Collisional quenching of Ga(5p) atoms by H2, D2 and CH4

Article abstract of DOI:10.1016/S0009-2614(98)00323-6

Collisional quenching of Ga(5p) atoms by H₂, D₂ and CH₄ has been studied. The gallium atoms were generated by photolysis of trimethyl gallium using a KrF laser. The Ga(5p) state was populated by two-photon excitation from the ground state and cascade fluorescence from Ga(5s) atoms was analyzed to extract quenching rate constants for Ga(5p) atoms. The apparent quenching rate constants for Ga(5p) atoms are (4.6±0.3)×10^-10, (3.4±0.3)×10^-10 and (7.8±0.2)×10^-11 cm³ molecule^-1 s^-1 by H₂, D₂ and CH₄, respectively. It is found that the predominant process for the large quenching rate constants for Ga(5p) atoms by H₂ and D₂ is the energy transfer for Ga(5s) formation.

Full text of DOI:10.1016/S0009-2614(98)00323-6

22 May 1998
Ž
.
Chemical Physics Letters 288 1998 531–537
ž /
Collisional quenching of Ga 5p atoms by H2, D2 and CH4
K. Lee, H.S. Son, S.C. Bae, J.K. Ku
Department of Chemistry, Pohang UniÕersity of Science and Technology, Pohang, Kyungbuk 790-784, South Korea
Received 26 January 1998; in final form 27 February 1998
Abstract
Collisional quenching of Ga 5p atoms by H2, D2 and CH4 has been studied. The gallium atoms were generated by
Ž
.
Ž
.
photolysis of trimethyl gallium using a KrF laser. The Ga 5p state was populated by two-photon excitation from the ground
Ž
.
Ž .
state and cascade fluorescence from Ga 5s atoms was analyzed to extract quenching rate constants for Ga 5p atoms. The
y
10
y
10
y11
Ž
.
Ž
.
Ž
.
Ž
.
apparent quenching rate constants for Ga 5p atoms are 4.6"0.3 =10 , 3.4"0.3 =10
and 7.8"0.2 =10
cm3 moleculey sy by H2, D2 and CH4, respectively. It is found that the predominant process for the large quenching rate
1
1
Ž
.
Ž .
constants for Ga 5p atoms by H2 and D2 is the energy transfer for Ga 5s formation. q 1998 Elsevier Science B.V. All
rights reserved.
Ž
.
1. Introduction
to investigate the reactivity of Ga 5p atoms with H2
and CH4.
The collisional quenching and reactions of elec-
tronically excited metal atoms have been an area of
In this Letter, we report the results of collisional
Ž
.
quenching studies of Ga 5p atoms in H2 , D2 and
w
x
Ž .
active research and of continuing interest 1,2 . Up to
date the low-lying excited states of Group-1, -2, and
CH4. The Ga 5p levels are located ;1 eV above
the Ga 5s state and ;0.2 eV below the Ga 4d
Ž
.
Ž .
w x
-12 metals are most extensively studied 1 , and
levels. They can be easily populated from the
w
x
Ž .
results for other metals are not so many 3–6 .
ground-state Ga 4p atoms by two-photon excitation.
Because of the much longer radiative lifetimes of the
Recently, it has been reported that the excited states
2
of Ga atoms 2 S or D react with H2 and CH4
Ga 5p atoms than that of the Ga 5s atoms, the
Ž
.
Ž .
Ž .
w
x
.
w x
Ž .
molecules in Ar matrices 3–5 . Mitchell et al. 6
kinetic behavior of the Ga 5p atoms can be obtained
Ž
studied the reactivity of Ga 5s atoms with small
molecules including H2 and CH4 in the gas phase.
They found that H2 was very inefficient for quench-
by analyzing the cascade fluorescence from the
Ž
.
Ga 5s level following two-photon excitation of the
w x
Ž
.
Ga 5p level 8 . Kinetic simulations were done to
Ž
.
