REACTIONS
IN RELATION TO A PROPOSED IONIC
MECHANISM OF SOOT FORMATION











BY

FEZA OZTtRK


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY



UNIVERSITY OF FLORIDA


1988 ; PVERS!OF FLORIDA LIBRARIES




STUDIES OF GAS-PHASE ION/MOLECULE REACTIONS
IN RELATION TO A PROPOSED IONIC
MECHANISM OF SOOT FORMATION
BY
FEZA ZTURK
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1988
' 1UN1VERSITY 0F FLORIDA LIBRARIES


TO ELIF
Digitized by the Internet Archive
in 2011 with funding from
University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation
http://www.archive.org/details/studiesofgasphasOOzt


ACKNOWLEDGEMENTS
This work is the final product of the efforts and
encouragement of many. First, I must thank my colleagues,
Bryan Hearn, Dr. Cliff Watson and Dr. Steve Bach, in the
Eyler group, including Dr. GOkhan Baykut and Dr. Mehdi Moini
who are no longer with the group, for their help and
suggestions. Each one deserves particular thanks for their
special efforts and friendship throughout these last years.
I have greatly benefitted particularly from their technical
experience and skills whenever questions and difficulties
arose in the lab.
Next, I wish to acknowledge my research advisor, Dr.
John Eyler, whose guidance and encouragement has enabled me
to experience the intellectual satisfaction and enjoyment of
scientific research. With his research funds, I had the
opportunity to spend my time exclusively doing research and
attend the annual meetings of the American Society of Mass
Spectrometry which provided the best setting for scientific
communication. I also would like to mention his editing
skills which have always assisted me and had a major role in
putting this manuscript to its final form.
ill


I would like to acknowledge Dr. Floyd Wiseman from the
Environics Division of Tyndall Air Force Base for his
interest and efforts in this research project. His
contribution to the work by the kinetic modeling study
deserves an important credit for providing a better
understanding of experimental results.
Special thanks are extended to Dr. William Weltner, Dr.
Robert Hanrahan, Dr. Merle Battiste, Dr. Willis Person and
Dr. Charles Proctor for serving as committee members. I
particularly wish to thank Dr. Calvin VanderWerf, Dr. Robert
Hanrahan, Dr. Kathryn Williams, and Dr. William Weltner for
their efforts and willingness to be supportive in every way
throughout these long years.
Another special person deserving particular thanks is
my friend, Zekiye Onsan. She has been an endless source of
encouragement and never failed to give her help whenever
needed. I also wish to thank Taghi Alizadeh Yekani for
sharing the difficult times with me with patience and
sincerity in my earlier years of study.
Finally, there is my five-year old, Elif. She made it
worhwhile by just being there for me.
iv


TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS ill
ABSTRACT vii
CHAPTER
1 INTRODUCTION 1
2 INSTRUMENTATION 15
3 ION/MOLECULE REACTIONS 29
Theory of Ion/Molecule Reactions 29
Experimental Study of Ion/Molecule Reactions
Using FTICR 38
4 REACTIONS OF CgHg + WITH ACETYLENE AND
DIACETYLENE IN THE GAS PHASE 45
Introduction 45
Experimental 48
Results 50
Discussion 64
5 KINETIC MODELING OF THE REACTIONS OF CgHg + .. 72
Introduction 72
Experimental 73
Results 74
Discussion 93
6 REACTIONS OF C5H5+ AND C5Hg+ WITH ACETYLENE
AND DIACETYLENE 101
Introduction 101
Experimental 104
Results 107
Discussion 123
v


7 REACTIONS OF GASEOUS C?H7 + IONS 132
Introduction 132
Experimental 136
Results 138
Discussion 148
8 CONCLUSIONS AND RECOMMENDATIONS 164
APPENDIX
I PROGRAM TO CALCULATE ABSOLUTE RATE CONSTANTS
AND THEIR 95% CONFIDENCE LIMITS FROM RAW OR
NORMALIZED INTEGRATED PEAK AREAS OF THE
REACTING ION AS A FUNCTION OF TIME IN FOURIER
TRANSFORM ION CYCLOTRON RESONANCE MASS
SPECTROMETRY 167
II ANALYTICAL EXPRESSIONS FOR KINETIC MODELING 181
BIBLIOGRAPHY 187
BIOGRAPHICAL SKETCH 196
vi


Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
STUDIES OF GAS-PHASE ION/MOLECULE REACTIONS IN RELATION TO
A PROPOSED IONIC MECHANISM OF SOOT FORMATION
By
FEZA ZTRK
August, 1988
Chairman: John R. Eyler
Major Department: Chemistry
The reactions of small hydrocarbon ions such as C3H3+,
c5h3+> c5h5+* and C?H7+ with acetylene and diacetylene have
been investigated using Fourier Transform Ion Cyclotron
Resonance (FTICR) mass spectrometry to provide qualitative
and quantitative information about a proposed ionic
mechanism of soot formation. Ion/molecule reaction pathways
and rate coefficients have been determined for several
isomers of each of the ions listed above, formed from a
variety of precursors, and reacting with precursors,
acetylene and diacetylene. Further understanding of
reaction mechanisms of some of the reactions proposed
experimentally was obtained from kinetic modeling studies.
All of the small hydrocarbon ions studied reacted with
diacetylene extensively while almost no production of larger
vii


ions was observed with acetylene. Linear C3H3 + was formed
by charge transfer ionization of propargyl iodide using Xe+,
and was found to isomerize to the cyclic form of C3H3+ in
reactions with both acetylene and diacetylene. The
isomerization was shown to take place via a long-lived
C5H5+* complex by isotope exchange reactions between linear
C3H3+ and deuterated acetylene. The reaction rate
coefficients for the reaction of C3H3+ with deuterated
acetylene and diacetylene were (4.5 + 1.9) x 10-10 cm3/s and
(1.4 + 0.7) x 10-9 cm3/s, respectively.
While different structures could be attributed to
C3H3+, C5H3+, and C7H7 + ions produced from different
precursors on the basis of reactivity, this could not be
done for C5H5+ ions, whose reactivity with acetylene and
diacetylene was similar within experimental error regardless
of precursor. Presence of two structural Isomers of C5H3+
was determined using different precursors and several
structures for these isomers were proposed. The reactive
isomer was observed to react with diacetylene with a rate
constant of (5.6 + 1.7) x 10-*9 cm3/s. Rate coefficients
for the ion/molecule reactions of C7H7 + were found to be
different when it was formed from various precursors, which
implied the involvement of different C7H7 + structures. All
experimental results are discussed in relation to
theoretical work involving structures of the ions studied
and a proposed ionic route to soot formation.
viii


CHAPTER 1
INTRODUCTION
Soot is a combustion product which has undesirable
effects both on human health and on the efficiency of fuel-
powered engines due to increased heat transfer to critical
engine components. Considering the fact that the use of
alternative fuels such as shale or coal-derived gas in the
near future would lead to increased soot emissions, search
for an effective way to reduce soot has been going on for a
long time. The design and development of advanced engines
to achieve soot suppression requires a sufficient
fundamental understanding of the mechanisms governing soot
formation. Soot formation in hydrocarbon flames involves a
succession of fast processes that occur within a few
milliseconds during the combustion of the hydrocarbon.
Although many investigations have been undertaken in
relation to the process of soot formation in fuel-rich
hydrocarbon flames, understanding of this process is still
limited. Experimental techniques such as mass spectrometry
(Calcte, 1963; Michaud et al., 1981), laser-light
scattering (Kent et al., 1981; D'Alessio et al., 1977),
laser induced ionization (Smith and Mallard, 1981), and
laser induced fluorescence (DiLorenzo et al., 1981) have
1


2
been used to study the molecular species and particles In
flames.
Soot collected from flames consists of chalnllke
aggregates of spherical units having diameters of 10-50 nm
with a carbon/hydrogen atom ratio in the range 8:1-12:1
(Calcte, 1981). Three distinct steps of soot formation
have been recognized over many years of research (Calcte,
1981) :
1. Nucleation- a phase change from molecular species where
chemical reactions dominate to incipient soot particles
where physical processes dominate;
2. Growth to spherical particles of 10-50 nm in diameter;
and
3. Aggregation or agglomeration of the spherical units to
form chains.
Among these, the first step, nucleation, is the least
understood in the process. Although many diverse theories
have been put forward to explain the nucleation process,
only two of these have received quantitative support:
1. Mechanisms involving neutral and free radical species;
and
2. Ionic mechanisms.
Neutral and Free Radical Mechanisms. A large number of
neutral and free radical mechanisms have been proposed to
describe the transition from molecular species to soot


3
(Palmer and Cullis, 1965; Lahaye and Prado, 1978; Gaydon and
Wo 1fhard, 1979).
One of the proposed paths Involves polyacetylenes
where acetylene reacts to form higher species (Bonne et al.,
1965) .
C4H2
C6H2
c8h2
-H
^2^2
C2H2
I
> c4h3 (+H)
c2h2
l-H
I
> c6h3 (+h2)
C2H2
l-H
I
> c8h3 (+h2)
It was suggested that the continuation of this series
leads to larger radicals which further react with each other
and with higher polyacetylenes forming even larger
molecules. However, because this mechanism leads to
formation of a giant chain molecule instead of a polycyclic
carbon structure, it was not accepted as being responsible
for soot formation (Homann, 1967). To account for the
problem of ring formation, Homann and Wagner (1967, 1968)
suggested that radicals such as CgH attack the
polyacetylenic species forming side chains which lead to
branched polymerization, and presumably ring closures. The
experimental support of this scheme comes from the
observation that in the oxidation region of the flame, the
concentration of polyacetylenes decreases while that of the
polycyclic aromatics increases. But the growth of
polyacetylenes was considered too slow by Calcte (1981), to


4
account for the rapid formation of soot particles.
Furthermore, as pointed out by Bonne et al. (1965), Thomas
(1965) and Cullis (1976), the rearrangement of a
polyacetylene to an aromatic graphite-1ike structure would
also be a slow process.
Another hypothesis proposed by Glassman (1980)
emphasized the importance of strongly conjugated molecules
such as butadiene in the formation of ring structures with
side chains to which butadiene-type molecules keep adding.
This mechanism did not receive much support on the basis of
concentration profiles in which the butadiene concentration
is observed to fall very rapidly even before the initiation
of soot formation (Cal cote,1981).
Some models considered C2, CgH and Cg radicals as
initial nuclei for soot formation which undergo condensation
reactions with each other or with acetylene (Jensen, 1974;
Smith, 1940; Carbannes, 1956). The main objection to these
mechanisms based on C2 and Cg condensation reactions was the
presence of a very strong C2 radiation in rich cyanogen-
oxygen flames which do not form soot.
Finally, direct condensation of aromatic rings was
proposed as being the most favored thermodynamic path to
soot formation (Bonne et al., 1965; Graham et al., 1975;
Stein, 1978). However, by a detailed analysis of the
concentration and the flux profiles of the species, Bittner
and Howard (1981a, 1981b) were able to show that soot is


5
produced via nonaromatic hydrocarbon intermediates rather
than via intact aromatic rings. But after a consideration
of many species, only a few intermediates were found to
favor the rearrangement to a ring structure over other
decomposition channels.
To conclude the discussion above, it is clear that all
the proposed neutral species mechanisms for soot formation
have serious problems with the nucleation step, and thus
none can be considered completely satisfactory in
understanding the soot formation process. Particularly it
is difficult in any of the proposed neutral schemes to
produce small cyclic and polycyclic species with a
sufficiently high rate to model the quite rapid soot
formation seen in flames. Recently, however, a
neutral/radical soot formation model has been proposed which
contains many steps and incorporates quite recently obtained
shock tube kinetic data (Frenklach et al., 1985). This
model is capable of yielding small ring compounds at a
higher rate than previously suggested radical mechanisms,
although there is some question as to the correct rate
constant for one or two of the crucial steps in formation of
the first ring.
Ionic Mechanisms. A number of experimental
observations in flames have led to a consideration of the


6
importance of ions in soot formation. Such observations in
flames include (Olson and Calcte, 1981a; Calcte, 1981):
1. Presence of a unit charge on soot particles;
2. A positive correlation between the growth of large ions
and the appearance of soot;
3. The increase both in the concentration of large ions and
the onset of soot formation by the addition of electrophilic
molecules;
4. Identical location for the peak concentrations of
molecular ions and soot precursors;
5. Production of larger particles by an increase in the
residence time of the positive ions; and
6. High ion concentrations in hydrocarbon pyrolysis.
As a consequence of the above observations, several
ionic mechanisms have been suggested (for references, see
Calcte, 1981). The postulated general growth of soot
particles from primary ions is shown in Figure 1.1. Calcte
(1962) proposed the chemiionlzation reactions (1.1) and
(1.2) for the formation of primary ions:
CH + 0 > CHO+ + e~ (1.1)
CH* + C2H2 > C3H3+ + e- (1.2)
The C3H3+ ion is the dominant ion observed in fuel-rich
flames (Knewstubb and Sugden, 1959; Goodings et al., 1979;
Olson and Calcte, 1981b; Michaud et al., 1981) and its


7
Primary flame
ins
C
C2H2
c3m3 +c4h2
etc.
Neutral flame
species
C5H5 +
C5H3+
>C5H5+
C7H3+'
C7H5+
-etc.
C^Hy species
etc.
-ION ELECTRON
RECOMBINATION
<3>
O
<3>
NUCLEATION
"incipient soot particles
SURFACE GROWTH
Small particles
^ THERMAL IONIZATION
Neutral and small
charged particles
SOOT
AGGLOMERATION
Figure 1-1. Growth of Soot Particles from Primary Molecular
Species.


8
concentration falls very rapidly at the critical equivalence
ratio of soot formation where the concentration of the
larger ions starts to increase (see Figure 1.2)
(Calcte, 1981). Unfortunately, the mechanism of C3H3+
formation is still not clear. An alternative mechanism
(Calcte, 1972) for C3H3 + formation is shown by reactions
(1.3) and (1.4):
CHO+ + C2H20 > C2H30+ + CO (1.3)
C2H30+ + c2H2 > C3H3+ + CH2 (1.4)
Reaction (1.5) is postulated (Calcte, 1972) to account for
the dominant H30+ observed in near stoichiometric and lean
flames :
CHO+ + H20 > H30+ + CO (1.5)
The C2H3+ ion was also considered as a possible nucleating
center for soot formation in flames and its formation is
shown by reaction (1.6) as proposed by Vinckier et al.
(1977 ) .
CHO+ + C2H2 > C2H3+ + CO (1.6)
The primary ions mentioned above are proposed to react
with CxHy molecules by fast ion/molecule reactions (Calcte,


9
Figure 1.2. Effect of Equivalence Ratio on Peak Ion
Currents for 2.0 kPa Acetylene-Oxygen Flames. The shaded
area indicates the minimum equivalence ratio for soot
formation.
Reprinted by permission of Elsevier Science Publishing Co.,
Inc. from the article by H. Calcte (1981). Copyright 1981
by the Combustion Institute.


10
1981; Olson and Calcte, 1981a). The typical set of
reactions for C3H3 + are shown below:
C3H3 +
+
C22
> C5H3+ + H 2
(1.7)
C3H3 +
+
c2h2
> C5H5+
(1.8)
c3h3 +
+
c2h -
---> C5H3+ + H
(1.9)
c3h3 +
+
C4H2
> c5h3+ + c2h2
(1.10)
C3h3 +
+
c 4 H 2
> CfjrHg
(1.11)
The next step is the further addition of neutral
building blocks, acetylene and diacetylene to the product
ions producing larger ions with increased C:H ratio.
Following are a few reactions representative of this step.
C5H3 +
+ C 2 H 2
> c7h5+
(1.12)
C5H3 +
+ c4h2
> c9h5+
(1.13)
C7H5 +
+ C4H2
> c9h5+ + c2h2
(1.14)
This series of reactions is suggested to lead to the
formation of polycyclic structures such as C13Hg+ and


11
The problem of rearrangement of linear structures to
polycyclic structures encountered in the neutral mechanism
is overcome in the ionic mechanism because of the general
observation that gaseous ions usually rearrange upon
formation to their most stable structure (Calcte, 1981).
Michaud et al. (1981) have made an alternate suggestion
that direct reactions of C3H3+ with aromatic neutrals such
as benzene, toluene, naphthalene, methylnaphthalenes, and
indene may be more important in forming polycyclic ions than
sequential reactions involving acetylene and diacetylene.
In fact, recent ion cyclotron resonance (ICR) studies of
reactions of C3H3+ with aromatic neutrals showed (Baykut et
al., 1986) that these reactions are fast enough to be
considered as possible bypass channels in ionic soot
formation pathways.
The main objection to the ionic mechanism is the lower
concentration of ions in flames compared to that of neutral
species. Figure 1.3 (Calcte, 1981) shows the concentration
profiles of primary neutrals and ions observed in flames as
a function of distance above the burner. One of the most
important features of the figure is that the soot
concentration is lower than that of the large positive ions
which implies that there are probably enough of these large
ions to produce the observed levels of soot. Several orders
of magnitude higher concentrations of neutral species
compared to those of ions in flames can be explained as a


12
DISTANCE ABOVE BURNER.Cm
Figure 1.3. Number Densities of Neutral and Ionic Species
Found within Flames.
Reprinted by permission of Elsevier Publishing Co., Inc.
from the article by H. Calcte (1981). Copyright 1981 by
the Combustion Institute.


13
requirement for the ion/molecule reactions to proceed fast
enough to account for the rapid formation of soot.
In this study, the reactions of primary ions with flame
neutrals have been investigated to identify different
reactant ion structures, reaction products and mechanisms.
One of the goals of this study was to determine how fast
these ion/molecule reactions proceed under laboratory
conditions, which hopefully leads to a better understanding
of the complex phenomena occurring under flame conditions.
Fourier Transform Ion Cyclotron Resonance (FTICR) mass
spectrometry, used in this study, is well suited to
investigate ion/molecule reactions due to its inherent
qualities which differ from other mass spectrometers. These
qualities include very clean isolation of the mass of
interest from a complicated reaction mixture and accurate
rate constant measurements along with reaction mechanism and
branching ratio studies. The basics of this technique are
discussed in Chapter 2 along with an explanation of the
determination of some experimental pressure measurement
parameters such as Baratron factors and the system factor
inherent to the instrument. The use of FTICR mass
spectrometry for studying ion/molecule reactions is
discussed in Chapter 3 along with some theoretical models
developed for ion-molecule reactions. The main body of the
experimental work, reported in Chapters 4-7, deals with
proposed nucleatlon steps of the ionic mechanism of soot


formation.
results is
14
An overall conclusion of the experimental
included in Chapter 8.


CHAPTER 2
INSTRUMENTATION
Fourier Transform Ion Cyclotron Resonance (FTICR) Mass
Spectrometry was introduced in the mid-1970s by Comisarow
and Marshall (1974a, 1974b, 1974c, 1975). It involves the
application of Fourier multiplex concepts (Griffiths, 1978;
Marshall, 1982) to ICR mass spectrometry. High speed, high
sensitivity, computerization, ultra-high mass resolution,
and wide mass range are some of the advantages of Fourier
Transform over continuous-wave spectrometry (Marshall,
1985). Basic principles and the vast applications of this
relative newcomer to mass spectrometry are summarized in
several recent review articles (Johlman et al., 1983; Gross
and Rempel, 1984; Comisarow, 1985; Marshall, 1985; Baykut
and Eyler, 1986; Laude et al.,1986). In this chapter, the
basic theory of operation of ICR which led to the concepts
and development of the FTICR technique will first be
discussed. Following that is a description of the
instrument along with typical experimental parameters and
the general sequence of operation.
Theory. An ion of charge, q, moving at velocity, v
when put in a uniform magnetic field, B, is subject to the
Lorentz force,
15


16
ma
q (v x B)
(2.1)
which acts perpendicular to the direction of ion motion.
Under the influence of this force, the ion follows a helical
path (Lawrence and Livingston, 1932) which, when projected
into a plane perpendicular to the magnetic field gives a
circle with a radius, r proportional to the velocity of the
ion, as shown in Figure 2.1. Substitution of the
centripetal acceleration in terms of angular frequency, w,
into equation (2.1) gives
and
o p
IF! = mlal = mv /r = mr = qcurB
0) = qB/m (mks units)
(2.2)
(2.3)
which relates the ion's characteristic cyclotron frequency
to its q/m (charge/mass). Equation (2.3) is called the
cyclotron equation and provides the basic principle of mass
measurement in terms of cyclotron frequency in the ICR mass
spectrometer. For a magnetic field of 3.0 Tesla, singly
charged ions with masses in the range of 18-5000 a.m.u. have
cyclotron frequencies in the radiofrequency range (10 kHz-
2.6 MHz), within which frequency can be measured with high
precision.
Operation. A schematic representation of the
commercial Nicolet FTMS-1000 mass spectrometer with a
superconducting solenoid magnet (3 Tesla) is shown in Figure


17
Figure 2.1. Motion of an Ion with Initial Velocity
Magnetic Field B.
in a


18
2.2. All data acquisition and processing and the selection
of various experimental parameters (except emission current)
are under computer control. Figure 2.3 shows a simplified
block diagram of an FTICR mass spectrometer. The simplicity
of operation results from the ability to form, excite, react
and detect ions in the same 1-inch cubic stainless steel
cell shown in Figure 2.4. This analyzer cell is located in
the center of a vacuum chamber which passes through the bore
of the magnet. The background pressure of 10 torr is
achieved by the use of a four-inch diameter oil diffusion
pump and by baking out the system at 250C for several hours
each night.
An inlet system which is evacuated with a three-inch
diameter diffusion pump permits the introduction of gas and
liquid samples into the high vacuum through precision leak
valves. The liquid samples are used after multiple freeze-
pump-thaw cycles to remove non-condensible gases. A solids
insertion probe is used for the introduction of solid
samples into the vacuum chamber and can be heated up to
250C to promote sublimation of the solid.
Ion formation is typically achieved in 5 ms by
collisions of electrons accelerated to 10-70 eV with
neutrals leaked into the vacuum chamber. The number of ions
is controlled by monitoring the emission current, measured
by means of an electron collector located behind the trap
plate opposite to the filament. When ions are formed, they


co
Figure 2.2. Schematic Diagram of FTICR-1000 Mass
Spectrometer.


20
Figure 2.3. Simplified Block Diagram of an FTICR Mass
Spectrometer.


21
electron
collector
V
transmitter
plate
receiver
trapping
plate
trapping
plate
receiver
plate
transmitter
plate
Figure 2.4. Cubic FT ICR Cell.


22
start cyclotron motion at their characteristic frequency
with a random phase. The trapping plates shown In Figure
2.4 constrain the ion motion in the direction parallel to
magnetic field lines. Positive and negative ions are trapped
by the application of, typically, positive and negative 1
volt potentials to the trapping plates, respectively.
To detect the ions, a fast sweep of oscillating voltage
in the radiofrequency range is applied to the transmitter
plates shown in Figure 2.4. Ions absorb energy at their
cyclotron frequency and are driven into coherent motion with
a larger radius, thus inducing an image current oscillating
at the frequency of their cyclotron motion on the receiver
plates (see Figure 2.5). The image current is amplified,
digitized and stored in the computer's memory as a time-
domain signal which contains the superimposed frequency
information of all the ions with different masses in the
analyzer cell. A fast Fourier Transform (Cooley and Tukey,
1965) is applied to the time-domain data to produce the
frequency-domain spectrum which can be plotted in terms of
the ion masses. Figure 2.6a shows a time-domain spectrum
of two superimposed sine waves of frequencies and aig
The decay of the signal results from the dephasing of ions
due to collisions with the neutral molecules. Fourier
transformation of this spectrum gives the mass-domain
spectrum shown in Figure 2.6b. In this procedure, the
lowest mass detected is limited by the sampling frequency of


23
Figure 2.5. Excitation and Detection of Ion Motion.
(a) Ion motion in magnetic field only, (b) motion during
radio-frequency pulse applied to the transmitter plates,
(c) larger radius of ion motion after excitation, and
(d) generation of an image current in the receiver plates by
a rotating ion "clump".


24
o
O
D
w
o.
E
<
Time
(a)
"I T
50 60 70
MASS IN A.M.U.
100
(b)
Figure 2.6. Ion Detection by Fourier Transform. (a) Time-
domain spectrum (Abscissa is time; ordinate is ion signal),
(b) Frequency-Domain Spectrum after Fast Fourier Transform
of the time-domain data (Abscissa is frequency; ordinate is
ion signal).


25
the analog-to-digital converter, which should be twice the
signal frequency according to the Nyquist criterion. Since
the highest cyclotron frequency detected is one-half the ADC
frequency, for a magnetic field of 3 Tesla used in this
work, the singly charged ion mass corresponding to this
frequency is 18 a.m.u., which sets the low mass limit.
A typical experimental sequence is shown in Figure 2.7.
Ions can be manipulated in various ways between the
formation and the excitation pulses. Ion ejection is used
to clean the cell of all ions except one of interest. Ions
are ejected by the same principle as excitation. The only
difference is that a higher amplitute of excitation voltage
is used. In this way ions achieve large enough radii to
strike the cell walls and be neutralized. Application of
either a single ejection pulse at a single cyclotron
frequency or a swept pulse covering a range of frequencies
is determined according to the user's purpose.
After selection of the ion of interest, different kinds
of ion chemistry can be performed. Among these, ion/molecule
reactions, co11isi onal1y activated dissociation, and
photodissociation are the most commonly used processes in
characterization of ion structures. Since the number of
stages of ion ejection and manipulation is not limited by
hardware or software, (MS)n (multiple stages of mass
selection and manipulation) experiments can be performed by
repeating the same processes for the various generations of


Ejection pulses
Quench
pulse
/
Excitation pulse
ir
Quench
pulse
T t
Electron beam
pulse
Reaction time
Detection
pulse
to
a
TIME
Figure 2.7.
Cell.
A Typical Experimental Sequence in the FTICR


27
offspring ions. Laser desorption of solid samples and laser
ionization are other techniques used in conjuction with
FTICR.
Experimental Parameters. In this study, the FTICR
technique was used mainly to determine ion/molecule reaction
rates and mechanisms. Ion formation was accomplished by
dissociative ionization using various charge transfer agents
instead of electron impact ionization, in order to form the
ions with well-defined internal energies. Reaction pathways
were delineated by using the ejection capabilities of FTICR
which make it possible to eject one ion from a complicated
reaction mixture to determine its contribution to the mass
spectrum of all the other ions.
Reaction rate coefficients were determined by
monitoring the intensity of the reactant ion as a function
of time (typically for at least 2s) after ejection of all
other ions from the analyzer cell. Neutral gas pressures
were measured with an ionizing gauge. Ionization gauge
readings were then corrected by constructing calibration
curves of ionization gauge vs. capacitance manometer (MKS-
Baratron) readings in the 1 x 10-6 to 1 x 10~4 Torr range.
In order to correct for the fact that the ionization gauge
and capacitance manometer were located at different points
on the vacuum system, somewhat removed from the FTICR
analyzer cell, a correction factor was required. This was


28
obtained by determining the rate coefficient of a well-
studied reaction (C2H4+ + C2H4 > products), where the
ionization gauge pressure readings were corrected by using
the capacitance manometer. This experimentally determined
rate coefficient was then compared with the average of
published values, kav = (1.0 + 0.3) x 10~9 cm3/s (Herod and
Harrison, 1970; Gross and Norbeck, 1971; Sieck and Ausloos,
1972; Warneck, 1972; Le Breton et al., 1975) and the ratio
of the measured value to the published, which was 0.3 + 0.1,
was used as a correction factor. This factor was used in
calculating the absolute rate coefficients reported in this
work. The large uncertainities (95% confidence limits)
reported for the correction factor and rate coefficients
calculated using it are primarily due to the wide range of
reported values for the C2H4 + + C2H4 reaction used to
determine the correction factor. The even more widely
studied "standard" calibration reaction of CH4+ with CH4
could not be employed because of the lowest accessible mass
limit in the FTICR instrument mentioned earlier. All
calculations of rate coefficients and 95% confidence limits
were performed with a menu-driven Fortran computer program
(given in Appendix I).


CHAPTER 3
ION/MOLECULE REACTIONS
In this chapter the various theoretical models which
have been developed for ion/molecule reactions will first be
discussed. Then follows a description of practical aspects
of studying such reactions by the use of FTICR mass
spectrometry.
Theory of Ion/Molecule Reactions
A number of both classical and statistical ion/molecule
collision theories have been introduced during the last two
decades to provide an adequate model explaining the
experimental observations of ion/molecule reactions.
Classical treatments mainly include the pure polarization
(ion-induced dipole) theory first developed by Langevin
(1905) and the various ion-dipole theories.
A. Pure Polarization Theory. Detailed discussions of
this model can be found in a number of articles (Gioumousls
and Stevenson, 1958; McDaniel, 1964; Futrell and Tiernan,
1968; Henglein, 1970). Langevin's model assumes that the
neutral has no permanent dipole moment, and that both the
ion and the neutral molecule are point particles with no
internal energy. The classical charge-induced dipole
potential at an ion-molecule separation r is
29


30
V(r) = aq2/2r4 (3.1)
where q is the charge on the ion and a is the polarizability
of the neutral. Since the energy of relative rotation,
Erot(r) the particles is associated with an outwardly
directed centrifugal force, the effective potential of the
ion/molecule system can be given by
veff(r) = V(r) + Erot(r) (3.2)
or
Veff(r) = -(q2a/2r4) + (L2/2//r2) (3.3)
where L is the classical orbiting angular momentum of the
two particles and \i is the reduced mass. The total relative
energy of the system is a sum of the translational energy
and the effective potential energy.
Er Etrans veff I3-4
Figure 3.1 shows a plot of Vgff(r) versus r at constant Er
for three different values of the impact parameter, b. When
b=0, since there is no centrifugal potential energy, the
effective potential is attractive at all ion/molecule
separations leading to a collision between two particles.
For b > 0, there is a critical value of the impact


31
O 2 4 6 8 10 12 14 16
r ¡ cm
Figure 3.1. Plot of Veff vs r from Equation (3.3) for N2
Colliding with N2.


32
paramater, bc at which the particles orbit around the
scattering center with a constant radius, rc. At this
ion/molecule separation, there is no contribution from the
attractive potential and Vgff is equal to centrifugal energy
which creates a "centrifugal barrier to a capture
collision. For all b < bc, a capture collision occurs,
whereas it is precluded by the centrifugal barrier for all
b > bc.
Capture cross section is defined as the area of a
circle with radius bc perpendicular to the line of collision
at infinite ion/molecule separation and a capture collision
occurs for all the ions that pass through the circle when
approaching the neutral molecule. Capture cross section can
be derived for a given relative velocity in terms of the
charge of ion, q, polarizability of the neutral, a, and the
reduced mass, n as shown in equation (3.5).
<7c(v) = 2nq(a/ii) 1/2/v (3.5)
Thus the collision rate constant is given by
k c = voc = 27tq(a//i) 1/2 (3.6)
The rate coefficients obtained from this expression are
generally good for some simple low energy ion/molecule


33
reactions but underestimate the rate constants of most
ion/polar molecule collisions.
B. Ion/Dipole Theory. Several different models were
proposed to describe the theory of ion/dipole collisions.
Among these are "The Locked Dipole Approximation" (Moran and
Hamill, 1963), "The Frozen Rotor Approximation" (Dugan and
Magee, 1966), "Ion/Dipole Trajectory Calculations" (Dugan
and Magee, 1967), "The Average Dipole Orientation (ADO)
Theory" (Bowers and Laudens1ager, 1972), "Barker-Ridge (BR)
Model" (Barker and Ridge, 1976) and "The Average Dipole
Orientation Theory with Conservation of Angular Momentum
(AADO)" (Su et al. 1978 ) .
Both the "Locked Dipole" and "The Frozen Rotor
approximations assume that the polar molecule is fixed at
angle 0 (0 = 0 for the "Locked Dipole" model) with respect
to the line of centers of the collision. The resulting rate
constants provide upper limits to the ion/dipole capture
collisions and overestimate the dipole effect (Su and
Bowers, 1973 ) .
Ion/Dipole Trajectory Calculations provide numerical
solutions for the equations of motion for the collision of
an ion with a rotating polar molecule. As a result of these
calculations, the numerical capture cross section was found
to depend on relative translational energy. When compared
with experimental results, this numerical approach seems to


34
be useful In the Investigation of nonreactive ion/dipole
phenomena such as energy transfer, but does not give a good
estimation of capture collision rates.
ADO theory assumes that there exists an overall average
orientation of the dipole with respect to the Ion and the
extent of locking of the dipole Increases as the dipole
moment of the molecule increases. Su and Bowers (1973) have
parametrized the ADO theory to calculate the ADO capture
rate constants. The results indicate that the ADO theory
gives the best prediction of rate constants in most cases
with respect to the other theories.
BR theory uses a simple statistical approach to study
the ion/dipole collisions and is based on the Langevin
model. BR results overestimate the dipole effect by almost
a factor of 2 for charge transfer and proton transfer as
well as momentum transfer reactions.
Su et al. (1978) modified the ADO theory by the
application of the conservation of angular momentum with the
assumption that there is no net angular momentum transfer
between the rotating molecule and the ion/molecule orbital
motion. This modified version of ADO theory is termed the
AADO theory. The capture rate constants obtained from AADO
model are larger than the ADO predictions, providing better
agreement between theory and experiment.


35
C. Ion/Quadrupole Theory. This theory makes
theoretical predictions of ion/quadrupole interactions for
the molecules having Dw symmetries. Similar to ADO theory,
the average quadrupole orientation theory, AQO, was
developed by Su and Bowers (1975). This model predicts
significant quadrupole effects for molecules with high
quadrupole moments and improves the agreement between theory
and experiment.
Statistical Treatments of ion/molecule reactions
include the statistical theory and the orbiting transition
state theory. Statistical Theory is divided into three
categories according to the type of reaction dynamics as
shown in Figure 3.2.
A. Transition State Theory. This theory is developed
for direct bimolecular reactions (Pelzer and Wigner, 1932;
Evans and Polanyi, 1935; Eyring, 1935). This method was
later refined by Pechukas and McLafferty (1972) and by
Miller (1974). The microcanonical rate constant is given by
k(E) = Wt(E-E0)/hp(E) (3.7)
where W^(E-Eq) is the total sum of states (vibrational and
rotational) of the transition state complex with nonfixed
energy less than or equal to E-Eq, where E is the total


36

Figure 3.2. Schematic Potential Surfaces for Various
Ion/Molecule Reactions, (a) Direct bimolecular, (b)
Unimolecular, and (c) Complex formation reactions.


37
system energy, and p(E) is the total density of states of
the reactants. For a given potential surface, transition
state theory provides a rigorous upper limit to the true
rate constant.
B. Unimolecular Theory. This theory involves two
approaches, RRKM and QET (quasi-equi1 ibrium theory) which
arrive at similar results for the unimolecular reaction of
an isolated energized molecule. These methods were
developed independently by Marcus and Rice (1951) using the
assumptions of transition state theory and by Rosenstock et
al. (1952) using the quasi-equilibrium hypothesis.
Experimental evidence suggests that most unimolecular
systems appear to behave according to the quasi-equi1ibrium
hypothesis which assumes a random distribution of excess
energy independent of the pattern of initial energization
prior to unimolecular decomposition.
C. Complex Formation Theory. This theory involves the
statistical treatment of reactions which form a long-lived
complex assuming quasi-equi1ibrium for the intermediate
complex (Keck, 1958; Light, 1967). Thus, the rate constant
for decomposition to each available channel is assumed to be
proportional to the flux through the transition state for
that channel.


