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The temperature dependence of ion-molecule association reactions
315
International Journal of Mass S’pectrometry and Ion Physics, 45 (1982) 315-322 Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
THE
TEMPERATURE
K.R.
JENNINGS,
Department cv4 7AL
DEPENDENCE
J.V.
OF ION-MOLECULE
HEADLEY
of Chemistry (ENGLAND)
and
and
R.S.
ASSOCIATION
REACTIONS
MASON
Molecular
Sciences,
University
of
Warwick,
Coventry
ABSTRACT The temperature dependence of five ion-molecule association reactions and three ion-molecule equilibria have been determined using a high pressure source in which the electron beam is pulsed. The temperature dependence of the rate constants takes the form k=CTem and values of m have been compared with literature values and theoretical predictions. No reason for the discrepancies between the various values can be given. Thermodynamic data derived from the variation of equilibrium constants with temperature are in excellent agreement with literature data.
INTRODUCTION In are
addition
of
to
clouds
(ref.1).
lieved
to
nuclear
in
paid features,
to
but in
strong
many
diatomic
such
as in
(i) glow In
the
and the
high
case,
of
increasing
is
to
assess
of
where
C and
region
of
the
species
but
higher
order
2-4
as
the
the
last of
(ref.3).
obtained
by
electron
beam
recently,
the
secondary
conditions
are
established
0 1982
Elsevier
found
these
the
use
source,
Scientific
ion
the
Above
characteristic for
the
the the
of
of
of
one (ii)
the
two
tube
(SIFT)
by working
at
Publishing
Company
of
reactions
of
reactants
value
and flow
is
constants.
of
ions,
reported
reactions
rate
complexity
been
0020-‘7381/82/0000-0000/$02.75
serious
theoretical
success
constants
are
cluster
been
thermal
their
are
over
relative
their
m are
have
more
has
over
there
association by
10 have
or
which
developed
the
ion-molecule exhibited
of
pulsed
attention
Several
been
be-
gas-cooled
agreement
for
(ref.3). have
results pressure,
general
processes in
observations.
m in
triatomic
years,
literature
dependence
of
ten
systems
interstellar
of
supports
there
early
feature
k=CTmm
formation
excess
recent
technique each
experimental
modeling
graphite
reactions too
striking
Values
in
the
the
reactions
and
of
several
in
present
reactions,
reaction.
Most
at
temperature
many
values
is
most
negative
150K,for the
it
the
although
association
explaining
Perhaps
and
reported
in
last
nevertheless
ion-molecule
years,
models
data
the
association
atmospheres
invoked
corrosion
During
are
ion-molecule
planetary
been
the
reactions
in of
of
also for
there
discrepancies models
have
(ref.2). these
interest,
chemistry
responsible
reactors
been
intrinsic the
They
be
main
few
their
importance
rises,
m rises
and
techniques: flowing
after-
technique.
a sufficiently
316 high,
pressure,
in
a SIFT
typically
80-600K.
The
ment,
the
ment,
it
in
1 - 5 Torr
apparatus;
each
techniques
third is
is
on
of
ture
end
of of
N;'+N2+M pressure
source
flowing
afterglow
and in
and
rate
in
a flowing in
and
or
in
is
unlikely
in
the
-1.5
Torr
the
range SIFT
pressure
experi-
source
a mixture
differences it
0.5
temperature
afterglow a high
system
expected,
and
the
of
experi-
third
bodies
stabilizing
that
effic-
their
dependence
four
reports
literature
of
the
tempera-
reaction
(1)
.
Two high
discrepancies
source cover
whereas
some
be
were
-+N;'+M
literature
that
pressure
principle
greatly.
there
the
in
Although to
differ
1981,
in
a one-component
are
would
the
dependence
the
in
bodies
a high
can
helium
system.
third
temperature At
usually
reactant
a multicomponent
iencies
differ
body
the
in
method
studies SIFT
the
we
(M=N2) gave
of
m reported
values
have
therefore
of
a number
constants
gave
study
m=1.7
m=1.5
and for
other
reinvestigated of
and 2.4
reactions.
a high
pressure
(refs.4,5)
systems
the
these
4.0
and
(M=He)(refs.6,7).
a
Similar
can
be
temperature
found
in
the
dependence
of
EXPERIMENTAL All
reactions
were
spectrometer
8).
The
source
Measurements the
was were
temperature
Ions
then
of
were
produced
ion
The
occurrence
of
at
the
Daly
a preamplifier erager
(Data
by the
after open
exit a high
which
they
construction
pulse
collision-induced were
of
bandwidth
shown
of
400
be
Laboratories
Ltd.)
5000-10000
cycles
were
ratios.
The
output
of
signal
recorder
or
transferred
the to
giving
to
a MINC-11
of
to
averager
using
mass (ref.
and
over
a "Baratron"
eV electrons
and
by
kHz
held the
at
a
into
was
minicomputer
with
were
respect
accelerating ion
ions.
allowed
They
-50V
full the
the
output
a "Biomac" of
minimizes
either
was
fed
through
Signal
per
Av-
channel.
signal-to-noise
displayed (D.E.C.
the
effects
1000 5 ys
acceptable
to
voltage
source
Discrimination
resolution give
were
conditions.
and
50 a time
required
MS50
gold-plated.
controlled
outside
negligible
than
and
were
grid
subjected
to
and
field-free
transmission
greater
an
controller.
decomposition
detector
to
previously
(1 Torr=133Nm-*)
measured
Inc.)
immediately
Usually,
processing.
were
under
are
Torr
pressure
slit
fitted described
flashed
- 3.2
Instruments
Automatic
as
nickel 0.5
Pressures
a 1 - 10 us
ion
towards
source
(MKS 216
source
Ltd.)
copper, of
K.
gauge
through
8kV.
of pressures
324-550
Series
accelerated
the
at
pressure
diffuse
Instruments
constructed
made range
capacitance
in
Analytical
Granville-Philips
to
studied
(Kratos
Ltd.)
on for
an
x-y
data
re-
317 The ion
pulse
of
source
certain
electrons
which
initially
number
urements
[made the
obtained
from
which sion
mode
only
after
quite of
pressure
by
had commonly
experiments
the
loss
of
charged
within
diffusion.
to
diffusion
free
been
established.