Ž .
ing of the Ga 5s atoms. They also observed a large
examine the relative magnitudes of the Ga 5s for-
mation and the sum of physical and chemical
quenching rate constants from the quenching of
Ž
.
quenching rate constant for the Ga 5s atoms by CH4
3.8"0.4 =10
y10
cm3 moleculey1 sy1 and re-
ŽŽ
.
.
Ž .
ported that ;27% of the total quenching rate con-
stant lead to a chemical reaction. Since the radiative
Ga 5p atoms by H2 , D2 and CH4. It was found that
Ž .
Ga 5p atoms are quenched very effectively by H2
Ž
.
Ž .
lifetimes of the Ga 5p levels are much longer than
and D2 , and Ga 5s atoms are formed predominantly
Ž
.
w
x
Ž .
that of Ga 5s state 7,8 , it would also be interesting
as the collisional product. The quenching of Ga 5p
0009-2614r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved.
Ž
.
PII: S0009-2614 98 00323-6

(
)
532
K. Lee et al.rChemical Physics Letters 288 1998 531–537
Ž
.
atoms by CH4 was less efficient than H2 and D2 , but
cooled Hamamatsu R928 photomultiplier PM tube.
The signal from the PM tube was digitized with a
Ž
.
Ga 5s was not formed.
Ž
.
transient digitizer Tektronix 7912HB and trans-
ferred to a laboratory computer for signal average
and storage.
2. Experimental
The experimental setup is similar to that previ-
3. Results
w x
ously reported 9 , but the ground-state Ga atoms are
Ž
.
generated by photolysis of trimethyl gallium TMGa
(
)
3.1. Cascade fluorescence kinetic scheme for Ga 5p
atoms
Ž
.
using a KrF laser Questek 2460 instead of a pulsed
discharge. Briefly, the cell was made of a 2 l Pyrex
bulb and two pairs of 1 in. Pyrex O-ring joints were
attached to allow laser beam paths. The sample gas
Ž
.
The direct emission from Ga 5p levels is difficult
to observe, because the emission wavelength for
Ž
.
0.1% TMGa in H2 , D2 or CH4 was premixed and
Ž
.
Ž .
Ga 5p ™Ga 5s transition is 1195 nm, which is
beyond the detection limits of most photomultiplier
tubes. Nevertheless, kinetic information for the
stored in a storage bulb on the vacuum rack. The
partial pressure of the TMGa in the cell was kept
Ž
.
constant ;1.0 mTorr by loading constant amounts
Ž
.
Ga 5p levels can be obtained by analyzing the
Ž
.
of the premixed sample gas 0.1% TMGa and adding
Ž
.
cascade fluorescence from the Ga 5s level following
additional amounts of H2 , D2 or CH4 to the cell to
Ž
.
the Ga 5p excitation. The kinetic scheme for the
Ž
.
Ž .
investigate the quenching of Ga 5s and Ga 5p atoms
by these gases. The cell was completely evacuated
after collection of one fluorescence time profile at a
specific pressure and filled with a new mixture to
obtain another time profile.
Ž
.
two-photon excitation of Ga 5p state in the presence
of a buffer gas M H2 , D2 or CH4 can be written as
followings.
Ž
.
Ga 4p q2hn 603.2 nm ™ Ga 5p, 2 P
,
1
Ž
.
Ž
.
Ž .
ž
/
3r 2
The pulse energy of the KrF laser was 55
mJrpulse and the laser beam was focused with a 50
cm focal length lens to generate free Ga atoms. Both
the excimer and YAG-DYE lasers were controlled
by a dual channel pulse generator and the delay time
1
rt1
Ga 5p ™ Ga 5s qhn 1195 nm ,
2
Ž
.
Ž
.
Ž
.
Ž .
kq1
Ga 5p qM ™ Ga 5s qM ,
3a
3b
Ž
.
Ž
.
Ž
Ž
.
.
Ž
between the photolysis and excitation laser pulses 8
kq2
.
ns FWHM was set 3–4 ms to allow the excited
species to decay. The Ga 5s atoms were formed by
™ Ga 4p qM ,
Ž
.