38
The Orbiting Transition State Theory is developed to
overcome the problem of determining the energy distribution
of reactants that leads to the formation of a given
transition state complex. In this method the transition
state is located at the maximum of the long range effective
potential where the reactants retain their original
identity. The orbiting rate constants for both bimolecular
reactions (Miller, 1976; Light, 1967), and unimolecular
reactions (Chesnavich and Bowers, 1977) can be obtained as a
function of translational, rotational, and vibrational
energy of the reacting system. Comparison with experiment
in general reveals that orbiting unimolecular rate constants
are unrealistically high while the orbiting bimolecular rate
constants are similar to experimental results at thermal
energies. This model also predicts the probability of a
given translational energy release (Chesnavich and Bowers,
1976) which in most cases is in good agreement with
experimental results for reactions with no reverse
activation energy.
Experimental Study of Ion/Molecule Reactions Using FT ICR
Rate Coefficients. ICR techniques cannot be used for
experimental tests of statistical theories since the
application of statistical models requires a detailed
knowledge of energy states of the system, which cannot be


39
obtained from ICR. On the other hand, theoretical
bimolecular rate constants using Langevin's model are
usually found to agree with the experimental results
obtained for low energy ion/molecule reactions using ICR
technique. Reactant ions with energies close to thermal can
be prepared by charge transfer ionization of a precursor
molecule followed by collisional relaxation of the ions by
inert gas molecules. Thus, this method provides the
determination of thermal bimolecular rate constants which
can be used to test the basic assumptions of the Pure
Polarization method.
The first step in the experimental determination of
rate coefficients by FTICR involves the ejection of all ions
except the one of interest from the analyzer cell following
charge transfer ionization. Next the decay of the ion
signal is monitored as a function of time long enough to
permit the ion of interest to react away completely.
Method of Data Analysis. The ion/molecule reactions
studied in FTICR most often involve bimolecular collisions
and follow second order kinetics. The rate expression for a
simple second order reaction is given by
-d[I]/dt = k2[i][R] (3.8)
where I is the ion and R is the reactant neutral. Since the
ion number density created in the FTICR instrument is at


40
least three orders of magnitude lower than the neutral
number density, a "pseudo-first order" rate coefficient,
I
kj can be substituted for the term k2[R] in equation (3.8).
d[I)/dt = kj [I] (3.9)
After integration, the rate expression giving the number
density of the reactant at any given time is obtained:
[I](t) = [I](0) exp(-kj t) (3.10)
where [I](0) is the initial number of ions present. Thus,
I
kj can be determined from the slope of the simple ln(ion
signal) vs time plot. The true rate coefficient, k2 can
f I
then be obtained from kj by dividing kj by the number
density of the reactant neutral. The number density of the
neutral is determined using the expression, (n/V) = P/RT,
where V and T are the volume and the temperature of the
analyzer cell respectively, and P is the pressure of the
reactant neutral measured by a capacitance manometer.
In an experimental situation, there is often a second
neutral present in the cell, which is the precursor neutral
of the ion of interest. Thus, the decay of the ion signal
includes ion/raolecule reactions with both the precursor and
the neutral molecules of interest. In this case the rate
expression becomes
40


41
-d[I]/dt = (k 2[R] + k3[P])[I]
(3.11)
where k3 is the bimolecular rate coefficient for the
reaction of the ion with the precursor molecule, P. The
integrated form is
(3.12)
[I](t) = [I](0) exp [-(k2 t R1 + k3[P])t]
In order to determine the rate coefficient of reactions of
the ion with the neutral reactant, it is necessary first to
monitor the reactions of the ion with precursor neutral with
no reactant neutral present in the analyzer cell and then to
subtract the rate coefficient for this reaction from the
total rate coefficient observed in the presence of both the
precursor neutral and the reactant of interest. If the
precursor neutral pressure is kept constant for the two
cases, only the pseudo-first order rate constants are used
in the subtraction step.
When two or more isomers of a particular ion are formed
from the same parent neutral, a single ion signal is
observed in the mass spectrometer whose intensity is the sum
of the intensities of all the isomers. For a simple case of
only two ion structures,
[ I ] (t ) = [A] (t) + [B) (t)
(3.13)


42
Thus, the integrated form of the rate expression is given by
[I](t) = [A](0) exp[-(k2[R] + k3[P])t]
+ t B](0) exp[-(k2'[R] + k3'[P])t] (3.14)
where A and B are the isomers of ion I. Consequently, the
decay curve of the ion signal is composed of segments with
two different exponential time constants, each slope
corresponding to the reaction rate of a different ion
structure. The sum of the rate coefficients (for reactions
with precursor and reactant neutrals) of the slower reacting
structure is calculated from the tail of the double decay
curve while that of the faster reacting structure is
determined by subtracting the amount of the slow reacting
isomer at each point in the initial part of the curve using
Equation (3.14). Often, one of the structures is completely
unreactive, while the other is reactive as shown in Figure
3.3, simplifying the data analysis for structure
identification.
Reaction Mechanisms. Reaction pathways leading to
final product ions from a ion/molecule reactant system can
be studied using the ejection capabilities of FTICR. The


lObJ SIG MAL
Figure 3.3. Ion Decay Curve with Reactive and Unreactive
Components .


44
method involves the ejection of each first generation
product ion continuously during the reaction time to see its
effect on the intensity distribution of the mass spectrum of
the final product ions. This method also can be used to
calculate the branching ratios for the product ions.
Studying reaction pathways and branching ratios of the ions
produced in different ways (either from different precursors
or different methods of ionization) provides an alternative
means to rate coefficient determination' for the
differentiation of structural isomers of the ion of
interest.


CHAPTER 4
REACTIONS OF C3H3+ WITH ACETYLENE AND DIACETYLENE
IN THE GAS PHASE
Introduction
The C3H3+ ion has received considerable attention in
recent years as a possible soot precursor because it is
found in quite high abundance in fuel-rich and sooting
flames (Goodings et al, 1979; Olson and Calcte, 1981b;
Michaud et al., 1981). Although substantial uncertainty
remains as to C3H3+ formation mechanisms in flames (Calcte,
1981), the ion is postulated (Calcte, 1981; Olson and
Calcte, 1981a) to react with neutrals such as acetylene,
diacetylene, and CgH in rapid, sequential condensation and
condensation/elimination reactions, forming successively
larger ions, which can rearrange to cyclic species during
the ion/molecule reaction chain.
Two isomeric structures of C3H3+ shown in Figure 4.1
are important in discussing the role of C3H3+ in
ion/molecule reaction mechanisms. The first is the
cyclopropenylium ion, recognized as the most stable isomer,
which has a theoretically calculated heat of formation of
253 kcal/mol (Radom et al., 1976), in quite good agreement
with the 256 kcal/mol determined by experiment (Lossing,
1972). A second and potentially more important C3H3+
45


46
H
J
(4.2)
Figure 4.1. The Most Stable C3H3 + Structures:
Cyclopropenylium (4.1) and Propargy1ium (4.2).


47
structure is that of the linear propargylium ion with a
calculated (Radom et al., 1976) heat of formation 31 to 34
kcal/mol higher than that of the cyclopropenylium ion, in
fair agreement with the 25 kcal/mol difference found
experimentally by Lossing (1972). Recent calculations have
shown several other stable isomeric structures of the C3h3 +
ion with higher heats of formation relative to the
cyclopropenylium and propargylium ions.
The importance of different precursors in affecting the
reactivity of C3H3+ ions was reported in a thermochemical
study by Holmes and Lossing (1979). In an ICR study of
C3H3+ reactions, Ausloos and Lias (1981) showed that
significant fractions of the linear isomer can be produced
by charge transfer reactions of small ions (Ar+, Xe+, C0+,
Ne+, etc.) with propargyl chloride and bromide. Later it
was reported (Baykut et al., 1986) that even higher
proportions of the propargylium isomer relative to the
cyclopropenylium isomer can be obtained with propargyl
iodide either by electron impact or charge exchange using
Xe+ .
A study by Smyth et al.(1982) demonstrated that the
cyclopropenylium ion was relatively unreactive toward simple
hydrocarbon fuels whereas the linear, propargylium ion was
quite reactive. In particular, reaction of propargylium
ions with acetylene was reported to produce CgH3+ and C5H5 +
ions with an overall C3H3+ disappearance rate coefficient of


48
1 x 10 cm /s. In the work discussed in this chapter,
results substantially different from those reported earlier
were found and the research was thus expanded to Investigate
possible production of CgHg + ions from ionic sources other
than C3h3+ present in the reaction media using the ejection
capabilities of Fourier transform ion cyclotron resonance
(FTICR) mass spectrometry. Reactions of propargylium ions
with C2D2 were also studied in order to delineate further a
proposed mechanism for the C3H3+/acetylene interaction.
Diacetylene is another important flame neutral which
has been postulated to react with C3H3+ ions in an
ion/molecule soot formation mechanism (Olson and Calcte,
1981a). Reaction pathways and the rate coefficient for the
reaction of propargylium ions with diacetylene near room
temperature were thus also investigated. In this chapter,
results for the reactions of C3H3+ ions with acetylene,
deuterated acetylene, and diacetylene are reported and
discussed in relation to previous work involving C3H3+
reactions (Ausloos and Lias, 1981; Smyth et al., 1982;
Baykut et al.,1986).
Experimental
Reactive and non-reactive C3H3^ ions were produced by
charge transfer reactions of various precursors with Xe+,
formed with an electron beam pulse of 5 ms duration at an
ionizing electron energy of ca. 15 eV. Propargyl iodide was


49
used as a precursor for CgHg + in studies of the reaction of
this ion with acetylene, deuterated acetylene, and
diacetylene, while a number of different precursors
(propargyl iodide, propargyl bromide, propargyl chloride,
propyne and aliene) were used to investigate the reaction
mechanisms leading to CgHg + ion formation. In some studies
CgHs+ ions were produced directly from the above-mentioned
precursors by electron impact to compare the effect of
ionization technique on the ratio of reactive to unreactive
isomers.
Propargyl iodide was prepared from propargyl chloride
by a halogen exchange reaction (March, 1977). The details
of purification are given elsewhere (Baykut et al., 1986).
Propargyl chloride, propargyl bromide, aliene, propyne and
acetylene were obtained commercially and their purity was
checked by obtaining wide mass range spectra. In the case
of acetylene, some production of protonated acetone was
observed at long delay times indicating the presence of a
small amount of acetone as an impurity. Propargyl bromide
was distilled before use in order to remove toluene which
was present as a stabilizing agent. Deuterated acetylene
was prepared from DgO and CaCg. Diacetylene was prepared by
the method of dehydrochlorination of 1,4-dichloro-3-butyne
in aqueous potassium hydroxide/dioxane solution (Snow,
1985). All the samples were used after multiple
freeze-pump-thaw cycles.


50
Results
C3I3- Reactions with Acetylene. Despite an earlier
report (Smyth et al., 1982) that C3H3 + is quite reactive
with acetylene, only very low intensities of C5H3 + and C5Hg+
produced via this reaction could be found in this work.
Experimental conditions of the earlier study were duplicated
as closely as possible, and then varied substantially with
respect to relative pressures of neutrals (from 1:1 to 8:1
C2H2:C3H3I) and overall system pressure (from 5 X 10 to 3
x 10~5 torr). The C3H3+ ions were formed from propargyl
chloride, bromide, and iodide by both charge transfer using
Xe+ and electron impact. In order to determine other
possible sources of C5H5+ observed under the earlier
reaction conditions, binary mixtures of acetylene and one of
the C3H3+ precursors reported (Ausloos and Lias, 1981; Smyth
et al., 1982; Baykut et al., 1986) earlier were used.
Intensities of C5H5+ and C5H3+ were first measured after a
125 ms reaction time. Then the parent ion, C2H2+, and C3H3+
were each ejected separately during the 125 ms reaction
period to assess their contribution to C5H5+ and C5H3+
formation.
For each different neutral precursor, the sources and
amounts of C5H5+ ions produced were found to be different.
Propyne and aliene were similar in producing large amounts
of CrjHg+ and no C5H3+ ion. However, the C3H3+ + C2H2


51
reaction was not responsible for C5H5+ formation. The main
reactions leading to CgH5+ were
C2H2+ + C3H4 > c5H5+ + H (4.1)
C3H4+ + C2H2 > C5H5+ + H (4.2)
in both cases. On the other hand, when propargyl iodide,
propargyl bromide and propargyl chloride were used as
precursors, relatively smaller amounts of CgH5+ ion
formation were observed along with C5H3 + ion production. In
the propargyl chloride case
C3H3C1+ + C2H2 > C5H5+ + Cl (4.3)
C2H2+ + C3H3C1 > C5H5+ + Cl (4.4)
were the major reactions leading to C5H5+ formation. For
propargyl bromide the
C3H3Br + C2H2 > C^H^ + Br (4.5)
reaction was the only source of C5H5+ ions observed. Any
contribution to C5H5 + formation from linear C3H3+ was less
than the experimental uncertainty. Finally, very little
(almost negligible) amounts of C5H5+ ions were observed when
propargyl iodide was used as a precursor and the reactions


52
C2H2+ + C3H31
--> c5h5+ + I
(4.6)
c3h3+ + c2h2 > c5h5+
(4.7)
were the major contributors in this case. An upper limit
for the rate constant, k, for reaction (4.7) was estimated
as 5 X 10-12 cm3/s by assuming that the very small C5H5 +
signal observed resulted from this reaction, and using the
expression [CgH3+](t) = [C3H3+](0) [C5H5+](t) =
[C3H3+](0)e-nkt, where n is the C2H2 number density.
Overall results for the production of C5H5+ and C5H3+ ions
in mixtures of acetylene and various neutrals used as the
precursors of C3H3+ are summarized in Table 4.1.
Because propargyl iodide was shown to produce the
highest reactive/unreactive ratio of C3H3+ ions both in
earlier (Baykut et al., 1986; Holmes and Lossing, 1979) and
the present work (see Table 4.2), it was used as a precursor
for C3H3+ ions in these reaction kinetics studies. Since
the precursor neutral molecule was always present in the
FTICR analyzer cell, it was a competitor with the reactant
neutral of interest in ion/molecule reactions involving
C3H3+. In order to determine the rate coefficient of
reactions of C3H3+ with the neutral reactant, it was
necessary first to monitor the reactions of this ion with
C3H31 and then to subtract the rate coefficient for this
reaction from the total rate coefficient observed in the
presence of both the precursor neutral and the reactant of


53
TABLE 4.1
Production of C5H5 + and C5H3+ Ions in Mixtures of
Various Neutrals and Acetylene3.
Neutral
Ionic sources**
of C5H3+ after
Xe+ charge
transfer
Ionization of
a mixture of
the neutral
and acetylene
Ratio of
C5H5+ prod,
relative to
that in
aliene casec
Ionic sources1*
of c5h3+
Intenslty
of C5h5+
vs. C5H3+
Percent
reactive
C33+
Ions
Aliene
C2h2+(4%)
C3H4+(60%)
1.0
-
-
<5
Propyne
C2H2+(40%)
C3H4+(60%)
0.75
-
-
30
Propargyl
chloride
C2H2+(40-50%)
C3H3Cl+(50-60%)
0.25
C3H3Cl+(20%)
C3H3+(20%)
c^H^eoS)
3.0
15
Propargyl
bromide
C3H3Br+(90-100%)
0.08
C2H2+(70%)
[c3h3+ *
C3H3Br+](30%)
2.0
85
Propargyl
Iodide
C2H2+(40%)
C3H3+(60%)
<0.02
C2Ho*(50%)
C3H3+(50%)
1.7
00
1 All ions were produced by chemical ionization charge transfer from Xe*.
3 Percentages show the relative contributions to C3i)3'' and production ns
determined by double resonance experiments and have an estimated uncertainty
of io%.
c Neutral reactants all had the same pressure (7 X 10-' torr) as measured by
the ionization gauge. Xenon and acetylene pressures were 5.U X lO-** and l.H
X 10 torr, respectively.


54
TABLE 4.2.
Percentages3 of reactive C3H3 + found from various precursors
by various ionization techniques (monitored by observing
reaction with the precursor neutral).
Ionizing
Technique
precursor
Propargy1
iodide
Propargy1
bromide
Propargy1
chloride
Electron impact (15eV)
90
40
10
Chemical ionization charge
90
85
15
transfer with Xe
aEstimated error is +5%.


55
interest. Reactions of C3H3 + with propargyl iodide were
monitored as a function of time following charge transfer
chemical ionization of CgHgl by Xe+ and ejection of all ions
but C3H3+ from the analyzer cell. Results obtained were
identical to CgH3 + reaction channels with propargyl iodide
which have been reported elsewhere (Baykut et al., 1986).
Isomerization of Linear In addition to the
absence of any significant C5H3+ and C5H5+ formed by
reaction of linear C3H3+ with C2H2, it was also observed
that C2H2 led to the isomerization of linear C3H3+ ions to
their cyclic form, thus rendering them unreactive toward
their parent neutral (C3H3I) as well as toward C2H2. This
Isomerization was followed as a function of C2H2 pressure
and a direct pressure dependence was found, as can be seen
in Figure 4.2.
C3H3+ Reactions with CgDg- To achieve a better
understanding of the isomerization of linear CgH3+, C2D2
instead of C2H2 was used as the neutral reactant. The
following isotope exchange reactions were observed:
C3H3+ +
C2D2
> c3h2d+ + c2dh
(4.8)
c3h3+
c2d2 -
^ c3hd2 + c2h2
(4.9)
c3h2d+
+ c2d2
> c3hd2+ + c2dh
(4.10)
c3h2d+
+ c2d2
> CgDg + C2H2
(4.11)


56
Deactivation of l-C3l-£ by acetylene at different pressures
Time/s
Figure 4.2. Isomerization of Linear C3H3 + Ions at Different
Pressures of CgHg. C3H3+ ions were produced by charge
transfer reactions with Xe^. p(C3H3I) = 1.1 x 10-7 torr;
p(Xe) was adjusted to maintain a constant total pressure of
2.6 x 10-6 torr as measured on the ionization gauge. (All
pressures are capacitance-manometer corrected.)


57
C^HDg + CgDg ^ C3D3 + C 2 D H
(4.12)
Using FTICR ejection capabilities, It was found that
reactions (4.9) and (4.10) contribute equally to the
production of C3HD2+ while reaction (4.12) produces more of
C3d3+ (80*) than reaction (4.11) (20*).
Ion intensity vs. time curves for the C3H3+/C2D2
reaction are shown in Figure 4.3. The overall rate
coefficient for the disappearance of C3H3+ was calculated by
subtracting the observed rate coefficient for the reaction
with propargyl iodide from the total observed rate
coefficient in the presence of C2D2. This observed rate
coefficient was then converted to the true rate coefficient
using the corrected pressure of C2D2. A value of (4.5+1.9)
x 10"10 cm^/s was found at a cell temperature of 373 K for
the disappearance of C3H3+ (reactions (4.8) and (4.9)). In
Figure 4.4, ion intensity vs. time curves of C3H3+ are
compared for reactions with and without C2D2.
L3L3 Reactions with Diacetylene. After ejection of
all ions except C3H3+ following charge transfer chemical
ionization by Xe+ of a mixture of diacetylene and propargyl
iodide, the ion/molecule reactions as a function of time
were monitored. Consecutive C2 and C4H2 addition reactions
were observed:
c3h3+ + c4h2 --
(4.13)


58
Reactions of I-C3H3 with C2D2
Time /s
Disappearance of C,H,
iodide.
Isotope Exchange Reactions of C3H3
with C2D2.
Figure 4.3.
ion includes reactions with propargyl
Note that the sum of all isotopic forms of C3H3+
remaining at the end of the reaction with C2D2 approximately
equals the total unreactive C3H3+ when C2H2 is used as a
neutral reactant at the same pressure (see Fig. 4.2).
p ( CoH/% I ) = 1 1 X 10
= 6.2 x 1 0-6 torr.
-7
torr ;
P ( C 2 D 2 ) -
1.2 x 10 6 torr; p(Xe)


59
Reactions of I-C3H3 with C3H3I and C2D2
Figure 4.4. C3H3+ Ion Decay Curves for Reaction with C3H3I
and C2D2 (Pressures are the same as given for Fig. 1.3.)


60
3+ + C4H2 >
C5H3+ + c2H2
(4.14)
C5H3 + c4h2
-> c9h5+
(4.15)
3+ + c4H2 >
c7h3+ + c2h2
(4.16)
c7h3+ + c4h2 ---
> C11H5+
(4.17)
5+ + c4h2 >
C11H5+ + C2H2
(4.18)
C9H5+ + C4H2
-> c13h7+
(4.19)
Some of these product ions were seen to react further
with propargyl iodide by displacement of atomic iodine:
C5H3 +
+
C3H3 i >
c8h6 +
+ I
(4.20)
C7H3 +
+
C3}i31 >
C10H6+
+
I
(4.21)
C75 +
+
C3h3 1 >
C10H8+
-f
I
(4.22)
c8h6 +
+
c3h3i >
C11H9+
+
I
(4.23)
C9H5 +
+
c3h3i >
C12H8+
+
I
(4.24)
Ion intensity vs. time curves for the c3H3+/C4H2
reaction are shown in Figure 4.5. The rate coefficient for
the disappearance of C3H3+ (reactions (4.13) and (4.14),
Figure 4.6) was calculated as described earlier, and a value
of k = (1.4 + 0.7) x 10-9 cm3/s was found. Propargyl
iodide, bromide, and chloride were all used as precursors of
C3H3+ in studying its reactions with diacetylene. For each
precursor, both electron impact and charge transfer chemical
ionization techniques were used. The percentages of
reactive isomer in the reaction with diacetylene are shown


61
Figure 4.5. Reactions of C3H3+ with C4H2. Disappearance of
C3H3+ and product ions include reactions with propargyl
iodide. p(C3H3I) = 1.1 x 10-7 torr; p(C4H2) = 4.8 x 10
torr; p(Xe) = 6.2 x 10~6 torr. (All pressures are
capacitance-manometer corrected.)


62
Figure 4.6. C3H3+ Decay Curves for the Reactions with C3H3I
and C4H,. (Pressures are the same as given for Fig. 4.5.)


63
TABLE 4.3
Percentages3
C4H2.b
of
reactive
c3h3
observed in the reaction with
precursor
Ionizing
Technique
Propargyl
iodide
Propargyl
bromide
Propargyl
chloride
Electron
impact (15eV)
75
30
5
Chemical
transfer
ionization
with Xe+
charge 75
65
5
aEstimated error is
+5%
bP(C4H2) =
4.8 x 10-7
torr


64
in Table 4.3. When these percentages of reactive isomer
were compared to those in the absence of C4H2 (see Table
4.2), it was clear that some isomerization of the reactive
linear C3H3+ ion, as well as reactions (4.13) and (4.14),
had taken place (see also Fig. 4.6). This isomerization was
followed as a function of C^H2 pressure and a direct
pressure dependence was found, as can be seen in Table 4.4.
The reactions of 1-C3H3+ with propargyl iodide and with
both acetylene and diacetylene have also been followed at
several elevated temperatures up to 500 K. All the rate
constants were found to be similar to their room temperature
value within experimental error.
Pi scussion
Effect of Different Precursors. Different percentages
of reactive C3H3+ were found from three different
precursors, propargyl iodide, propargyl bromide and
propargyl chloride as shown in Table 4.2. To explain the
differences observed in reactivity, schematic potential
energy surfaces for these precursors are shown in Figure
4.7. Experimental thermochemical data reported by Holmes
and Lossing (1978) were used in the generation of the
potential surfaces. Reverse activation energies for c-C3H3+
formation from propargyl bromide and chloride were
determined by the difference between the experimental and
the calculated appearance potentials. Since the appearance


65
TABLE 4.4
Changes in CoH3 + reactivity3 at different pressures of
diacetylene.H
C4H2 pressure/10'7 Torr
% unreactive C3H3+
0.8
16
1.6
17
4.8
25
7.2
32
8.0
35
9.6
40
al-CgH3+ ions were produced from propargyl iodide by
chemical ionization charge transfer with Xe+. (p(C3H3I) =
1.1 X 10~7 torr; pXe was adjusted to maintain a constant
total pressure of 2.6 X 10 torr as read on the ionization
are capacitance-manometer corrected.
gauge)
BA11 "
pressures


66
Figure 4.7. Schematic Potential Energy Surfaces for
C3H3+/C3H3X+ System from Different Precursors. Propargyl
Iodide (a), Propargyl Bromide (b). and Propargyl Chloride
(c) .


67
potential of C3H3+ produced from propargyl iodide very
closely corresponds to the calculated threshold for 1-C3H3+
rather than c-C3H3+, the dissociation to the latter is
assumed to have a significant energy barrier. Thus, reverse
activation energy for the dissociation channel giving
unreactive c-C3H3+ decreases in the order Ej0(j0 > Ebromo >
Echloro as s^own *n the figure. Production of almost
exclusively reactive 1-C3H3+ by both electron impact and Xe+
charge transfer ionization from propargyl iodide suggests
that Ej0Cj0 is so large that the fragmentation channel
leading to 1-C3H3+ becomes the lowest energy channel. In
the case of propargyl bromide, there is enough excess energy
to dissociate to both 1-C3H3+ and c-C3H3+. Production of
80% 1-C3H3 + by Xe+ chemical ionization suggests no
significant energy barrier for the 1-C3H3+ channel. It is
interesting to note that dissociation to 1-C3H3+ reduces by
a factor of two when electron impact ionization is used,
which demonstrates the effect of a large distribution of
electron energies from an electron impact ionization source
on the relative abundances of two channels almost equally
accessible energetically. The very small reactive 1-C3H3+
percentage produced from propargyl chloride by both electron
impact and Xe+ charge transfer ionization suggests at least
a small energy barrier for this dissociation channel, as
indicated schematically in Figure 4.7c.


68
Internal Energy of the Ions In Relation to Rate
Coefficient Measurements. In studying reactions it is
desirable to have knowledge of the internal energy
distribution of the reactant ions. The reactions studied
here are bimolecular addition reactions followed by
unimolecular decomposition. As shown in Figure 4.7a, when
1_c3h3+ *8 formed from propargyl iodide by Xe+ charge
transfer chemical ionization, 1.5 eV of excess energy is
available. Much of this excess energy will be converted
into translational motion of the heavy Xe and I neutrals
resulting from the charge transfer in the collision process.
6
Under typical experimental conditions (ca. 2 3 x 10 torr
total pressure), about 125 ms was allowed for the charge
transfer process and for ejecting intermediates. For these
conditions the C3H3 + ions collided a number (10-15) of times
with the excess Xe present in the FTICR cell, leading to
near therma1 ization of internal energy before the
ion/molecule reactions were monitored. Since the reaction
time scale was on the order of seconds, it can be assumed
that any slight initial deviation from Boltzmann behavior
presents no serious error. On the other hand, the
observation that the rate constants for the reactions of 1-
C3H3+ with propargyl iodide and with both diacetylene and
acetylene are temperature independent implies that
thermalization of the ions is not complete under the
conditions reported and there is still some internal energy


69
in 1-CgH3+, which is comparable in magnitude to that
contributed from the range of temperatures studied.
Reactivity of I-C3H3. with Acetylene. Although the
results of C3H3 + + C2H2 reaction are not in agreement with
the earlier report (Smyth et al.t 1982) of C3H3+/C2H2
reactivity, the discrepancy is most likely due to
limitations of the older pulsed ICR (Smyth et al., 1982)
instrumentation for studying ion/molecule reaction pathways
in complicated systems when compared to newer FTICR
capabilities. Facile ejection of all ions except the one
whose ion/molecule reactions are being investigated offers a
very clean monitoring opportunity for product-parent
relationships even in complicated consecutive and
competitive reaction systems. Various alternative pathways
for the production of C5H3+ and C5H5+ which have been
described above probably contributed significantly to the
intensities of these ions seen in the earlier work.
Additional support for the low reactivity of C3H3+ with C2H2
is found in a recent report (Anicich et al., 1986) of the
rate coefficient for this reaction as less than 0.01 X 10~
O x
cm /s, although the isomeric form of C3H3 was not given.
It is also possible that the highest pressures used in this
work did not reach those of the earlier study due to
differences in the location of capacitance manometers,
ionization gauges, etc. Thus third body stabilization of


70
CgH5+ collision complexes might have been occurring to some
extent in the earlier work and not in that reported here.
In fact, such collisional stabilization of the association
complexes for the reactions of C3H3 + and C4H4 + with C2H2 has
been shown to occur in higher pressure SIFT studies (Smith
and Adams, 1987; Knight et al., 1987).
The most likely mechanism of the observed isomerization
of C3H3+ ions by collisions with acetylene is a "reactive"
rather than a "non-reactive" one. That is, it results from
an intimate encounter of the ion and neutral in the CgH5 +
collision complex. This hypothesis is confirmed by the fact
that deuterated forms of CgH3+ were produced when C2D2 was
the neutral reactant (see Figure 4.4). Kinetic modeling
studies (discussed in Chapter 5) indicate that in some cases
the CgHg+ collision complex dissociates to give the cyclic,
unreactive, C3H3+ isomer, instead of the reactive, linear
form which reacted initially. The possibility of
non-reactive collisional isomerization of linear C3H3+ to
the cyclic isomer has been ruled out because experiments at
elevated pressures of xenon (to ca. 1 X 10-5 torr) showed no
interconversion. Similar interconversion of C4H4+ ions from
a linear to cyclic form has also been reported (Jarrold et
al., 1984) in the reaction with C2H2 and has also been shown
to take place via complex formation by using isotopically
labeled C2H2. To confirm the hypothesis that energetically
less stable, reactive, (linear) CgH3+ ions interconvert to


71
more stable, unreactlve ones, cyclic C3H3 + Ions were also
reacted with C2D2 and no Isotope exchange reactions were
observed.
Reactivity of 1-C3H3+ with Dlacetylene. Plots of C3H3+
ion intensity vs. time for reaction with dlacetylene (C4H2)
(Figure 4.5) indicate a 10-12* increase in the intensity of
the unreactive isomer relative to the reaction when the
parent precursor only is present. Isomerization of reactive
C3H3+ was also seen when different precursors were used
(compare Tables 4.2 and 4.3). A similar mechanism involving
complex formation may be responsible for this isomerization
as well, although it was not investigated in any detail.


CHAPTER 5
KINETIC MODELING OF THE REACTIONS OF C3H3+
Introduction
As reported in the last chapter, bimolecular reactions
of the propargylium form of C3H3+ with acetylene most often
result in an isomerization to the cyclopropenylium isomer.
To help understand this isomerization process, C3H3+
reactions with deuterated acetylene were investigated.
These studies showed that the isomerization proceeds via the
C5H5+ ion/molecule reaction complex, which is sufficiently
long-lived under the experimental conditions employed that
deuterium exchange, as well as isomerization, takes place.
Thus with time the reactive propargylium C3H3+ isomer is
converted to both reactive and unreactive species containing
one, two, and three deuterium atoms. There is no evidence,
either experimental or theoretical, that the propargylium
cation converts into the cyc1opropeny1iurn cation in the
absence of the C5H5 + reaction complex. In order to better
understand the isomerization which converts the reactive
to the unreactive form of C3H3+. kinetic modeling studies of
the ion intensity vs. time curves reported in Chapter 4 were
72


73
carried out.* It was also hoped that fitting procedures
would produce improved ion/molecule reaction rate
coefficients. Quantum mechanical calculations2 on C3H3 + and
C5H5+ structures and reactivity were used to guide the
modeling effort.
Experimental
A mixture (predominantly propargy1ium) of the C3H3 +
isomers was in most cases formed by charge transfer from
propargyl iodide to Xe+, produced by 15 eV electron
ionization of Xe (present at pressures > lOx those of other
gases). Other conditions such as neutral partial pressures,
pulse sequences and reaction times, and the sources of
chemicals were kept as close as possible to those reported
in Chapter 4 for the duplicate kinetics experiments reported
and modeled here. Any significant deviations are given in
the text, table headings, or figure captions. All pressures
reported in this chapter were determined by a capacitance
manometer, and then multiplied by a "system factor" of 0.30
which corrects for the fact that the pressure read by the
capacitance manometer is not the same as that in the FTICR
*The kinetic modeling studies were performed in the
Environics Division of Air Force Engineering and Services
Center, Tyndall Air Force Base, Florida by F. Wiseman using
multiple experimental data sets produced at identical
conditions to those reported in Chapter 4.
2A. Cameron, J. Leszczynski, M. C. Zerner and B Weiner,
submitted. J. Feng, J. Leszczynski and M. C. Zerner, submitted.


74
cell. Non-linear least-squares fitting routines employing
Marquardt's algorithm (Annino and Driver, 1986), implemented
on two different computers3, were used for kinetic modeling.
Complete analytical solutions were obtained from the
chemical models developed below for the systems C3h3+ + CgHg
and C3H3+ + C4H2. A complete analytical solution was not
possible when an isotope effect was included in the chemical
model for the C3H3+ + C2D2 system. Numerical integrations
used the finite difference method (Annino and Driver, 1986).
Results
Models of C3H3+ + CqHq Reaction. As reported in
Chapter 4, collision of the propargylium cation, 1-C3H3+,
with acetylene forms the cyclopropenylium cation, c-C3H3+,
which is unreactive on the time scale of the experiments,
given the pressures attainable in the FTICR cell.
Experiments with C2D2 showed that an encounter complex which
allows for isotopic scrambling is formed. Hence, whatever
the isomeric form of this complex, a structure having the
chemical formula C5H3+ can be postulated. Since no species
of m/z 65 is observed in the mass spectrum, the (CgH5+)
species must be in steady-state and of low concentration.
The simplest scheme which takes into account this
information is given in Figure 5.1.
3Tektronix Model 4054 and Hewlett Packard Model 150.


75
kf
i-c3H3+ + c2h2 > c5H5+
k
c2h2i p
->
sink
k.
_ + £
C5H5
-> £-C3H3 +
+
C2h2
k
c5h5+
^ c
+
C2H2
Figure 5.1. Reaction Scheme Postulated for the Kinetic
Modeling of the Reaction of linear C3h3+ with Acetylene.


76
Applying steady-state kinetics to this scheme yields
I (t) = Io kp'Ij0 (1 e~9t)/0
(5.1)
In which Io and I(t) are Ion Intensities Initially and as a
function of time, respectively, Ij refers only to the linear
form,
and
kp = kppC3H3I
(5.2)
0 = [kfkcPC2H2/(k1 + kc)] + kp' (5.3)
Equation (5.1) was fitted to several kinetic runs reported
in Chapter 4. Table 5.1 shows results of these fits. A
plot of 0 vs. Pc H should be linear, as implied by equation
2 2
(5.3), and this is demonstrated in Figure 5.2. Results
yield kfkc/(kj + kc) = 2.3(.2) x 106 torr-1s-1 and kp' =
1.4(0.2) s_1.
Models of -CaiU--t-CgP2- Reaction. Reaction of C3H3+ +
C2D2 is complicated by the observation that isotopic
scrambling occurs and isotope effects are possible. Several
models were tried, including those which allowed for
complete isotopic scrambling and those which allowed only
partial scrambling. The simplest model allowed for complete
scrambling and no isotope effects4.
4Lampe and Field (1959) studied the reaction of CD4 + +
C2H4, and observed the following yields: C3HD4+ : 1/10,
C3H3D2+ : 2/5, c3H2d3+ : 2/5> and C3HD4+ : 1/10. Statistical
yields with no isotope effect would have been: C3H4D+ :
1/14, C3H5D2+ : 3/7, C3H2D3+ : 3/7, and CgHD4+ : 1/14, very


77
TABLE 5.1
Results of fits of equation (5.3) to kinetic data for the
C3H3+ + c2**2 reaction.a
Pr u /torr
l2m2
kp'I/Arb. units s 1
e/s'1
0
1.53( 06 )
1.58( 08)
4.4 x 10-7
1.65( .20)
2.40(.31)
1.0 x 10~6
1 74( 12)
3.60(.24)
1.6 x 10'6
1 71( 08 )
4.82(.23)
2.0 x 10-6
1.71( 11)
6.33(.38)
aThe standard error of estimate computed by the fitting
program is shown in parentheses.
close to the observed values. Hence, since the C3Lq +
complex exhibited almost complete scrambling, it is
reasonable to expect the CgL5 + complex modeled here to
undergo complete, or nearly complete scrambling.