used
in
can
primary
species
ambipolar
changes
condition
source for
of
rapidly
procedure
explicitly
density
diffusion
this
normalization high
allows
a high
decays
density,the
were
conditions,
produces
be
ions
the
Below and
by
by
these of
an
a
meas-
Under processing
replaced both
the
data
analysis
reaction
and
diffu-
(ref.9). In
A+.
a one-component
+
+2
2A -IA
t
A'+
system,
wall--t
If
the
rate
to
the
total
-dlA+-I dt-
primary
be
lost
by
two
processes,
(2)
A of
(3)
diffusion
to
the
wall
is
+
k31A+~JlAl-1
assumed
to
be
inversely
proportional
pressure,
-
k'
may
+A
kr,A+.,[A,’ L
= k’[A+‘] t k”[A+‘] where
ions
= k2[Aj2
and
(4)
at
k"=k3[A]-'
.
constant
pressure
Integrating
and
replacing
]A+.]
hy
I(A+')
yields ;n
I(A+')
so
that
:n
= a plot
of
S=-(k't-
k").
k,[AJ-l)
~r S[A]= 3 should
(Pressure)
with
reaction
mixture
the
temperature
be extracted.
each
published
In do
not
system,
two
line
of
the
it
of
k2 be
-(S
+ against
intercept
extracted
dependence
S where
x Pressure)
and
components.
slope S= -(k,[A]*
k3
For
a
from
plots
obtained
By working
with
different
of
k3
on
composition
of
the
(ref.10). over
dependences
with
of
slope may
two
repeated
case,
line dependent,
a plot of
the
be obtained
is
a straight pressure
so that
components,
was
each
gives both
information
ratio
interfere this
are
a straight
could procedure
processes for
the
(5) t
k"
similar
above
results
and
+ k3),
give
of
+ k")t
against
k'
a fixed
fractions
(k'
I(A+)
-(k,[A]'
system,
by working
The
:n
-
Because
two-component
mole
I,(A")
of is
of
the
discussed
a range and
k2 course
observation fully
in
of
temperatures
k3 for
each
necessary on a more
to the
and
reaction ensure
reactions
complete
that of
account
from mixture
these could
competing interest of
this
and work
elsewhere.
RESULTS One-Component cO2-.
Systems In
pure
CO2,
(ref.9) the
rates
of
the
forward
and
back
reactions
are
so
high
318 that
equilibrium
be
is From
obtained.
values in
of
good
AS0
Good
good
of Data
work
are
SP against for
compared
This
procedure
and are
closely
analysis
compared
*
Systems
The
System.
CO/CO, varied
erature the
only
from
obtained
and
the was
k3 over
very
system
similar. in
a range
rise
of
obtained
tempfrom
Third Body
and
the
from
this
table: Third Body
----1.5 3.320.2
Source Source
experimental
obtained
following
Source
12 6 5 4 7 9
N2
m in k = CT-m
Pressure Tube Pressure Pressure
Ref.
He N2 2
Results
the
Method High Drift High High
gave
below:
nitrogen
values
and
constant,
--_ 1.5 4.0 1.7 2.4 3.8kO.3
of
considered
in
5.5
K.
by the
Ref.
co
13 14 4 9
co CO
were
at
total
This
is
switching
are
reactions.
stages
on
pressures a complex
abundance
early
made
of
the
mixtures of
0.4-2.0
system
and,
CO;' These reaction,
and
for
which Torr
in
(CO);., are
rapid
the
only
over
the
CO/CO2 the
temp-
the
late
afterglow,
the
latter
ion
compared processes
with which
being back need
are:
+ M -~~~~
co;.
+ M pm->
+ CO
to
significant
co;.
+ co2
Observations
534
(CO*);' and
be
k2
derive
(ref.10)
0.1
388-
ions
reactions to
from
range
formed
of
may
estimate.
Two-Component
ratio
NC were
obtained, -1 and mol
kJ one
of
rate
constant,
6.3
Drift Tube Flowing Afterglow High Pressure Source High Pressure Source SIFT High Pressure Source
results
298 300 300 300
Indirect
i
m in k =CT-m
T/K
14.8" 12.5 11.4 13.0
results,
could
were
Method
literature
k/10-2gcm6mol-2s-1
K-'mol-'
67.8
values
resembled
of with
equilibrium
reaction
T/K
system
the
these
values
information
f 4.65 AH'=-
decay
literature
ambient 280 300 300 287 300
of
kinetic
of
the give
no
From
association
with
5.0 1.9 8.0 10.0 1.9 4.5
study
for
P3 to the
k2,
and
AS’=-%.4
values
plots
k/10-2gcm6mol-2s-1
Q.
and
(ref.11). -1 kJ mol .
-t 2.5
ps
dependence
mol-'
literature
first-order
plots
eratures.
500
mol -'
JK-l
= 475.3
N2L
kJ
with
c 8.4
within
temperature
+ 2.9
agreement
AH&02);J
this
the
AH"=-66.1
= -88.3
to
established
+
(C02);' (C02.CO)+'
+ M + M
(7)
319
co;-
+
wall
Putting of
by
reaction
of
Q by
By working of
of
300
2.1
available
for
k7 for
the
the
The
of
range
the
451-537
from
K.
abstraction
by
the
rate
described k6 and
constant
for
k7 may
(k6+
k7Q) for
for
a given
a one-component
be
evaluated
loss
system.
and
k8 as
a
In
in
4.520.2;
no
previous
reports
no
linearity
that
reactions
CO2
containing
of other
plots
than
the
(refs.
at for
may
H2 was
used
are
measurement
found
(8)
values
literature
obtained
(6)-
with
values
of was
the
the
literature
x 10-28cm6molecules-2s-1
good
agreement
reported
CTmm was are
excellent
be
of
300K
and
this
system
for
neglected
in
data.
System.
H(C02)l
Q,
constant
loss
that
of
kg=
3.5
assumption
CO2/H2
to
There of The
of
a diffusive
x 10-28cm6molecule-2s-1 m in
a value
analysis
mation
HCOZ
Rapid CO;'
over
3% and the
protonation
to
form
of
the
5% of
pressure
same
range
CO2 ion
to
1 - 2.5
give
was
HCO;
followed
to
Torr
coupled by the
study and
the
for-
temperature
with
hydrogen
rapid
establishing
equilibrium
HCO; so
2.5 of
m=3.8?0.4.
support
rate
x 10-28cm6molecule-2s-1,
comparison.
which
which
of
and
overall
obtained.