Ž
.
single-photon excitation at 403.3 nm, and the fluo-
kc1
™ other products chemical quenching ,
Ž
.
Ž
.
rescence was monitored at 417.2 nm. The Ga 5p
atoms, however, were generated by two-photon exci-
tation at either 605.3 or 603.2 nm and the cascade
3c
Ž
.
1
rt2
Ž
.
fluorescence from the Ga 5s state was monitored at
417.2 nm. The pulse energy of the visible laser beam
was 5.5 mJrpulse and the laser beam was loosely
focused using a 1 m focal length lens to generate
Ga 5s ™ Ga 4p qhn 417.2 and 403.3 nm ,
Ž
.
Ž
.
Ž
.
4
Ž .
kq3
Ž
.
Ga 5p atoms. The line width of the dye laser
Ga 5s ™ Ga 4p qM ,
5a
Ž
.
Ž
.
Ž
.
Ž
.
Quantel YG681-TDL60 with NBP and DGO was
narrow -0.1 cm
y1
Ž
.
enough to excite a single
kc2
™ other products chemical quenching .
Ž
.
spin-orbit state selectively.
Ž
.
The fluorescence from the Ga 5s atoms was de-
5b
Ž
.
tected at 908 from the laser beam direction through a
Ž
.
0.5 m monochromator Spex 1870C equipped with a
The formation and decay of the excited states of Ga

(
)
K. Lee et al.rChemical Physics Letters 288 1998 531–537
533
(
)
(
)
atoms can be expressed by the following coupled
differential equations.
3.2. Collisional quenching of Ga 5s and Ga 5p
atoms in H2 , D2 and CH4
d Ga 5p
Ž
.
sF t
Ž .
Ž
.
The Ga 5s state was excited at 403.3 nm and the
fluorescence was monitored at 417.2 nm. The pres-
sure dependence of the fluorescence decay rates
dt
1
w x
y
q kq1 qkq2 qkc1
M
Ž
.
½
5
Ž
.
from Ga 5s excitation is shown in Fig. 1a. Because
of the large difference in the pressure range, the
pressure dependence of the decay rate in CH4 is
shown in the insert. The total quenching rate con-
t1
= Ga 5p
,
6
Ž
.
Ž .
d Ga 5s
Ž
.
Ž
.
stants for the Ga 5s state by H2 , D2 and CH4 are
dt
y12
y12
Ž
.
Ž
.
Ž
1.1"0.2 =10 , 1.6"0.2 =10
and 3.8"
y10
1
.
0.3 =10
cm3 moleculey1 sy1, respectively. The
w x
M
s
qkq1
Ga 5p
Ž
.
½
5
total quenching rate constants obtained in this work
t1
1
w x
M
.
y
q kq3 qkc2
Ga 5s
,
7
Ž .
Ž
.
Ž
½
5
t2
Ž .
where F t denotes the formation rates for the laser
excited state. The chemical quenching rate constants
Ž
.
Ž .
for the Ga 5p and Ga 5s atoms are included in the
kc1 and kc2 , respectively. If the deactivation rates for
Ž
.
the Ga 5p atoms were much slower than the forma-
Ž .
tion rates, F t could be assumed to be a d-function
and could be dropped from the rate equation. In that
Ž
.
case, the concentration of the Ga 5p atoms vs. time
Ž .
can be expressed by Eq. 8 ,
Ga 5p t s Ga 5p exp yb t ,
8
Ž .
Ž
. Ž .
Ž
.
Ž
.
1
0
Ž
.w
x
where b1 s1rt1 q kq1 qkq2 qkc1 M . Substitut-
Ž . Ž .
ing Eq. 8 into Eq. 7 , and solving for the time
dependence of the Ga 5s concentrations, Eq. 9 is
Ž
.
Ž .
obtained,
b2
Ga 5s t s
. Ž .
Ga 5p
Ž
Ž
.
0
b3 yb1
= exp yb t yexp yb t
4
.
,
Ä
Ž
.