0/s-
78
Figure 5.2. The Plot of 0 as a Function of Acetylene
Pressure (see Equation (5.3)).


79
Complete scrambling occurs when fragmentation of the
complex, CgLg+ (L = H, D), yields precursors having a
statistical distribution of hydrogen and deuterium atoms.
C5h3D2+ then yield the following ratios of precursors:
C3h3+ = 1/10, C3H2D+ = 3/5, and C3HD2+ = 3/10. Using these
statistics for obtaining the isotopic distribution in the
C3L3+ precursors, we obtain the scheme shown in Figure 5.3.
With the assumption again that all four CgL5+ complexes are
in steady-state, a full analytical solution is possible for
the set of kinetic differential rate equations. The
solutions to the set of equations are given in Appendix
II.A. Figure 5.4 shows the best fit curves to a typical
data set. Table 5.2 shows the fitted parameters, errors,
and residual sum of squares from fits of a typical data set.
An examination of Figure 5.4 shows that the model given
by Figure 5.3 does not adequately explain the production of
C3HD2+. In an attempt to examine this, incomplete, or
partial isotopic scrambling was next assumed. To do this
correctly requires a detailed knowledge of the chemistry of
the system, which is not available. A somewhat crude
application of isotope effects applies multiplicative
factors to the individual rate constants and this procedure
requires but a nominal knowledge of the structure of the


80
k-
t-CjH3+ C202 > C5H3D2 +
t-CjHj* C3H3I > sink
SH32+ > T3 l^3H3+ + T C2D2 I l^3H2D+ +
lc2HD + ^l-C3HD2+^c2H2
C5H3D2
> TO C^3H3+ + TO C22 + T C-3H2D+ +
I C2HD + TO C-C3HD2+ + T C2H2
i-C3H2D+ + C2D2 > C5H2D3+
i-C3H2D + C3H3I > sink
C5H23 > 10 l_C3D3+ + T C2H2 + I t_C3HD2+ +
T C2HD + To t-C3H2D+ + TO C2D2
C5H2D3< > TO C-3D3+ + To C2H2 + T 32+ +
? C2HD + T C^3H2D+ + TO C22
t-C3HD2+ c2o2 > cshd4+
1-C3HD2* C3H3I 2_> sink
C5HD4+ I C3HD2+ i C2D2 | t-C3D3+ + f C2HD
+ kc
C5HD4 ~E_> 5 C'C3HD2+ T C22 + f C-C3D3+ + f C2HD
i-c3o3 c2d2 > c5d5
+ kt +
C5D5 > l^33 + C22
* C^H^I :> sink
kc
C5D5 > cC33 C22
Figure 5.3. Reaction Scheme Postulated for the Kinetic
Modeling of the Reaction of linear C3H3+ with Deuterated
Acetylene Assuming Complete Scrambling and No Isotope
Effects.


81
(a)
Figure 5.4. Model Fit (using the
Typical Data Set for C3H3 + + CgDg
vs. time curves for (a) C3h3 + and
c3d3+.
scheme of Figure 5.3) to a
Reactions. Ion Intensity
C3H3D+ and (b) C3HD3+ and


TABLE 5.2
Results uf Model Fits (Figures 5.3 and 5.7) for the System c3113 +
+ C2n2 under Various Experimental Conditions.
Pressures (torr)
C2D2
C22
C D
U2
C2n2
C2U2
1.2 X 10~6;
1.2 X 10'6;
7.8 X 10-7;
6.2 X 10-7;
1.1 X 10'6;
PC3,,3I
P(w
PW
t>C3H3I
"W
1.1 X 10"7
1.1 X 10"7
1.1 X io7
1.1 X 10~7
1.3 X 107
4.17(.15 )
1.1K.14)
920(.098)
1.30(.12)
1.86(.34)
:c/kt
F
kPPc33I
(s-1)
(arb units)
(arb units)
SOS*
212( .030)
1(fixed)
O
H

CO
o
N
.707(.007)
063(fixed)
.017
308(.026 )
1.86(.11 )
2.16(.08)
.703(.005)
.067(fixed)
.0069
318( .032)
1.71 (.08)
2.20(.09)
.671( .007 )
.057(.008)
.0023
389(.026)
1.53(.06)
2.74(.07)
.881(.006 )
. 100(.006)
.0038
.363(.034)
1.58( .13)
2.18(. 11 )
.856(.007 )
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00
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83
species involved5. This simple scheme was applied as
described below.
£
Quantum mechanical calculations indicate that C2H2
does not readily react with the cyclopropenylium cation, but
does react with the propargylium cation (1-C3H3+) without
barrier with formation of the four possible products shown
in Figure 5.5. Thermodynamically, only Structure (5.1) is
stable with respect to decomposition to c-C3H3+ + C2H2.
However, since the 1-C3H3+ + C2H2 > Structure (5.1)
reaction is at least 60 kcal/mol exothermic6 in the
absence of stabilizing collisions this energy then permits
many different isomeric forms to be sampled before
decomposition back to C3H3+ + C2H2. If the sampling of all
isomers is fast, complete isotopic scrambling is expected.
Given the uncertainity in C5H5+ structures, total
equivalence of carbon atoms in the complex is assumed. For
ease of understanding, a cyclic C5H5+ complex, in which all
C atoms are sp2 hybridized, might be visualized. With these
assumptions, it is a simple matter to determine which carbon
atoms undergo hybridization changes during the reaction.
For instance, in the attack of C2H2 on 1-C3H3+, three carbon
5
Although somewhat crude, applying a multiplicative factor
to the rate constant for each deuterated site is in keeping with
experimental evidence. For instance, in the acetolysis of some
identical tosylates, each deuterium atom substitution changed the
rate constant by ca. 0.84 (Streitwei ser et. al. 1958).
Details of these studies are given in: J. Feng, J.
Leszczynski and M. C. Zerner, submitted; and J. Leszczinski, M.
C. Zerner and F. Wiseman, submitted.


84
(5.1)
(5.2)
(5.3) (5.4)
Figure 5.5. Structures which are Proposed to Form by
the Reaction of Propargylium Ion with Acetylene Without an
Energy Barrier.


85
atoms change from sp to sp2 hybridized. Upon fragmentation,
some carbon atoms remain sp2 hybridized; others become sp
hybridized.
In general, for a-secondary isotope effects, an
increase in hybridization in going from the reactant state
to the transition state yields an inverse isotope effect (kR
< kjj), whereas a decrease in hybridization yields a normal
isotope effect (kjj > kp) (Dreuth and Kwart, 1980). In this
system the bimolecular addition reaction will have an
inverse isotope effect, and the fragmentation reaction
should have a normal isotope effect. Figure 5.6 shows how
the isotope effects for the reaction of 1-C3H3+ + C2L2 can
arise. For the forward addition reaction, EpH > EpD and for
the fragmentation reaction, ERR < ERD, in which the
subscripts "F" and "R" refer to forward and reverse,
respectively, and "H" and "D" refer to protonated and
deuterated species, respectively. Since the bimolecular
addition is very exothermic for the formation of most CgL5 +
isomers, it might be expected that the "average" transition
state structure might closely resemble the reactants and not
any of the C5L5 + isomers. This in turn implies that ERD -
ERh > EpR Epjj (zero-point effects). However, the excess
energy in the reaction will allow longer sampling times for
the more energetic CgL5+ isomers. The less energetic
isomers which are sampled will undoubtedly be in higher
rotational and vibrational levels. The overall effect is to


86
+
Figure 5.6. A Schematic Representation showing the
Qualitative Differences in the Zero-Point Vibration Energy
Levels for the Reactants, Transition-State, and a
Representative C5L5+ Isomer for the Reaction of linear C3H3+
with C2H2/C2D2. (E f h > ^FD ^RH a n ^ ^rd are explained in
the text. )


87
lessen the normal Isotope effects expected in the
fragmentation of the C5L5+ isomers, unless there are
sufficient collisions to stabilize the isomers prior to
fragmentation.
In the model development outlined below, only
a-secondary isotope effects will be considered important.
0-secondary isotope effects, arising predominantly from
hyperconjugation, can sometimes be important (Melander,
I960), but will be assumed here to be minor compared to the
o-effects. It is also possible that hydride/deuteride
shifts may be occurring in the transition- state. However,
hydride transfers often exhibit small isotope effects
(Melander, and Saunders, 1980) and hydride shifts, if they
occur at all, will be assumed here to give negligible
contributions to the isotope effects.
Even though the different reactions in Figure 5.3 will
have different isotope effects, the introduction of an
independent fitting parameter for each type of reaction is
not justified. Though crude, only one additional parameter
was introduced into the model to account for all potential
a-secondary isotope effects. The method for introducing
this parameter is outlined as follows.
If a carbon atom bearing a deuterium atom undergoes a
hybridization change from sp to sp2 (force field becoming
stronger), the "isotope effect factor", F, is introduced as
a multiplicative factor in the rate constant. For two


88
deuterium atoms, F2 is the multiplicative factor, etc. If
the deuterium atom is attached to an atom changing from sp2
to sp hybridized, the rate constant is divided by F, for two
deuteriums, F2, etc. Introducing the same factor for both
addition and fragmentation reactions implies a constraint
which is at best only qualitatively correct. Applied in the
numerator the factor corrects for a single deuterium atom
(F2 for two, etc.) attached to a center undergoing
hybridization change from sp to sp2 in the transition-state
complex. Applied in the denominator, it corrects for a
change from sp2 to sp hybridization. Since the
transition-state complex has a stronger force field than the
reactant state (1-C3L3+ + C2L2) at these centers, the
-secondary isotope effect will be "inverse" and F should
therefore be greater than unity.
Using the structural notation,
H\ H\
1-HDC3H+ = [ C-C=C-H]+, 1-H2C3D+ = [ C-C=C-D]+,
D7 H7
H\ D\
1-HDC3D+ = [ C-C=C-D]+, and 1-D2C3H+ = [ C-C=C-H]+,
D7 D7
the full kinetic scheme is shown in Figure 5.7. The neutral
fragmentation products, C2H2, C2HD, and C2D2, have not been
included for brevity. It is assumed that 1-C3L3+ undergoes
the same kind of hybridization changes when reacting with
C3H31 as it does with C2L2. As shown in Chapter 4, the


89
FTc
i-c3h3* c2d2 L> c5h3d2+
t-C33 + C3H3I > sink
C5H3D2
* ^7 ^3H3+ + IF -HDC3H+ + I -W* ' sF V* T *D2C3^
5F
C5H3D2+ > ~2 C^3H3+ + IF C^3H2D> + To
1 OF
F2k
t-HDC3H+ + C2D2 i> C5H2D3+
F3k,
i-H2C3D+ c2D2 L> C5H2D3*
t-HDCjH + C^I > sink
* F*p
i-H2C3D C3H3I Sn*
C5H2D3* > ^ ^ £-HDC3D+ IF l-2C3H" * ^5 W*
C5H2D3* > TO C^33+ IF C-C3HD2> "4 C^3H2+
1 OF
F3k
t-HDC D+ CD, -> C HD +
3 2 2 5 4
F2k
t-D,C,H+ CD, -> C_ HD +
2 3 2 2 5 4
Fk
i-HDC3D C3H3I -> sink
* F\
t-c3D3 C202 1> c,D
S 5
l-D C H C3H3I :> sink
Fk
i-C3D3 C3H3I :> sink
V/ -J_> JL¡ t-C^* JL_ t.HOC3D^ -L t-D C
SF 5F 5F
VF
CS5 >
C'H* 5F C_C33 C_C3IID2
'5 4
k /F*
C.D. > c-C3D3
5 5
Figure 5.7. Reaction Scheme Postulated for the Kinetic
Modeling of the Reaction of linear C g H g + with Deuterated
Acetylene Assuming Complete Scrambling and a-secondary
Isotope Effects.


90
products of the 1-C3L3+ + C3H3I reaction are of higher mass
and do not enter further into the kinetic schemes modeled
here.
Steady-state conditions are applied for all four C5L5+
isotopic species as before (without regard for isomeric
differentiation) and the differential rate equations for
scheme shown in Figure 5.7 are given in Appendix II.B.
Table 5.2 shows fitting results for several data sets using
the same kinetic scheme. Figure 5.8 shows plots of the best
fit of this model to the same data set as fitted in Figure
5.4.
Some experiments were conducted where certain ions were
ejected from the analyzer cell using FTICR double resonance
techniques (Comisarow et. al., 1978) as they formed. Among
the ions ejected were C3H2D+ and C3HD2+. Without further
fitting, this model was used to predict the behavior of the
kinetic system if these ions were ejected. Figure 5.9 shows
predicted results and data points.
Models for 4H2. The reaction of C3H3+ with
C4H2 (diacetylene) is kinetically more complicated than that
of C3H3+ with C2H2. There are more isomeric possibilities,
and ion/molecule reaction products of higher m/z are
detected. Several models were tried in attempts to fit the
experimental data, and the best of these made the
assumptions that C7H5+ and the excited forms of CgH5+ and


91
(b)
Figure 5.8. Model Fit (using the scheme of Figure 5.7) to
Typical Data set for linear C3H3+ + C2D2 Reactions. Ion
intensity vs. time curves for (a) C~H~ + and C~H0D+ and (b)
C3HD2+ and C3D3+. 32
a


Full Text
UNIVERSITY of FLORIDA
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FILES


STUDIES OF GAS-PHASE ION/MOLECULE REACTIONS
IN RELATION TO A PROPOSED IONIC
MECHANISM OF SOOT FORMATION
BY
FEZA ÃœZTURK
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1988
' 1UN1VERSITY 0F FLORIDA LIBRARIES

TO ELIF
Digitized by the Internet Archive
in 2011 with funding from
University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation
http://www.archive.org/details/studiesofgasphasOOzt

ACKNOWLEDGEMENTS
This work is the final product of the efforts and
encouragement of many. First, I must thank my colleagues,
Bryan Hearn, Dr. Cliff Watson and Dr. Steve Bach, in the
Eyler group, including Dr. GOkhan Baykut and Dr. Mehdi Moini
who are no longer with the group, for their help and
suggestions. Each one deserves particular thanks for their
special efforts and friendship throughout these last years.
I have greatly benefitted particularly from their technical
experience and skills whenever questions and difficulties
arose in the lab.
Next, I wish to acknowledge my research advisor, Dr.
John Eyler, whose guidance and encouragement has enabled me
to experience the intellectual satisfaction and enjoyment of
scientific research. With his research funds, I had the
opportunity to spend my time exclusively doing research and
attend the annual meetings of the American Society of Mass
Spectrometry which provided the best setting for scientific
communication. I also would like to mention his editing
skills which have always assisted me and had a major role in
putting this manuscript to its final form.
ill

I would like to acknowledge Dr. Floyd Wiseman from the
Environics Division of Tyndall Air Force Base for his
interest and efforts in this research project. His
contribution to the work by the kinetic modeling study
deserves an important credit for providing a better
understanding of experimental results.
Special thanks are extended to Dr. William Weltner, Dr.
Robert Hanrahan, Dr. Merle Battiste, Dr. Willis Person and
Dr. Charles Proctor for serving as committee members. I
particularly wish to thank Dr. Calvin VanderWerf, Dr. Robert
Hanrahan, Dr. Kathryn Williams, and Dr. William Weltner for
their efforts and willingness to be supportive in every way
throughout these long years.
Another special person deserving particular thanks is
my friend, Zekiye Onsan. She has been an endless source of
encouragement and never failed to give her help whenever
needed. I also wish to thank Taghi Alizadeh Yekani for
sharing the difficult times with me with patience and
sincerity in my earlier years of study.
Finally, there is my five-year old, Elif. She made it
worhwhile by just being there for me.
iv

TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS ill
ABSTRACT vii
CHAPTER
1 INTRODUCTION 1
2 INSTRUMENTATION 15
3 ION/MOLECULE REACTIONS 29
Theory of Ion/Molecule Reactions 29
Experimental Study of Ion/Molecule Reactions
Using FTICR 38
4 REACTIONS OF C3H3+ WITH ACETYLENE AND
DIACETYLENE IN THE GAS PHASE 45
Introduction 45
Experimental 48
Results 50
Discussion 64
5 KINETIC MODELING OF THE REACTIONS OF CgH3+ .. 72
Introduction 72
Experimental 73
Results 74
Discussion 93
6 REACTIONS OF C5H5+ AND C5H3+ WITH ACETYLENE
AND DIACETYLENE 101
Introduction 101
Experimental 104
Results 107
Discussion 123
v

7 REACTIONS OF GASEOUS C?H7 + IONS 132
Introduction 132
Experimental 136
Results 138
Discussion 148
8 CONCLUSIONS AND RECOMMENDATIONS 164
APPENDIX
I PROGRAM TO CALCULATE ABSOLUTE RATE CONSTANTS
AND THEIR 95% CONFIDENCE LIMITS FROM RAW OR
NORMALIZED INTEGRATED PEAK AREAS OF THE
REACTING ION AS A FUNCTION OF TIME IN FOURIER
TRANSFORM ION CYCLOTRON RESONANCE MASS
SPECTROMETRY 167
II ANALYTICAL EXPRESSIONS FOR KINETIC MODELING 181
BIBLIOGRAPHY 187
BIOGRAPHICAL SKETCH 196
vi

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
STUDIES OF GAS-PHASE ION/MOLECULE REACTIONS IN RELATION TO
A PROPOSED IONIC MECHANISM OF SOOT FORMATION
By
FEZA ÃœZTÃœRK
August, 1988
Chairman: John R. Eyler
Major Department: Chemistry
The reactions of small hydrocarbon ions such as C3H3+,
c5h3+> c5h5+* and C?H7+ with acetylene and diacetylene have
been investigated using Fourier Transform Ion Cyclotron
Resonance (FTICR) mass spectrometry to provide qualitative
and quantitative information about a proposed ionic
mechanism of soot formation. Ion/molecule reaction pathways
and rate coefficients have been determined for several
isomers of each of the ions listed above, formed from a
variety of precursors, and reacting with precursors,
acetylene and diacetylene. Further understanding of
reaction mechanisms of some of the reactions proposed
experimentally was obtained from kinetic modeling studies.
All of the small hydrocarbon ions studied reacted with
diacetylene extensively while almost no production of larger
vii

ions was observed with acetylene. Linear C3H3 + was formed
by charge transfer ionization of propargyl iodide using Xe+,
and was found to isomerize to the cyclic form of C3H3+ in
reactions with both acetylene and diacetylene. The
isomerization was shown to take place via a long-lived
C5H5+* complex by isotope exchange reactions between linear
C3H3+ and deuterated acetylene. The reaction rate
coefficients for the reaction of C3H3+ with deuterated
acetylene and diacetylene were (4.5 + 1.9) x 10-10 cm3/s and
(1.4 + 0.7) x 10-9 cm3/s, respectively.
While different structures could be attributed to
C3H3+, C5H3+, and C7H7 + ions produced from different
precursors on the basis of reactivity, this could not be
done for C5H5+ ions, whose reactivity with acetylene and
diacetylene was similar within experimental error regardless
of precursor. Presence of two structural isomers of C5H3+
was determined using different precursors and several
structures for these isomers were proposed. The reactive
isomer was observed to react with diacetylene with a rate
constant of (5.6 + 1.7) x 10-*9 cm3/s. Rate coefficients
for the ion/molecule reactions of C7H7 + were found to be
different when it was formed from various precursors, which
implied the involvement of different C7H7 + structures. All
experimental results are discussed in relation to
theoretical work involving structures of the ions studied
and a proposed ionic route to soot formation.
viii

CHAPTER 1
INTRODUCTION
Soot is a combustion product which has undesirable
effects both on human health and on the efficiency of fuel-
powered engines due to increased heat transfer to critical
engine components. Considering the fact that the use of
alternative fuels such as shale or coal-derived gas in the
near future would lead to increased soot emissions, search
for an effective way to reduce soot has been going on for a
long time. The design and development of advanced engines
to achieve soot suppression requires a sufficient
fundamental understanding of the mechanisms governing soot
formation. Soot formation in hydrocarbon flames involves a
succession of fast processes that occur within a few
milliseconds during the combustion of the hydrocarbon.
Although many investigations have been undertaken in
relation to the process of soot formation in fuel-rich
hydrocarbon flames, understanding of this process is still
limited. Experimental techniques such as mass spectrometry
(Calcóte, 1963; Michaud et al., 1981), laser-light
scattering (Kent et al., 1981; D'Alessio et al., 1977),
laser induced ionization (Smith and Mallard, 1981), and
laser induced fluorescence (DiLorenzo et al., 1981) have
1

2
been used to study the molecular species and particles In
flames.
Soot collected from flames consists of chalnllke
aggregates of spherical units having diameters of 10-50 nm
with a carbon/hydrogen atom ratio in the range 8:1-12:1
(Calcóte, 1981). Three distinct steps of soot formation
have been recognized over many years of research (Calcóte,
1981) :
1. Nucleation- a phase change from molecular species where
chemical reactions dominate to incipient soot particles
where physical processes dominate;
2. Growth to spherical particles of 10-50 nm in diameter;
and
3. Aggregation or agglomeration of the spherical units to
form chains.
Among these, the first step, nucleation, is the least
understood in the process. Although many diverse theories
have been put forward to explain the nucleation process,
only two of these have received quantitative support:
1. Mechanisms involving neutral and free radical species;
and
2. Ionic mechanisms.
Neutral and Free Radical Mechanisms. A large number of
neutral and free radical mechanisms have been proposed to
describe the transition from molecular species to soot

3
(Palmer and Cullis, 1965; Lahaye and Prado, 1978; Gaydon and
Wo 1fhard, 1979).
One of the proposed paths Involves polyacetylenes
where acetylene reacts to form higher species (Bonne et al.,
1965) .
C4H2
C6H2
c8h2
-H
^2^2
C2H2
I
> c4h3 (+H)
c2h2
l-H
I
> c6h3 (+h2)
C2H2
l-H
I
> c8h3 (+h2)
It was suggested that the continuation of this series
leads to larger radicals which further react with each other
and with higher polyacetylenes forming even larger
molecules. However, because this mechanism leads to
formation of a giant chain molecule instead of a polycyclic
carbon structure, it was not accepted as being responsible
for soot formation (Homann, 1967). To account for the
problem of ring formation, Homann and Wagner (1967, 1968)
suggested that radicals such as CgH attack the
polyacetylenic species forming side chains which lead to
branched polymerization, and presumably ring closures. The
experimental support of this scheme comes from the
observation that in the oxidation region of the flame, the
concentration of polyacetylenes decreases while that of the
polycyclic aromatics increases. But the growth of
polyacetylenes was considered too slow by Calcóte (1981), to

4
account for the rapid formation of soot particles.
Furthermore, as pointed out by Bonne et al. (1965), Thomas
(1965) and Cullis (1976), the rearrangement of a
polyacetylene to an aromatic graphite-1ike structure would
also be a slow process.
Another hypothesis proposed by Glassman (1980)
emphasized the importance of strongly conjugated molecules
such as butadiene in the formation of ring structures with
side chains to which butadiene-type molecules keep adding.
This mechanism did not receive much support on the basis of
concentration profiles in which the butadiene concentration
is observed to fall very rapidly even before the initiation
of soot formation (Cal cote,1981).
Some models considered C2, CgH and Cg radicals as
initial nuclei for soot formation which undergo condensation
reactions with each other or with acetylene (Jensen, 1974;
Smith, 1940; Carbannes, 1956). The main objection to these
mechanisms based on C2 and Cg condensation reactions was the
presence of a very strong C2 radiation in rich cyanogen-
oxygen flames which do not form soot.
Finally, direct condensation of aromatic rings was
proposed as being the most favored thermodynamic path to
soot formation (Bonne et al., 1965; Graham et al., 1975;
Stein, 1978). However, by a detailed analysis of the
concentration and the flux profiles of the species, Bittner
and Howard (1981a, 1981b) were able to show that soot is

5
produced via nonaromatic hydrocarbon intermediates rather
than via intact aromatic rings. But after a consideration
of many species, only a few intermediates were found to
favor the rearrangement to a ring structure over other
decomposition channels.
To conclude the discussion above, it is clear that all
the proposed neutral species mechanisms for soot formation
have serious problems with the nucleation step, and thus
none can be considered completely satisfactory in
understanding the soot formation process. Particularly it
is difficult in any of the proposed neutral schemes to
produce small cyclic and polycyclic species with a
sufficiently high rate to model the quite rapid soot
formation seen in flames. Recently, however, a
neutral/radical soot formation model has been proposed which
contains many steps and incorporates quite recently obtained
shock tube kinetic data (Frenklach et al., 1985). This
model is capable of yielding small ring compounds at a
higher rate than previously suggested radical mechanisms,
although there is some question as to the correct rate
constant for one or two of the crucial steps in formation of
the first ring.
Ionic Mechanisms. A number of experimental
observations in flames have led to a consideration of the

6
importance of ions in soot formation. Such observations in
flames include (Olson and Calcóte, 1981a; Calcóte, 1981):
1. Presence of a unit charge on soot particles;
2. A positive correlation between the growth of large ions
and the appearance of soot;
3. The increase both in the concentration of large ions and
the onset of soot formation by the addition of electrophilic
molecules;
4. Identical location for the peak concentrations of
molecular ions and soot precursors;
5. Production of larger particles by an increase in the
residence time of the positive ions; and
6. High ion concentrations in hydrocarbon pyrolysis.
As a consequence of the above observations, several
ionic mechanisms have been suggested (for references, see
Calcóte, 1981). The postulated general growth of soot
particles from primary ions is shown in Figure 1.1. Calcóte
(1962) proposed the chemiionlzation reactions (1.1) and
(1.2) for the formation of primary ions:
CH + 0 > CHO+ + e~ (1.1)
CH* + C2H2 > C3H3+ + e- (1.2)
The C3H3+ ion is the dominant ion observed in fuel-rich
flames (Knewstubb and Sugden, 1959; Goodings et al., 1979;
Olson and Calcóte, 1981b; Michaud et al., 1981) and its

7
Primary flame
i°ns
°C
C2H2
^CH+
c3m3 +c4h2
etc.
Neutral flame
species
C5H5 +
C5H3+
>C5H5+
C7H3+'
C7H5+
-etc.
C^Hy species
etc.
-ION ELECTRON
RECOMBINATION
<3>

<3>
NUCLEATION
"incipient soot particles
SURFACE GROWTH
Small particles
^ THERMAL IONIZATION
Neutral and small
charged particles
.—--AGGLOMERATION
\ ‘V N
SOOT
Figure 1-1. Growth of Soot Particles from Primary Molecular
Species.

8
concentration falls very rapidly at the critical equivalence
ratio of soot formation where the concentration of the
larger ions starts to increase (see Figure 1.2)
(Calcóte, 1981). Unfortunately, the mechanism of C3H3+
formation is still not clear. An alternative mechanism
(Calcóte, 1972) for C3H3 + formation is shown by reactions
(1.3) and (1.4):
CHO+ + C2H20 > C2H30+ + CO (1.3)
c2h3o+ + c2h2 > c3h3+ + CH20 (1.4)
Reaction (1.5) is postulated (Calcóte, 1972) to account for
the dominant H30+ observed in near stoichiometric and lean
flames :
CHO+ + H20 > H30+ + CO (1.5)
The C2H3+ ion was also considered as a possible nucleating
center for soot formation in flames and its formation is
shown by reaction (1.6) as proposed by Vinckier et al.
(1977 ) .
CHO+ + C2H2 > C2H3+ + CO (1.6)
The primary ions mentioned above are proposed to react
with CxHy molecules by fast ion/molecule reactions (Calcóte,

9
Figure 1.2. Effect of Equivalence Ratio on Peak Ion
Currents for 2.0 kPa Acetylene-Oxygen Flames. The shaded
area indicates the minimum equivalence ratio for soot
formation.
Reprinted by permission of Elsevier Science Publishing Co.,
Inc. from the article by H. Calcóte (1981). Copyright 1981
by the Combustion Institute.

10
1981; Olson and Calcóte, 1981a). The typical set of
reactions for C3H3 + are shown below:
C3H3 +
+
C2»2
> C5H3+ + H 2
(1.7)
C3H3 +
+
c2h2
> C5H5+
(1.8)
c3h3 +
+
c2h -
---> C5H3+ + H
(1.9)
c3h3 +
+
C4H2
> c5h3+ + c2h2
(1.10)
C3h3 +
+
c 4 H 2
> CfjrHg
(1.11)
The next step is the further addition of neutral
building blocks, acetylene and diacetylene to the product
ions producing larger ions with increased C:H ratio.
Following are a few reactions representative of this step.
C5H3 +
+ ^ 2 H 2
> c7h5+
(1.12)
C5H3 +
+ c4h2
> c9h5+
(1.13)
C7H5 +
+ C4H2
> c9h5+ + c2h2
(1.14)
This series of reactions is suggested to lead to the
formation of polycyclic structures such as C13Hg+ and

11
The problem of rearrangement of linear structures to
polycyclic structures encountered in the neutral mechanism
is overcome in the ionic mechanism because of the general
observation that gaseous ions usually rearrange upon
formation to their most stable structure (Calcóte, 1981).
Michaud et al. (1981) have made an alternate suggestion
that direct reactions of C3H3+ with aromatic neutrals such
as benzene, toluene, naphthalene, methylnaphthalenes, and
indene may be more important in forming polycyclic ions than
sequential reactions involving acetylene and diacetylene.
In fact, recent ion cyclotron resonance (ICR) studies of
reactions of C3H3+ with aromatic neutrals showed (Baykut et
al., 1986) that these reactions are fast enough to be
considered as possible bypass channels in ionic soot
formation pathways.
The main objection to the ionic mechanism is the lower
concentration of ions in flames compared to that of neutral
species. Figure 1.3 (Calcóte, 1981) shows the concentration
profiles of primary neutrals and ions observed in flames as
a function of distance above the burner. One of the most
important features of the figure is that the soot
concentration is lower than that of the large positive ions
which implies that there are probably enough of these large
ions to produce the observed levels of soot. Several orders
of magnitude higher concentrations of neutral species
compared to those of ions in flames can be explained as a

12
DISTANCE ABOVE BURNER.Cm
Figure 1.3. Number Densities of Neutral and Ionic Species
Found within Flames.
Reprinted by permission of Elsevier Publishing Co., Inc.
from the article by H. Calcóte (1981). Copyright 1981 by
the Combustion Institute.

13
requirement for the ion/molecule reactions to proceed fast
enough to account for the rapid formation of soot.
In this study, the reactions of primary ions with flame
neutrals have been investigated to identify different
reactant ion structures, reaction products and mechanisms.
One of the goals of this study was to determine how fast
these ion/molecule reactions proceed under laboratory
conditions, which hopefully leads to a better understanding
of the complex phenomena occurring under flame conditions.
Fourier Transform Ion Cyclotron Resonance (FTICR) mass
spectrometry, used in this study, is well suited to
investigate ion/molecule reactions due to its inherent
qualities which differ from other mass spectrometers. These
qualities include very clean isolation of the mass of
interest from a complicated reaction mixture and accurate
rate constant measurements along with reaction mechanism and
branching ratio studies. The basics of this technique are
discussed in Chapter 2 along with an explanation of the
determination of some experimental pressure measurement
parameters such as Baratron factors and the system factor
inherent to the instrument. The use of FTICR mass
spectrometry for studying ion/molecule reactions is
discussed in Chapter 3 along with some theoretical models
developed for ion-molecule reactions. The main body of the
experimental work, reported in Chapters 4-7, deals with
proposed nucleatlon steps of the ionic mechanism of soot

formation.
results is
14
An overall conclusion of the experimental
included in Chapter 8.

CHAPTER 2
INSTRUMENTATION
Fourier Transform Ion Cyclotron Resonance (FTICR) Mass
Spectrometry was introduced in the mid-1970s by Comisaron
and Marshall (1974a, 1974b, 1974c, 1975). It involves the
application of Fourier multiplex concepts (Griffiths, 1978;
Marshall, 1982) to ICR mass spectrometry. High speed, high
sensitivity, computerization, ultra-high mass resolution,
and wide mass range are some of the advantages of Fourier
Transform over continuous-wave spectrometry (Marshall,
1985). Basic principles and the vast applications of this
relative newcomer to mass spectrometry are summarized in
several recent review articles (Johlman et al., 1983; Gross
and Rempel, 1984; Comisarow, 1985; Marshall, 1985; Baykut
and Eyler, 1986; Laude et al.,1986). In this chapter, the
basic theory of operation of ICR which led to the concepts
and development of the FTICR technique will first be
discussed. Following that is a description of the
instrument along with typical experimental parameters and
the general sequence of operation.
Theory. An ion of charge, q, moving at velocity, v
when put in a uniform magnetic field, B, is subject to the
Lorentz force,
15

16
ma
q (v x B)
(2.1)
which acts perpendicular to the direction of Ion motion.
Under the influence of this force, the ion follows a helical
path (Lawrence and Livingston, 1932) which, when projected
into a plane perpendicular to the magnetic field gives a
circle with a radius, r proportional to the velocity of the
ion, as shown in Figure 2.1. Substitution of the
centripetal acceleration in terms of angular frequency, w,
into equation (2.1) gives
and
o p
IF! = mlal = mv /r = mr» = qcurB
0) = qB/m (mks units)
(2.2)
(2.3)
which relates the ion's characteristic cyclotron frequency
to its q/m (charge/mass). Equation (2.3) is called the
cyclotron equation and provides the basic principle of mass
measurement in terms of cyclotron frequency in the ICR mass
spectrometer. For a magnetic field of 3.0 Tesla, singly
charged ions with masses in the range of 18-5000 a.m.u. have
cyclotron frequencies in the radiofrequency range (10 kHz-
2.6 MHz), within which frequency can be measured with high
precision.
Operation. A schematic representation of the
commercial Nicolet FTMS-1000 mass spectrometer with a
superconducting solenoid magnet (3 Tesla) is shown in Figure

17
Figure 2.1. Motion of an Ion with Initial Velocity
Magnetic Field B.
in a

18
2.2. All data acquisition and processing and the selection
of various experimental parameters (except emission current)
are under computer control. Figure 2.3 shows a simplified
block diagram of an FTICR mass spectrometer. The simplicity
of operation results from the ability to form, excite, react
and detect ions in the same 1-inch cubic stainless steel
cell shown in Figure 2.4. This analyzer cell is located in
the center of a vacuum chamber which passes through the bore
of the magnet. The background pressure of 10”® torr is
achieved by the use of a four-inch diameter oil diffusion
pump and by baking out the system at 250°C for several hours
each night.
An inlet system which is evacuated with a three-inch
diameter diffusion pump permits the introduction of gas and
liquid samples into the high vacuum through precision leak
valves. The liquid samples are used after multiple freeze-
pump-thaw cycles to remove non-condensible gases. A solids
insertion probe is used for the introduction of solid
samples into the vacuum chamber and can be heated up to
250°C to promote sublimation of the solid.
Ion formation is typically achieved in 5 ms by
collisions of electrons accelerated to 10-70 eV with
neutrals leaked into the vacuum chamber. The number of ions
is controlled by monitoring the emission current, measured
by means of an electron collector located behind the trap
plate opposite to the filament. When ions are formed, they

co
Figure 2.2. Schematic Diagram of FTICR-1000 Mass
Spectrometer.