2.0
value
an
with
values
be
k6=
The
(8) derive
similar
different
x 1o-28
15,16).
. may
together
Q may
K,
CO2 one
an analysis
with
function At
>
[CO]/[CO2]
co;.
value
---
Q=
+
co2
that
no
pendence
+
M _
kinetic
of
data
the
AH0
CO/H2
= -84.1
M
obtained
-1 i
System.
+
were
6.3
(9)
for
constant,
K-lmol
of
The
were
equilibrium
AS'=-113.4+6.35 values
H(C02);
this
system.
values
of
obtained,
kJ mol-'
in
and
CO containing
ES0
5% and
From
AH0 good
of
temperature
2 2.9
agreement
= -121.3
6.5%
the
= -79.9
kJ
with
?r 12.5 H2 were
mol
de-1
and
literature -'
J K-'mol used
to
study
(ref.11). the
reaction HCO+
+
CO
over
the
high
pressures
from
a study
values
of
of AHo in
slow conditions,
walls
and
the
component k,O
system at
300K
-2.5
I
(10)
Torr
of
2.5
and
the
the
temperature
with
was
equilibrium
kJ mol-'
agreement mol-'
M
equilibrium
variation
pressures
these
for
the
J K-'
sufficiently
0.4
+
temperatures,
= -45.2 good
lower
H(C0);
range and
= - 87.4 At
M e
pressure
obtained, AS0
f
and
!,S"
literature
range
established constant
= - 94.1 values
of
223-320
within with
K.
500
At
us
and
temperature,
+ 8.0
J K-'
mol-'
LH"
= -48.9
kJ
mol
were -1
and
(ref.4). and
for HCO'
analysis (ref.9). compared
the
temperatures, rate
of
is
removed
of
the This with
however, the
forward
either
data
by
closely
leads a literature
to
the
approach
reaction
to
to
be measured.
reaction
(10)
or
resembles
that
used
a value value,
of
0.93 estimated
equilibrium
by
Under
diffusion for
x 10e3'
was
to
a onecm6
indirectly,
mol
-2s-1 of
the
320
1.6
x 10-30cm6molecule-2s-1 -m was measured k,O= CT
as
values
(M=H2),
2.9
from
a comparison
of
3.0
(ref.16). 6.9
The
(M=CO,H2)
(M=CO),
value
of
which and
6.2
m in
the
compares
equation
with
(M=H2)
(refs.
obtained
in
literature 11,17).
DISCUSSION It those ent
is
clear
in
the
literature
laboratories
reactions.
This
perimental
pulsed
using
flow
M.
that the
temperature
is
not
obviously
The
since source,
afterglow data
and
using
a high-pressure
several
reactions
complicated
by the
that
tween
the
results
of
the
gests
that
there
are
no
the
measurement
the
equilibrium
entirely
tion plicit rather
own
Meot-Ner
in
the
assumed
for
the
loss
analysis
m.
work,
was
when
thermore,
the block
use
of
should
reduce reported
primary ion
have
a similar
of
obtain
data
a gold-plated have
both
only
that
block
establishing
diffusion,
to
a lower on
data,
reac-
The
and
taken
ex-
absothe
excited
species
although
in
in
the
than
thermal
our
late
established.
rather of
arise
for
effect
were
that
experiments, 3.25
leads
of
in
assumed
Field.
little
readings
source
to
and
source
sugor
differences own
only
set
bewhich
is
vibrationally
each
the
Field
reaction
has
for
further
agreement
it
our
usually
from
in
the
3.8
or
copper
facilitated
and
by
but
on
conditions
if
by Meot-Ner
effect
is
effects
example,
electronically
dependence
and
in
third-body, all
This
Meot-Ner
m from
~25%
the
discrimination
currents, of
in
obtained
ourselves,
good
correct
ions
a high data
very
temperature
1.7
constants
to
are of
would
rate
diffusion
of
For
Field
with
groups.
from
pressure.
of of
those
ex-
Field,usinq
and
is
differ-
a particular
temperature
other
and
association
differences
a higher
coming
normalising
taken
free
and
and
participation should
care
afterglow,
by
reactive The
work
error
and
there
measurement
allowance
reaction
steel
of
value
for
to from
errors and
the
of the
present
above
value
value
this
lead data
work between
of
Hiraoka
equilibria,
serious
well
than
lute
errors
for (1),
for
temperature
data
from
allowance
in
of
on
use
agreement
coworkers,
source, based
the
despite
and
present
ion-molecule
Yeot-Ner good
techniques,
Kebarle
that
fact
by in
the
disagreement of to
obtained general
SIFT
pulsed than
considerable
attributable
in
by
is
dependencies
data are
obtained
results
there
on
technique
pressure
of
Fur-
a stainless
equilibrium
(ref.9). There can work
be
remains
showed
errors
and
was
defined
and
since
resolution ment
the
measured
was
question
of
the
as a function
of
time.
that
the
use
a bandwidth by the
in signal
observations of
at
independently
of
excess
of
50
for
in
50
1 part
kHz
which
made
calibrated
with
which
Preliminary
bandwidth
averager were
least
a low
accuracy
of
was gave
the
primary in
pre-amplifier
a minimum
against
the
experiments
total other
could
therefore a time of
used. resolution
observation
current present
lead
to
serious
The
time
scale
of 5ps/channel
25Cps,this
pulsing
ion the
corresponds time. equipment
to
This and
equipit
is
a
321 therefore
unlikely
that
any
significant
error
in
the
measurement
of
time
was
present. Another
possible
presence to
of
exclude we the
from
our
and
is
For
the
Field SIFT
CO:
with
2.3
and
and
ourselves.
+ AB
AB +.*
t
+
AB
M
----+
overall
AB+.
sion,
since
these
not
all
Classical
tmodel
is
Imuch
Bates
(ref.18)
plex.
in When
degrees 1,
which
a reaction
non-linear
of reflects of
two
species, the
AB'. to
lower
kS
(stabilization).
k,= '*
the
is
taken
freedom the
than
usual ks
(1-S)
be
are
afterglow of of
CH< and
m between
Kebarle,
usually
Hiraoka
given
in
T
reactants of
species, between higher
of
the
lie
3 and
4. of
expresEach
to
of
This
r is
by and
and
excited
the
sum
ion-molecule
are com-
collisions, of
usually step.