Ž
1
3
9
Ž .
w
x
Ž
where b2 s1rt1 qkq1 M , and b3 s1rt2 q kq3
q
.w
x
kc2 M . Since t1 4t2 for the present case, the
Ž .
effect of second exponential term in Eq. 9 on the
Ga 5s t can be neglected when b3 t4b1t. Thus,
w
Ž
.xŽ .
the pressure dependence of the time constant b1 can
be obtained by analyzing the latter part of the cas-
cade fluorescence time profiles at low pressures, and
the radiative lifetime and the total quenching rate
2
Ž .
Ž
.
.
Fig. 1. Pressure dependence of decay rates of
and
a
Ga 5s, S1r2
2
Ž . Ž . Ž . Ž
b Ga 5p, P3r2 states in H2 ^——^ , D2 B——B
and CH4 `——` . The apparent quenching rate constants are
Ž
.
Ž
.
constant for the Ga 5p states can be obtained.
shown in Table 1.

(
)
534
K. Lee et al.rChemical Physics Letters 288 1998 531–537
are in good agreement with those of Mitchell et al.
w x
6 . The zero-pressure intercepts, 7.1"0.2 ns, also
are in good agreement with those previously reported
Ž
.
w
x
radiative lifetimes of Ga 5s state 6,8 .
2
Ž
.
The Ga 5p, P3r2 level was populated by two-
photon excitation at 603.2 nm, and the cascade fluo-
Ž
.
rescence from Ga 5s state was monitored at 417.2
nm. The pressure dependence of the decay rate
constants of the cascade fluorescence is plotted in
Ž
.
Fig. 1b. Since the radiative lifetimes for the Ga 5s
Ž
.
w
x
state is much shorter than that for Ga 5p state 6–8 ,
the pressure dependence of the decay rate constants
Ž
.
shown in Fig. 1b corresponds to the Ga 5p state. As
shown in Fig. 1b, H2 and D2 are very efficient for
Ž
.
Fig. 2. Cascade fluorescence intensities from Ga 5s vs. pulse
Ž
.
quenching of the Ga 5p state. The apparent total
energies of the photolysis laser at constant TMGa concentration
Ž
.
quenching rate constants for the Ga 5p state by H2 ,
D2 and CH4 are shown in Table 1. The zero-pres-
sure intercepts correspond to 56"2 ns, which is in
good agreement with the previously reported radia-
Ž
.
1.2 mTorr .
Ž
.
w
x
tive lifetimes of the Ga 5p state 7,8 . When the
we attempted to assign the relative magnitude of kq1
and kq2 qkc1. The relative magnitude of kq1 and
kq2 qkc1 can be assigned if one can generate the
2
Ž
.
Ga 5p, P1r2 level was excited at 605.3 nm, the
same results were obtained. Since the energy differ-
Ž
.
ence between the two spin-orbit states of Ga 5p
Ž
.
same amounts of Ga 5p atoms at different total
atom is only 111 cmy1, collisional mixing between
the two levels seemed to be very fast.
Ž
.
pressures. When the same amounts of Ga 5p atoms
are generated, then the time-integrated emission in-
Ž
.
tensities from Ga 5s state can be used to extract the
relative magnitude of kq1 and kq2 qkc1. For this
purpose, we have investigated the dependence of the
(
)
3.3. Branching fractions for E–V transfer for Ga 5p
qH2 rD2 rCH4
Ž
.
The apparent total quenching rate constants for
Ga 5s emission intensities on the pulse energies of
the photolysis laser at constant concentration of
Ž
.
the Ga 5p state by H2 and D2 are very large, and
Table 1
Ž
.
Ž .
Apparent quenching rate constants and branching fractions for collisional quenching of Ga 5p and Ga 5s atoms
Apparent quenching rate constant
s a
Process
Branching fractions
3
cm moleculey1 sy1
˚
Ž .
A
Ž
.
y10
Ž
.
Ž
.
Ž .
H2
4.6"0.3 =10
25.6"1.7
Ga 5p qH2 ™ Ga 5s qH2
)0.9
-0.1
™ othersb
y12
Ž
Ž
.