20
Figure 2.3. Simplified Block Diagram of an FTICR Mass
Spectrometer.

21
electron
collector
V
trapping
plate
transmitter
plate
receiver
trapping
plate
receiver
plate
transmitter
plate
Figure 2.4. Cubic FT ICR Cell.

22
start cyclotron motion at their characteristic frequency
with a random phase. The trapping plates shown In Figure
2.4 constrain the ion motion in the direction parallel to
magnetic field lines. Positive and negative ions are trapped
by the application of, typically, positive and negative 1
volt potentials to the trapping plates, respectively.
To detect the ions, a fast sweep of oscillating voltage
in the radiofrequency range is applied to the transmitter
plates shown in Figure 2.4. Ions absorb energy at their
cyclotron frequency and are driven into coherent motion with
a larger radius, thus inducing an image current oscillating
at the frequency of their cyclotron motion on the receiver
plates (see Figure 2.5). The image current is amplified,
digitized and stored in the computer's memory as a time-
domain signal which contains the superimposed frequency
information of all the ions with different masses in the
analyzer cell. A fast Fourier Transform (Cooley and Tukey,
1965) is applied to the time-domain data to produce the
frequency-domain spectrum which can be plotted in terms of
the ion masses. Figure 2.6a shows a time-domain spectrum
of two superimposed sine waves of frequencies and aig •
The decay of the signal results from the dephasing of ions
due to collisions with the neutral molecules. Fourier
transformation of this spectrum gives the mass-domain
spectrum shown in Figure 2.6b. In this procedure, the
lowest mass detected is limited by the sampling frequency of

23
Figure 2.5. Excitation and Detection of Ion Motion.
(a) Ion motion in magnetic field only, (b) motion during
radio-frequency pulse applied to the transmitter plates,
(c) larger radius of ion motion after excitation, and
(d) generation of an image current in the receiver plates by
a rotating ion "clump".

24
D
TD
O
â– *-*
O.
E
<
Time
SflííiMírft"
(a)
100
(b)
Figure 2.6. Ion Detection by Fourier Transform. (a) Time-
domain spectrum (Abscissa is time; ordinate is ion signal),
(b) Frequency-Domain Spectrum after Fast Fourier Transform
of the time-domain data (Abscissa is frequency; ordinate is
ion signal).

25
the analog-to-digital converter, which should be twice the
signal frequency according to the Nyquist criterion. Since
the highest cyclotron frequency detected is one-half the ADC
frequency, for a magnetic field of 3 Tesla used in this
work, the singly charged ion mass corresponding to this
frequency is 18 a.m.u., which sets the low mass limit.
A typical experimental sequence is shown in Figure 2.7.
Ions can be manipulated in various ways between the
formation and the excitation pulses. Ion ejection is used
to clean the cell of all ions except one of interest. Ions
are ejected by the same principle as excitation. The only
difference is that a higher amplitute of excitation voltage
is used. In this way ions achieve large enough radii to
strike the cell walls and be neutralized. Application of
either a single ejection pulse at a single cyclotron
frequency or a swept pulse covering a range of frequencies
is determined according to the user's purpose.
After selection of the ion of interest, different kinds
of ion chemistry can be performed. Among these, ion/molecule
reactions, co11isi onal1y activated dissociation, and
photodissociation are the most commonly used processes in
characterization of ion structures. Since the number of
stages of ion ejection and manipulation is not limited by
hardware or software, (MS)n (multiple stages of mass
selection and manipulation) experiments can be performed by
repeating the same processes for the various generations of

Ejection pulses
Quench
pulse
/
Excitation pulse
ir
Quench
pulse
T t
Electron beam
pulse
Reaction time
Detection
pulse
to
a
TIME —»
Figure 2.7.
Cell.
A Typical Experimental Sequence in the FTICR

27
offspring ions. Laser desorption of solid samples and laser
ionization are other techniques used in conjuction with
FTICR.
Experimental Parameters. In this study, the FTICR
technique was used mainly to determine ion/molecule reaction
rates and mechanisms. Ion formation was accomplished by
dissociative ionization using various charge transfer agents
instead of electron impact ionization, in order to form the
ions with well-defined internal energies. Reaction pathways
were delineated by using the ejection capabilities of FTICR
which make it possible to eject one ion from a complicated
reaction mixture to determine its contribution to the mass
spectrum of all the other ions.
Reaction rate coefficients were determined by
monitoring the intensity of the reactant ion as a function
of time (typically for at least 2s) after ejection of all
other ions from the analyzer cell. Neutral gas pressures
were measured with an ionizing gauge. Ionization gauge
readings were then corrected by constructing calibration
curves of ionization gauge vs. capacitance manometer (MKS-
Baratron) readings in the 1 x 10-6 to 1 x 10~4 Torr range.
In order to correct for the fact that the ionization gauge
and capacitance manometer were located at different points
on the vacuum system, somewhat removed from the FTICR
analyzer cell, a correction factor was required. This was

28
obtained by determining the rate coefficient of a well-
studied reaction (C2H4+ + C2H4 > products), where the
ionization gauge pressure readings were corrected by using
the capacitance manometer. This experimentally determined
rate coefficient was then compared with the average of
published values, kav = (1.0 + 0.3) x 10~9 cm3/s (Herod and
Harrison, 1970; Gross and Norbeck, 1971; Sieck and Ausloos,
1972; Warneck, 1972; Le Breton et al., 1975) and the ratio
of the measured value to the published, which was 0.3 + 0.1,
was used as a correction factor. This factor was used in
calculating the absolute rate coefficients reported in this
work. The large uncertainities (95% confidence limits)
reported for the correction factor and rate coefficients
calculated using it are primarily due to the wide range of
reported values for the C2H4 + + C2H4 reaction used to
determine the correction factor. The even more widely
studied "standard" calibration reaction of CH4+ with CH4
could not be employed because of the lowest accessible mass
limit in the FTICR instrument mentioned earlier. All
calculations of rate coefficients and 95% confidence limits
were performed with a menu-driven Fortran computer program
(given in Appendix I).

CHAPTER 3
ION/MOLECULE REACTIONS
In this chapter the various theoretical models which
have been developed for ion/molecule reactions will first be
discussed. Then follows a description of practical aspects
of studying such reactions by the use of FTICR mass
spectrometry.
Theory of Ion/Molecule Reactions
A number of both classical and statistical ion/molecule
collision theories have been introduced during the last two
decades to provide an adequate model explaining the
experimental observations of ion/molecule reactions.
Classical treatments mainly include the pure polarization
(ion-induced dipole) theory first developed by Langevin
(1905) and the various ion-dipole theories.
A. Pure Polarization Theory. Detailed discussions of
this model can be found in a number of articles (Gioumousls
and Stevenson, 1958; McDaniel, 1964; Futrell and Tiernan,
1968; Henglein, 1970). Langevin's model assumes that the
neutral has no permanent dipole moment, and that both the
ion and the neutral molecule are point particles with no
internal energy. The classical charge-induced dipole
potential at an ion-molecule separation r is
29

30
V(r) = - aq2/2r4 (3.1)
where q is the charge on the ion and a is the polarizability
of the neutral. Since the energy of relative rotation,
Erot(r) °* the Particles is associated with an outwardly
directed centrifugal force, the effective potential of the
ion/molecule system can be given by
veff(r) = V(r) + Erot(r) (3.2)
or
Veff(r) = -(q2a/2r4) + (L2/2//r2) (3.3)
where L is the classical orbiting angular momentum of the
two particles and (i is the reduced mass. The total relative
energy of the system is a sum of the translational energy
and the effective potential energy.
Er * Etrans * veff I3-4»
Figure 3.1 shows a plot of Vgff(r) versus r at constant Er
for three different values of the impact parameter, b. When
b=0, since there is no centrifugal potential energy, the
effective potential is attractive at all ion/molecule
separations leading to a collision between two particles.
For b > 0, there is a critical value of the impact

31
O 2 4 6 8 10 12 14 16
r ¡ cm
Figure 3.1. Plot of Veff vs r from Equation (3.3) for N2
Colliding with N2.

32
paramater, bc at which the particles orbit around the
scattering center with a constant radius, rc. At this
ion/molecule separation, there is no contribution from the
attractive potential and Vgff is equal to centrifugal energy
which creates a "centrifugal barrier” to a capture
collision. For all b < bc, a capture collision occurs,
whereas it is precluded by the centrifugal barrier for all
b > bc.
Capture cross section is defined as the area of a
circle with radius bc perpendicular to the line of collision
at infinite ion/molecule separation and a capture collision
occurs for all the ions that pass through the circle when
approaching the neutral molecule. Capture cross section can
be derived for a given relative velocity in terms of the
charge of ion, q, polarizability of the neutral, a, and the
reduced mass, n as shown in equation (3.5).
<7c(v) =â–  2nq(a//i) 1/2/v (3.5)
Thus the collision rate constant is given by
k c = voc = 27rq(a//i) 1/2 (3.6)
The rate coefficients obtained from this expression are
generally good for some simple low energy ion/molecule

33
reactions but underestimate the rate constants of most
ion/polar molecule collisions.
B. Ion/Dipole Theory. Several different models were
proposed to describe the theory of ion/dipole collisions.
Among these are "The Locked Dipole Approximation" (Moran and
Hamill, 1963), "The Frozen Rotor Approximation" (Dugan and
Magee, 1966), "Ion/Dipole Trajectory Calculations" (Dugan
and Magee, 1967), "The Average Dipole Orientation (ADO)
Theory" (Bowers and Laudens1ager, 1972), "Barker-Ridge (BR)
Model" (Barker and Ridge, 1976) and "The Average Dipole
Orientation Theory with Conservation of Angular Momentum
(AADO) " (Su et al., 1978 ) .
Both the "Locked Dipole" and "The Frozen Rotor”
approximations assume that the polar molecule is fixed at
angle 0 (0 = 0 for the "Locked Dipole" model) with respect
to the line of centers of the collision. The resulting rate
constants provide upper limits to the ion/dipole capture
collisions and overestimate the dipole effect (Su and
Bowers, 1973 ) .
Ion/Dipole Trajectory Calculations provide numerical
solutions for the equations of motion for the collision of
an ion with a rotating polar molecule. As a result of these
calculations, the numerical capture cross section was found
to depend on relative translational energy. When compared
with experimental results, this numerical approach seems to

34
be useful In the Investigation of nonreactive ion/dipole
phenomena such as energy transfer, but does not give a good
estimation of capture collision rates.
ADO theory assumes that there exists an overall average
orientation of the dipole with respect to the Ion and the
extent of locking of the dipole Increases as the dipole
moment of the molecule increases. Su and Bowers (1973) have
parametrized the ADO theory to calculate the ADO capture
rate constants. The results indicate that the ADO theory
gives the best prediction of rate constants in most cases
with respect to the other theories.
BR theory uses a simple statistical approach to study
the ion/dipole collisions and is based on the Langevin
model. BR results overestimate the dipole effect by almost
a factor of 2 for charge transfer and proton transfer as
well as momentum transfer reactions.
Su et al. (1978) modified the ADO theory by the
application of the conservation of angular momentum with the
assumption that there is no net angular momentum transfer
between the rotating molecule and the ion/molecule orbital
motion. This modified version of ADO theory is termed the
AADO theory. The capture rate constants obtained from AADO
model are larger than the ADO predictions, providing better
agreement between theory and experiment.

35
C. Ion/Quadrupole Theory. This theory makes
theoretical predictions of ion/quadrupole interactions for
the molecules having Dw symmetries. Similar to ADO theory,
the average quadrupole orientation theory, AQO, was
developed by Su and Bowers (1975). This model predicts
significant quadrupole effects for molecules with high
quadrupole moments and improves the agreement between theory
and experiment.
Statistical Treatments of ion/molecule reactions
include the statistical theory and the orbiting transition
state theory. Statistical Theory is divided into three
categories according to the type of reaction dynamics as
shown in Figure 3.2.
A. Transition State Theory. This theory is developed
for direct bimolecular reactions (Pelzer and Wigner, 1932;
Evans and Polanyi, 1935; Eyring, 1935). This method was
later refined by Pechukas and McLafferty (1972) and by
Miller (1974). The microcanonical rate constant is given by
k(E) = Wt(E-E0)/hp(E) (3.7)
where W^(E-Eq) is the total sum of states (vibrational and
rotational) of the transition state complex with nonfixed
energy less than or equal to E-Eq, where E is the total

36
í
Figure 3.2. Schematic Potential Surfaces for Various
Ion/Molecule Reactions, (a) Direct bimolecular, (b)
Unimolecular, and (c) Complex formation reactions.

37
system energy, and p(E) is the total density of states of
the reactants. For a given potential surface, transition
state theory provides a rigorous upper limit to the true
rate constant.
B. Unimolecular Theory. This theory involves two
approaches, RRKM and QET (quasi-equi1 ibrium theory) which
arrive at similar results for the unimolecular reaction of
an isolated energized molecule. These methods were
developed independently by Marcus and Rice (1951) using the
assumptions of transition state theory and by Rosenstock et
al. (1952) using the quasi-equilibrium hypothesis.
Experimental evidence suggests that most unimolecular
systems appear to behave according to the quasi-equi1ibrium
hypothesis which assumes a random distribution of excess
energy independent of the pattern of initial energization
prior to unimolecular decomposition.
C. Complex Formation Theory. This theory involves the
statistical treatment of reactions which form a long-lived
complex assuming quasi-equi1ibrium for the intermediate
complex (Keck, 1958; Light, 1967). Thus, the rate constant
for decomposition to each available channel is assumed to be
proportional to the flux through the transition state for
that channel.

38
The Orbiting Transition State Theory is developed to
overcome the problem of determining the energy distribution
of reactants that leads to the formation of a given
transition state complex. In this method the transition
state is located at the maximum of the long range effective
potential where the reactants retain their original
identity. The orbiting rate constants for both bimolecular
reactions (Miller, 1976; Light, 1967), and unimolecular
reactions (Chesnavich and Bowers, 1977) can be obtained as a
function of translational, rotational, and vibrational
energy of the reacting system. Comparison with experiment
in general reveals that orbiting unimolecular rate constants
are unrealistically high while the orbiting bimolecular rate
constants are similar to experimental results at thermal
energies. This model also predicts the probability of a
given translational energy release (Chesnavich and Bowers,
1976) which in most cases is in good agreement with
experimental results for reactions with no reverse
activation energy.
Experimental Study of Ion/Molecule Reactions Using FT ICR
Rate Coefficients. ICR techniques cannot be used for
experimental tests of statistical theories since the
application of statistical models requires a detailed
knowledge of energy states of the system, which cannot be

39
obtained from ICR. On the other hand, theoretical
bimolecular rate constants using Langevin's model are
usually found to agree with the experimental results
obtained for low energy ion/molecule reactions using ICR
technique. Reactant ions with energies close to thermal can
be prepared by charge transfer ionization of a precursor
molecule followed by collisional relaxation of the ions by
inert gas molecules. Thus, this method provides the
determination of thermal bimolecular rate constants which
can be used to test the basic assumptions of the Pure
Polarization method.
The first step in the experimental determination of
rate coefficients by FTICR involves the ejection of all ions
except the one of interest from the analyzer cell following
charge transfer ionization. Next the decay of the ion
signal is monitored as a function of time long enough to
permit the ion of interest to react away completely.
Method of Data Analysis. The ion/molecule reactions
studied in FTICR most often involve bimolecular collisions
and follow second order kinetics. The rate expression for a
simple second order reaction is given by
-d[I]/dt = k2[i][R] (3.8)
where I is the ion and R is the reactant neutral. Since the
ion number density created in the FTICR instrument is at

40
least three orders of magnitude lower than the neutral
number density, a "pseudo-first order" rate coefficient,
I
kj can be substituted for the term k2[R] in equation (3.8).
— d[I)/dt = kj'[I] (3.9)
After integration, the rate expression giving the number
density of the reactant at any given time is obtained:
[I](t) = [I](0) exp(-kj t) (3.10)
where [I](0) is the initial number of ions present. Thus,
I
kj can be determined from the slope of the simple ln(ion
signal) vs time plot. The true rate coefficient, k2 can
f I
then be obtained from kj by dividing kj by the number
density of the reactant neutral. The number density of the
neutral is determined using the expression, (n/V) = P/RT,
where V and T are the volume and the temperature of the
analyzer cell respectively, and P is the pressure of the
reactant neutral measured by a capacitance manometer.
In an experimental situation, there is often a second
neutral present in the cell, which is the precursor neutral
of the ion of interest. Thus, the decay of the ion signal
includes ion/raolecule reactions with both the precursor and
the neutral molecules of interest. In this case the rate
expression becomes
40

41
-d[I]/dt = (k 2[R] + k3[P])[I]
(3.11)
where k3 is the bimolecular rate coefficient for the
reaction of the ion with the precursor molecule, P. The
integrated form is
(3.12)
[I](t) = [I](0) exp [-(k2(R] + k3[P])t]
In order to determine the rate coefficient of reactions of
the ion with the neutral reactant, it is necessary first to
monitor the reactions of the ion with precursor neutral with
no reactant neutral present in the analyzer cell and then to
subtract the rate coefficient for this reaction from the
total rate coefficient observed in the presence of both the
precursor neutral and the reactant of interest. If the
precursor neutral pressure is kept constant for the two
cases, only the pseudo-first order rate constants are used
in the subtraction step.
When two or more isomers of a particular ion are formed
from the same parent neutral, a single ion signal is
observed in the mass spectrometer whose intensity is the sum
of the intensities of all the isomers. For a simple case of
only two ion structures,
[ I ] (t ) = [A] (t) + [B) (t)
(3.13)

42
Thus, the integrated form of the rate expression is given by
[I](t) = [A](0) exp[-(k2[R] + k3[P])t]
+ t B](0) exp[-(k2'[R] + k3'[P])t] (3.14)
where A and B are the isomers of ion I. Consequently, the
decay curve of the ion signal is composed of segments with
two different exponential time constants, each slope
corresponding to the reaction rate of a different ion
structure. The sum of the rate coefficients (for reactions
with precursor and reactant neutrals) of the slower reacting
structure is calculated from the tail of the double decay
curve while that of the faster reacting structure is
determined by subtracting the amount of the slow reacting
isomer at each point in the initial part of the curve using
Equation (3.14). Often, one of the structures is completely
unreactive, while the other is reactive as shown in Figure
3.3, simplifying the data analysis for structure
identification.
Reaction Mechanisms. Reaction pathways leading to
final product ions from a ion/molecule reactant system can
be studied using the ejection capabilities of FTICR. The

lObJ SlGhJ AL
Figure 3.3. Ion Decay Curve with Reactive and Unreactive
Components .

44
method involves the ejection of each first generation
product ion continuously during the reaction time to see its
effect on the intensity distribution of the mass spectrum of
the final product ions. This method also can be used to
calculate the branching ratios for the product ions.
Studying reaction pathways and branching ratios of the ions
produced in different ways (either from different precursors
or different methods of ionization) provides an alternative
means to rate coefficient determination' for the
differentiation of structural isomers of the ion of
interest.

CHAPTER 4
REACTIONS OF C3H3+ WITH ACETYLENE AND DIACETYLENE
IN THE GAS PHASE
Introduction
The C3H3+ ion has received considerable attention in
recent years as a possible soot precursor because it is
found in quite high abundance in fuel-rich and sooting
flames (Goodings et al, 1979; Olson and Calcóte, 1981b;
Michaud et al., 1981). Although substantial uncertainty
remains as to C3H3+ formation mechanisms in flames (Calcóte,
1981), the ion is postulated (Calcóte, 1981; Olson and
Calcóte, 1981a) to react with neutrals such as acetylene,
diacetylene, and CgH in rapid, sequential condensation and
condensation/elimination reactions, forming successively
larger ions, which can rearrange to cyclic species during
the ion/molecule reaction chain.
Two isomeric structures of C3H3+ shown in Figure 4.1
are important in discussing the role of C3H3+ in
ion/molecule reaction mechanisms. The first is the
cyclopropenylium ion, recognized as the most stable isomer,
which has a theoretically calculated heat of formation of
253 kcal/mol (Radom et al., 1976), in quite good agreement
with the 256 kcal/mol determined by experiment (Lossing,
1972). A second and potentially more important C3H3+
45

46
H
J
(4.2)
Figure 4.1. The Most Stable C3H3 + Structures:
Cyclopropenylium (4.1) and Propargy1ium (4.2).

47
structure is that of the linear propargylium ion with a
calculated (Radom et al., 1976) heat of formation 31 to 34
kcal/mol higher than that of the cyclopropenylium ion, in
fair agreement with the 25 kcal/mol difference found
experimentally by Lossing (1972). Recent calculations have
shown several other stable isomeric structures of the C3h3 +
ion with higher heats of formation relative to the
cyclopropenylium and propargylium ions.
The importance of different precursors in affecting the
reactivity of C3H3+ ions was reported in a thermochemical
study by Holmes and Lossing (1979). In an ICR study of
C3H3+ reactions, Ausloos and Lias (1981) showed that
significant fractions of the linear isomer can be produced
by charge transfer reactions of small ions (Ar+, Xe+, C0+,
Ne+, etc.) with propargyl chloride and bromide. Later it
was reported (Baykut et al., 1986) that even higher
proportions of the propargylium isomer relative to the
cyclopropenylium isomer can be obtained with propargyl
iodide either by electron impact or charge exchange using
Xe+ .
A study by Smyth et al.(1982) demonstrated that the
cyclopropenylium ion was relatively unreactive toward simple
hydrocarbon fuels whereas the linear, propargylium ion was
quite reactive. In particular, reaction of propargylium
ions with acetylene was reported to produce CgH3+ and C5H5 +
ions with an overall C3H3+ disappearance rate coefficient of

48
1 x 10 cm /s. In the work discussed in this chapter,
results substantially different from those reported earlier
were found and the research was thus expanded to Investigate
possible production of CgHg + ions from ionic sources other
than C3h3+ present in the reaction media using the ejection
capabilities of Fourier transform ion cyclotron resonance
(FTICR) mass spectrometry. Reactions of propargylium ions
with C2D2 were also studied in order to delineate further a
proposed mechanism for the C3H3+/acetylene interaction.
Diacetylene is another important flame neutral which
has been postulated to react with C3H3+ ions in an
ion/molecule soot formation mechanism (Olson and Calcóte,
1981a). Reaction pathways and the rate coefficient for the
reaction of propargylium ions with diacetylene near room
temperature were thus also investigated. In this chapter,
results for the reactions of C3H3+ ions with acetylene,
deuterated acetylene, and diacetylene are reported and
discussed in relation to previous work involving C3H3+
reactions (Ausloos and Lias, 1981; Smyth et al., 1982;
Baykut et al.,1986).
Experimental
Reactive and non-reactive C3H3^ ions were produced by
charge transfer reactions of various precursors with Xe+,
formed with an electron beam pulse of 5 ms duration at an
ionizing electron energy of ca. 15 eV. Propargyl iodide was

49
used as a precursor for CgH3+ in studies of the reaction of
this ion with acetylene, deuterated acetylene, and
diacetylene, while a number of different precursors
(propargyl iodide, propargyl bromide, propargyl chloride,
propyne and aliene) were used to investigate the reaction
mechanisms leading to C5Hg+ ion formation. In some studies
C3H3+ i°ns were produced directly from the above-mentioned
precursors by electron impact to compare the effect of
ionization technique on the ratio of reactive to unreactive
isomers.
Propargyl iodide was prepared from propargyl chloride
by a halogen exchange reaction (March, 1977). The details
of purification are given elsewhere (Baykut et al., 1986).
Propargyl chloride, propargyl bromide, aliene, propyne and
acetylene were obtained commercially and their purity was
checked by obtaining wide mass range spectra. In the case
of acetylene, some production of protonated acetone was
observed at long delay times indicating the presence of a
small amount of acetone as an impurity. Propargyl bromide
was distilled before use in order to remove toluene which
was present as a stabilizing agent. Deuterated acetylene
was prepared from D30 and CaC2* Diacetylene was prepared by
the method of dehydrochlorination of 1,4-dichloro-3-butyne
in aqueous potassium hydroxide/dioxane solution (Snow,
1985). All the samples were used after multiple
freeze-pump-thaw cycles.

50
Results
C3I3I- Reactions with Acetylene. Despite an earlier
report (Smyth et al., 1982) that C3H3 + is quite reactive
with acetylene, only very low intensities of C5H3 + and C5Hg+
produced via this reaction could be found in this work.
Experimental conditions of the earlier study were duplicated
as closely as possible, and then varied substantially with
respect to relative pressures of neutrals (from 1:1 to 8:1
C2H2:C3H3I) and overall system pressure (from 5 X 10 to 3
x 10~5 torr). The C3H3+ ions were formed from propargyl
chloride, bromide, and iodide by both charge transfer using
Xe+ and electron impact. In order to determine other
possible sources of C5H5+ observed under the earlier
reaction conditions, binary mixtures of acetylene and one of
the C3H3+ precursors reported (Ausloos and Lias, 1981; Smyth
et al., 1982; Baykut et al., 1986) earlier were used.
Intensities of C5H5+ and C5H3+ were first measured after a
125 ms reaction time. Then the parent ion, C2H2+, and C3H3+
were each ejected separately during the 125 ms reaction
period to assess their contribution to C5H5+ and C5H3+
formation.
For each different neutral precursor, the sources and
amounts of C5H5+ ions produced were found to be different.
Propyne and aliene were similar in producing large amounts
of CrjHg+ and no C5H3+ ion. However, the C3H3+ + C2H2

51
reaction was not responsible for C5H5+ formation. The main
reactions leading to CgH5+ were
C2H2+ + C3H4 > c5H5+ + H (4.1)
C3H4+ + c2H2 > C5H5+ + H (4.2)
in both cases. On the other hand, when propargyl iodide,
propargyl bromide and propargyl chloride were used as
precursors, relatively smaller amounts of CgH5 + ion
formation were observed along with C5H3+ ion production. In
the propargyl chloride case
C3H3C1+ + C2H2 > C5H5+ + Cl (4.3)
C2H2+ + C3H3C1 > C5H5+ + Cl (4.4)
were the major reactions leading to C5H5+ formation. For
propargyl bromide the
C3H3Br+ + C2H2 > C5H5+ + Br (4.5)
reaction was the only source of C5H5+ ions observed. Any
contribution to C5H5+ formation from linear C3H3+ was less
than the experimental uncertainty. Finally, very little
(almost negligible) amounts of C5H5+ ions were observed when
propargyl iodide was used as a precursor and the reactions

52
C2H2+ + C3H3I
--> c5h5+ + I
(4.6)
c3h3+ + c2h2 > c5h5+
(4.7)
were the major contributors in this case. An upper limit
for the rate constant, k, for reaction (4.7) was estimated
as 5 X 10-12 cm3/s by assuming that the very small C5Hg +
signal observed resulted from this reaction, and using the
expression [C3H3+](t) = [C3H3+](0) - [C5H5+](t) =
[C3H3+](0)e-nkt, where n is the C2H2 number density.
Overall results for the production of C5H5+ and C5H3+ ions
in mixtures of acetylene and various neutrals used as the
precursors of C3H3+ are summarized in Table 4.1.
Because propargyl iodide was shown to produce the
highest reactive/unreactive ratio of C3H3+ ions both in
earlier (Baykut et al., 1986; Holmes and Lossing, 1979) and
the present work (see Table 4.2), it was used as a precursor
for C3H3+ ions in these reaction kinetics studies. Since
the precursor neutral molecule was always present in the
FTICR analyzer cell, it was a competitor with the reactant
neutral of interest in ion/molecule reactions involving
C3H3+. In order to determine the rate coefficient of
reactions of C3H3+ with the neutral reactant, it was
necessary first to monitor the reactions of this ion with
C3H3I and then to subtract the rate coefficient for this
reaction from the total rate coefficient observed in the
presence of both the precursor neutral and the reactant of

53
TABLE 4.1
Production of C5H5 + and C5H3+ Ions in Mixtures of
Various Neutrals and Acetylene3.
Neutral
Ionic sources**
of C5H3+ after
Xe+ charge
transfer
Ionization of
a mixture of
the neutral
and acetylene
Ratio of
C5H5+ prod,
relative to
that in
aliene casec
Ionic sources**
of c5h3+
Intenslty
of C5h5+
vs. C5H3+
Percent
reactive
C3»3+
Ions
Aliene
C2h2+(4°%)
C3H4+(605)
1.0
-
-
<5
Propyne
C2H2+(40%)
C3H4+(60%)
0.75
-
-
30
Propargyl
chloride
C2H2+(40-50%)
C3H3Cl+(50-60%)
0.25
C3H3Cl+(20%)
c3H3+(20%)
c2'h2+(60%)
3.0
15
Propargyl
bromide
C3H3Br4'(90-100%)
0.08
C2h2+(70%)
[c3h3+ *
C3H3Br+](30%)
2.0
85
Propargyl
Iodide
C2H2+(40%)
C3H3+(60%)
<0.02
C2Ho*(50%)
C3H3+(50%)
1.7
â– JO
1 All ions were produced by chemical ionization charge transfer from Xe*.
3 Percentages show the relative contributions to C3i)3'' and production ns
determined by double resonance experiments and have an estimated uncertainty
of ±io%.
c Neutral reactants all had the same pressure (7 X 10-' torr) as measured by
the ionization gauge. Xenon and acetylene pressures were 5.0 X lO-** and l.H
X 10"° torr, respectively.

54
TABLE 4.2.
Percentages3 of reactive C3H3 + found from various precursors
by various ionization techniques (monitored by observing
reaction with the precursor neutral).
Ionizing
Technique
precursor
Propargy1
iodide
Propargy1
bromide
Propargy1
chloride
Electron impact (15eV)
90
40
10
Chemical ionization charge
90
85
15
transfer with Xe
aEstimated error is +5%.

55
interest. Reactions of C3H3 + with propargyl iodide were
monitored as a function of time following charge transfer
chemical ionization of CgHgl by Xe+ and ejection of all ions
but C3H3+ from the analyzer cell. Results obtained were
identical to CgH3 + reaction channels with propargyl iodide
which have been reported elsewhere (Baykut et al., 1986).
Isomerization of Linear In addition to the
absence of any significant C5H3+ and C5H5+ formed by
reaction of linear C3H3+ with C2H2, it was also observed
that C2H2 led to the isomerization of linear C3H3+ ions to
their cyclic form, thus rendering them unreactive toward
their parent neutral (C3H3I) as well as toward C2H2. This
Isomerization was followed as a function of C2H2 pressure
and a direct pressure dependence was found, as can be seen
in Figure 4.2.
C3H3+ Reactions with CgDg- To achieve a better
understanding of the isomerization of linear CgH3+, C2D2
instead of C2H2 was used as the neutral reactant. The
following isotope exchange reactions were observed:
C3H3+ +
C2D2 “
—> c3h2d+ + c2dh
(4.8)
c3h3+ ♦
c2d2 -
^ c3hd2 + c2h2
(4.9)
c3h2d+
+ c2d2
> c3hd2+ + c2dh
(4.10)
c3h2d+
+ c2d2
> CgDg + C2H2
(4.11)

56
Deactivation of l-C3H^ by acetylene at different pressures
Time/s
Figure 4.2. Isomerization of Linear C3H3 + Ions at Different
Pressures of CgHg. C3H3+ ions were produced by charge
transfer reactions with Xe^. p(C3H3I) = 1.1 x 10-7 torr;
p(Xe) was adjusted to maintain a constant total pressure of
2.6 x 10-6 torr as measured on the ionization gauge. (All
pressures are capacitance-manometer corrected.)

57
C^HDg + CgDg ^ C3D3 + C 2 D H
(4.12)
Using FTICR ejection capabilities, It was found that
reactions (4.9) and (4.10) contribute equally to the
production of C3HD2+ while reaction (4.12) produces more of
C3d3+ (80*) than reaction (4.11) (20*).
Ion intensity vs. time curves for the C3H3+/C2D2
reaction are shown in Figure 4.3. The overall rate
coefficient for the disappearance of C3H3+ was calculated by
subtracting the observed rate coefficient for the reaction
with propargyl iodide from the total observed rate
coefficient in the presence of C2D2. This observed rate
coefficient was then converted to the true rate coefficient
using the corrected pressure of C2D2. A value of (4.5+1.9)
x 10"10 cm^/s was found at a cell temperature of 373 K for
the disappearance of C3H3+ (reactions (4.8) and (4.9)). In
Figure 4.4, ion intensity vs. time curves of C3H3+ are
compared for reactions with and without C2D2.
ÍL3ÍL3—- Reactions with Diacetylene. After ejection of
all ions except C3H3+ following charge transfer chemical
ionization by Xe+ of a mixture of diacetylene and propargyl
iodide, the ion/molecule reactions as a function of time
were monitored. Consecutive C2 and C4H2 addition reactions
were observed:
c3h3+ + c4h2 --
(4.13)

58
Reactions of I-C3H3 with C2D2
Time /s
Disappearance of C,H,
iodide.
Isotope Exchange Reactions of C3H3
with C2D2.
Figure 4.3.
ion includes reactions with propargyl
Note that the sum of all isotopic forms of C3H3+
remaining at the end of the reaction with C2D2 approximately
equals the total unreactive C3H3+ when C2H2 is used as a
neutral reactant at the same pressure (see Fig. 4.2).
p(C~H~I) = 1.1 X 10
= 6.2 x 1 0-6 torr.
-7
torr ;
P ( C 2 D 2 ) -
1.2 x 10 6 torr; p(Xe)

59
Reactions of I-C3H3 with C3H3I and C2D2
Figure 4.4. C3H3+ Ion Decay Curves for Reaction with C3H3I
and C2D2 . (Pressures are the same as given for Fig. 1.3.)