3 and
for
therefore been
the between
On this
2 and
have
the
treatments
RRKM model
theory
kd. of
form,
a parameter,
between
of
number
recent the
in
111 which
that
correct
stabilization
m should
values
due
reactants
where
6 is
is
be equated
this
effective the
the
barriers -(r/Z+'?) and
is
the of
a development
kf
temperature-dependent
More
of
ka can of
stabilization.
kf
S is
value.
of
that
to
is
where
fraction
of
this
functions
kf=kakS/kd
weakly
, where
centrifugal
lie
Meot-Ner
discrepancy.
assume
some
only
predictive
efficiency
the
to is
lead
Although
of
flowing
by
is
to
dependence
dependence
linear
is that
to
partition of
reasonably of
values
this
leads
necessarily
CT
report m obtained of
theory
(ref.19)
of
m should rather
(dissociation)
It
be of
a temperature
rotational
kd
and
to
Herbst
account
predicts
0 and
crude
terms
(association)
temperature
leads
in
Kebarle
results
reactions
reactions
ka
expected the
Field,
(ref.3):
will
complex
and
formulated
this
of
the too
ion-molecule
expression
therefore
RRK theory in
no explanation
steady-state
collisions
source
oscillators
have
constant.
ADO
is
major
of
M
rate or
processes the
t limit,
forward
Langevin
Smith
and
of
is
using
association
and
error. m obtained
results
hand,
obtained
values
of
of
dependence
any
mechanism
the
other
Adams
of
value
em-
by Meot-Ner
with
than
tB
pressure
results
the difficult
consistency.
temperature
ion-molecule
+.*
>A "
low
we
treatment
+.*
the
a*ld
present,
source the
such
is
very
procedures
m obtained to
On the
the of
lower
energy-transfer
B
the
the to
the
with
(ref.7),
appreciably At
the
is
purification
agreement
Hiraoka.
a study
of
lend
good
(lo),
accord
the
type
it
possible,
value
this
a significant
is
the
of systems,
of
were
is
of
most
view
would
there
neutrals
in
times
data
in
measurement In
comparison
reaction
in
theoretical of
0.05
the
more
several
The terms
In
for
any
impurities
which
impurities
techniques;
3.4,
that
i
with
are
but
system,
and
and
completely
that
agreement
A+.
2.25
nitrogen
and
ports
is
in
reactants.
for
unlikely
error
the
believe
systems
coworker,
good
for
not
data
it
and
do
three
of
in
impurities
ployed, For
source
impurities
determined
basis, two sup-
322 experimentally.
A shortcoming
conserve
angular
phase
space
which
the
for
are
the
to
of
m in
the
two
We thank tricity and
for
reason
for
of
values.
Science
and
Generating Or.
A.
J.
each favor
Board Wickham
for
of
"low"
this
for
financial
helpful
systems
in
for
Research support
will
the of
which
no
during
between
fall them
is there
and the
data
reactions.
choice
Council
interesting
experimental
present firm
two
future.
comparison
at
the
laboratories
ratio
of in
data
be
near
different
but and
of
association
the
terms
systems
experimental it
body
in
values,
discrepancy
Engineering
with and
rigorously in
for
predictions
amines
values,
systems
lower
not
reactions
the
accepted
does
but
ion-molecule
m determined
three the
other
of
and
these
agreement of
generally
kf=CT-
to
sets the
no
values
good
to
it
shortcoming low,
dimers
dependence
equation
appears
experimental
tween
as yet
"high" 2.25
RRKM theory ous
the
groups:
approximately
is
gives
proton
that
of
this
relatively
application
temperature
is
description
is
theory of
its
there the
two
The
of
RRKM theory
removes
momentum
formation
results
summary,
Values into
of
the
describing
20,Zl)
similar.
the
A recent
(refs. angular
rates
see In
momentum.
theory total
theories
of
can
the
course
being
possible. is
no
be
made
obvi-
Central
Elec-
of
work,
this
be-
discussions.
REFERENCES 1 2 3 4 5 6
9
l? 12 13 14
1': 17 18 19 20 21
W.T. Huntress, Chem. Sot. Rev. 6, (1977), 295. A.J. Wickham, Chemistry in Britain, Is, (1979), 286. M. Meot-Ner in "Gas Phase Ion Chemistry", Vol.1, M.T. Bowers, ed., Academic Press, New York, 1979, pp. 198-271. M. Meot-Ner and F.H. Field, J. Chem. Phys., 61, (1974), 3742. J.D. Payzant and P. Kebarle, J. Chem. Phys., 53, (1970), 4723. D.K. BEhme, D.B. Dunkin, F.C. Fehsenfeld and E.E. Ferguson, J. Chem. Phys., 51, (1969), 863. N.G. Adams and D. Smith, Chem. Phys. Lett., 79, (1981), 563. D.K. BGhme, J.A. Stone, R.S. Mason, R.S. Stradling and K.R. Jennings, Int. J. Mass Spectrom. Ion Phys., 37-, (1981), 283. J. Chem. Sot. Faraday Trans. I, J.V. Headley, R.S. Mason and K.R. Jennings, 78, (1982), 933. J.V. Headley, R.S. Mason and K.R. Jennings (unpublished work). M. Meot-Ner and F.H. Field, J. Chem. Phys., 66-, (1977), 4527. J.T. Moseley, R.M. Snuggs, D.W. Martin, and E.W. McDaniel, Phys. Rev., 178, (1969), 240. L.W. Sieck and R. Gorden, J. Res. Natl. Bur. Stand., Sec.A, 78, (1974), 315. J.H. Schummers, G.M. Thomson, D.R. James, I.R. Gatland and E.W. McDaniel, Phys. Rev. A, 7, (1973), 683. A.B. Rakshit and P. Warneck, Z. Naturforsch., a, (1979), 1410. L.W. Sieck, Int. J. Chem. Kin., lo, (1978), 335. K. Hiraoka, Int. J. Mass Spectrom. Ion Phys., 2, (1980), 73. D.R. Bates, J. Phys., E, (1979), 4135; J.Chem.Phys., 73, (1980) 1000. E. Herbst, J. Chem. Phys., 2, (1979), 2201; 72, (198Or; 5284. L.M. Bass, W.J. Chesnavich and M.T. Bowers, J. Am. Chem. Sot., 101, (1979), 5493. L.M. Bass, P.R. Kemper, V.G. Anicich and M.T. Bowers, J. Am. Chem. Sot., lOJ, (1981), 5283.