60
3+ + C4H2 >
C5H3+ + c2H2
(4.14)
C5H3 + c4h2
-> c9h5+
(4.15)
3+ + c4H2 >
c7h3+ + c2h2
(4.16)
c7h3+ + c4h2 ---
“> C11H5+
(4.17)
5+ + c4h2 >
C11H5+ + C2H2
(4.18)
C9H5+ + C4H2
-> c13h7+
(4.19)
Some of these product ions were seen to react further
with propargyl iodide by displacement of atomic iodine:
C5H3 +
+
C3H3 i >
c8h6 +
+ I
(4.20)
C7H3 +
+
C3}i31 >
C10H6+
+
I
(4.21)
C7«5 +
+
C3h3 1 >
C10H8+
â– f
I
(4.22)
c8h6 +
+
c3h3i >
C11H9+
+
I
(4.23)
C9H5 +
+
c3h3i >
C12H8+
+
I
(4.24)
Ion intensity vs. time curves for the c3H3+/C4H2
reaction are shown in Figure 4.5. The rate coefficient for
the disappearance of C3H3+ (reactions (4.13) and (4.14),
Figure 4.6) was calculated as described earlier, and a value
of k = (1.4 + 0.7) x 10-9 cm3/s was found. Propargyl
iodide, bromide, and chloride were all used as precursors of
C3H3+ in studying its reactions with diacetylene. For each
precursor, both electron impact and charge transfer chemical
ionization techniques were used. The percentages of
reactive isomer in the reaction with diacetylene are shown

61
Figure 4.5. Reactions of C3H3+ with C4H2. Disappearance of
C3H3+ and product ions include reactions with propargyl
iodide. p(C3H3I) = 1.1 x 10-7 torr; p(C4H2) = 4.8 x 10
torr; p(Xe) = 6.2 x 10~6 torr. (All pressures are
capacitance-manometer corrected. )

62
Figure 4.6. C3H3+ Decay Curves for the Reactions with C3H3I
and C4H,. (Pressures are the same as given for Fig. 4.5.)

63
TABLE 4.3
Percentages
C4H2.b
a
of reactive C3H3‘
observed in the reaction with
precursor
Ionizing
Technique
Propargyl
iodide
Propargyl
bromide
Propargyl
chloride
Electron
impact (15eV)
75
30
5
Chemical
transfer
ionization
with Xe+
charge 75
65
5
aEstimated error is
+5%
bP(C4H2) =
4.8 x 10-7
torr

64
in Table 4.3. When these percentages of reactive isomer
were compared to those in the absence of C4H2 (see Table
4.2), it was clear that some isomerization of the reactive
linear C3H3+ ion, as well as reactions (4.13) and (4.14),
had taken place (see also Fig. 4.6). This isomerization was
followed as a function of C^H2 pressure and a direct
pressure dependence was found, as can be seen in Table 4.4.
The reactions of 1-C3H3+ with propargyl iodide and with
both acetylene and diacetylene have also been followed at
several elevated temperatures up to 500 K. All the rate
constants were found to be similar to their room temperature
value within experimental error.
Pi scussion
Effect of Different Precursors. Different percentages
of reactive C3H3+ were found from three different
precursors, propargyl iodide, propargyl bromide and
propargyl chloride as shown in Table 4.2. To explain the
differences observed in reactivity, schematic potential
energy surfaces for these precursors are shown in Figure
4.7. Experimental thermochemical data reported by Holmes
and Lossing (1978) were used in the generation of the
potential surfaces. Reverse activation energies for c-C3H3+
formation from propargyl bromide and chloride were
determined by the difference between the experimental and
the calculated appearance potentials. Since the appearance

65
TABLE 4.4
Changes in CoH3 + reactivity3 at different pressures of
diacetylene.H
C4H2 pressure/10'7 Torr
% unreactive C3H3+
0.8
16
1.6
17
4.8
25
7.2
32
8.0
35
9.6
40
al-CgH3+ ions were produced from propargyl iodide by
chemical ionization charge transfer with Xe+. (p(C3H3I) =
1.1 X 10-7 torr; pXe was adjusted to maintain a constant
total pressure of 2.6 X 10“® torr as read on the ionization
are capacitance-manometer corrected.
gauge)
BA11 «
pressures

66
Figure 4.7. Schematic Potential Energy Surfaces for
C3H3+/C3H3X+ System from Different Precursors. Propargyl
Iodide (a), Propargyl Bromide (b). and Propargyl Chloride
(c) .

67
potential of C3H3+ produced from propargyl iodide very
closely corresponds to the calculated threshold for 1-C3H3+
rather than c-C3H3+, the dissociation to the latter is
assumed to have a significant energy barrier. Thus, reverse
activation energy for the dissociation channel giving
unreactive c-C3H3+ decreases in the order Ej0(j0 > E|;)romo >
Echloro as s^own 'the figure. Production of almost
exclusively reactive 1-C3H3+ by both electron impact and Xe+
charge transfer ionization from propargyl iodide suggests
that Ej0Cj0 is so large that the fragmentation channel
leading to 1-C3H3+ becomes the lowest energy channel. In
the case of propargyl bromide, there is enough excess energy
to dissociate to both 1-C3H3+ and c-C3H3+. Production of
80% 1-C3H3 + by Xe+ chemical ionization suggests no
significant energy barrier for the 1-C3H3+ channel. It is
interesting to note that dissociation to 1-C3H3+ reduces by
a factor of two when electron impact ionization is used,
which demonstrates the effect of a large distribution of
electron energies from an electron impact ionization source
on the relative abundances of two channels almost equally
accessible energetically. The very small reactive 1-C3H3+
percentage produced from propargyl chloride by both electron
impact and Xe+ charge transfer ionization suggests at least
a small energy barrier for this dissociation channel, as
indicated schematically in Figure 4.7c.

68
Internal Energy of the Ions In Relation to Rate
Coefficient Measurements. In studying reactions it is
desirable to have knowledge of the internal energy
distribution of the reactant ions. The reactions studied
here are bimolecular addition reactions followed by
unimolecular decomposition. As shown in Figure 4.7a, when
1_c3h3+ *8 formed from propargyl iodide by Xe+ charge
transfer chemical ionization, 1.5 eV of excess energy is
available. Much of this excess energy will be converted
into translational motion of the heavy Xe and I neutrals
resulting from the charge transfer in the collision process.
— fi
Under typical experimental conditions (ca. 2 - 3 x 10 torr
total pressure), about 125 ms was allowed for the charge
transfer process and for ejecting intermediates. For these
conditions the C3H3 + ions collided a number (10-15) of times
with the excess Xe present in the FTICR cell, leading to
near therma1 ization of internal energy before the
ion/molecule reactions were monitored. Since the reaction
time scale was on the order of seconds, it can be assumed
that any slight initial deviation from Boltzmann behavior
presents no serious error. On the other hand, the
observation that the rate constants for the reactions of 1-
C3H3+ with propargyl iodide and with both diacetylene and
acetylene are temperature independent implies that
thermalization of the ions is not complete under the
conditions reported and there is still some internal energy

69
in 1-CgH3+, which is comparable in magnitude to that
contributed from the range of temperatures studied.
Reactivity of I-C3H3Í. with Acetylene. Although the
results of C3H3 + + C2H2 reaction are not in agreement with
the earlier report (Smyth et al.f 1982) of C3H3+/C2H2
reactivity, the discrepancy is most likely due to
limitations of the older pulsed ICR (Smyth et al., 1982)
instrumentation for studying ion/molecule reaction pathways
in complicated systems when compared to newer FTICR
capabilities. Facile ejection of all ions except the one
whose ion/molecule reactions are being investigated offers a
very clean monitoring opportunity for product-parent
relationships even in complicated consecutive and
competitive reaction systems. Various alternative pathways
for the production of C5H3+ and C5H5+ which have been
described above probably contributed significantly to the
intensities of these ions seen in the earlier work.
Additional support for the low reactivity of C3H3+ with C2H2
is found in a recent report (Anicich et al., 1986) of the
rate coefficient for this reaction as less than 0.01 X 10~®
O x
cm /s, although the isomeric form of C3H3 was not given.
It is also possible that the highest pressures used in this
work did not reach those of the earlier study due to
differences in the location of capacitance manometers,
ionization gauges, etc. Thus third body stabilization of

70
CgH5+ collision complexes might have been occurring to some
extent in the earlier work and not in that reported here.
In fact, such collisional stabilization of the association
complexes for the reactions of CgHg + and C4H4 + with C2H2 has
been shown to occur in higher pressure SIFT studies (Smith
and Adams, 1987; Knight et al., 1987).
The most likely mechanism of the observed isomerization
of C3H3+ ions by collisions with acetylene is a "reactive"
rather than a "non-reactive" one. That is, it results from
an intimate encounter of the ion and neutral in the CgH5 +
collision complex. This hypothesis is confirmed by the fact
that deuterated forms of CgHg + were produced when C2D2 was
the neutral reactant (see Figure 4.4). Kinetic modeling
studies (discussed in Chapter 5) indicate that in some cases
the C5H5+ collision complex dissociates to give the cyclic,
unreactive, C3H3+ isomer, instead of the reactive, linear
form which reacted initially. The possibility of
non-reactive collisional isomerization of linear C3H3+ to
the cyclic isomer has been ruled out because experiments at
elevated pressures of xenon (to ca. 1 X 10-5 torr) showed no
interconversion. Similar interconversion of C4H4+ ions from
a linear to cyclic form has also been reported (Jarrold et
al., 1984) in the reaction with C2H2 and has also been shown
to take place via complex formation by using isotopically
labeled C2H2. To confirm the hypothesis that energetically
less stable, reactive, (linear) CgHg + ions interconvert to

71
more stable, unreactlve ones, cyclic C3H3 + Ions were also
reacted with C2D2 and no Isotope exchange reactions were
observed.
Reactivity of 1-C3H3+ with Dlacetylene. Plots of C3H3+
ion intensity vs. time for reaction with dlacetylene (C4H2)
(Figure 4.5) indicate a 10-12* increase in the intensity of
the unreactive isomer relative to the reaction when the
parent precursor only is present. Isomerization of reactive
C3H3+ was also seen when different precursors were used
(compare Tables 4.2 and 4.3). A similar mechanism involving
complex formation may be responsible for this isomerization
as well, although it was not investigated in any detail.

CHAPTER 5
KINETIC MODELING OF THE REACTIONS OF C3H3+
Introduction
As reported in the last chapter, bimolecular reactions
of the propargylium form of C3H3+ with acetylene most often
result in an isomerization to the cyclopropenylium isomer.
To help understand this isomerization process, C3H3+
reactions with deuterated acetylene were investigated.
These studies showed that the isomerization proceeds via the
C5H5+ ion/molecule reaction complex, which is sufficiently
long-lived under the experimental conditions employed that
deuterium exchange, as well as isomerization, takes place.
Thus with time the reactive propargylium C3H3+ isomer is
converted to both reactive and unreactive species containing
one, two, and three deuterium atoms. There is no evidence,
either experimental or theoretical, that the propargylium
cation converts into the cyc1opropeny1iurn cation in the
absence of the C5H5 + reaction complex. In order to better
understand the isomerization which converts the reactive
to the unreactive form of C3H3+, kinetic modeling studies of
the ion intensity vs. time curves reported in Chapter 4 were
72

73
carried out.* It was also hoped that fitting procedures
would produce improved ion/molecule reaction rate
coefficients. Quantum mechanical calculations2 on C3H3 + and
C5H5+ structures and reactivity were used to guide the
modeling effort.
Experimental
A mixture (predominantly propargy1ium) of the C3H3+
isomers was in most cases formed by charge transfer from
propargyl iodide to Xe+, produced by 15 eV electron
ionization of Xe (present at pressures > lOx those of other
gases). Other conditions such as neutral partial pressures,
pulse sequences and reaction times, and the sources of
chemicals were kept as close as possible to those reported
in Chapter 4 for the duplicate kinetics experiments reported
and modeled here. Any significant deviations are given in
the text, table headings, or figure captions. All pressures
reported in this chapter were determined by a capacitance
manometer, and then multiplied by a "system factor" of 0.30
which corrects for the fact that the pressure read by the
capacitance manometer is not the same as that in the FTICR
*The kinetic modeling studies were performed in the
Environics Division of Air Force Engineering and Services
Center, Tyndall Air Force Base, Florida by F. Wiseman using
multiple experimental data sets produced at identical
conditions to those reported in Chapter 4.
2A. Cameron, J. Leszczynski, M. C. Zerner and B Weiner,
submitted. J. Feng, J. Leszczynski and M. C. Zerner, submitted.

74
cell. Non-linear least-squares fitting routines employing
Marquardt's algorithm (Annino and Driver, 1986), implemented
on two different computers3, were used for kinetic modeling.
Complete analytical solutions were obtained from the
chemical models developed below for the systems C3h3+ + CgHg
and C3H3+ + C4H2. A complete analytical solution was not
possible when an isotope effect was included in the chemical
model for the C3H3+ + C2D2 system. Numerical integrations
used the finite difference method (Annino and Driver, 1986).
Results
Models of C3H3+ + CqHq Reaction. As reported in
Chapter 4, collision of the propargylium cation, 1-C3H3+,
with acetylene forms the cyclopropenylium cation, c-C3H3+,
which is unreactive on the time scale of the experiments,
given the pressures attainable in the FTICR cell.
Experiments with C2D2 showed that an encounter complex which
allows for isotopic scrambling is formed. Hence, whatever
the isomeric form of this complex, a structure having the
chemical formula C5H3+ can be postulated. Since no species
of m/z 65 is observed in the mass spectrum, the (CgH5+)
species must be in steady-state and of low concentration.
The simplest scheme which takes into account this
information is given in Figure 5.1.
3Tektronix Model 4054 and Hewlett Packard Model 150.

75
kf
i-c3H3+ + c2h2 > c5H5+
k
C3h3x P
->
sink
k.
_ + X.
C5H5
-> £-C3H3 +
+
C2h2
k
c5h5+
^ c
+
C2H2
Figure 5.1. Reaction Scheme Postulated for the Kinetic
Modeling of the Reaction of linear C3h3+ with Acetylene.

76
Applying steady-state kinetics to this scheme yields
I (t) = Io - kp'Ij0 (1 - e~9t)/0
(5.1)
in which Io and I(t) are ion intensities initially and as a
function of time, respectively, Ij refers only to the linear
form,
and
kp’ = kppC3H3I
(5.2)
0 = [kfkcPC2H2/(k1 + kc)] + kp' (5.3)
Equation (5.1) was fitted to several kinetic runs reported
in Chapter 4. Table 5.1 shows results of these fits. A
plot of 0 vs. Pc H should be linear, as implied by equation
2 2
(5.3), and this is demonstrated in Figure 5.2. Results
yield kfkc/(kj + kc) = 2.3(.2) x 106 torr-1s-1 and kp' =
1.4(0.2) s_1.
Models of -CaiU--t-CgP2- Reaction. Reaction of C3H3+ +
C2D2 is complicated by the observation that isotopic
scrambling occurs and isotope effects are possible. Several
models were tried, including those which allowed for
complete isotopic scrambling and those which allowed only
partial scrambling. The simplest model allowed for complete
scrambling and no isotope effects4.
4Lampe and Field (1959) studied the reaction of CD4 + +
C2H4, and observed the following yields: C3HD4+ : 1/10,
C3H3D2+ : 2/5> c3H2d3+ : 2/5> and C3HD4+ : 1/10. Statistical
yields with no isotope effect would have been: C3H4D+ :
1/14, C3H5D2+ : 3/7, C3H2D3+ : 3/7, and CgHD4+ : 1/14, very

77
TABLE 5.1
Results of fits of equation (5.3) to kinetic data for the
C3H3+ + C2H2 reaction.3
Pr u /torr
l2m2
kp'I°/Arb. units s 1
e/s'1
0
1.53( . 06 )
1.58( . 08)
4.4 x 10-7
1.65( .20)
2.40(.31)
1.0 x 10~6
1 . 74( . 12 )
3.60(.24)
1.6 x 10~6
1 . 71( . 08 )
4.82(.23)
2.0 x 10"6
1.71( . 11)
6.33(.38)
aThe standard error of estimate computed by the fitting
program is shown in parentheses.
close to the observed values. Hence, since the C3Lq +
complex exhibited almost complete scrambling, it is
reasonable to expect the CgL5 + complex modeled here to
undergo complete, or nearly complete scrambling.

0/s-
78
Figure 5.2. The Plot of 6 as a Function of Acetylene
Pressure (see Equation (5.3)).

79
Complete scrambling occurs when fragmentation of the
complex, CgLg+ (L = H, D), yields precursors having a
statistical distribution of hydrogen and deuterium atoms.
C5h3D2+ then yield the following ratios of precursors:
C3h3+ = 1/10, C3H2D+ = 3/5, and C3HD2+ = 3/10. Using these
statistics for obtaining the isotopic distribution in the
C3L3+ precursors, we obtain the scheme shown in Figure 5.3.
With the assumption again that all four CgL5+ complexes are
in steady-state, a full analytical solution is possible for
the set of kinetic differential rate equations. The
solutions to the set of equations are given in Appendix
II.A. Figure 5.4 shows the best fit curves to a typical
data set. Table 5.2 shows the fitted parameters, errors,
and residual sum of squares from fits of a typical data set.
An examination of Figure 5.4 shows that the model given
by Figure 5.3 does not adequately explain the production of
C3HD2+. In an attempt to examine this, incomplete, or
partial isotopic scrambling was next assumed. To do this
correctly requires a detailed knowledge of the chemistry of
the system, which is not available. A somewhat crude
application of isotope effects applies multiplicative
factors to the individual rate constants and this procedure
requires but a nominal knowledge of the structure of the

80
k-
t-CjH3+ ♦ C202 > C5H3D2 +
IV
t-CjHj* ♦ C3H3X ——> sink
SH3°2+ —> T3 ‘-C3H3> + Tó C2D2 * I l^3H2D+ +
TC2HD + T0t-C3HD2+ + T0C2H2
C5H3D2
—> TO C^3H3+ + TO C2°2 + T C-C3H2D+ +
I C2HD + To c_C3hd:+ + TÓ C2H2
i-C3H2D+ + C2D2 —> C5H2D3+
t-C3H2Dr + C3H3I ——> sink
C5H2D3 > 10 l_C3D3+ + To C2H2 + I t_C3HD2+ +
I c2h° ♦ ^ í-c3„2d+ ♦ 2_ c2d2
C5H2D3<‘ —> To C-°3D3+ + To C2H2 + T c^3«°2+ +
? C2HD + To C^3H2°+ + TO C2°2
t-C3HD2+ ♦ c2o2 > cshd4+
1-C3HD2* ♦ C3H3I —2-> sink
C5HD4+ I l^3HD2+ ♦ i c2°2 * I *-C3D3+ + f CjHD
+ kc
C5HD4 ~E_> 5 C'C3HD2+ * T C2°2 + f C-C3D3+ + f C2HD
i-c3o3 ♦ c2d2 — > c5d5
+ kt +
C5D5 > l^3°3 + C2°2
♦ C^H^I —:—> sink
♦ kc
C5ds > C"c3°3 * C:D:
Figure 5.3. Reaction Scheme Postulated for the Kinetic
Modeling of the Reaction of linear C3H3+ with Deuterated
Acetylene Assuming Complete Scrambling and No Isotope
Effects.

81
(a)
Figure 5.4. Model Fit (using the
Typical Data Set for C3H3 + + CgDg
vs. time curves for (a) C3H3 + and
c3d3+.
scheme of Figure 5.3) to a
Reactions. Ion Intensity
C3H3D+ and (b) C3HD3+ and

TABLE 5.2
Results uf Model Fits (Figures 5.3 and 5.7) for the System c3113 +
+ C2n2 under Various Experimental Conditions.
Pressures (torr)
C2D2
C2°2
C D
L2U2
C2n2
C2°2
1.2 X 10~6;
1.2 X 10'6;
7.8 X io-7;
6.2 X 10-7;
1.1 X 10'6;
pw
P(W
Va1
Pc3H3I
Va1
1.1 x io-7
1.1 X 10"7
1.1 X io-7
1.1 X IO-7
1.3 X IO"7
kfPc2D2
(s‘h
kc/kt
F
kPPc3,l3I
(S-1)
l°t
(arb units)
(arb units)
SOS*
4.17(.15 )
. 212(.030)
1(fixed)
o
H
V-r
CO
o
.707(.007)
.063(fixed)
.017
1.1K.14)
. 308(.026)
1.86(.11 )
2.16(.08)
.703(.005)
.067(fixed)
.0069
.920(.098)
.318(.032)
1.71 (.08)
2.20(.09)
.671( .007 )
.057(.008)
.0023
1.30(.12)
.389(.026)
1.53 (.06)
2.74(.07)
.881(.006 )
. 100(.006)
.0038
1.86(.34)
.363(.034)
1.58(.13)
2.18(. 11 )
.856(.007 )
.061(fixed)
.024
00
fo
Rum of squares.

83
species involved5. This simple scheme was applied as
described below.
Quantum mechanical calculations indicate that C2H2
does not readily react with the cyclopropenylium cation, but
does react with the propargylium cation (1-C3H3+) without
barrier with formation of the four possible products shown
in Figure 5.5. Thermodynamically, only Structure (5.1) is
stable with respect to decomposition to c-C3H3+ + C2H2.
However, since the 1-C3H3+ + C2H2 > Structure (5.1)
reaction is at least 60 kcal/mol exothermic6 , in the
absence of stabilizing collisions this energy then permits
many different isomeric forms to be sampled before
decomposition back to C3H3+ + C2H2. If the sampling of all
isomers is fast, complete isotopic scrambling is expected.
Given the uncertainity in C5H5+ structures, total
equivalence of carbon atoms in the complex is assumed. For
ease of understanding, a cyclic C5H5+ complex, in which all
C atoms are sp^ hybridized, might be visualized. With these
assumptions, it is a simple matter to determine which carbon
atoms undergo hybridization changes during the reaction.
For instance, in the attack of C2H2 on 1-C3H3+, three carbon
5
Although somewhat crude, applying a multiplicative factor
to the rate constant for each deuterated site is in keeping with
experimental evidence. For instance, in the acetolysis of some
identical tosylates, each deuterium atom substitution changed the
rate constant by ca. 0.84 (Streitwei ser et. al. , 1958).
Details of these studies are given in: J. Feng, J.
Leszczynski and M. C. Zerner, submitted; and J. Leszczinski, M.
C. Zerner and F. Wiseman, submitted.

84
(5.1)
(5.2)
(5.3) (5.4)
Figure 5.5. Structures which are Proposed to Form by
the Reaction of Propargylium Ion with Acetylene Without an
Energy Barrier.

85
atoms change from sp to sp2 hybridized. Upon fragmentation,
some carbon atoms remain sp2 hybridized; others become sp
hybridized.
In general, for a-secondary isotope effects, an
increase in hybridization in going from the reactant state
to the transition state yields an inverse isotope effect (kR
< kjj), whereas a decrease in hybridization yields a normal
isotope effect (kjj > kp) (Dreuth and Kwart, 1980). In this
system the bimolecular addition reaction will have an
inverse isotope effect, and the fragmentation reaction
should have a normal isotope effect. Figure 5.6 shows how
the isotope effects for the reaction of 1-C3H3+ + C2L2 can
arise. For the forward addition reaction, EpH > EpD and for
the fragmentation reaction, ERR < ERD, in which the
subscripts "F" and "R" refer to forward and reverse,
respectively, and "H" and "D" refer to protonated and
deuterated species, respectively. Since the bimolecular
addition is very exothermic for the formation of most C5L5+
isomers, it might be expected that the "average" transition
state structure might closely resemble the reactants and not
any of the C5L5 + isomers. This in turn implies that ERD -
Erh > EpR - Epjj (zero-point effects). However, the excess
energy in the reaction will allow longer sampling times for
the more energetic CgL5+ isomers. The less energetic
isomers which are sampled will undoubtedly be in higher
rotational and vibrational levels. The overall effect is to

86
+
Figure 5.6. A Schematic Representation showing the
Qualitative Differences in the Zero-Point Vibration Energy
Levels for the Reactants, Transition-State, and a
Representative C5L5+ Isomer for the Reaction of linear C3H3+
with C2H2/C2D2. (E f h > E p p > ^RH’ a n ^ ^rd are explained in
the text.)

87
lessen the normal Isotope effects expected in the
fragmentation of the C5L5+ isomers, unless there are
sufficient collisions to stabilize the isomers prior to
fragmentation.
In the model development outlined below, only
a-secondary isotope effects will be considered important.
0-secondary isotope effects, arising predominantly from
hyperconjugation, can sometimes be important (Melander,
I960), but will be assumed here to be minor compared to the
o-effects. It is also possible that hydride/deuteride
shifts may be occurring in the transition- state. However,
hydride transfers often exhibit small isotope effects
(Melander, and Saunders, 1980) and hydride shifts, if they
occur at all, will be assumed here to give negligible
contributions to the isotope effects.
Even though the different reactions in Figure 5.3 will
have different isotope effects, the introduction of an
independent fitting parameter for each type of reaction is
not justified. Though crude, only one additional parameter
was introduced into the model to account for all potential
a-secondary isotope effects. The method for introducing
this parameter is outlined as follows.
If a carbon atom bearing a deuterium atom undergoes a
hybridization change from sp to sp2 (force field becoming
stronger), the "isotope effect factor", F, is introduced as
a multiplicative factor in the rate constant. For two

88
deuterium atoms, F2 is the multiplicative factor, etc. If
the deuterium atom is attached to an atom changing from sp2
to sp hybridized, the rate constant is divided by F, for two
deuteriums, F2, etc. Introducing the same factor for both
addition and fragmentation reactions implies a constraint
which is at best only qualitatively correct. Applied in the
numerator the factor corrects for a single deuterium atom
(F2 for two, etc.) attached to a center undergoing
hybridization change from sp to sp2 in the transition-state
complex. Applied in the denominator, it corrects for a
change from sp2 to sp hybridization. Since the
transition-state complex has a stronger force field than the
reactant state (1-C3L3+ + C2L2) at these centers, the
«-secondary isotope effect will be "inverse" and F should
therefore be greater than unity.
Using the structural notation,
H\ H\
1-HDC3H+ = [ C-C=C-H]+, 1-H2C3D+ = [ C-C=C-D]+,
D7 H7
H\ D\
1-HDC3D+ = [ C-C=C-D]+, and 1-D2C3H+ = [ C-C=C-H]+,
D7 D7
the full kinetic scheme is shown in Figure 5.7. The neutral
fragmentation products, C2H2, C2HD, and C2D2, have not been
included for brevity. It is assumed that 1-C3L3+ undergoes
the same kind of hybridization changes when reacting with
C3H31 as it does with C2L2. As shown in Chapter 4, the

89
FTc
i-c3H3* * c2d2 s> c5h3d2+
t-C3”3 + C3H3I ——> sink
C5H3D2
* ^7 ^3H3+ + IF ‘-HDC3H+ + ¿I ‘-W* «V* * TÓ ‘*D2C3^
5F
C5H3D2+ —> Z~2 C-C3H3+ + If C-C3H2D* + To
1 OF
P2k
t-HDC3H+ + C2D2 -> C5H2D3+
F3k,
i-H2C3D+ ♦ c2D2 L> C5H2D3+
t-HDCjH + C^I —> sink
♦ F*P
i_H2C3D * C3H3I —£~> sin*
C5H2D3* —> T5F ^3°3+ * -¿2 £-HDC3D+ * ¥F
C5H2D3* —> TO C^3°3+ * If C-C3HD2+ * ^~2 ^2
1 OF
F3k
t-HDC D+ * CD, -> C HD +
J 2 2 5 4
F2k
t-D,C,H+ ♦ CD, -> C HD *
2 J 2 2 5 4
Fk
i-HDC3D ♦ C3H3I -> sink
* F\
t-C3D3 * C2°2 ~> C'D
S 5
l'°2C3H * C3H3I —~> Sin)C
♦ Fk
t_C3D3 * C3H3I :—> sink
V°/ —> -¿I l*lDS * ~J t*HDC D* ♦ -L
SF 5F 5F
„VF
CS°5 >
C'H°* * 5F C_C3°3 * C_C3IID2
'5 4
k /F*
C.D. * — > c-C3D3‘
5 5
Figure 5.7. Reaction Scheme Postulated for the Kinetic
Modeling of the Reaction of linear C g H g + with Deuterated
Acetylene Assuming Complete Scrambling and a-secondary
Isotope Effects.

90
products of the 1-C3L3+ + C3H3I reaction are of higher mass
and do not enter further into the kinetic schemes modeled
here.
Steady-state conditions are applied for all four C5L5+
isotopic species as before (without regard for isomeric
differentiation) and the differential rate equations for
scheme shown in Figure 5.7 are given in Appendix II.B.
Table 5.2 shows fitting results for several data sets using
the same kinetic scheme. Figure 5.8 shows plots of the best
fit of this model to the same data set as fitted in Figure
5.4.
Some experiments were conducted where certain ions were
ejected from the analyzer cell using FTICR double resonance
techniques (Comisarow et. al., 1978) as they formed. Among
the ions ejected were C3H2D+ and C3HD2+. Without further
fitting, this model was used to predict the behavior of the
kinetic system if these ions were ejected. Figure 5.9 shows
predicted results and data points.
Models for 4. The reaction of C3H3+ with
C4H2 (diacetylene) is kinetically more complicated than that
of C3H3+ with C2H2. There are more isomeric possibilities,
and ion/molecule reaction products of higher m/z are
detected. Several models were tried in attempts to fit the
experimental data, and the best of these made the
assumptions that C7H5+ and the excited forms of CgH5+ and

91
(b)
Figure 5.8. Model Fit (using the scheme of Figure 5.7) to
Typical Data set for linear C3H3+ + C2D2 Reactions. Ion
intensity vs. time curves for (a) C~H~ + and C~H0D+ and (b)
C3HD2+ and C3D3+. 32
a

92
(a)
(b)
Figure 5.9. Data from Ejection Studies and Model
Prediction. (a) C3HD2+ ion is ejected, (b) C3H2D+
ejected. (Poor signal/noise ralos of experimental
points are due to the effect of the ejection pulse
neighboring ion.)
ion is
data
on the

93
C11H5+ are in steady state, while C5H3+ and C7H3+ are not.
In order to account for the build-up of CgH5 + and C11H5+
ions, it was necessary to include stabilization steps for
the excited forms of these ions. A further assumption was
made that the stabilized forms of CgHg + and C11H5+ are not
reactive within the time frame (2s) of the experiments. The
resulting scheme is shown in Figure 5.10. Reactions
involving CgHgI+ are included because CgHg + is detected in
the ICR experiments. Applying steady-state assumptions to
the C?H5+, CgH5+, C11H5+, and CgHg+ ions yields a model with
a full analytical solution (Appendix II.C). Figure 5.11
shows results of the model fit to a typical data set. The
kinetic parameters have been grouped as exponential and
pre-exponential terms in the equations, yielding 9 fitting
parameters. Table 5.3 shows results of model fits of two
data sets. The term kp2pc3H3I'*s
— (0 2 + k_21^2 + ^sl*^)’ anc* hence can be calculated from the
parameters. The results of the first data set fit in Table
5.3 yield k 2Pc H I = 1-2(0.3) s-1; from the second data set
flt* kp2PC3H3I = 1,3 (°-2) 8
Discussion
C3V.,+„C2H g/CgDo• Several insights into the mechanism
of the C3H3+ + CgHg/CgDg reactions are obtained from these
modeling studies. First, a value of 1.4 (0.2) s-1 is
obtained for kp' from the intercept of Figure 5.2 (values

94
l^3H3+ * C4H2 ~* C7H5*
l^3H3+ * C3H3I “> W+
SH5+ —■* SH3+ + C2H2
C7Hs+ -^> t-CjH/ ♦ C4H2
Jq
SH5+ —■> C^3H3+ + C4H2
C5H3+ + C4H2 —> C9HS*
CSH3+ + C3H3I —J C8H6I+
+ -21 +
C H > C-H- ♦ C.H0
9 5? 7 3 2 2
c9h5+ -11> c5h3+ ♦ c4h2
C H + Sl-> c H + (stabilized)
9 5 9 5
C7H3+ + C4H2 —> C11H5+
C7H3+ + C3H3I —> C10H6I+
C1,H5+—> C9«3+ + C2H2
♦ -32 ♦
C,,H5 >C7H3 +C4lI2
k
CnH5‘ —-—> (stabilized)
W* —> ca"6+ * 1
♦ kJ
C H > sink
3 6
Figure 5.10. Reaction Scheme Postulated for the Kinetic
Modeling of the Reaction of linear C g H g * with Diacetylene

95
Figure 5.11. Model
a Typical data Set
Intensity vs. time
and CgHg+, and (c)
Fit (using the scheme of Figure 5.10) to
for linear C3H3+ + C4H2 Reactions. Ion
curves for (a) C~H.,+ and Cc-H«+, (b) C7HQ +

TABLE 5.3
Results of Model Fits (Figure 5.10) foj the System C3H3+ + C4H2
under Various Experimental Conditions.
Pressures (torr)
fijCs-1 )*
02(s-1)+
flais’1)*
(Arb units)
k-ll*lIt/«12*
(Arb units)
P„ „ . = 1.1 X 10“7;
^3n3A _7
Pr M = 4.8 X 10 ;
^4 n9
Px = 6.2 X 10 b;
e
-8.1(.2)
-3.9(.2)
-1.9(.7 )
.743(.007)
-.93(.07)
pc,H,i - * lo:7:
Pc H = 5.7 X lO-';
?x = 5.3 X 10 b;
e
-8.4(.2)
-3.9(.1)
-3.4(.7)
.8 29( .007)
-1.23(.08)
k-21♦2(s~1)*
ksl*2*
ks2*3(s-1)*
kd(S_1)
SOS
l.Q(.l)
1.79(.07)
1.0(.3 )
• 5 ( . 1)
.0051
1•2(•1)
1.45(.05)
• 7 (. 2)
.2(.2)
.015
* Initial readings were
scaled to one
arbitrary unit for
comparison.
* ®1 “ ”(k-ll + k-13)kf1
PC.H /(k-ll +
4 2
k-12 + k-13> “ kpl
PC3H3X1 92 =
“(k-21 + ksl)kf2 pc Hn/(k-21
4 2
♦ k-22 + ksl) ~
kp2 PC„H„I ' fi3 " -(k-31 + ks2>kf3 PC.H,/(k-31 + k-32 + ks2> - kp3 PC„H„I • *1 “ kfl PC.H0^k-ll + k-12 + k13^ 012 = 01
J J T ft «5») 4 ft
- *2 = kf2 pc II ! (k-21 + k-22 + ksl): *3 “ kf3 PC H / (k-31 + k-32 + ks2)*
4 2 4 2

97
for kp1 are a little higher from model fits shown In Table
5.2). Assuming a cell temperature of 363K and given that
PC H I = 3,3 x 10~8 torr (after system factor correction),
3 3
kp = 1.6 (0.2) x 10-9 cm3 s~1 , in good agreement with an
experimentally determined value7. Second, the model gives
branching ratios for the complex C5L5+. The ratio, kc/kj, ,
is ca. 0.34 (.03) (Table 5.2), implying that C5L5 + fragments
to 1-C3H3+ at a rate three times that of fragmentation to
c-C3H3+. Since c-CgH3+ is thermodynamically more stable
than 1-C3H3+ by ca. 25 kcal mol-1 (Lossing, 1972), any
factor affecting the internal energy of CgL5+, such as a
collisional stabilization, will undoubtedly affect the ratio
kc/kj. Hence, k^kj is probably very sensitive to
experimental conditions (method of ionization, total
pressure, and temperature). Finally the "direction" and
magnitude of F (1.67 (.10)) suggest not only that the model
is reasonable, but that the isotope effect plays an
important part in the overall kinetics.
It should be remembered that F is not an overall
isotope effect; isotope effects are ratios of rate
constants. The magnitude of F does, however, indicate the
kinetic contribution of replacing one hydrogen atom with a
deuterium atom on a hydrogenic site undergoing a
hybridization change in the transition-state structure. F is
7kp = (3.0 + 1.2) x 10"9 cm3 mol-1 s-1 was determined
experimentally using a typical reaction conditions given in
Chapter 4.

98
the a-secondary kinetic isotope effect for the elementary
bimolecular addition reactions per hydrogenic site (only
those sites giving rise to a-secondary effects included).
1/F is the isotope effect for the elementary
fragmentation reactions (to 1-C3H3+ and c-C3H3+) per
hydrogenic site (again only those sites giving rise to
a-secondary effects included). Because of the complexity of
the scheme in Figure 5.7, overall isotope effects cannot be
obtained by determining product ratios, as is often done in
isotopic studies of more elementary ion/molecule reactions.
However, F can be compared to isotope effects found in
elementary ion/molecule reactions.
a-secondary kinetic isotope effects can be quite large
(Mead, et.al., 1980; Turnas, et. al., 1987). The larger
effects found in ion/molecule reactions are due to a narrow
(non- Boltzmann) energy distribution centered close to the
threshold energy (Derrick, 1983). The magnitude of the
isotope effect factor, F, indicates a fair amount of bond
rearrangement in the transition state structures. Due to the
number of assumptions and the indirect method for obtaining
F, it is not attempted to calculate isotope effects from
molecular models and calculated vibrational frequencies.
CgHs* + ClH2. Kinetic data and modeling of this system
reveal some insight into the mechanism for the reaction of
C3H3+ and C4H2- Although the scheme shown in Figure 5.10

99
does not account for specific isomeric reactivities, the
scheme does account reasonably well for the data. The
signal-to-noise ratios of the available data do not warrant
further refinements of the model. Several crude models were
attempted, and the model reported here may not be the best
or only model which can adequately explain the results.
However, of the variations of the scheme in Figure 5.10
which were tried, the one reported gave the best fitting
results. In particular, a scheme was tried in which stable
forms of CgH5+ and C11H5+ were formed from the corresponding
bimolecular additions reactions rather than requiring
stabilization steps of "hot" CgH5+ and C11H5+ ions. This
scheme did not fit the data. Apparently, only in the ions
larger than C7H5 + are there enough internal vibrational
modes to give rise to an ion/molecule collision complex of
sufficient lifetime to allow collisional stabilization at
these pressures.
Interestingly, the value for kp2 in the scheme of
Figure 5.10 is the same, within error, as the value for kp
in the scheme of Figure 5.7. The ratio of the reduced
masses of the two reacting systems (C3H3+ + C3H31 )/(C5H3+ +
C3H3I) is 0.83, which is well within the error for the value
of kp2/kp. Hence, it cannot be determined from this
comparison whether the reactions with C3H3I are
collision-controlled or not. However, if the reactions of
C3L3+ with C3H3I and C2L2 are co11 ision-contro 11ed, there

100
would only be a small kinetic isotopes effect arising from
the rotational partition functions. If the scheme in Figure
5.7 is correct, there is a transition-state structure for
the reaction of C3H3 + and C2H2. and undoubtedly with C3H3+
and C4H2 as well, which does have bond changes. This
implies that the rate is predicted to be lower than
collision-controlled.
Figure 5.10 does not show CgH5 + and C?H3+ fragmenting
to any products. Undoubtedly any isomers of CgH3+ and C7H3 +
which form are all resonance-stabilized. Any fragmentation
product would be highly energetic and unlikely to form, even
at the energy levels available in these reacting systems.
Hence, once CgH3+ and C7H3 + are formed, they will react only
in bimolecular addition reactions, which are orders of
magnitude slower than the unimolecular fragmentation
reactions of C7H5+, CgH5+, and CjjHg'1". Hence, there is a
non-steady-state build up of C5H3 + and C7H3+ ions at the
first part of the reaction.

CHAPTER 6
REACTIONS OF C5H3+ AND C5Hg+ IONS WITH ACETYLENE AND
DIACETYLENE
Introduction
According to the proposed ion/molecule mechanism of
soot formation (Calcóte, 1981; Olson and Calcóte, 1981a),
C3H3+ forms CgH3 + and CgH5+ in reactions with acetylene, and
C7Hg+ when reacting with diacetylene. However, as seen in
Chapter 4, investigation of the reactions of C3H3+ with
acetylene and diacetylene did not reveal facile formation of
CgH3+ or CgH5+ by reaction of this ion with acetylene,
although C3H3+ did react readily with diacetylene, yielding
CgH3+ and C?H3+. All three of the postulated products of
C3H3+ reactions with acetylene and diacetylene (CgH3+,
CgH5+, C7Hg+) have been identified by mass spectrometry
(Michaud et al., 1981; Olson and Calcóte, 1981b) in flames,
but it remains to be determined which, if any, of them may
be important in soot formation mechanisms.
Heats of formation of the CgH3+ ion from different
precursors have been reported in three experimental studies
(Franklin and Carroll, 1969; Dannacher et al., 1979; Baer et
al., 1979). Dannacher, et al (1979) suggested the presence
of two different linear structures, CH3-C;C-C=C+ and
HC=C-C;C-CH2+ for the CgH3 + ions produced by .CH3 and H.
101

102
loss from 2,4-hexadiyne and 1,3-pentadiyne parent Ions,
respectively.
There are many possible structures for the C5H5 + ion,
and despite a number of theoretical and experimental studies
involving it, few definitive results exist regarding the
specific relative energies of various isomeric forms.
Experimental studies concentrated on determining the
appearance potential and heats of formation of CgH5 + ions
from different sources by mass spectrometric methods (Pottle
and Lossing 1963; Dorman, 1965; Harrison et al., 1965;
Occolowitz and White, 1968; Franklin and Carroll, 1969;
Lossing and Traeger, 1975; McCreary and Freiser, 1978).
These resulted in heat of formation values ranging from 239
to 309 kcal/mole depending on the source and technique of
C5H5+ production. Probably the best estimate of heat of
formation is for the eye 1opentadieny1 ion (AH^ = 255
kcal/mole), obtained by Lossing and Traeger (1975) from
measurement of the ionization potential of the
cyclopentadienyl radical with an electron monochromator-mass
spectrometer. Other than this, all the AHf's measured from
different sources using electron impact techniques fall into
two categories: 270-290 kcal/mole and 300-309 kcal/mole.
Evaluating these differences in terras of different isomeric
structures cannot be justified considering the large
uncertainty in the internal energies of ions which may be
present following electron impact ionization. Early ICR

103
experiments were carried out to identify structures of C5H5 +
according to their reactivity with different neutrals (Brill
and Eyler, 1981; Buckley, 1982; Brill, 1983, Eyler, 1984).
Several precursors were used in the formation of ions
and the results of the reactivity studies indicated the
possibility of four different isomers of C5H5+ (Brill,
1983). Acetylene reacted quite slowly with the C5H5+ ions
(Buckley, 1982; Brill, 1983) while diacetylene and aromatics
with side chains reacted at an appreciable rate (Buckley,
1982). As a result, it has been suggested that soot
nucleation may proceed by adding a few large molecules
rather than through addition of many smaller ones (Buckley,
1982; Baykut et al., 1986). No definitive assignment of
C5H5+ isomeric structure was possible in the earlier studies
(Buckley, 1982; Brill, 1983). Proton-transfer reactions
involving one relatively unreactive C5H5+ isomer gave
(Buckley, 1982) a proton affinity of 227.9 + 0.3 kcal/mole
for the C5H4 neutral which remained after proton transfer.
When combined with estimates of the heats of formation of
possible C5H4 species, the results were consistent with (but
did not conclusively prove) a vinylcyclopropenylium form for
the C5H5+ isomer.
A number of theoretical studies have examined C5H5+
structures (Stohrer and Hoffman, 1972; Hehre and Schleyer,
1973; Dewar and Haddon, 1973; Kollmar et al, 1973; Borden
and Haddon, 1979). Schleyer and co-workers located two

104
minimum energy forms on the CgHg + potential surface, the
more stable one corresponding to planar cyclopentadlenyl,
the other one to a square-based pyramid structure (Hollinar
et al, 1973; Hehre and Schleyer, 1973). Similar results
were reported by Stohrer and Hoffman (1972) although they
proposed the pyramidal structure as the more stable form
compared to the planar cyclopentadlenyl. Recent
calculations8 have shown that the vinylcyclopropenyl1um ion
has the lowest energy (AH^ = 256.7 kcal/mole) among a number
of other possible structures as shown In Figure 6.1. All of
these structures were found to be no more than 30 kcal/mole
n
higher In energy than the lowest energy structure .
In this work, the kinetics and reaction mechanisms of
CgH3+ and GgH5+ Ions produced from different precursors and
reacting with acetylene and diacetylene have been studied in
order to identify isomeric structures and to obtain rate
coefficients. Also, the energetics of CgH5 + formation from
norbornadiene and cycloheptatriene were followed to
investigate two possible competing pathways of CgHg +
formation which could lead to different isomeric structures.
Experimental
Reaction rate coefficients were determined by
monitoring the intensity of the CgH3 + or CgH5 + ions,
respectively, as a function of time after ejection of all
O
J. Feng, J. Leszczynski and M. C. Zerner, submitted.

(6.1)
AHf = 256.7kcal/mol
(6.2) is triplet, and
(6.3) is singlet3
AHf = 265.9kcal/mo 1
(6.4)
AHf = 269.6kcal/mol
(6.6)
AHf = 274 . 7kcal/mol
(6.7)
AHf = 277.7kcal/mol
(6.8)
AHf = 278.3kcal/mo 1
(6.9)
AHf = 283.0kcal/mol
Figure 6.1. C5H5 + Structures and Theoretical Heats of
Formation. a(6 5) is also a singlet cyc1opentad ieny1
structure with AHf = 273.1 kcal/mol.
105

106
other Ions from the analyzer cell. Excitation amplitude and
total pressure were kept constant at optimized values for
all the kinetic runs in order to minimize the unwanted
effects of such factors on ion intensities, which have been
discussed in detail elsewhere.9
C5H3+ ions were produced by 50 eV electron ionization
of 2,4-hexadiyne and by the reaction of C3H3 + with
diacetylene. C3H3+ ions used to produce CgH3 + were formed
by Xe+ charge transfer reactions with propargyl iodide at an
ionizing energy of 15 eV. After 30 ms reaction time with
C4H2. all the other ions except CgH3+ were ejected from the
cell to follow the reactions of this ion with diacetylene as
a function of time. C5H5 + ions were produced by charge
transfer reactions of various precursors (dicyclopentadiene,
cyclopentadiene, norbornadiene, 1-penten-3-yne,
cycloheptatriene) with different charge transfer agents
(Xe+, N2+. Ar+) formed with an electron beam pulse of 5 ms
duration at an ionizing energy of 13, 16.5, and 20 eV,
respectively.
Cyclopentadiene was prepared by cracking
dicyclopentadiene and was kept in dry ice when not used to
prevent the dimerization process. All the other compounds
used were obtained commercially and their purity was checked
9M. Moini and J. R. Eyler, to be published.

107
by obtaining wide mass range spectra. All the samples were
used after multiple freeze-pump-thaw cycles.
All reactions were followed at a cell temperature of
363 K. Some C5H3 + and all C5H5 + ions used in rate constant
determination studies were produced by chemical reactions in
order to minimize the internal energy imparted to the ions.
Also, since the total pressure in the reaction cell was
almost 1 x 10-5 torr and the reactant ion formation time was
>30 ms, substantial collislonal relaxation of the ions took
place before kinetic data were collected.
Results
Reactions of CgHg'1'. A very low number of C5H3 + ions
were produced from 2,4-hexadiyne at electron energies above
30 eV. Reactivity of these ions was monitored at an
electron energy of 50 eV although the ion intensity was
still very low. Although almost all of the C5H3+ ions
produced reacted with the 2,4-hexadiyne precursor, no
reaction was observed with either C2H2 or C4H2> Reactions
of C5H3+ with 2,4-hexadiyne were:
C5H3 +
+
C6H6
—->
C6H6 +
+
[C5H3]
(6.1)
C5H3 +
+
c6h6
>
c9h7 +
+
[C2H2]
(6.2)
C5H3 +
+
C6H6
>
C6H5 +
+
[C5H4]
(6.3)
C5H3 +
+
C6H6
>
c7h7 +
+
[C4H2]
(6.4)
C5H3 +
+
C6H6
>
C11H9+
(6.5)

108
CgH?+ + C6H6 > C15H13+ (6.6)
C5H3+ Ions produced as products of the reaction of
C3H3+ + C4H2 were 100% reactive with both propargyl iodide
and with diacetylene (the neutrals present in the reaction
medium).
C5H3+ reactions with C4H2 were:
C5H3 +
+
c4h2
>
c7h3+ + [C2H2]
(6.7)
C5H3 +
+
C4H2
>
C9H5 +
(6.8)
C?H3 +
+
C4H2
>
C11H5+
(6.9)
C9H5 +
+
C4H2
>
Ci3h7+
(6.10)
Some of the product ions were observed to react further with
propargyl iodide by displacing atomic iodine:
c7h3+ ♦ c3h3i > c10H6+ + I
c9h5+ + c3h3i > c12H8+ + I
C5H3+ reactions with propargyl iodide were:
C5H3+ + C3H3I > CgHg+ + I (6.13)
C8H6+ + C3H3I > C11H9+ + I (6.14)
The CgHg+ ion reacted further with C4H2:
(6.11)
(6.12)

109
C8H6+ + C4H2
> c12H8
(6.15)
Ion Intensity vs. time curves for the C5H3+/(C4H2 +
C 3 H 31) system are shown in Figure 6.2. The decay of C5H3 +
ions involved reaction with both C4H2 and propargyl iodide.
The procedure for rate coefficient determination used
in previous studies of C3H3 + and C5H5+ ion/molecule
reactions required subtraction of the observed rate constant
for the reaction of the ion with the precursor neutral from
the observed rate constant for the sum of the reactions with
precursor and reactant neutrals. In this case, however, the
reactant neutral (C4H2) was also the precursor of the ion of
interest (C5H3+), and thus the subtraction procedure could
not be used. An alternative method for rate constant
determination was thus required. Following ejection of all
other ions from the FTICR cell, the decay of C«jH3+ as a
function of time is given by:
tC5H3+^t = [C5H3+^0e
“(npkP
ndkd^t
(6.16)
where npkp and ndkd refer to the products of the number
densities and ion/molecule rate coefficients for propargyl
iodide and diacetylene, respectively (Reactions (6.7), (6.8)
and (6.13)). The quantity ndkd + npkp can thus be
determined from the slope of a semilog plot of C5H3 + decay
as a function of time. At short reaction times, the
following expressions hold true:

110
c5^3+ + c4^2 Reactions
Time (s)
Figure 6.2. Reactions of CgH3 + with C4H2. Disappearance of
C5H3 and product ions includes reactions with propargyl
iodide. C5H3+ ions were produced from the reaction of C3H3+
with diacetylene within 30 ms reaction time. C3H3+ ions'3
were produced from propargyl iodide by charge transfer
reactions with Xe+. p(C3H3I) = 1.9 x 10-7 torr, p(C,H?) =
1.3 x 10 6 torr, p(Xe) = 5.4 x 10-6 torr.

Ill
dD/dt
ndkd tC5H3+Ioe
" ( npkp + ndkd^
(6.17)
and
dP/dt
npkp tc5H3+^0e
- (6.18)
where D and P refer to product Ions of the reaction with
diacetylene (C7Hg+ and CgH5+, Reactions (6.7) and (6.8)) and
with propargyl Iodide (CgH6+, Reaction 6.13) respectively.
Thus, the ratio ndkd/npkp was calculated from the ratio of
slopes of product formation as a function of time. Next
ndkd was obtained using the calculated sum and ratio of the
two rate constants. Finally the absolute rate constant was
determined following the usual procedure. It was found that
C5H3+ ions reacted with C4H2 with a rate constant of (5.6 +
1.7) x 10-10 cm3/s.
Kinetic Modeling of C5H3* reactions with diacetylene.
In order to better understand the reaction mechanisms
involved in the C5H3+ + C4H2 system, kinetic modeling
studies of the ion intensity vs. time curves shown in Figure
6.2 were carried out.10 Details of the modeling methodology
are given in Chapter 5. A kinetic model involving the
10The kinetic modeling studies were performed in the
Environics Division of Air Force Engineering and Services
Center, Tyndall Air Force Base, Florida by F. Wiseman using
multiple experimental data sets produced at identical
conditions to those reported for Figure 6.2.

112
reactions above was fitted to the experimental data assuming
steady-state concentrations for the excited forms of
(C9H5+)* and (C11H5+)* Intermediate complexes. The complete
reaction scheme used for modeling Is shown in Figure 6.3.
Comparison of the model fit with the experimental data
Is shown In Figures 6.4a and 6.4b.
Effect of Precursor Neutrals. C5H5+ ions produced from
different precursors exhibited behavior indicative of both
reactive and unreactive populations toward both the
precursors and the reactant neutrals. Figures 6.5a and 6.5b
show CgHg+ normalized ion intensity vs. time curves for two
(cycloheptatriene and l-penten-3-yne) of the five precursors
used to form ions before reaction with diacetylene and
acetylene. Following an exponential decay indicative of
pseudo-first order kinetics, a substantial fraction of
unreactive ions remains at long reaction times, particularly
in Figure 6.5b. Table 6.1 shows the method of preparation
of CgH5+ ions from different precursors and the percent of
unreactive ions remaining at long reaction times.
Two (norbornadiene and cycloheptatriene) of the five
precursors mentioned above produce C7H8 + rather than C5H6+
parent ions. The C7H8 + ions produced from norbornadiene
were reported (Davidson and Skell, 1973; Ausloos, 1982)

113
. Kf2 + *
C5H3 + C4H2 >
"p2
C5H3+ + C3H3I > CgHgI+
> ^5H3 + C4Ii2
(C9H5+)* ----> c7h3+ + c2h2
k.
* ----> CqHr+ (stabilized)
'9 5
9 5
k94
C9H5+ + C4H2 ~ > C13H7+
. f3 +
Cr^Hg + C4H2 ^ C^ j^5
C7H3+ + C3H3I “ > C10H6I
(C11H5+) > C7H3+ + C4H;
(cHH5+) " > ^9H3 + C2H2
k s 2
(C11H*+) > C11H=+ (stabilized)
Figure 6.3. Reaction Scheme Postulated for the Kinetic
Modeling of the Reaction of CgH3+ with Diacetylene.

114
TIME/s
Figure 6.4. Model Fit to Typical Data Set for CgH3 + + C4H2
Reactions.3 (a) Ion intensity vs time curves for C5H3 + and
C7H3+. (b) Ion intensity vs time curves for CgHg+, CgHg4-,
and Cj -j H5+ .
aThe best fit values for the fitting parameters were:
6g = - 8.7( .2)/s, 03 = - 4.6( .4)/s, k_210j = 2.8(.l)/s. kg1<¡>1
= 3.7(.1)/s, ks202 = 2.9(.2)/s, k94 = .04(.06)/s, and kd =
.8(.2)/s where
°2 = ~(k-21 + ksl)kf2PC4H2/_kp2PC3H3I’
^1 = kf2PC4H2/ and
^2 = kf3PC4H2/(k-31 + k-32 + ks2)-

115
Figure 6.5. CgH^ Ion Decay Curves for Various Reactions.
(a) with cycloheptatriene(O), with cycloheptatriene
and acetyl ene( + ), and with cycloheptatriene and diacetylene
(tn) . C5H5+ ions were produced from cycloheptatriene by
charge transfer reactions with Ar+. p(C7Hg) = 1.3 x 10-7
torr, p(C2H2) = 1.1 x 10-6 torr, p(C4H2) = 6.6 x 10-7 torr,
p(Ar) = 10.4 x 10"6 torr.
(b) C5H5+ with 1-penten-3-yne(O) . with 1- penten-3-yne and
acetylene(+), and with 1-penten-3-yne and diacetylene(â–¡).
C5H5+ ions were produced from l-penten-3-yne by charge
transfer reactions with Xe+ . p(C5Hg) = 4.2 x 10-7 torr,
p(C2H2) = 1.4 x 10-6 torr, p(C4H2) = 8.4 x 10"7 torr, p(Xe)
= 5.4 x 10-6 torr.

116
TABLE 6.1
Percentages3 of unreactlve C5H5+ found from various
precursors by charge transfer chemical ionization monitored
by observing reaction
with the precursor
neutral.
Precursor
Neutral
Charge Transfer
Agent
% unreactive
C5H5 +
dicyclopentadiene
N2+/Ar+
20
cyclopentadiene
Xe +
17
l-penten-3-yne
Xe +
65-70
cycloheptatriene
Ar +
0-5
norbornadiene
N2+/Ar+
Kr +
18-20
5-10
aEstimated error is 5%.

117
earlier to lead to two different channels (Reactions (6.19)
and (6.20)) for C5H5+ Ion formation.
C7H8+ > C7H7+ + H
(6.19a)
c7h7+ > c5h5+ + c2h2
(6.19b)
or
C7H8+ > C5H6+ + C2H2
(6.20a)
C5H6+ > C5H5+ + H
(6.20b)
Thus, C5H5+ ion formation pathways were studied in more
detail for norbornadlene and cycloheptatriene. When
different charge transfer gases were used for ionization of
norbornadiene, different percentages of reactive C«jH5+ were
observed, as is noted in Table 6.1. Also the abundances of
C7H7+, C5Hg+ and C5H5 + ions were measured following charge
transfer ionization, and different behavior was observed for
compounds with ionization potentials in the range of 14 to
16 eV. Table 6.2 shows this effect for two reagent gases
(Kr+ and N2+) which have ionization energies of 14.0 and
15.7 eV respectively.
In order to further investigate this behavior, the
relative ion abundances vs. electron energy for
cycloheptatriene and norbornadiene were obtained (see
Figures 6.6 and 6.7). *
1:1Electron impact ionization was used for this study and
therefore the energy scale in Figures 6.6 and 6.7 should be
considered as approximate with at least +1 eV uncertainty.

118
TABLE 6.2
Changes In Ion abundances at two different Ionization
energies for norbornadiene.
Ionizing energy/eV
(charge transfer agent)
Abundances as a
total ion
fraction
signal3
of
c7h8 +
C rj H rj
C5H6 +
C5H5 +
14.0 (Kr+)
0.07
0.45
0.32
0.16
15.7 (N2+)
0.09
0.28
0.16
0.47
aEstimated error Is +0.02.

119
(a)
(b)
Figure 6.6. Relative Ion Intensities Produced from
Cycloheptatriene as a Function of Electron Impact Energy,
(a) C7Hg* and C ^ H ^ and (b) CgHg , CgHg • and C g H g .

120
Energy (eV) ( a )
Figure 6.7. Relative Ion Intensities Produced from
Norbornadiene as a Function of Electron Impact Energy, (a)
C7H8+ and C7H7 + and (b) C5H6+, C5H5+, and C3H3+.

121
^5Ü5— reactions with dlacetylene. After ejection of
all Ions except CgH5 + following charge transfer chemical
Ionization of a mixture of diacetylene and a precursor
compound, the ion/molecule reactions as a function of time
were monitored. Independent of the precursor used, the main
reaction was the addition of C4H2 to C5H5 + to produce the
C9H7+ ion.
C5H5+ + C4H2 > C9H7+ (6.21)
Other minor reactions observed were:
C5H5 +
+
C4H2
>
C7H5+ +
[c2h2]
(6.22)
C5H5 +
+
C4H2
>
c7h7+ +
[c2]
(6.23)
C7H7 +
+
C4»2
c11Hg+
(6.24)
c9h7 +
+
C4H2
>
C13H9+
(6.25)
For CgHg+ ions produced from cyclopentadiene, the C2
addition reaction (6.22) was not observed with C4H2.
The rate coefficient for the disappearance of C5H5+
was calculated as described earlier in Chapter 3 and the
values found for C5H5+ ions produced from different
precursors are given in Table 6.3.
reactions with acetylene. C5H5+ ions formed from
four of the five precursors (cyclopentadiene,

122
TABLE 6.3
Rate coefficients for the reaction of C5Hc+ ions from
different precursors3 with diacetylene and acetylene.
Precursor
Absolute rate
C4H2/(10-10 cm3/s )
coefficient with
C2H2/(10_11 cm3/s
cyclopentadiene
(1.0
+ 0.5)
(4.8
+ 1.9)
l-penten-3-yne
(2.0
+ 1.0)
(2.7
+ 1.0)
norbornadiene
(2.9
+ 1.4)
(3.1
+ 1.3)
cycloheptatriene
(3.3
+ 1.9)
(1.8
+ 0.7)
dicyclopentadieneb
(1.6
+ 0.8)
aC5H5+ ions were produced by charge transfer chemical
ionization using different gases as shown in Table 6.1.
bIon signal for dicyclopentadiene was too small to produce
reproducible results for the rate coefficient of the
reaction with acetylene.

123
l-penten-3-yne, norbornadlene, cycloheptatrlene) reacted
very slowly with C2H2, producing very small amounts of C7H7 +
and CgHg+.
C5H5 +
+ c2h2
-> c7h7+
(6
. 26)
C7H7 +
+ C 2 H 2
-> CgHg+
(6
. 27 )
Rate
constants for
the CgHg+
+ C2H2 reaction were
about
one
order
of magnitude
less than
those for reactions
with C4
h2
(see Table 6.3).
Discussion
Two different CgH3 + structures were postulated
(Dannacher et al., 1979) based on PIPECO measurements of
appearance energies of C5H3+ ions from 1,3-pentadiyne and
2.4-hexadiyne. In the work reported here, C5H3+ ions were
produced from 2,4-hexadiyne and by reaction of C3H3+ with
diacetylene. Although CgH3+ ions produced either way were
reactive toward their precursor neutrals, C5H3 + ions from
2.4-hexadiyne were unreactive with both C4H2 and C2H2, while
those formed as ion/molecule reaction products reacted with
C4H2 with the relatively high rate constant of (5.6 + 1.7) x
10-10 cm3/s. Dannacher et al. (1979) suggested the
structures CH3~C=C-C=C+ and HC=C-C=C-CH2+ for the C5H3+ ions
produced from 2,4-hexadiyne and 1,3-pentadiyne respectively.
Experimental appearance potentials for these ions suggested

124
that the former probably had a higher heat of formation,
<1431 kJ/mole (Baer et al., 1979), compared to the latter,
1317 kJ/mole (Dannacher et al., 1979). In this study,
enhanced reactivity of CgH3 + ions produced by the C3H3 + +
C4H2 reaction compared to those produced by electron
ionization of 2,4-hexadiyne suggests that the former have a
higher heat of formation with a stable structure different
from those reported earlier for C5H3+ ions from both
2,4-hexadiyne and 1,3-pentadiyne. Enhanced reactivity does
not always correlate with a higher heat of formation, but
this has often been found true for isomers of other small
hydrocarbon ions. Our observation that CgH3+ is formed in
an exothermic reaction of linear C3H3+ with diacetylene
leads to an upper limit of 1375.9 kJ/mole for AHj. of the
CgH3+ ion formed in this manner.12 This value is not
inconsistent with either of those reported earlier.
Although no structural assignment can be made for the
C5H3+ ion produced by reacting C3H3+ with diacetylene based
on the results of this study, several structures can be
considered possible on the basis of initial charge
distribution on C3H3+ leading to the formation of three
product ion structures by reaction mechanisms shown in
Figure 6.8. The three possible CgH3+ product ions shown in
-“This calculation assumes no significant internal
energy in the C3H3 + ions prior to reaction and heats of
formation of 281 kcal mol-1 (Lossing, 1972), for 1-C3H3+.
54.2 kcal mol-1 (Wagman et al., 1968), and 102 kcal mol-*
for C4H2 (Coats and Anderson, 1957).

125
+
C=C=C-H
IK
H-C=C-C=C-H
>
;;c = c = c-^ +
Hx ^C=C-C=C-H
H
>
% = C = C/H C = C-H >
H/ nc=q/ "
+
iK
C = C = C
^C=C-H
+ H-C=C-H
(6.10)
Hv +
iK
C-C=C-H + H-C=C-C=C-H
H
+ JtC /H
> H-C=C-C^
iK ^C = C-H
>
H
cr ,h
H-C = C-cf ^C<
H ^C=C-H
H
XC<
> H-C = CX ^C = C-H + H-C = C-H
and/or
(6.11)
H-C=C-C^I
'C +
H-C=C-H
(6.12)
Figure 6.8. Proposed Reaction Mechanisms for the Reaction
of the Propargylium Cation with Diacetylene, Leading to
Three Different C5H3 + Product Ions with Resultant Loss of
Acetylene.

126
Figure 6.8 have structures which differ from those
postulated (Dannacher et al., 1979) earlier. While no
definitive theoretical or experimental evidence as to the
relative stability of these (or other) C5H3 + isomers Is
available. Structure (6.12) Is most similar to the
vinylcyclopropenyl1 urn ion found most stable among the CgHg +
Isomers. Thus Structure (6.10) or (6.11) might be the
unstable, reactive structure formed In these experiments.
When deuterated diacetylene was reacted with C3H3 + ion, the
deuterated product ratios, CgH2D+:CgHD2+:CgH3+ were found to
be 6:3:1. This result is also consistent with the reaction
mechanisms of formation of the three CgH3 + structures shown
in Figure 6.8 assuming complete scrambling of hydrogens in
the intermediate C7H5+ complex.
CgüS- ion structures produced from different
precursors. CgHg + ions produced from different precursors
all exhibited at least two populations, one reactive, other
unreactive. This behavior for numerous other ionic
reactants has been used previously (Ausloos and Lias, 1981;
Smyth et al., 1982; Wagner-Redeker et al., 1983; Smith and
Adams, 1987) to argue for the existence of at least two
different structural isomers; one reactive and one
non-reactive. These results are in agreement with the
earlier reactivity study of C5H5+ ions from different
precursors (Brill, 1983). To distinguish the reactive CgHg +

127
structures, their reaction mechanisms and reaction rates
with acetylene and diacetylene were studied. Although they
reacted with their precursor neutrals with different rates,
they all reacted with acetylene and diacetylene at similar
rates within the experimental error limits, as shown in
Table 6.3. Thus no isomeric differentiation based on
reactivity can be made. Rate coefficients for the reaction
with acetylene were similar to those determined earlier
(Buckley, 1982; Brill, 1983), i.e. in the range of 10-11
cm3/s. Reaction mechanisms were similar for all C5H5+ ions
with the exception of cyclopentadiene, which didn't give C2
addition reactions with C4H2.
Although no definitive structure assignment can be made
for the CgHg+ ions produced, several suggestions are
possible from the results of this study. Similar reaction
rates within experimental error suggest the formation of the
same reactive C5H5+ structure from all precursors. Assuming
that the latest theoretical information13 on the energies of
different C5H5 + structures is fairly accurate, we can
identify the possible structures which are energetically
accessible by the initial internal energy transferred to
neutral parents by chemical ionization. As shown in Table
6.4 , simple calculation using the thermochemical data14
13J. Feng, J. Leszczynski and M. C. Zerner, submitted.
14This calculation assumed heats of formation of 31.8
kcal mol-1 for cyclopentadiene (Harrison et al., 1960), 43.5
kcal mol-1 for cycloheptatriene (Finke et al., 1956), and

128
TABLE 6.4
Comparison of the energy transferred to neutral precursors
by chemical ionization with theoretical appearance energies
(assuming no reverse activation energy) of different C5h5 +
structures from the corresponding precursors.
| Neutral
charge
transfer
1
structure3 |
theoretical|
| precursor
I _
agent and (IP/eV)
1
1
1
_ I
AP/eV
(Cyclopentadiene
Xe +
(12.1)
1
1
6.1
1
1
12.0
i
1
6
. 2&6 .
3 I
12.4
i
1
6.4
1
12.6
i
I
6.5
1
12.7 |
i
1
6.6
!
12.8
i
1
6.7
I
12.9
i
1
6.8
!
13.0
i
i
1
I
6.9
1
1
13.2
i
|Norbornadiene
Kr +
(14.0)
1
!
6.1
l
1
13.1
1
Ar +
(15.8)
!
6
. 2&6 .
3 I
13.5
1
1
6.4
1
13.6 |
1
1
6.5
1
13.8
1
1
6.6
1
13.8
1
1
6.7
1
14.0
1
1
6.8
1
14.0
1
I __ _
1
6.9
1
I
14.2
1
|Cycloheptatriene
N2 +
(15.6)
I
1
6.1
I
1
13.9
1
!
6
. 2&6 .
3 !
14.2 |
!
!
6.4
1
14.4 |
1
I
6.5
1
14.6 |
1
1
6.6
1
14.6
I
1
6.7
!
00
1
1
6.8
1
14.8 |
1
!
6.9
!
15.0 |
aNumbers refer to the structures shown in Figure 6.1.
-1
62.3 kcal mol
for norbornadiene (Lifshitz and Bauer, 1963).

129
available for cyclopentadiene, norbornadiene and
cycloheptatriene indicates that C5H5+ formed from
cyclopentadiene by Xe+ charge transfer chemical ionization
can only have the lowest energy structure (Structure 6.1).
On the other hand, C5h5+ ions produced from norbornadiene
and cycloheptatriene by N2+/Ar+ charge transfer chemical
ionization have enough excess energy to sample almost all
the isomeric structures shown in Figure 6.1. Since the
energy barriers between these structures are not yet known,
nothing can be said concerning the possibility of
isomerization between these structures. Experimental data
indicates that at least two stable (reactive and unreactive)
structures are formed in all the cases studied. More
definitive identification of CgH5+ structures may be
forthcoming when better theoretical calculations are
reported, although identification of the
vinylcyclopropenylium ion as (one of) the unreactive
structure(s) seems reasonable in the light of the recent
calculations and earlier ICR studies.
To compare the behavior of ions produced from
cycloheptatriene and norbornadiene precursors (both having
the formula C^Hg), relative abundances as a function of
electron energy shown in Figures 6.6 and 6.7 were obtained.
As shown, the curves for C?H?+ (Figures 6.6a and 6.7a) and
CgHg^ and C3H3 + (Figures 6.6b and 6.7b) are very similar
both in terms of energetics and of general shape.

130
Differences in C5H5 + relative intensities are probably due
to the normalization procedure used in each case. An
increase in the relative intensity of CgHg + ions in both
cases in the energy range of 15-25 eV along with the fact
that the C7h7 + curves no longer increase in this energy
range implies that most of the C5H5+ ions are produced from
C7H7+. Similar behavior is seen for C3H3 + ions, i.e., the
intensity of these ions increases at about 22 eV (on the
energy scale shown on Figures 6.6b and 6.7b) where the rate
of increase in the intensity of C5H5+ is decreased. This
similar behavior implies that C7H7 + ions formed from
cycloheptatriene and norbornadiene follow the same
fragmentation pathways in the same energy range. Similar
behavior for C7H7 + ions from these two compounds has also
been reported earlier in collisional activation studies
(Winkler and McLafferty, 1973).
As seen in Figures 6.6b and 6.7b, formation of C5Hg+,
both in terms of energetics and relative intensity, is
different for cycloheptatriene and norbornadiene, indicating
that C7Hg+ ions formed from these compounds by electron
impact have different structures (according to Reaction
(6.20a). Based on the significantly higher relative
intensity of C5Hg+ for norbornadiene along with the results
shown in Tables 6.1 and 6.2, there exists the possibility of
formation of CgH5 + ions from the CgHg + channel by Reaction
(6.20b) for norbornadiene. As shown in Table 6.1, the

131
percent of unreactlve C5H5 + increases from (5-10)% to (18-
20)% with changing ionizing charge transfer energy for
norbornadiene while no such change in C5H5 + reactivity was
observed for cycloheptatriene under the same conditions.
Relative ion intensities at two different energies of charge
transfer chemical ionization are shown in Table 6.2 for
norbornadiene. The results indicate that when Ar+/N2+
replaces Kr+ as the charge donor, the relative intensity of
the observed C5H5 + increases while there is a corresponding
decrease in the yield of the C5Hg+ ion. Thus, evaluation of
the results on C5H5 + reactivity (Table 6.1) together with
the results on relative ion intensity (Table 6.2) implies
that C5H5+ formed from CgHg + channel has a higher percent of
unreactive isomer compared to that formed from CyH?+
channel .