International Journal of Mass S’pectrometry and Ion Physics, 45 (1982) 315-322 Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
THE
TEMPERATURE
K.R.
JENNINGS,
Department cv4 7AL
DEPENDENCE
J.V.
OF ION-MOLECULE
HEADLEY
of Chemistry (ENGLAND)
and
and
R.S.
ASSOCIATION
REACTIONS
MASON
Molecular
Sciences,
University
of
Warwick,
Coventry
ABSTRACT The temperature dependence of five ion-molecule association reactions and three ion-molecule equilibria have been determined using a high pressure source in which the electron beam is pulsed. The temperature dependence of the rate constants takes the form k=CTem and values of m have been compared with literature values and theoretical predictions. No reason for the discrepancies between the various values can be given. Thermodynamic data derived from the variation of equilibrium constants with temperature are in excellent agreement with literature data.
INTRODUCTION In are
addition
of
to
clouds
(ref.1).
lieved
to
nuclear
in
paid features,
to
but in
strong
many
diatomic
such
as in
(i) glow In
the
and the
high
case,
of
increasing
is
to
assess
of
where
C and
region
of
the
species
but
higher
order
2-4
as
the
the
last of
(ref.3).
obtained
by
electron
beam
recently,
the
secondary
conditions
are
established
0 1982
Elsevier
found
these
the
use
source,
Scientific
ion
the
Above
characteristic for
the
the the
of
of
of
one (ii)
the
two
tube
(SIFT)
by working
at
Publishing
Company
of
reactions
of
reactants
value
and flow
is
constants.
of
ions,
reported
reactions
rate
complexity
been
0020-‘7381/82/0000-0000/$02.75
serious
theoretical
success
constants
are
cluster
been
thermal
their
are
over
relative
their
m are
have
more
has
over
there
association by
10 have
or
which
developed
the
ion-molecule exhibited
of
pulsed
attention
Several
been
be-
gas-cooled
agreement
for
(ref.3). have
results pressure,
general
processes in
observations.
m in
triatomic
years,
literature
dependence
of
ten
systems
interstellar
of
supports
there
early
feature
k=CTmm
formation
excess
recent
technique each
experimental
modeling
graphite
reactions too
striking
Values
in
the
the
reactions
and
of
several
in
present
reactions,
reaction.
Most
at
temperature
many
values
is
most
negative
150K,for the
it
the
although
association
explaining
Perhaps
and
reported
in
last
nevertheless
ion-molecule
years,
models
data
the
association
atmospheres
invoked
corrosion
During
are
ion-molecule
planetary
been
the
reactions
in of
of
also for
there
discrepancies models
have
(ref.2). these
interest,
chemistry
responsible
reactors
been
intrinsic the
They
be
main
few
their
importance
rises,
m rises
and
techniques: flowing
after-
technique.
a sufficiently
316 high,
pressure,
in
a SIFT
typically
80-600K.
The
ment,
the
ment,
it
in
1 - 5 Torr
apparatus;
each
techniques
third is
is
on
of
ture
end
of of
N;'+N2+M pressure
source
flowing
afterglow
and in
and
rate
in
a flowing in
and
or
in
is
unlikely
in
the
-1.5
Torr
the
range SIFT
pressure
experi-
source
a mixture
differences it
0.5
temperature
afterglow a high
system
expected,
and
the
of
experi-
third
bodies
stabilizing
that
effic-
their
dependence
four
reports
literature
of
the
tempera-
reaction
(1)
.
Two high
discrepancies
source cover
whereas
some
be
were
-+N;'+M
literature
that
pressure
principle
greatly.
there
the
in
Although to
differ
1981,
in
a one-component
are
would
the
dependence
the
in
bodies
a high
can
helium
system.
third
temperature At
usually
reactant
a multicomponent
iencies
differ
body
the
in
method
studies SIFT
the
we
(M=N2) gave
of
m reported
values
have
therefore
of
a number
constants
gave
study
m=1.7
m=1.5
and for
other
reinvestigated of
and 2.4
reactions.
a high
pressure
(refs.4,5)
systems
the
these
4.0
and
(M=He)(refs.6,7).
a
Similar
can
be
temperature
found
in
the
dependence
of
EXPERIMENTAL All
reactions
were
spectrometer
8).
The
source
Measurements the
was were
temperature
Ions
then
of
were
produced
ion
The
occurrence
of
at
the
Daly
a preamplifier erager
(Data
by the
after open
exit a high
which
they
construction
pulse
collision-induced were
of
bandwidth
shown
of
400
be
Laboratories
Ltd.)
5000-10000
cycles
were
ratios.
The
output
of
signal
recorder
or
transferred
the to
giving
to
a MINC-11
of
to
averager
using
mass (ref.
and
over
a "Baratron"
eV electrons
and
by
kHz
held the
at
a
into
was
minicomputer
with
were
respect
accelerating ion
ions.
allowed
They
-50V
full the
the
output
a "Biomac" of
minimizes
either
was
fed
through
Signal
per
Av-
channel.
signal-to-noise
displayed (D.E.C.
the
effects
1000 5 ys
acceptable
to
voltage
source
Discrimination
resolution give
were
conditions.
and
50 a time
required
MS50
gold-plated.
controlled
outside
negligible
than
and
were
grid
subjected
to
and
field-free
transmission
greater
an
controller.
decomposition
detector
to
previously
(1 Torr=133Nm-*)
measured
Inc.)
immediately
Usually,
processing.
were
under
are
Torr
pressure
slit
fitted described
flashed
- 3.2
Instruments
Automatic
as
nickel 0.5
Pressures
a 1 - 10 us
ion
towards
source
(MKS 216
source
Ltd.)
copper, of
K.
gauge
through
8kV.
of pressures
324-550
Series
accelerated
the
at
pressure
diffuse
Instruments
constructed
made range
capacitance
in
Analytical
Granville-Philips
to
studied
(Kratos
Ltd.)
on for
an
x-y
data
re-
317 The ion
pulse
of
source
certain
electrons
which
initially
number
urements
[made the
obtained
from
which sion
mode
only
after
quite of
pressure
by
had commonly
experiments
the
loss
of
charged
within
diffusion.
to
diffusion
free
been
established.