CHAPTER 7
REACTIONS OF GASEOUS C?H7 + IONS
Introduction
The C7H7+ ion has been proposed as one species
involved in an ion/molecule mechanism of soot formation
(Olson and Calcóte, 1981a; Calcóte, 1981). Mass
spectrometric measurements have shown that as premixed
flames approach a sooting condition, the predominant C3H3 +
ion is replaced by larger ions (Olson and Calcóte, 1981b)
including C7H7+. These ions in turn have been postulated
to react with neutrals such as acetylene and diacetylene,
forming still larger ions (Olson and Calcóte, 1981a).
According to the proposed ion/molecule mechanism, C5H5+
forms C7H7+ in reactions with acetylene. However, the
reactions of CgH5 + with acetylene did not reveal significant
formation of C7H7 + (see Chapter 6). Much higher
concentrations of C7H7+ than observed experimentally were
predicted (Olson and Calcóte, 1981a) by a simple model which
assumed a benzyl structure for the ion. To account for this
difference between experiment and theory, it was suggested
that the actual ion in the flame, presumably formed by
ion/molecule reactions of C3HX+ and CgHx + ions, is some
132

133
other C7H7+ Isomer less stable than benzyl (Olson and
Calcóte, 1981a).
There have been a significant number of both
theoretical and experimental studies on structural
characterization of CyH7+ ions. Theoretical studies
(Abbaund et al., 1976; Cone et al.,1977) on the
determination of heats of formation for C?H7+ ions indicated
that tropylium, with AHf=207.9 kcal/mol (Abbaund et al . ,
1976), and 195.6 kcal/mol (Cone et al.,1977) and benzyl,
with AH^=217.1 kcal/mol (Abbaund et al., 1976), and 220.4
kcal/mol (Cone et al.,1977) are the most stable structures
with an activation energy of 32.7 kcal/mol (Cone et al.,
1977) for benzyl > tropylium isomerization. Experimental
measurements of ionization potentials for tropylium and
benzyl radicals by monoenergetic electron impact gave
calculated values of AH^=209 and 211 kcal/mol (Thrush and
Zwolenik, 1963; Elder and Parr, 1969; Lossing, 1971)
respectively. Studies of metastable ions (Cooks et al.,
1973; Mclafferty and Winkler, 1974; Grotemeyer and
Grueitzmacher, 1981) collisional activation (Winkler and
McLafferty, 1973; Koeppel et al., 1978McLafferty and
Bockhoff, 1979), gas phase radiolysis (Yamamoto et al.,
1969; Takamuku et al., 1972; Takamuku et al., 1973; Sagi et
al . , 1974 ), photoionization/photodissociation ( Dunbar,
1975; Traeger and McLoughlin, 1977; McCreary and Preiser,
1978; Traeger and McLoughlin, 1978; McLoughlin et al., 1979;

134
Yaroslavtsev et al., 1984), PEPICO (Bombach et al., 1983a,
and b), and lon/molecule reactions (Shen et al., 1974;
Jackson, 1977; Jackson et al., 1977; Ausloos et al., 1980;
Sharma and Kebarle, 1981) of C7H7 + ions from different
precursors were used to characterize the different
structures. General experimental evidence including the
determination of appearance potentials and heats of
formation (Traeger and McLoughlin, 1977; Traeger and
McLoughlin, 1978; McLoughlin et al., 1979; Bombach et al.,
1983a,and b) supported that these ions exist in the gas
phase with at least two structures; tropylium, and benzyl.
Unreactive and reactive C7H7 + observed in ion/molecule
reactions have been attributed to the tropylium and benzyl
structures, respectively (Shen et al., 1974; Jackson, 1977;
Jackson et al., 1977; Ausloos et al., 1980; Sharma and
Kebarle, 1981). Furthermore, it was proposed that there is
an equilibrium between these two structures (McLafferty and
Bockhoff, 1979; Andrews and Keelan, 1981) similar to that
proposed between the parent ions toluene and
cycloheptatriene (Mclafferty and Bockhoff, 1979; Ausloos,
1982) (see Figure 7.1). Several groups studied the effect
of the energy above C?H7+ formation threshold on the
dominance of one structure over the other (McLafferty and
Winkler, 1974; Shen and Dunbar, 1974; Dunbar, 1975; Ausloos,
1982). Their results in general were supportive of the
equilibria between different structures mentioned above.

135
+
ch3
CHo
1
/>N - H-
(jQj 2.2 ev^
6
Toluene ion
AHf = 2|5.4 kcal/mol
Benzyl
AHj = 2|| kcal/mol
/
/
0.9 ev
0.5 ev
1.8 ev •
>
f
y
2.0,
1.0 ev
Cyclohepfatriene
ion
AHf = 235.1 kcal/mol
Tropy lium
AHj = 209 kcal/mol
Figure 7.1. Proposed (Mclafferty and Bockhoff, 1979;
Ausloos, 1982) Equllbriums between Different C7Hg + and C7H7 +
Structures .

136
Although McLafferty et al (Winkler and McLafferty, 1973;
McLafferty and Winkler, 1974) reported evidence for stable
tolyl and norbornadienyl structures in their earlier
collisional activation studies no definitive indication for
stable structures other than benzyl and tropylium was
provided by later studies using different precursors
(Jackson et al.; 1977; Koeppel et al., 1978; McLafferty and
Bockhoff, 1979; Ausloos, 1982). In the work reported here
C7H7 + ions have been produced from three different
precursors using different charge transfer gases. Reaction
pathways and the rate coefficients for the reaction of C7H7 +
ions with precursor neutrals, acetylene and diacetylene
near room temperature were investigated.
Experimental
C7H7+ ions were produced from toluene, cycloheptatriene
and norbornadiene by dissociative charge transfer .
Percentages of reactive/unreactlve isomers were determined
when the three neutrals above reacted with different charge
transfer agents (C4H2+, Xe+, Kr+ and Ar+) formed with an
electron beam pulse of 5ms duration at an ionizing energy of
11.5, 13, 15, and 20eV, respectively. To do this, all ions
except C7H7+ were ejected from the cell and enough reaction
time (typically 3s) at the pressures used (typically 10-6-
10 torr) was allowed so that the reactive structures could

137
be lost via ion/molecule reactions, thus leaving an
unreactive population.
However, in the case of cycloheptatriene, as reported
earlier (Jackson et al., 1977; Ausloos, 1982), because of
the growth of unreactive C?H7+ by time as a result of the
ion/molecule reactions (7.1a) and (7.1b), this approach
required some adjustments in the experimental sequence in
order to obtain accurate percentages of C7H7 + populations
c7h7+ + c7h8 --
> C7H8 + C7H7
(7.1a)
c7h8+ + c7h8 --
> C7H7+ (unreactive) + C7Hg
(7.1b)
Thus, at long reaction times C7Hg + was ejected continously
during reaction time in order to avoid reaction (7.1b).
All reactions were followed at a cell temperature of
363K. In order to avoid any possible effect of differences
in initial internal energy distribution of C7H7 + ions on
rate coefficient determination, charge transfer agents
which produce C7H7+ ions with similar internal energies
from different precursors were used for kinetic runs.
Also, since the total pressure in the reaction cell was
almost 1 x 10-5 torr and the charge transfer time was
100ms, substantial collisional relaxation of the ions took
place before kinetic data were collected.

138
Results
Effect of Precursor Neutrals: C7H7 + ions produced from
different precursors exhibited behavior indicative of both
reactive and unreactive populations toward the precursors.
Figures 7.2a, 7.2b, and 7.2c show normalized ion intensities
of C7H7+ and product ions vs time for reactions with
precursor neutrals; toluene, norbornadiene and
cycloheptatriene respectively. Following an exponential
decay indicative of first order kinetics, a substantial
fraction of unreactive ions remains at long reaction times.
Table 7.1 shows the charge transfer agents used to produce
C7H7+ ions from different precursors, the initial internal
energy imparted to the ions, and the percent of unreactive
ions remaining at long reaction times.
The major reaction of C7H7 + produced by charge transfer
from toluene with the toluene neutral gives CgHg+ (reaction
(7.2)); when norbornadiene is used as a precursor and
neutral reactant, reaction (7.3) is observed.
C7H7 + C7Hg
> C8H9 + C6H6
(7.2)
C7H7 + C7Hg
---> c9h9+ + c5h6
CO
[>
C7H7+ from norbornadiene also reacted to give small amounts
of higher molecular weight products. On the other hand,
C7H7+ produced from cycloheptatriene reacted with its
precursor neutral to give significant amounts of higher

NORMAUZCO INTENSITY
TOLUENE + C7H7+
CYCLOHEPTATRIENE + CyH 7+
Figure 7.2. Reactions of C7H7 + Ions with Their Precursor
Neutrals, (a) C7H7 + + toluene, (b) C7H7 + + norbornadiene and
(c) C 7 H 7 + + cycloheptatriene.
139

140
TABLE 7.1
Percentages of unreactive C7H7 + found from various precursors by
different ionization methods monitored by observing reaction with
the precursor neutral.3
1 1
Precursor lionizing charge|
1 1
Neutral (transfer agents |
1 1
Maximum Internal
Energy (eV)^
| Percent
| Unreactive
1
Toluene |
L
Xe +
1
!
1
1.4
45-50
1
1
L
Kr +
1
1
1
3.3
25-30
1
Ar +
1
1
1
1
5.0
25-30
1
Norbornadiene |
L
c4h
2 +
\
0.9
70-75
1
| Xe +
1
1
1
1
2.5
30-35
1
1 Kr +
1
1
I
1
4.4
25-30
1
Cycloheptatriene|
L
c4h
2 +
1
1 . 1
70-75
1
| Xe +
1
1
1
1
2.8
35-40
1
1
1
Kr +
1
1
1
4.6
35-40
aFor those ions produced by C4H2 + charge transfer, reactions with
both precursor neutral and diacetylene were monitored. ^Based on
C7H7+ appearance energies given Traeger and McLoughlin, (1978).

141
molecular weight product Ions along with smaller amounts of
CqH9+ and CgH9+ product Ions:
c7h7 +
+
00
s
C-
0
>
c8h9+ +
C6H6
(7.4)
C7H7 +
+
c7h8 --
>
C9H9+ +
c5h6
(7.5)
c7h7 +
+
c7h8
>
C10H9+
+ c4h6
(7.6)
c7h7 +
+
c 7 H 8
>
C11H9+
+ c3h6
(7.7)
c?h7 +
+
c7h8 --
>
C12H11+
+ c2H4
(7.8)
c7h7 +
+
c7h8
>
C13H11+
+ CH4
(7.9)
C7H7 +
+
c7h8 --
>
C14H11+
+ 2H2
(7.10)
c7h7 +
+
c7h8
>
C14H13+
+ h2
(7.11)
Deuteratlon Studies: In order to further investigate
the mechanisms of some of the reactions shown above,
deuterated toluene was used both to produce C7D7 + for
reactions with neutral precursors and as a neutral reactant
for reactions of C7H7 + produced from different precursors.
Reactions of C7D7 + with toluene and norbornadiene were
respectively:
C 7D7 + CyHg (toluene) > CgH^Dg + C 8 H D 8 (7.12)
C7D7+ + C7Hq (NBD) > C9D?H2+ + C5H6 (7.13)
When C7D7+ reacted with cycloheptatriene, the major product

142
observed was unreactive C7H7 + due to reactions (7.14) and
(7.15).
c7d7+ + c7h8 -
> c7h8 + c7d7
(7.14)
C7H8+ + C7H8 "
> C7H7+ (unreactive) + C7Hg
(7.15)
Other reactions observed were:
C 7 D 7 + C7H8
>
C9D6H3+ + C5H5D
(7.16)
c7d7 + c7h8
>
C10D6H3+ + C4H5D
(7.17)
c7d7 + c7h8
>
Ch¥3+ + C3H5D
(7.18)
c7d7 + c7h8
>
C12D7H4+ + C2H4
(7.19)
C7H7+ ions produced
toluene as shown by
from toluene reacted with
equation (7.20):
deuterated
c7h7 + c7d8
>
C8D7H2+ + C6H5D
(7.20)
Very low intensities of this product ion were also observed
in the mass spectra of C7H7 + ions produced from
eye 1oheptatri ene and norbornadiene. The rate coefficients
for the disappearance of C7H7+/C7D7+ by reactions with
precursor neutrals were calculated as described earlier and
the values are shown in Table 7.2.

143
TABLE 7.2
Rate coefficients for different C7H7+/C7Hg reaction systems.
1
|Precursor
1
k /10-10
cm3s_1
1
1
1
| \ Ion
1
1
1
\
Toluene-dg |
NBD
1
CHT
1
1Neutral\
1
1
1 \
.. . 1
.1.
1
1
| Toluene-dg
1
(3.5 + 1.0)a |
. . 1
(0.8 + 0.3)
1
1
.1.
(1
.7 +
1
0.5)|
1
1
| NBD
1
1
(3.2 + 1.0) |
1
(5.4 + 1.7)
1
1
. |_
1
1
1
1
| CHT
1
1
( 4.6 + 1 . 5 ) |
1
1
1
_ 1 _
(8
.2 +
1
2.6)|
1
Previously reported as 4.0 x
10“10 cm3/s
for
the
reaction
of benzyl ions with toluene (Dunbar, 1975).

144
C 7 H 7 *** Reactions with Acetylene: C7H7 + Ions produced by
Xe+ dissociative charge transfer of norbornadiene and
cycloheptatriene reacted slowly with acetylene to produce
very small amounts of CgHg+.
C7H7+ + CgHg > CgHg+ (7.21)
The following reaction was also observed with the ions
produced from cycloheptatriene:
C7H7+ + C2H2 > C7H9+ + c2 (7.22)
The rate coefficients for the disappearance of C7H7+ ions
produced from norbornadiene and cycloheptatriene were found
to be (1.0 + 1.0) * 10-11 and (3.6 + 1.3) x 10-*1 cm3/s
respectively. However, when toluene was used as a precursor
for C7H7+ production by Kr+ dissociative charge transfer, no
reaction with acetylene was observed.
C7H7+ Reactions with Diacetylene: C7H7+ ions from
different precursors were reacted with both diacetylene and
deuterated diacetylene in order to identify the reaction
products from those with the precursor neutral (for instance
the reactions with both diacetylene and cycloheptatriene
give C1;1Hg+). The following reactions of C?H7+ with
diacetylene were observed.

145
C7H7+ + C4H2 > C9H7+ + C2H2 (7.23a)
C7H7 + C4D2 > CgHgD2 + C2H2 (7.23b)
C7H7 + C4H2 > CijHg (7.24a)
C 7 H 7 + C4D2 > Cj jH7D2 (7.24b)
CgH7+ + C4H2 > C13Hg+ (7.25a)
c9h5d2+ + C4D2 > c13h5d4+ (7.25b)
In the toluene case, the following reaction was also
observed:
C8Hg+ + C4H2 > C12Hg+ + H2 (7.26a)
C8H9+ + C4D2 > C12H7D2+ + H2 (7.26b)
Ion intensity vs time curves of C7H7+ (produced by Kr+
charge transfer from toluene) and product ions for the
reaction with diacetylene are shown in Figure 7.3. The rate
coefficients for the disappearance of C7H7+ by the sum of
reactions (7.23) and (7.24) for different precursors are
given in Table 7.3.
When C7H7+ ions were produced in a 100ms reaction time
by Xe+ dissociative charge transfer from norbornadiene and
cycloheptatriene in the presence of C4H2, production of
unreactive C7H7+ was observed by the following reactions.
Xe+ + C4H2
>
C4H2
+
+ Xe
(7.27)

NORMALIZED INTENSITY
146
+
“ T T *T* J I » I I 1 1 1 1 |
0 0.4 0.8 1.2 1.6 2 2.4 2.8
TIME (s)
Figure 7.3. Reactions of C?H7+ Ions Formed from Toluene by
Kr+ Chemical Ionization with Diacetylene.

147
TABLE 7.3
Reaction rate coefficients for C?H7+ + C4H2 reaction.
| Precursor
1 l_
k/10"10
cm^s 1
I 1
|Toluene |
1 1
( 1.50
+ 0.50
)
1 1
|Norbornadiene
1 1
( 0.25
+ 0.19
)
1 1
|Cycloheptatriene|
1 1
( 0.75
+ 0.25
)

148
C4H2+ + C^Hg > C7H7+(unreactive) + C4H2 + H (7.28)
Thus In order to obtain accurate Information on
reaction kinetics of the C?H7+ + C4H2 reaction, the C4H2+
ion was continuously ejected during C7H7 + ion formation by
dissociative charge transfer using Xe+.
Also in this study, the relative abundances of the
ions produced from toluene as a function of electron impact
energy were determined for the purpose of comparison with
results obtained for norbornadiene and cycloheptatriene (see
Chapter 6). Relative abundances of C5H5+ and C3H3+ as a
function of energy for toluene are shown in Figure 7.4.
Results of the earlier study given in Chapter 6 for
norbornadiene and cycloheptatriene are also included in the
figure for comparison.
Discussion
Since numerous earlier investigations ^Dunbar, 1975;
Jackson et al., 1977; Traeger and McLoughlin, 1978;
McLafferty and Bockhoff, 1979; Sharma and Kebarle, 1981)
have demonstrated that C7H7+ ions have at least two stable
structures, one reactive and the other unreactive, the
results of this study are interpreted in terms of the
possibility of other stable structure(s).

149
Figure 7.4. Relative Intensities of Fragment Ions from
Different C?h7 + Precursors as a Function of Electron Energy.
Toluene, norbornadiene and cycloheptatri ene are abbreviated
as ÍTOL), (NBD) and (CHT) respectively.

150
The nature of the reaction products observed for the
reactions of C7H7 + ions with their precursor neutrals,
toluene, norbornadlene and eye 1oheptatri ene, were
significantly different, as shown in Figures 7.1a, 7.1b and
7.1c respectively. In order to determine whether these
differences were due to the neutral or ion structures
deuterated toluene was used to monitor the reaction
mechanisms with different neutral precursors. As seen in
equations (7.12 )-(7.19 ) , C7D7 + ions reacted with the
precursor neutrals, producing deuterated analogues of the
same product ions observed for each non-deuterated
ion/precursor reaction system. This result showed that the
differences in reaction products are the result of the
different structures of neutral precursors, and not
necessarily of different ion structures. Then deuterated
toluene was used as a reactant neutral for C7H7 + ions
produced from different precursors. As seen from equation
(7.20), C7H7+ ions produced from all three precursors
reacted with C7Dg to produce C8D7H2+. although very low ion
intensities were produced with eye 1oheptatri ene and
norbornadiene precursorsors. The reaction mechanism which
gives this product ion is also operative in reaction (7.12)
and is believed (Shen and Dunbar, 1974; Dunbar, 1975;
Jackson et al., 1977; McCreary and Freiser, 1978) to be
indicative of the benzyl structure for C7H7+ ions (see
Figure 7.5). This mechanism has also been studied earlier

151
CH2
(m/z s 105)
Figure 7.5. Proposed (Shen and Dunbar, 1974; Dunbar, 1975;
Jackson et al., 1977; McCreary and Frelser, 1978) Mechanism
of CgHg+ Formation from the Reaction of Benzyl Ion with
Toluene.

152
by similar isotopic labeling experiments (Jackson et al.,
1977; Ausloos et al.p 1980). The only important difference
in the behavior of reactive C7H7 + ions produced from
different precursors was their reaction rates with precursor
neutrals. C7h7+/C7D7+ ions produced from toluene/deuterated
toluene reacted at similar rates with toluene, norbornadiene
and cycloheptatriene whereas C7H7 + ions produced either from
norbornadiene and cycloheptatriene reacted at much slower
rates with toluene than with their own precursor neutrals
(see Table 7.2).
Reactions of C7H7 + and product ions with diacetylene
are represented by equations (7.23 )-(7.25) independent of
the precursor used. An interesting mechanism is observed
for C2 and C4 addition reactions shown by equations (7.23b)
and (7.26b) which is indicative of an ion/molecule complex
from which C2H2 and H2, respectively, rather than C2D2 and
D2 are the apparent neutral products. Since complete
scrambling of product ions is not observed, preferential
retention of C2D2 and D2 is probably due to a specific
structure of the intermediate complex which does not
rearrange fast enough to give complete scrambling before
falling apart to give the products. Reaction rates with
diacetylene followed a different trend than those with
precursor neutrals for C7H7 + ions from different
precursors. In this case, C7H7+ ions from toluene reacted

153
faster than those from norbornadlene and cyc1oheptatr1 ene
(see Table 7.3).
Different behavior was observed when C2H2 was used as a
reactant neutral. C7H7 + from norbornadiene and
cycloheptatriene reacted slowly with acetylene as shown by
equations (7.21) and (7.22). On the other hand, no reaction
products were observed with C7H7 + from toluene.
Table 7.1 shows the percent of unreactive C7H7 + as a
function of the internal energy of the ion formed from
different precursors. At the lowest internal energies
above the C7H7+ formation threshold, C7H7+ from toluene had
a much smaller percentage of unreactive isomer than C7H7+
from norbornadiene and cycloheptatriene. Formation of
unreactive C7H7+ from all three precursors decreased with
increasing internal energy and stayed constant at high
enough energy. This behavior is different from that
observed previously for toluene and norbornadiene (Dunbar,
1975; Ausloos, 1982) in which the unreactive percent first
decreased and then increased with internal energy. The
previous results were interpreted in terms of the interplay
between the two equilibria involving different C7Hg+ and
C7H7+ structures (Sagi et al., 1974; McLafferty and
Bockhoff, 1979; Andrews and Keelan, 1981; Ausloos, 1982).
The different behavior observed in an earlier ICR study
(Jackson et al., 1977), which is similar to that observed in
this work, was suggested (McLafferty and Bockhoff, 1974;

154
Ausloos, 1980) to be the result of the displacement of the
equilibrium between two C7H7 + structures by the removal of
the reactive C7H7 + ions through chemical reaction.
In Chapter 6, the relative abundances of ions
produced from norbornadiene and cycloheptatriene as a
function of ionizing electron energy were reported.
Similarities of C7H7+, C5Hg + and CgHg + appareance curves
were interpreted to imply that C7H7+ formed from these two
compounds behaves similarly, i.e., follows the same
fragmentation pathways in the same energy range.
Differences in the appareance curve of C5Hg + for
norbornadiene and cycloheptatriene were interpreted as
suggesting that C7Hg + formed from these compounds by
electron impact may have different structures. Extensive
fragmentation of C7Hg + to give C5Hg+ was also reported
earlier for norbornadiene (Ausloos, 1982). In this study,
the relative abundances of the ions produced from toluene as
a function of energy were determined for the purpose of
comparison with earlier results obtained for norbornadiene
and cycloheptatriene. In contrast to the observed
similarity mentioned above between norbornadiene and
cycloheptatriene fragment ion appareance curves, those of
toluene were significantly different both in terms of
energetics and of general shape. For example, the onsets of
formation for both CgH5 + and CgH3+ were different than those
values observed for the other two precursors. Furthermore,

155
the relative Intensities for C5H5+ and C3H3 + increased much
more slowly with energy relative to those from norbornadiene
and cycloheptatriene. The maximum relative intensities for
C5H5+ and C3H3 + ions were respectively 0.017 and 0.005 for
toluene and 0.10 and 0.035 for norbornadiene and
cycloheptatriene (see Figure 7.4). This different behavior
in the fragmentation of C7H7 + produced from toluene suggests
the involvement of a different structure (benzyl+) for C7H7 +
in the case of toluene.
A possible potential energy surface for C7H7+/C7H3+
system is shown in Figure 7.6. Based on the differences in
behavior observed in this study for C7H7+ ions produced from
three precursors, the possibility of stable structure(s)
other than benzyl and tropylium must be considered. The
unreactive structure which was observed in all three cases
has been shown to be cyclic tropylium by a number of
previous experimental (see for example, Jackson et al.,
1977) and theoretical (Abbaund and Hehre, 1976; Cone et
al . , 1977 ) studies. Similarly, the reactive isomer produced
from toluene was identified as the benzyl structure numerous
times previously (see for example, Ausloos et al., 1980;
Bombach et al., 1983). However, the results of this study
have shown that it behaves somewhat differently from the
reactive C7H7+ isomers produced from norbornadiene and
cycloheptatriene. Although no definitive assignment for
reactive C7H7+ ion structure(s) produced from norbornadiene

I50.6b
Figure 7.6. Potential Energy Surface for C7H7+/C7Hg+
System. Numbers refer to heats of formation values in units
of kcai/mol. aMINDO, ^AMl and cexperimental.
156

157
and cycloheptatriene can be made at this point, the most
probable structures will be discussed considering the
energetics of C7H7 + ions.
Cycloheptatriene. AMI calculations for the C7H8+/C7H7+
surface15 suggest the structure produced by hydrogen loss
from the bieye 1o[3.2.0]heptadiene radical cation (BCH+), is
a possible stable C7H7 + isomer, accessible at about 2.8 eV
above the appearance potential of tropylium from
cycloheptatriene (see Figure 7.6). This structure is in a
sufficiently deep potential well that it might reasonably be
expected to live for an extended time. It was also
suggested14 that this structure is most probably formed from
cycloheptatriene by isomerization on the radical cation
surface followed by hydrogen loss from (BCH+).
Isomerization of (BCH-H) + , (AHf = 274.4kcal/mo 1)14 to
tropylium is considered unlikely due to the high energy
barrier between two structures as seen in Figure 7.6.
Although the barrier to form the toluene ion is lower than
that for (BCH+), it was suggested14 that the simplicity of
the rearrangement to the latter, compared to the convoluted
surface leading to benzyl or toluene radical ion may make
formation of BCH+, a faster rearrangement at high enough
energy. Consistent with these calculations, our
experimental results show that the percent of unreactive
1
J. E. Bartmess, private communication.

158
C7H7+ from cycloheptatrlene decreases very rapidly with
Increasing internal energy. This can be interpreted as a
result of increased isomerization of the cycloheptatrlene
cation to (BCH+). At high energy, when the equilibrium
between these two parent ions is established, the percent of
unreactive Isomer stays constant due to the absence of
isomerization between two C7H7+ structures with an energy
barrier of 14.1 kcal/mol16. Other experimental evidence for
the involvement of different structures for C7Hg + ions
formed from toluene and cycloheptatrlene comes from the
strikingly different photodissociation curves of these ions
(Dunbar and Fu, 1973).
Norbornadiene. In spite of the general similarity of
the behavior of C7H7+ ions from cycloheptatrlene and
norbornadiene, differences in reactivity (see Tables 7.2 and
7.3) suggest the formation of a C7H?+ structure different
from that discussed above for cycloheptatrlene. A simple
bond breakage in norbornadiene can directly form an
ipso-protonated benzyl radical, CgH5(H+)CH2 ion, in which a
1.2-hydrogen shift leads to the intermediate, 5-methylene-
1.3-cyclohexadiene ion, (MCH+) with a theoretical AHf * 219
kcal/mol (Dewar and Landman, 1977) (see Figure 7.6). This
ion was proposed to account for the ring expansion of the
toluene ion in the toluene+ > eye 1oheptatri ene +
1 fi
J. E. Bartmess, private communication.

159
isomerization process (Dewar and Landman, 1977). The
formation of (MCH+) from other precursor cations at least
with a transitory existence has been indicated by previous
experimental evidence (Leusen et al., 1973). After the
availability (Gajewski and Gortva, 1982) of 5-methylene-l,3-
cyclohexadiene, experimental determination of its ionization
potential indicated a heat of formation value 18 kcal/mol
higher than that of the toluene ion (Bartmess, 1982).
Once this intermediate ion is formed, it can rearrange
to another structure or decompose directly to the C7H7+ ion.
In fact, it was suggested that direct decomposition of this
ion is in competition with rearrangement to other
structures, cycloheptatriene cation being the most probable
rearrangement product (Bursey et al., 1973). The
competition between these two processes is believed to
depend on the internal energy with rearrangement being
favored at lower energies (Dunbar and Klein, 1977). Thus at
low energies, fragmentation to C7H?+ after rearrangement to
cycloheptatriene but not to toluene ion is expected due to
the lower activation barrier for fragmentation of
cycloheptatriene ion relative to toluene parent ion (Dunbar,
1975). This is consistent with our results which indicate a
high percent of unreactive C?H7+ (tropylium+) formed from
norbornadiene at low energy (see Table 7.1). Furthermore, as
a result of the photodissociation study of C7Hg + structures
(Dunbar and Fu, 1973), possibility for conversion of about

160
half the norbornadiene cations to the cycloheptatriene
structure was not inconsistent with the data. On the other
hand, it has been reported that there is no rearrangement of
this ion to toluene ion on a time scale of 10~^ s (Bursey et
al. , 1971).
Photodissociation spectra of n-butylbenzene and 2-
phenylethanol ions which are believed to form (MCH+) were
studied in order to identify any possible rearrangement
products (Dunbar and Klein, 1977). The results were
consistent with the retention of the (MCH+) structure, with
less than 20 percent rearrangement to cycloheptatriene ion.
Although there was not any evidence for ready
interconversion among C7Hg + structures for nondecomposing
methylenecyclohexadiene ions, it was suggested the that more
energetic, decomposing ions may interconvert to other
structures. In this study, the decrease in the percent of
tropylium structure with the increase in energy is
interpreted as a result of decomposition of (MCH+) becoming
competitive with rearrangement to the cycloheptatriene ion.
Thus, the C7H7 + structure formed by hydrogen loss from
(MCH+) can be suggested as the reactive isomer observed for
norbornadiene. The overall results of this study in terms
of the proposed structures for C7H7 + ions formed from
different precursors are given in Table 7.4.

161
TABLE 7.4
Proposed C7H7 + structures from different precursors.
| Unreactive
| Reactive|
AHf
| Precursor
| structure
1
|structure|
1 1
(kcal/mo 1) |
¡Toluene
1
| Tropylium+
1
1 1
| Benzyl+ |
1 1
211
| NBD
1
| Tropylium+
1
1 1
| ( BCH-H)+a|
1 1
271
| CHT
!
| Tropyllum+
!
|(MCH-H)+b|
.1 1
7(236)
aStructure produced by hydrogen loss from
bicyclo[3.2.0]heptadiene.
^Structure produced by hydrogen loss from 5-methylene-l,3-
cyclohexadiene Ion.

162
An ICR study (Bartmess, 1982) Involving the formation
of (MCH)+ from its precursor neutral at 30eV electron energy
indicated ion/molecule chemistry different from that of
toluene. C7H7 + produced from (MCH+) was reported to have a
different rate coefficient and reaction efficiency for the
formation of CqH9+. It is interesting to note that the rate
coefficient reported (0.6 x 10-10 cm3/s) (Bartmess, 1982)
for this reaction agrees very closely with the value, (0.8 +
0.3) x 10-10 cm3/s found in this work for the reaction of
C7H7+ formed from norbornadiene with toluene (see Table
7.2). Although a definitive structure can not be assigned
to C^H7 + formed from (MCH+) yet, one possible structure is
the norcaradieny1 ion, which was calculated to be stable
with AHf = 235.9 kcal/mol (Cone et al., 1977) (see Figure
7.6).
Supporting experimental evidence for the existence of
stable C7H7+ structures other than benzyl and tropylium
comes from a UV absorption study of C7H7+ ions in solid
argon (Andrews and Keelan, 1981). In relation to rate
coefficient data for reactions with precursor neutrals,
acetylene, and diacetylene the same trend was observed for
norbornadiene and cycloheptatriene. In all three cases, the
reactive structure formed from norbornadiene reacted more
slowly than that formed from cycloheptatriene. This is
consistent with the general observation that less reactive
structures of small hydrocarbon ions have lower heats of

163
formation since the C7H7 + structure formed from (MCH+) has a
lower heat of formation than that formed from (BCH+).
Finally, in relation to the Ionic soot formation
mechanism, the existence of a different C7H7 + ion less
stable than benzyl in flames would account for the
disagreement between experiment and theory in relation to
C7H7+ concentration in flames (Olson and Calcóte, 1981a).

CHAPTER 8
CONCLUSIONS AND RECOMMENDATIONS
The experimental work reported here contributes
significantly to an understanding of the reactivity,
energetics, and structures of small hydrocarbon ions.
However, it does not prove or disprove an ionic mechanism of
soot formation. It does lead to several clarifications of
the ionic mechanism, which will be discussed below.
The extensive ion/molecule condensation reactions at
rates approaching the Langevin limit observed when C3H3+,
CgHg+ and C7H7 + react with C4H2 suggest that this aspect of
the proposed (Calcóte, 1981; Olson and Calcóte, 1981a) ionic
path to soot formation is quite credible. The general
reaction
CxHy+ + c4H2 —> Cx+2Hy+ + C2H2 (8.1)
appeares to occur in a facile manner and could be quite
important in soot nucleation. Some of the product ions
formed (e.g. CgH3 + and C7Hg+) have been seen to be abundant
in both nonsooting and sooting flames (Olson and Calcóte,
1981b). Furthermore, product ions with increased C:H ratios
having as many as 13 carbon atoms have been observed in the
164

165
reaction of C7H7 + with diacetylene. On the other hand, the
observation of C3H3 + isomerization and not condensation with
acetylene as well as low bimolecular reactivity of acetylene
with CgHg+ and C7H7 + suggests that the proposed sequential
acetylene addition reactions to CgH3+ in the ionic soot
formation mechanism be reconsidered. Other channels such as
direct reaction of neutral aromatics with C3H3+ (Michaud et
al., 1981; Baykut et al., 1986) may be as important in the
formation of small polycyclic ions.
These experiments were carried out at significantly
lower temperatures (363K) and pressures (p < 5 X 10-5 torr)
than those found in most combustion environments. It is
thus quite possible that third-body collisions in
atmospheric pressure flames can stabilize a fraction of the
reaction complexes leading to significant termolecular
reactivity of the ions studied with acetylene. In fact,
such collisional stabilization of the association complexes
for the reactions of C3H3 + and C4H4 + with C2H2 has been
shown to occur in higher pressure SIFT studies (Smith and
Adams, 1987; Knight et al., 1987).
Continuation of this work in several directions could
have a major impact on assessing the importance of an ionic
mechanism of soot formation. First, experiments should be
carried out at higher pressures, using a high pressure
source for the FTICR mass spectrometer, to assess the
importance of third-body stabilization of ion/molecule

166
collision complexes. Actual sampling of ions from flames
into the FTICR mass spectrometer, in order to probe their
structures and reactivity, would extend the isolated studies
done here to an actual combustion environment.
A crucial argument in favor of an ion/molecule soot
nucleation route is the ease with which cyclic ions, which
could lead to polycyclic aromatic hydrocarbons, are formed.
Yet the work reported here did not identify definitively
when the first cyclic ions were formed. Predicted spectra
from theoretical calculations on C5H5+, C5H3 + and C7HX+ ions
should be combined with laser spectroscopic studies on these
ions to determine which, if any, have cyclic structures.
Also, theoretical studies which probe the geometries of the
ion/molecule collision complexes, such as those reported in
Chapter 5 for C3H3 + + acetylene, should be extended to other
important reactions, e.g. with diacetylene, and the nature
of the proposed chemi-ionization reaction which forms the
C3H3+ ion (see Chapter 1) should be investigated.