used
in
can
primary
species
ambipolar
changes
condition
source for
of
rapidly
procedure
explicitly
density
diffusion
this
normalization high
allows
a high
decays
density,the
were
conditions,
produces
be
ions
the
Below and
by
by
these of
an
a
meas-
Under processing
replaced both
the
data
analysis
reaction
and
diffu-
(ref.9). In
A+.
a one-component
+
+2
2A -IA
t
A'+
system,
wall--t
If
the
rate
to
the
total
-dlA+-I dt-
primary
be
lost
by
two
processes,
(2)
A of
(3)
diffusion
to
the
wall
is
+
k31A+~JlAl-1
assumed
to
be
inversely
proportional
pressure,
-
k'
may
+A
kr,A+.,[A,’ L
= k’[A+‘] t k”[A+‘] where
ions
= k2[Aj2
and
(4)
at
k"=k3[A]-'
.
constant
pressure
Integrating
and
replacing
]A+.]
hy
I(A+')
yields ;n
I(A+')
so
that
:n
= a plot
of
S=-(k't-
k").
k,[AJ-l)
~r S[A]= 3 should
(Pressure)
with
reaction
mixture
the
temperature
be extracted.
each
published
In do
not
system,
two
line
of
the
it
of
k2 be
-(S
+ against
intercept
extracted
dependence
S where
x Pressure)
and
components.
slope S= -(k,[A]*
k3
For
a
from
plots
obtained
By working
with
different
of
k3
on
composition
of
the
(ref.10). over
dependences
with
of
slope may
two
repeated
case,
line dependent,
a plot of
the
be obtained
is
a straight pressure
so that
components,
was
each
gives both
information
ratio
interfere this
are
a straight
could procedure
processes for
the
(5) t
k"
similar
above
results
and
+ k3),
give
of
+ k")t
against
k'
a fixed
fractions
(k'
I(A+)
-(k,[A]'
system,
by working
The
:n
-
Because
two-component
mole
I,(A")
of is
of
the
discussed
a range and
k2 course
observation fully
in
of
temperatures
k3 for
each
necessary on a more
to the
and
reaction ensure
reactions
complete
that of
account
from mixture
these could
competing interest of
this
and work
elsewhere.
RESULTS One-Component cO2-.
Systems In
pure
CO2,
(ref.9) the
rates
of
the
forward
and
back
reactions
are
so
high
318 that
equilibrium
be
is From
obtained.
values in
of
good
AS0
Good
good
of Data
work
are
SP against for
compared
This
procedure
and are
closely
analysis
compared
*
Systems
The
System.
CO/CO, varied
erature the
only
from
obtained
and
the was
k3 over
very
system
similar. in
a range
rise
of
obtained
tempfrom
Third Body
and
the
from
this
table: Third Body
----1.5 3.320.2
Source Source
experimental
obtained
following
Source
12 6 5 4 7 9
N2
m in k = CT-m
Pressure Tube Pressure Pressure
Ref.
He N2 2
Results
the
Method High Drift High High
gave
below:
nitrogen
values
and
constant,
--_ 1.5 4.0 1.7 2.4 3.8kO.3
of
considered
in
5.5
K.
by the
Ref.
co
13 14 4 9
co CO
were
at
total
This
is
switching
are
reactions.
stages
on
pressures a complex
abundance
early
made
of
the
mixtures of
0.4-2.0
system
and,
CO;' These reaction,
and
for
which Torr
in
(CO);., are
rapid
the
only
over
the
CO/CO2 the
temp-
the
late
afterglow,
the
latter
ion
compared processes
with which
being back need
are:
+ M -~~~~
co;.
+ M pm->
+ CO
to
significant
co;.
+ co2
Observations
534
(CO*);' and
be
k2
derive
(ref.10)
0.1
388-
ions
reactions to
from
range
formed
of
may
estimate.
Two-Component
ratio
NC were
obtained, -1 and mol
kJ one
of
rate
constant,
6.3
Drift Tube Flowing Afterglow High Pressure Source High Pressure Source SIFT High Pressure Source
results
298 300 300 300
Indirect
i
m in k =CT-m
T/K
14.8" 12.5 11.4 13.0
results,
could
were
Method
literature
k/10-2gcm6mol-2s-1
K-'mol-'
67.8
values
resembled
of with
equilibrium
reaction
T/K
system
the
these
values
information
f 4.65 AH'=-
decay
literature
ambient 280 300 300 287 300
of
kinetic
of
the give
no
From
association
with
5.0 1.9 8.0 10.0 1.9 4.5
study
for
P3 to the
k2,
and
AS’=-%.4
values
plots
k/10-2gcm6mol-2s-1
Q.
and
(ref.11). -1 kJ mol .
-t 2.5
ps
dependence
mol-'
literature
first-order
plots
eratures.
500
mol -'
JK-l
= 475.3
N2L
kJ
with
c 8.4
within
temperature
+ 2.9
agreement
AH&02);J
this
the
AH"=-66.1
= -88.3
to
established
+
(C02);' (C02.CO)+'
+ M + M
(7)
319
co;-
+
wall
Putting of
by
reaction
of
Q by
By working of
of
300
2.1
available
for
k7 for
the
the
The
of
range
the
451-537
from
K.
abstraction
by
the
rate
described k6 and
constant
for
k7 may
(k6+
k7Q) for
for
a given
a one-component
be
evaluated
loss
system.
and
k8 as
a
In
in
4.520.2;
no
previous
reports
no
linearity
that
reactions
CO2
containing
of other
plots
than
the
(refs.
at for
may
H2 was
used
are
measurement
found
(8)
values
literature
obtained
(6)-
with
values
of was
the
the
literature
x 10-28cm6molecules-2s-1
good
agreement
reported
CTmm was are
excellent
be
of
300K
and
this
system
for
neglected
in
data.
System.
H(C02)l
Q,
constant
loss
that
of
kg=
3.5
assumption
CO2/H2
to
There of The
of
a diffusive
x 10-28cm6molecule-2s-1 m in
a value
analysis
mation
HCOZ
Rapid CO;'
over
3% and the
protonation
to
form
of
the
5% of
pressure
same
range
CO2 ion
to
1 - 2.5
give
was
HCO;
followed
to
Torr
coupled by the
study and
the
for-
temperature
with
hydrogen
rapid
establishing
equilibrium
HCO; so
2.5 of
m=3.8?0.4.
support
rate
x 10-28cm6molecule-2s-1,
comparison.
which
which
of
and
overall
obtained.