APPENDIX I
PROGRAM TO CALCULATE ABSOLUTE RATE CONSTANTS AND THEIR 95%
CONFIDENCE LIMITS FROM RAW OR NORMALIZED INTEGRATED PEAK
AREAS OF THE REACTING ION AS A FUNCTION OF TIME IN FOURIER
TRANSFORM ION CYCLOTRON RESONANCE MASS SPECTROSCOPY.
WRITTEN JULY AND AUGUST 1986 BY FEZA OZTURK AND BRYAN HEARN
Adapted for use with the IBM pc on 9-17-87 by CLIFF WATSON.
UNDER THE DIRECTION OF DR. JOHN EYLER
DEPARTMENT OF CHEMISTRY
UNIVERSITY OF FLORIDA
GAINESVILLE, FLORIDA 32611
TYPICAL ORDER OF EXECUTION:
A. Calculation of the system factor using the literature
value of a well-known rate constant for a reference reaction
(this Involves calculating the observed rate constant for
the reference reaction, *3, the actual pressure, #1, then
the system factor, #4, which uses the literature value for
the absolute rate constant along with your experimental
observed rate constant and actual pressure just calculated
using *3 and *1). The system factor will be used later in
the absolute rate constant calculation, so it should be
noted. If this calculation is not desired, a value of 1 may
be input for the system factor.
B. Running the program a second time, calculate the
observed rate constant for the reaction of the ion with its
precursor neutral, #3.
Step 3 should be followed by step 9 here if the no
baseline correction option is chosen in the calculation of
k.
C. Calculation of the observed rate constant for the
reaction of the ion with reactant neutral (gives the sum and
individual rate constants with precursor and reactant
neutrals, # 5). This should be followed by step 10 if the
no baseline correction option is chosen in the calculation
of k2 .
D. Determination of the actual pressure for the reactant
neutral by entering the ionization gauge and capacitance
manometer readings manually (Baratron factor is determined
from the slope by linear least squares, # 1).
E. Calculation of the absolute rate constant using the
actual pressure and system factor (# 6).
167

168
For steps B and C, raw or normalized Integrated peak areas
of the reacting ion as a function of time should be entered
manually.
System factor is a correction factor for pressure
calibration due to the fact that ionization gauge and
capacitance manometer are located at different points of the
instrument.
Options 2, 8, 11 and 12 can be used to input the
appropriate values once they are calculated. This allows
one to calculate absolute rate constants without going
through the entire process by entering the precalculated
values.
Baseline correction is needed to correct for the
unreactive population of the reacting ion when both reactive
and unreactive isomers exist (#'s 9 and 10 are used when
there is no unreactive isomer ).
DIMENSION
RDATA(50,50).TIMES(100).TIC(50),TMPDAT(50),TMP2DT(50)
DIMENSION
YP(100) , XP(100) .TEMP(50) ,ETEMP(50) ,CMA(100) ,TXGRAF(52) ,
&TYGRAF(52)
REAL K.IG.LITK.K2
INTEGER FLAG
CHARACTER*1 YESNO
10 WRITE(*,*)' '
WRITE(*
WRITE(*
WRITE(*
WRITE(*
CONSTANT '
WRITE(*
WRITE(*
CORR(K2) '
WRITE(*
953» CL '
*) '
*) '
•) '
*) '
*) '
*) '
1
3
5
7
9
PRESSURE CALC (MANUAL) 2
K AND 95% CONFIDENCE 4
K2 AND 95% CONFIDENCE 6
ENTER BF '
SYSTEM FACTOR
ABSOLUTE RATE
STOP 8 INPUT SYSTEM FACTOR
NO BASELINE C0RR(F0R K) 10 NO BASELINE
*)' 11 ENTER K AND 95% CL
12 ENTER K2 AND
WRITE(*,*)' '
WRITE(*,*)' INPUT CHOICE
READ(*,*)I
GOTO(100,200.300,400,500,600,700,800.900,1000,1300,
& 1400 ) I
GOTO 10
100 WRITE(*,*)1 NUMBER OF POINTS TO ENTER MANUALLY FOR
PRESSURE '
READ(*,*)NPRESS
DO 123 1=1,NPRESS
WRITE(*,120)1
120 FORMAT(' INPUT IG READING # ',15)
READ(*,*)XP(I)

169
WRITE(*,129)I
129 FORMAT(' INPUT BARATRON READING * '.15)
123 READ(*,*)YP(I)
CALL GRAF2D(XP,YP,NPRESS)
WRITE(*,*)' INPUT THE NUMBER OF POINTS FOR LLSQ '
READ(*,*)NPRESS
FLAG=3
CALL LLSQ(XP,YP,EYP,NPRESS,BF.EBF,FLAG,I NT)
DO 196 1=1,NPRESS
TYGRAF(I)=YP(I)
196 TXGRAF(I)=XP(I )
TXGRAF(NPRESS+1)=XP(NPRESS)
TYGRAF(NPRESS+1)=BF*XP(NPRESS)
TXGRAF(NPRESS+ 2)=XP(1 )
TYGRAF(NPRESS+2)=BF*XP(1)
CALL GRAF2D(TXGRAF,TYGRAF,(NPRESS+2))
WRITE(*,*)1 THE BARATRON FACTOR IS'
WRITE(*,*)BF
WRITE(*,*)' THE 95% CONFIDENCE LIMIT FOR BARATRON
FACTOR IS '
WRITE(*,*)EBF
150 WRITE(*,*)' INPUT THE IONIZATION GAUGE READING '
READ(*,*)IG
P=IG * BF
WRITE(*,*)' THE PRESSURE IS '
WRITE(*,*)P
WRITE(*,*)' DEFAULT 95% CON.LIMIT FOR IG IS 0.1*GAUGE:
CHANGE=Y '
READ(*,88)YESNO
IF(YESNO.EQ.'Y')THEN
WRITE(*,*)1 INPUT THE % MULTIPLIER DESIRED 95% CON.
LIMIT FOR IG '
READ(*,*)EI
EI = EI *IG
GOTO 152
END IF
El = 0.1 *IG
C DEFAULT 95% CONF.LIMIT FOR ION. GAUGE READING IS EST'ED AS
0.1 * ION.GAUGE
152 EP=SQRT(BF*BF*EI*EI+IG*IG*EBF*EBF)
WRITE(*,*)' THE 95% CONFIDENCE LIMIT FOR PRESSURE IS'
WRITE(*,*)EP
GOTO 10
200 WRITE(*,*)' ENTER THE BARATRON FACTOR '
READ(*,*)BF
WRITE(*,*)' ENTER THE 95% CONF. LIMIT OF BF '
READ(*,*)EBF
GOTO 150
300 WRITE(*,*)' NUMBER OF POINTS TO ENTER MANUALLY ='
READ(*,*)NT IM
DO 366 1=1,NTIM
WRITE(*,364)I

170
364 FORMAT(' ENTER TIME #',I5)
READ(*,*)TIMES(I)
WRITE(*,*)' ENTER THE CIN OR CIN NORMALIZED TO TOTAL
ION CIN '
READ(*,*)TEMP(I)
366 CONTINUE
345 WRITE(*,*)' DO YOU WISH BASELINE CORRECTION? YES=1 '
READ(*,*)NANS
IF(NANS.NE.1) GOTO 10
CALL CNIC(NTIM,TEMP.ETEMP.XMAX,EXMAX)
390 YLSTPT=TEMP(1)
KOUNT =1
DO 391 1=2,(NTIM-1)
IF(TEMP(I).GT.YLSTPT)GOTO 392
YLSTPT=TEMP(I)
391 KOUNT=KOUNT + 1
392 CALL GRAF2D(TIMES,TEMP,KOUNT)
WRITE( * , * )' INPUT THE NUMBER OF POINTS TO USE '
READ(*,*)NPOINT
395 CALL LLSQ(TIMES,TEMP,ETEMP,NPOINT,K,ERRK,FLAG,YINT)
DO 396 1=1,NPOINT
TYGRAF(I)=TEMP(I)
396 TXGRAF(I)=TIMES(I)
TXGRAF(NPOINT+1)=TIMES(NPOINT)
TYGRAF(NPOINT+1)= K*TIMES(NPOINT)+YINT
TXGRAF(NPOINT+2)=TIMES(1)
TYGRAF(NPOINT+2)=K*TIMES(1)+YINT
CALL GRAF2D(TXGRAF,TYGRAF,(NPOINT+2))
K = -K
WRITE(*,*)' K AND 95% CONFIDENCE LIMIT IN K='
WRITE(*,*)K,ERRK
GOTO 10
400 WRITE(*,*)' HAVE YOU CALCULATED THE PRESSURE? YES=1'
READ(*,*)NANS
IF (NANS.NE.l)GOTO 10
WRITE(*,*)' INPUT THE LITERATURE VALUE K '
READ(*,*)LITK
WRITE(*,*)1 INPUT THE LITERATURE ERROR VALUE '
READ(*,*)EL IT
WRITE(*,*)1 INPUT THE TEMPERATURE '
READ(* , * )T
WRITE(* , * ) 1 THE DEFAULT ERROR IN TEMP IS 2 DEGREES.
CHANGE=Y '
READ(*,88)YESNO
IF(YESNO.EQ.'Y')THEN
WRITE(*,*)1 INPUT THE DESIRED ERROR IN TEMP. '
READ(*.*)ET
GOTO 415
END I F
ET= 2
C DEFAULT ERROR IN TEMPERATURE IS ESTIMATED AS 2 DEGREES
415 K=1.036E-19*T*K/P

171
EK=SQRT(ET*ET/(T*T)+EK*EK/(K*K)+EP*EP/(P*P))*K
SF=K/LITK
ESF=SQRT(EK*EK/(K*K)+ELIT*ELIT/(LITK*LITK))*SF
WRITE(*,*)1 THE SYSTEM FACTOR AND ITS 95% CONFID.
LIMIT IS '
WRITE(*,*)SF,ESF
GOTO 10
500 WRITE(*,*)1 NUMBER OF POINTS TO ENTER MANUALLY ='
READ(*,*)NTIM
DO 566 1=1,NTIM
WRITE(*,564)I
564 FORMAT(1 ENTER TIME #',I5)
READ(*,*)TIMES(I)
WRITE(*,*)' ENTER THE CIN OR CIN NORMALIZED TO TOTAL
CIN '
READ(*,*)TEMP(I)
566 CONTINUE
545 WRITE(*,*)' DO YOU WANT BASELINE CORRECTION? YES=1 '
READ(*,*)NANS
IF(NANS.NE.1)GOTO 10
CALL CNIC(NTIM,TEMP.ETEMP,XMAX.EXMAX)
590 YLSTPT=TEMP(1)
KOUNT =1
DO 591 1=2,(NTIM-1)
IF(TEMP(I).GT.YLSTPT)GOTO 592
YLSTPT=TEMP(I)
591 KOUNT=KOUNT + 1
592 CALL GRAF2D(TIMES,TEMP,KOUNT)
WRITE(*,*)' INPUT THE NUMBER OF POINTS TO USE '
READ(*,*)NPOINT
CALL LLSQ(TIMES,TEMP,ETEMP,NPOINT,K2,ERRK2.FLAG,YI NT)
DO 596 1=1,NPOINT
TYGRAF(I)=TEMP(I)
596 TXGRAF(I)=TIMES(I)
TXGRAF(NP0INT+1)=TIMES(NPOI NT)
TYGRAF(NPOINT+1)=K2*TIMES(NPOINT)+ YINT
TXGRAF(NPOINT+2)=TIMES(1)
TYGRAF(NP0INT+2)=K2*TIMES(1)+YINT
CALL GRAF2D(TXGRAF,TYGRAF,(NPOINT+2))
K2=-K2
WRITE(*,*)1 THE OBSERVED SLOPES (K1 AND K2) ARE '
WRITE(*,*)K,K2
WRITE(*,*)1 THE ERRORS IN K1 AND K2 ARE '
WRITE(*,*)ERRK,ERRK2
598 K=K2-K
EK=SQRT(ERRK*ERRK+ERRK2*ERRK2)
WRITE(*,*)' THE NET RATE CONSTANT IS'
WRITE ( * , * )K
WRITE(*,*)' THE 95% CON. LIMIT IN THE OBSERVED RATE
CONSTANT IS'
WRITE(*,* ) EK
GOTO 10

172
600 WRITE(*,*)'CALCULATED THE SYSTEM FACTOR AND PRESSURE?
Y= 1 '
READ(*,*)NANS
IF(NANS.NE.1)GOTO 10
WRITE(*,*)' INPUT THE TEMPERATURE'
READ(*,*)T
TRUEK=1.036E-19*K*T/(SF*P)
WRITE(*,*)' THE TRUE K IS '
WRITE(*,*)TRUEK
WRITE(*,*)' THE DEFAULT ERROR IN TEMP IS 2 DEGREES.
CHANGE=Y '
READ(*,88)YESN0
IF(YESNO.EQ.'Y')THEN
WR I TE(*,*) ' INPUT THE DESIRED ERROR IN TEMP. '
READ(*,*)ET
GOTO 615
END IF
ET= 2
C DEFAULT ERROR IN TEMPERATURE IS ESTIMATED AS 2 DEGREES
615
ETRUEK=SQRT(EK*EK/(K*K)+ET*ET/(T*T)+ESF*ESF/(SF*SF)+EP*EP/
&(P*P))*TRUEK
WRITE(*,*)' THE 95% CONFIDENCE LIMIT FOR TRUE K IS ’
WRITE(*,*)ETRUEK
GOTO 10
800 WRITE( * , * )' INPUT SYSTEM FACTOR'
READ(*,*)SF
WRITE(*,*)' INPUT THE ERROR IN THE SYSTEM FACTOR ’
READ(*,*)ESF
GOTO 10
900 WRITE(*,*)'* * * *N0 BASELINE CORRECTION****'
WRITE(*,*)'DEFAULT ERROR MULTIPLIER IN CIN IS 0.1
CHANGE=Y'
READ(*,88)YESN0
IF(YESNO.EQ.'Y')THEN
WRITE(*,*)' INPUT THE DESIRED MULTIPLIER OF ERROR
IN CIN '
READ(*,*)ECIN
GOTO 915
END I F
ECIN=0.1
915 DO 910 1=1,NTIM
ETEMP(I)=ECIN*TEMP(I)
ETEMP(I)=ETEMP(I)/TEMP(I)
910 CONTINUE
DO 920 1=1,NTIM
920 TEMP(I)=LOG(TEMP(I))
990 YLSTPT=TEMP(1)
KOUNT =1
DO 991 1=2,NTIM
IF(TEMP(I).GT.YLSTPT)GOTO 992
YLSTPT=TEMP(I)

173
991 KOUNT=KOUNT + 1
992 CALL GRAF2D(TIMES,TEMP,KOUNT)
WRITE(*,*)' INPUT THE NUMBER OF POINTS TO USE IN LLSQ
CALC. ’
READ(*,*)NPOINT
FLAG=2
CALL LLSQ(TIMES,TEMP,ETEMP,NPOINT,K,ERRK,FLAG,YINT)
DO 996 1=1,NPOINT
TYGRAF(I)=TEMP(I)
996 TXGRAF(I)=TIMES(I)
TXGRAF(NPOINT+l)-TIMES(NPOINT)
TYGRAF(NPOINT+l)=K*TIMES(NPOINT)+YINT
TXGRAF(NPOINT + 2)=TIMES(1 )
TYGRAF(NPOINT+2)=K*TIMES(1)+YINT
CALL GRAF2D(TXGRAF,TYGRAF, (NPOINT + 2) )
K = -K
WRITE(*,*)' OBSERVED RATE CONSTANT AND 95* CONFIDENCE
LIMIT IS '
WRITE(*,*)K,ERRK
GOTO 10
1000 WRITE(*,*)'****N0 BASELINE CORRECTION****'
WRITE(*,*)'DEFAULT ERROR MULTIPLIER IN CIN IS 0.1
CHANGE=Y1
READ(*,88)YESN0
88 format(a)
IF(YESNO.EQ.'Y')THEN
WRITE(*,*)' INPUT THE DESIRED MULTIPLIER OF ERROR
IN CIN '
READ(*,*)ECIN
GOTO 1015
END IF
ECIN=0.1
1015 DO 1060 1=1,NTIM
ETEMP(I)=ECIN*ETEMP(I)
ETEMP(I)=ETEMP(I)/TEMP(I)
1060 CONTINUE
DO 1070 1=1,NTIM
1070 TEMP(I)=LOG(TEMP(I))
1090 YLSTPT=TEMP(1)
KOUNT =1
DO 1091 1=2,NTIM
IF(TEMP(I).GT.YLSTPT)GOTO 1092
YLSTPT=TEMP(I)
1091 KOUNT=KOUNT + 1
1092 CALL GRAF2D(TIMES,TEMP,KOUNT)
WRITE(*,*)1 INPUT THE NUMBER OF POINTS TO USE IN LLSQ
CALC. '
READ(*,*)NPOINT
FLAG = 2
CALL LLSQ(TIMES,TEMP,ETEMP,NPOINT,K2.ERRK2,FLAG,YINT)
DO 1096 1=1,NPOINT
TYGRAF(I)=TEMP(I )

174
1096 TXGRAF(I)=TIMES(I)
TXGRAF(NP0INT+1)=TIMES(NP0INT)
TYGRAF(NP0INT+1)=K2*TIMES(NPOINT)+YINT
TXGRAF(NPOINT+2)=TIMES(1)
TYGRAF(NPOINT+2)=K2*TIMES(1)+YINT
CALL GRAF2D(TXGRAF.TYGRAF,(NPOINT+2))
K2=-K2
WRITE(*,*)'OBSERVED RATE CONSTANT AND 95% CONFIDENCE
LIMITS ARE '
WRITE(*,*)K2,ERRK2
GOTO 10
1300 WRITE(*,*)' ENTER OBSERVED RATE CONSTANT '
READ(*,*)K
WRITE(*,*)' ENTER 95% CONF. LIMIT OF K '
READ(*,*)ERRK
GOTO 10
1400 WRITE( * , * )' ENTER K2 '
READ(*,*)K2
WRITE(*,*)1 ENTER 95% CONF. LIMIT IN K2 '
READ( * , * )ERRK2
GOTO 598
700 STOP
END
SUBROUTINE LLSQ(T,D,ERRD,NPOI NT,SLOPE.ERRS.FLAG,YINT)
C THIS SUBROUTINE CALCULATES THE SLOPE AND ITS 95%
CONFIDENCE LIMITS.
C EITHER ESTIMATED OR "T TEST" GENERATED ERR Y IS USED.
DIMENSION D(100),T(100).ERRD(100)
INTEGER FLAG
CHARACTER*1 YESNO
DIMENSION CT(31)
DOUBLE PRECISION
SUMX,SUMY,SUMXY,SUMYS.SUMXS.BOTTOM,SIGMAY,SUMRS
DATA
CT(1),CT(2),CT(3),CT(4),CT(5)/12.706,4.303,3.182,2.776,
&2.571/
DATA
CT(6) ,CT(7) ,CT(8) ,CT(9) ,CT(10)/2.447,2.365,2.306,2.262,
& 2.228/
DATA
CT(ll),CT(12),CT(13),CT(14),CT(15)/2.201,2.179,2.160,2.145,
& 2.131/
DATA
CT(16),CT(17),CT(18),CT(19),CT(20)/2.120,2.110,2.101,2.093,
&2.086/
DATA
CT(21) ,CT(22) ,CT(23) ,CT(24) ,CT(25)/2.080,2.074,2.069,2.064,
&2.060/
DATA
CT(26),CT(27),CT(28),CT(29),CT(30)/2.056,2.052,2.048.2.045,
&2.042/
IF(FLAG.EQ.2)G0T0 600

175
IF(FLAG.EQ.3)G0T0 100
WRI TE(*,*) 1 0 = ZER0 INTERCEPT 1=N0N-ZER0 INTERCEPT
I
READ(*,*)N
IF(N.EQ.0)GOTO 100
C ************Non ZERO INTERCEPT LEAST SQUARES**********
600 SUMX=0
SUMY = 0
SUMXY=0
SUMXS=0
SUMYS=0
SUMRS=0
DO 870 1=1,NPOINT
SUMX=SUMX+T(I)
SUMY=SUMY+D(I)
SUMXS=SUMXS+T(I)*T(I)
SUMYS=SUMYS+D(I)*D(I)
SUMXY=SUMXY+D(I)*T(I)
870 CONTINUE
B0TT0M=FLOAT(NPOINT)*SUMXS-SUMX*SUMX
SLOPE=(FLOAT(NPOINT)*SUMXY-SUMX*SUMY)/BOTTOM
YINT=(SUMY*SUMXS-SUMXY*SUMX)/BOTTOM
DO 900 1=1,NPOINT
SUMRS=SUMRS+((SLOPE*T(I)+YINT)-D(I))*((SL0PE*T(I)+YINT)
-D(I ) )
900 CONTINUE
WRITE(*,*) 'DO YOU WISH TO USE THE ESTIMATED ERRY?
YES=1 '
READ(*,*)NANS
IF(NANS.EQ.1) GOTO 910
SIGMAY=SUMRS/(NP0INT-2)
SIGMAY=SQRT(SIGMAY)
ERRY=CT(NP0INT-2)*SIGMAY/SQRT(FLOAT(NPOINT))
ERRS=ERRY*(SQRT(NPOINT/BOTTOM))
RETURN
910 EDMAX=ERRD(1)
DO 930 I= 2,NPOI NT
930 EDMAX=MAX(ERRD(I),EDMAX)
ERRY=EDMAX
ERRS = ERRY*SQRT(FLOAT(NPOI NT)/BOTTOM)
RETURN
100 WRITE(*,*)' ****ZERO INTERCEPT LEAST SQUARES**** '
SUMXY=0
YINT = 0.0
SUMXS=0
SUMRS=0
DO 200 1=1,NPOINT
SUMXY = SUMXY + D(I)* T(I)
SUMXS = SUMXS + T(I)* T(I)
SLOPE=SUMXY/SUMXS
SUMRS=SUMRS+(SL0PE*T(I)-D(I))*(SL0PE*T(I)-D(I))

176
200 CONTINUE
WRITE(*,*) ' DO YOU WISH TO USE ESTIMATED ERRY? YES = 1 '
READ(*,*)NANS
IF (NANS.EQ.l) GOTO 300
SIGMAY=SUMRS/FLOAT(NPOINT-1)
SIGMAY=SQRT(SIGMAY)
ERRY = CT(NPOINT-1)*SIGMAY/SQRT(FLOAT(NPOI NT) )
WRITE(*,*)'ERRY IS '
WRITE(*,*)ERRY
ERRS=ERRY/SQRT(SUMXS)
RETURN
300 WRITE(*,*)' DETERMINING THE BARATRON FACTOR? YES=1 '
READ(*,*)NANS
IF (NANS.EQ.l) GOTO 500
EDMAX=ERRD(1)
DO 400 1=2,NPOINT
400 EDMAX=MAX(ERRD(I),EDMAX)
ERRY=EDMAX
ERRS=ERRY/SQRT(SUMXS)
RETURN
500 WRITE(*,*)'DEFAULT ERROR IN BARATRON IS 2E-6.
CHANGE=Y'
88 FORMAT(A)
READ(*,88)YESN0
IF(YESNO.EQ . 'Y' )THEN
WRITE(*,*)' INPUT THE DESIRED MULTIPLIER OF ERROR
IN CIN '
READ(*,*)ERRY
GOTO 515
ENDIF
ERRY=2E-6
C DEFAULT ERROR IN BARATRON READING IS ESTIMATED AS 2E-6
TORR
515 ERRS=ERRY/SQRT(SUMXS)
RETURN
END
SUBROUTINE CNIC(NT IM,TEMP,ETEMP,XMAX.EXMAX)
C THIS SUBROUTINE MAKES BASELINE CORRECTION AND FINDS ERROR
BARS OF Y VALUES FOR BOTH ZERO AND NONZERO INTERCEPT LLSQ
CALC .
DIMENSION TEMP(100),ETEMP(100)
CHARACTER*1 YESNO
WRITE(*,*)'DEFAULT ERROR MULTIPLIER IN CIN IS 0.1
CHANGE=Y'
READ(*,88)YESN0
IF(YESNO.EQ.'Y')THEN
WRITE(*,*)1 INPUT THE DESIRED MULTIPLIER OF ERROR
IN CIN '
READ(*,*)ECIN
GOTO 915
ENDIF
ECIN=0.1

177
915 DO 500 1=1,NTIM
500 ETEMP(I)=ECIN*TEMP( I )
XMIN = TEMP(1 )
DO 600 1=2,NTIM
600 XMIN=MIN(TEMP(I),XMIN)
EXMIN=ECIN*XMIN
XMAX = TEMP(1 )
DO 625 1=2,NTIM
625 XMAX=MAX(TEMP(I),XMAX)
EXMAX=ECIN*XMAX
DO 700 1=1,NTIM
700 TEMP(I)=TEMP(I)-XMIN
DO 750 1=1,NTIM
ETEMP(I)= SQRT(ETEMP(I)* ETEMP(I)+ EXMIN*EXMIN )
WRITE(*,*)I
WRITE(*,*)TEMP(I),ETEMP(I)
750 CONTINUE
WRITE(*,*)'LLSQ CALC: NON-ZERO INTERCEPTS ZER0=0'
READ(*,*)NANS
IP(NANS.EQ.1 ) GOTO 950
XMAX=XMAX-XMIN
EXMAX = SQRT(EXMAX*EXMAX+EXMIN*EXMIN )
DO 900 1=1,(NTIM-1)
900
ETEMP(I)=SQRT(ETEMP(I)*ETEMP(I)/(TEMP(I)*TEMP(I))+EXMAX*
&EXMAX/(XMAX*XMAX))*TEMP(I)
DO 910 1=1,(NTIM-1)
910 TEMP(I)=TEMP(I)/XMAX
950 DO 960 1 = 1, (NTIM-1 )
960 ETEMP(I)=ETEMP(I)/TEMP(I)
DO 970 1 = 1, (NTIM-1 )
970 TEMP(I)=LOG(TEMP(I ) )
88 FORMAT(A)
RETURN
END
SUBROUTINE GRAF2D(XR,YR,NDP)
C General plotting routine for cga adaptor.
C Must be linked with GRAF.OBJ which contains the
1anguage
C subroutines WRITDOT, and SETDIS.
C Written by Cliff Watson 9-17-1987.
DIMENSION XR( 1024 ) ,YR( 1024 )
CHARACTER YESNO*l
COMMON /SCALE/ XMIN,XMAX,XS,YMIN.YMAX.YS
YMAX = YR( 1 )
YMIN = YR(1)
XMIN = XR(1)
XMAX = XR(1 )
C
AND MIN VALUES
DO 10 I =
assembly
FIND XAW
1 , NDP

178
IF
(XR(I)
. GT .
XMAX)
XMAX
= XR(I)
IF
(XR(I)
. LT .
XMIN)
XMIN
= XR(I )
IF
(YR(I)
. LT .
YMIN)
YMIN
= YR(I)
IF
(YR(I)
, GT .
YMAX)
YMAX
= YR(I )
10 CONTINUE
WRI TE(*,*)XMAX,XMIN,YMAX,YMIN
PAUSE
C
SET SCALE
XS = 639 / (XMAX - XMIN)
YS = 199 / (YMAX - YMIN)
C ENTER GRAPHICS MODE
C SET DISPLAY TO HIGH
RESOLUTION GRAPHICS
CALL SETDIS(6 )
CALL B0X(0,0,639,199)
C
PLOT DATA
DO 20 I = 1,NDP
IX = (XR(I) - XMIN) * XS
IY = (YR(I) - YMIN) * YS
CALL PSET(IX,IY,1,IERR)
CALL BOX(IX-5,IY-5,IX+5,IY+5)
20 CONTINUE
C PAUSE
TO DISPLAY PLOT
READ(*,'(A)') YESNO
C SET
DISPLAY TO TEXT
CALL SETDIS(2 )
RETURN
END
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
SUBROUTINE PSET(IX,IY,ICOLOR,IERR)
C Subroutine to set pixel on high resolution graphics
screen.
C x = 0,639; y = 0,199
IERR = 0
IP( (IX.LT.0) .OR. (IX.GT.639 ) ) IERR = 1
IF((IY.LT.0).OR.(IY.GT.199)) IERR = 1
IF ((ICOLOR.LT.-1).OR.(ICOLOR.GT.1)) IERR = 1
IF(IERR.EQ.1) GO TO 100
INVY
199
I Y

179
CALL WRIDOKIX,INVY,ICOLOR)
100 CONTINUE
RETURN
END
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
SUBROUTINE LRL(IXMIN,IXMAX,IY,I ERR)
C Subroutine to draw horizontal line
DO 100 I = IXMIN,IXMAX
CALL PSET(I,IY,1,I ERR)
100 CONTINUE
RETURN
END
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
SUBROUTINE LUD(IYBOT,IYTOP,IX,IERR)
C Subroutine to draw vertical line
DO 100 I = IYBOT,IYTOP
CALL PSET(IX,1,1,I ERR)
100 CONTINUE
RETURN
END
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
SUBROUTINE BOX(IXMIN,IYMIN,IXMAX,IYMAX)
C Subroutine to draw box
C Draw top of box
CALL LRL(IXMIN,IXMAX,IYMAX,IERR)
C Draw bottom

180
CALL LRL(IXMIN,IXMAX,IYMIN,I ERR)
C Draw left side
CALL LUD(IYMIN,IYMAX,IXMIN,IERR)
C Draw right side
CALL LUD(IYMIN,IYMAX,IXMAX,IERR)
RETURN
END

APPENDIX II
ANALYTICAL EXPRESSIONS FOR KINETIC MODELING IN CHAPTER 5
A. Kinetic Differential Rate Equations for the Scheme Shown
in Figure 5.3.
I = 1° +1°
C3H3+ C3H3+ £-°3H3
+ [1 + 6/(1O01 ) ] [exp( 0^ t) - 1]
I =31
C H D+
3 2 3 3
+ [exP( ~ exp “To 84’1° + {[exp( 0 t)
Z-°3H3
-1]/01 - 3[exp(02t) - l]/02}
1 + = 31 [exp(0 t) - 2exp(0 t) + exp(0 t)1 +
c3hd2 í-c3h3+ 2 3
{[exp(0 t) - l]/0 - 6[exp(0 t) - 1]/0,
l-C H ¿ *
3 3
+ 6[exp(03t) - 1]/@3}
= I [3 exp(0 t) + exp(0 t) - exp(0 t) - 3 exp(0.,t)l
C3D3 £^3H3 3
- 84>I° . {[exp( 0 t) - 1 1/(100.) - 9[exp( 0 t) -
l-e3H3
1]/(1002) + 9[exP(02t) - 1 ]/(503) - [exp(04t) - i]/9 }f
181

182
in which s = kc/k£, $ = k£kfPc D /(k£ + kc), 0, = k£(j,/10 - kfPc D - k pc H x
2 2 2 2 p 3 3 '
9 2 = 31W° - kfPC2D2 - kpPC3H3I' 03 = 3k¿4>/5 - kfPc2D2 " kpPC3H3I' and 04 =
kZ^ ~ kfpC2D2 “ kppC3»3i* Thefitting parameters for this model are
I. +' kfpc7D,'and kppC-,H,I* l0 . is fixed at its
£^3H3 3 3 C3H3
experimental value if the initial point is at t=0; otherwise
it is also a fitting parameter.
B. Kinetic Differential Rate Equations for the Scheme Shown
in Figure 5.7.
dl
+/dt = 01
*-C3h3- £-C3H3
dl
+/dt = 81 +/(1 OF j
c-C3H3 ^3
dl /dt =
£-HDC3H
- (F2k^ + kj I + + 4>2(i + +
f p â– 
£-HDC3H' £-HDC3H
FI
£-H2C3d
)/(5F ) + 2^ I +/(5F)
£-C3H3
dl /dt =
£-H2C3d
-F(F2k* + kj I + + $2 {I +
f P
£-H2C3D
£-HDC3H
FI )/(1 OF3) + A I /(5F2)
£-H2C3d+ ¡í-C3H3
/dt = 38[-(I + + FI + ) / (2F) +
c-C3H2D+ £-HDC3H ¿-H2C3D
♦,I +]/<5F)
*-C3H3

183
di /dt = -F(F2k' + k' )I + 2$ (FI +
£-hdc3d+ p a-hdc3d £-hdc3d
I )/(5F ) + 2 (I +
!í-D2C3H 2.-HDC 3H
FI
<í-h2c3d
+ )/(5F2) + 4>11 +/(5F)
¿-C3H3
di
I I
+/dt = -3(FI +
-D2C3h P £-D2C3H £-HDC D
£-D2C3h
+ )/(5F<4) + 2(I + +
£-HDC3H
FI )/(5F) + * I /10
£-H^C„D £-C H.
2 3
3 3
di /dt = 38 [<(i (FI + I
L 3 _ _ +
r3 + • * , )/F + *,(I
c-C3HD2 £-HDC3D+ £-D2C3H £-HDC.
+ FI +}/F + 1 ¿_c H +/2J/5
£-H2C3d 33
di /dt = [ P £-C3D3 £-HDC3C
'3 2
+ I
£-D2C3h
+ )/(5F ) + 4>2 (I + +
FI
£-HDC3H £-H2C3D'
+
)/(1 OF)

184
di /dt = 8[*4i +/f2 + 24> (FI +
c~C2D3 £-C3D3 ¿-HDC..D
i +)/(5F) + (J> (I + FI )/10,
£~D2C3H ¿-HDC3H Jt_H2C3D
in which 0
■ - "S - V \ - Vc„D ' kp - Vc "S'
2' 2 1 2 2 3 3
(X1
+ BV
/ 2 = F kf/^3 + BA,), 3 = F kf/(X4 + 0X5), <(>4 = F6kf/(1 + F0),
and
the ^
t's are given as:
X1
= (1 +
6/F + 3/F2)/10
X2
= (3 +
6/F + 1/F2)/10
X3
= *2/f
)
X4
= (3 +
2/F)/5F2)
X5
= (2 +
3/F)/(5F).
The fitting parameters for this model are ^ .* 2# k » k , and F.
£-c3H3 1 P
1° Is fixed if the initial point is at t=0; otherwise it is
C3H3+
also a fitting parameter.
C. Kinetic Differential Rate Equations for the Scheme Shown
in Figure 5.10.
C H + + Cc H +[' + k-31*1/6l ]ie='P 3 3 3 3
k-1lV° [exp(0 t) - exp( 0 t) ]/0
t-C 2 12
C3H3
C5H3

185
C7H3
= k_11k_2l(í,l*2l0 +[exp(01t)/013 - exp(02t)/023 +
£-C3H3
(1 /023 ~ 1/9-| 3 )exp( 03t) ]/01 2
I + = k_i n ks1 <í>n 4>2i0 +{[exp(01t) - 1]/01 - [exp(02t)
CgH5 (s)
^C3H3
1 ]/e9}/0
2J' 1 2
C11H5+(S)
-k-11k-2,ka2*lW° + H««> -’V<6,813>
^3H3
[exp(02t) - 1 ]/(e2023) “ (1 /023 “ 1/013)[exp(03t)
^]/®3}/®i2'
1 + = k_!kA201 x° +[exp(0 t)/0 - exp(0 t)/@’ + (1/e’
CH * Q-c u z z ¿
8 6 £ C3H3
-1/01)exp(-k2t)]/012

186
■in * k.,2 ♦ k_n), *2 = k£2PCA/(k_2t ♦ k_22 ♦
ksl>. ^3 = kf3Pc H ^(k-31 + k-32 + ks2); “91 ' -02' and _03 are Parameters
(1), (2), and (3), in that order, in equations <“>■ 812 * 9, - V 913 *
91 “ 03' 023 = 02 " 03' 81 = 81 + kd' 3nd 02 = 02 + kd* The fitting
parameters are 0^ 02, @3, 1° (1 + k_31*1/01>» k_i1'f>1I° +/012'
2-“C3H3 " ~ ¿-C H
ks2<*>3' k-21^2' ks1‘í,2' and kd. It can be seen that k¿2 = -01 - k 212 -
ks1^2' in which kp2 = kp2pc H^.

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BIOGRAPHICAL SKETCH
Up until 1982, Feza Oztiirk's educational background
originated in Turkey. She received a Bachelor of Science
degree in chemistry in 1976 and Master of Science degree in
1977 from Ege University in Izmir. After teaching for five
years at the same university, she came to the United States
and started the Ph.D program at the University of Florida in
Gainesville in 1982. Three years later, she began working
in Dr. John Eyler's lab in the area of gas-phase
ion/molecule reactions. She completed her graduate studies
during the summer of 1988.
196

I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Willis B. Person
Professor of Chemistry
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Merle A. Battiste
Professor of Chemistry

I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Associate Professor of
Mechanical Engineering
This dissertation was submitted to the Graduate Faculty
of the Department of Chemistry in the College of Liberal
Arts and Sciences and to the Graduate School and was
accepted as partial fulfillment of the requirements for the
degree of Doctor of Philosophy.
August, 1988
Dean, Graduate School

UNIVERSITY of florida
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