2.0
value
an
with
values
be
k6=
The
(8) derive
similar
different
x 1o-28
15,16).
. may
together
Q may
K,
CO2 one
an analysis
with
function At
>
[CO]/[CO2]
co;.
value
---
Q=
+
co2
that
no
pendence
+
M _
kinetic
of
data
the
AH0
CO/H2
= -84.1
M
obtained
-1 i
System.
+
were
6.3
(9)
for
constant,
K-lmol
of
The
were
equilibrium
AS'=-113.4+6.35 values
H(C02);
this
system.
values
of
obtained,
kJ mol-'
in
and
CO containing
ES0
5% and
From
AH0 good
of
temperature
2 2.9
agreement
= -121.3
6.5%
the
= -79.9
kJ
with
?r 12.5 H2 were
mol
de-1
and
literature -'
J K-'mol used
to
study
(ref.11). the
reaction HCO+
+
CO
over
the
high
pressures
from
a study
values
of
of AHo in
slow conditions,
walls
and
the
component k,O
system at
300K
-2.5
I
(10)
Torr
of
2.5
and
the
the
temperature
with
was
equilibrium
kJ mol-'
agreement mol-'
M
equilibrium
variation
pressures
these
for
the
J K-'
sufficiently
0.4
+
temperatures,
= -45.2 good
lower
H(C0);
range and
= - 87.4 At
M e
pressure
obtained, AS0
f
and
!,S"
literature
range
established constant
= - 94.1 values
of
223-320
within with
K.
500
At
us
and
temperature,
+ 8.0
J K-'
mol-'
LH"
= -48.9
kJ
mol
were -1
and
(ref.4). and
for HCO'
analysis (ref.9). compared
the
temperatures, rate
of
is
removed
of
the This with
however, the
forward
either
data
by
closely
leads a literature
to
the
approach
reaction
to
to
be measured.
reaction
(10)
or
resembles
that
used
a value value,
of
0.93 estimated
equilibrium
by
Under
diffusion for
x 10e3'
was
to
a onecm6
indirectly,
mol
-2s-1 of
the
320
1.6
x 10-30cm6molecule-2s-1 -m was measured k,O= CT
as
values
(M=H2),
2.9
from
a comparison
of
3.0
(ref.16). 6.9
The
(M=CO,H2)
(M=CO),
value
of
which and
6.2
m in
the
compares
equation
with
(M=H2)
(refs.
obtained
in
literature 11,17).
DISCUSSION It those ent
is
clear
in
the
literature
laboratories
reactions.
This
perimental
pulsed
using
flow
M.
that the
temperature
is
not
obviously
The
since source,
afterglow data
and
using
a high-pressure
several
reactions
complicated
by the
that
tween
the
results
of
the
gests
that
there
are
no
the
measurement
the
equilibrium
entirely
tion plicit rather
own
Meot-Ner
in
the
assumed
for
the
loss
analysis
m.
work,
was
when
thermore,
the block
use
of
should
reduce reported
primary ion
have
a similar
of
obtain
data
a gold-plated have
both
only
that
block
establishing
diffusion,
to
a lower on
data,
reac-
The
and
taken
ex-
absothe
excited
species
although
in
in
the
than
thermal
our
late
established.
rather of
arise
for
effect
were
that
experiments, 3.25
leads
of
in
assumed
Field.
little
readings
source
to
and
source
sugor
differences own
only
set
bewhich
is
vibrationally
each
the
Field
reaction
has
for
further
agreement
it
our
usually
from
in
the
3.8
or
copper
facilitated
and
by
but
on
conditions
if
by Meot-Ner
effect
is
effects
example,
electronically
dependence
and
in
third-body, all
This
Meot-Ner
m from
~25%
the
discrimination
currents, of
in
obtained
ourselves,
good
correct
ions
a high data
very
temperature
1.7
constants
to
are of
would
rate
diffusion
of
For
Field
with
groups.
from
pressure.
of of
those
ex-
Field,usinq
and
is
differ-
a particular
temperature
other
and
association
differences
a higher
coming
normalising
taken
free
and
and
participation should
care
afterglow,
by
reactive The
work
error
and
there
measurement
allowance
reaction
steel
of
value
for
to from
errors and
the
of the
present
above
value
value
this
lead data
work between
of
Hiraoka
equilibria,
serious
well
than
lute
errors
for (1),
for
temperature
data
from
allowance
in
of
on
use
agreement
coworkers,
source, based
the
despite
and
present
ion-molecule
Yeot-Ner good
techniques,
Kebarle
that
fact
by in
the
disagreement of to
obtained general
SIFT
pulsed than
considerable
attributable
in
by
is
dependencies
data are
obtained
results
there
on
technique
pressure
of
Fur-
a stainless
equilibrium
(ref.9). There can work
be
remains
showed
errors
and
was
defined
and
since
resolution ment
the
measured
was
question
of
the
as a function
of
time.
that
the
use
a bandwidth by the
in signal
observations of
at
independently
of
excess
of
50
for
in
50
1 part
kHz
which
made
calibrated
with
which
Preliminary
bandwidth
averager were
least
a low
accuracy
of
was gave
the
primary in
pre-amplifier
a minimum
against
the
experiments
total other
could
therefore a time of
used. resolution
observation
current present
lead
to
serious
The
time
scale
of 5ps/channel
25Cps,this
pulsing
ion the
corresponds time. equipment
to
This and
equipit
is
a
321 therefore
unlikely
that
any
significant
error
in
the
measurement
of
time
was
present. Another
possible
presence to
of
exclude we the
from
our
and
is
For
the
Field SIFT
CO:
with
2.3
and
and
ourselves.
+ AB
AB +.*
t
+
AB
M
----+
overall
AB+.
sion,
since
these
not
all
Classical
tmodel
is
Imuch
Bates
(ref.18)
plex.
in When
degrees 1,
which
a reaction
non-linear
of reflects of
two
species, the
AB'. to
lower
kS
(stabilization).
k,= '*
the
is
taken
freedom the
than
usual ks
(1-S)
be
are
afterglow of of
CH< and
m between
Kebarle,
usually
Hiraoka
given
in
T
reactants of
species, between higher
of
the
lie
3 and
4. of
expresEach
to
of
This
r is
by and
and
excited
the
sum
ion-molecule
are com-
collisions, of
usually step.
3 and
for
therefore been
the between
On this
2 and
have
the
treatments
RRKM model
theory
kd. of
form,
a parameter,
between
of
number
recent the
in
111 which
that
correct
stabilization
m should
values
due
reactants
where
6 is
is
be equated
this
effective the
the
barriers -(r/Z+'?) and
is
the of
a development
kf
temperature-dependent
More
of
ka can of
stabilization.
kf
S is
value.
of
that
to
is
where
fraction
of
this
functions
kf=kakS/kd
weakly
, where
centrifugal
lie
Meot-Ner
discrepancy.
assume
some
only
predictive
efficiency
the
to is
lead
Although
of
flowing
by
is
to
dependence
dependence
linear
is that
to
partition of
reasonably of
values
this
leads
necessarily
CT
report m obtained of
theory
(ref.19)
of
m should rather
(dissociation)
It
be of
a temperature
rotational
kd
and
to
Herbst
account
predicts
0 and
crude
terms
(association)
temperature
leads
in
Kebarle
results
reactions
reactions
ka
expected the
Field,
(ref.3):
will
complex
and
formulated
this
of
the too
ion-molecule
expression
therefore
RRK theory in
no explanation
steady-state
collisions
source
oscillators
have
constant.
ADO
is
major
of
M
rate or
processes the
t limit,
forward
Langevin
Smith
and
of
is
using
association
and
error. m obtained
results
hand,
obtained
values
of
of
dependence
any
mechanism
the
other
Adams
of
value
em-
by Meot-Ner
with
than
tB
pressure
results
the difficult
consistency.
temperature
ion-molecule
+.*
>A "
low
we
treatment
+.*
the
a*ld
present,
source the
such
is
very
procedures
m obtained to
On the
the of
lower
energy-transfer
B
the
the to
the
with
(ref.7),
appreciably At
the
is
purification
agreement
Hiraoka.
a study
of
lend
good
(lo),
accord
the
type
it
possible,
value
this
a significant
is
the
of systems,
of
were
is
of
most
view
would
there
neutrals
in
times
data
in
measurement In
comparison
reaction
in
theoretical of
0.05
the
more
several
The terms
In
for
any
impurities
which
impurities
techniques;
3.4,
that
i
with
are
but
system,
and
and
completely
that
agreement
A+.
2.25
nitrogen
and
ports
is
in
reactants.
for
unlikely
error
the
believe
systems
coworker,
good
for
not
data
it
and
do
three
of
in
impurities
ployed, For
source
impurities
determined
basis, two sup-
322 experimentally.
A shortcoming
conserve
angular
phase
space
which
the
for
are
the
to
of
m in
the
two
We thank tricity and
for
reason
for
of
values.
Science
and
Generating Or.
A.
J.
each favor
Board Wickham
for
of
"low"
this
for
financial
helpful
systems
in
for
Research support
will
the of
which
no
during
between
fall them
is there
and the
data
reactions.
choice
Council
interesting
experimental
present firm
two
future.
comparison
at
the
laboratories
ratio
of in
data
be
near
different
but and
of
association
the
terms
systems
experimental it
body
in
values,
discrepancy
Engineering
with and
rigorously in
for
predictions
amines
values,
systems
lower
not
reactions
the
accepted
does
but
ion-molecule
m determined
three the
other
of
and
these
agreement of
generally
kf=CT-
to
sets the
no
values
good
to
it
shortcoming low,
dimers
dependence
equation
appears
experimental
tween
as yet
"high" 2.25
RRKM theory ous
the
groups:
approximately
is
gives
proton
that
of
this
relatively
application
temperature
is
description
is
theory of
its
there the
two
The
of
RRKM theory
removes
momentum
formation
results
summary,
Values into
of
the
describing
20,Zl)
similar.
the
A recent
(refs. angular
rates
see In
momentum.
theory total
theories
of
can
the
course
being
possible. is
no
be
made
obvi-
Central
Elec-
of
work,
this
be-
discussions.
REFERENCES 1 2 3 4 5 6
9
l? 12 13 14
1': 17 18 19 20 21
W.T. Huntress, Chem. Sot. Rev. 6, (1977), 295. A.J. Wickham, Chemistry in Britain, Is, (1979), 286. M. Meot-Ner in "Gas Phase Ion Chemistry", Vol.1, M.T. Bowers, ed., Academic Press, New York, 1979, pp. 198-271. M. Meot-Ner and F.H. Field, J. Chem. Phys., 61, (1974), 3742. J.D. Payzant and P. Kebarle, J. Chem. Phys., 53, (1970), 4723. D.K. BEhme, D.B. Dunkin, F.C. Fehsenfeld and E.E. Ferguson, J. Chem. Phys., 51, (1969), 863. N.G. Adams and D. Smith, Chem. Phys. Lett., 79, (1981), 563. D.K. BGhme, J.A. Stone, R.S. Mason, R.S. Stradling and K.R. Jennings, Int. J. Mass Spectrom. Ion Phys., 37-, (1981), 283. J. Chem. Sot. Faraday Trans. I, J.V. Headley, R.S. Mason and K.R. Jennings, 78, (1982), 933. J.V. Headley, R.S. Mason and K.R. Jennings (unpublished work). M. Meot-Ner and F.H. Field, J. Chem. Phys., 66-, (1977), 4527. J.T. Moseley, R.M. Snuggs, D.W. Martin, and E.W. McDaniel, Phys. Rev., 178, (1969), 240. L.W. Sieck and R. Gorden, J. Res. Natl. Bur. Stand., Sec.A, 78, (1974), 315. J.H. Schummers, G.M. Thomson, D.R. James, I.R. Gatland and E.W. McDaniel, Phys. Rev. A, 7, (1973), 683. A.B. Rakshit and P. Warneck, Z. Naturforsch., a, (1979), 1410. L.W. Sieck, Int. J. Chem. Kin., lo, (1978), 335. K. Hiraoka, Int. J. Mass Spectrom. Ion Phys., 2, (1980), 73. D.R. Bates, J. Phys., E, (1979), 4135; J.Chem.Phys., 73, (1980) 1000. E. Herbst, J. Chem. Phys., 2, (1979), 2201; 72, (198Or; 5284. L.M. Bass, W.J. Chesnavich and M.T. Bowers, J. Am. Chem. Sot., 101, (1979), 5493. L.M. Bass, P.R. Kemper, V.G. Anicich and M.T. Bowers, J. Am. Chem. Sot., lOJ, (1981), 5283.