Ž .
1.1"0.2 =10
0.06"0.01
26.4"2.3
Ga 5s qH2 ™ quenching
y10
.
Ž
.
Ž .
D2
3.4"0.3 =10
Ga 5p qD2 ™ Ga 5s qD2
)0.9
-0.1
™ othersb
y12
Ž
Ž
.
Ž .
1.6"0.2 =10
0.12"0.02
11.2"0.3
Ga 5s qD2 ™ quenching
y11
.
Ž
.
Ž .
CH4
7.8"0.2 =10
Ga 5p qCH4 ™ Ga 5s qCH4
-0.1
)0.9
0.73c
0.27c
™ othersb
y10
Ž
.
Ž
.
Ž .
3.8"0.3 =10
54.6"4.3
Ga 5s qCH4 ™ Ga 4p qCH4
™ chemical quenching
a
1r2
² :
² :
Ž
.
sskqr Õ at 298 K; Õ s 8 kTrpm
.
bSum of physical and chemical quenching processes.
c
w x
Ref. 6 .

(
)
K. Lee et al.rChemical Physics Letters 288 1998 531–537
535
Ž
.
TMGa 1.2 mTorr . The pulse energy of the pump
laser was also kept constant during this series of
experiments. The cascade fluorescence intensities vs.
pulse energies of the photolysis laser are plotted in
Fig. 2, which shows the second-order dependence at
low energies and saturation effects at high energies.
Based on Fig. 2, we have collected a new set of time
The pressure dependence of the cascade fluores-
cence intensities following two-photon excitation of
Ž
.
Ga 5p atoms in H2 and D2 is shown in Fig. 3a and
that in CH4 is plotted in Fig. 3b. The time-integrated
cascade fluorescence intensities are effectively con-
stant in H2 and D2 as shown in Fig. 3a. Kinetic
simulations were done to find out the relative magni-
tudes of kq1 and kq2 qkc1. The solid lines in Fig. 3a
are the expected variation of the cascade fluores-
Ž
.
profiles at constant ;1.0 mTorr TMGa concentra-
tion, and reinvestigated the dependence of the cas-
cade fluorescence intensities on the H2rD2rCH4
pressures. To ensure the saturation condition shown
in Fig. 2, 55 mJrpulse was used to photolyze the
TMGa in the cell.
Ž .
cence intensities in H2 calculated from assigning i
Ž .
Ž .
Ž .
100%, ii 90%, iii 80% and iv 0% of the appar-
ent quenching rate constant to kq1, respectively. The
calculated results in D2 are almost overlapped with
those in H2. It is seen that the experimental data
points match pretty well with the calculated results
Ž .
i , and the dominant quenching channel is that given
Ž
.
by Eq. 3a .
On the other hand, the cascade fluorescence inten-
sities in CH4 decrease with pressure as shown in
Fig. 3b. The expected fluorescence intensities calcu-
Ž .
Ž .
Ž .
lated from assigning i 100%, ii 20% and iii 0%
of the total quenching rate constant to kq1 also are
shown as solid lines. The experimental data points in
Ž .
CH4 match well with the calculated results iii ,
which implies the dominant quenching processes are
Ž
.
Ž .
those given by Eqs. 3b and 3c . Comparison of the
experimental and calculated results shows that the
Ž
.
collisional branching fractions for the Ga 5s forma-
Ž
.
tion from Ga 5p states are larger than 0.9 in H2 and
D2 , but less than 0.1 in CH4 as shown in Table 1.
4. Discussion
The absorption coefficient of TMGa at 248 nm is
w
x
not large 10–12 . Thus, slight focusing of the KrF
laser beam was needed to generate bare Ga atoms in
the gas phase. The excited states of Ga atoms formed
by the photolysis laser, however, decay very effec-
tively to the ground state by direct or cascade fluo-
rescence. Hence, 3–4 ms delay time was long enough
to ensure exclusion of these excited species for the
present work.
Since H2 , D2 and CH4 do not absorb photons at
248 nm, the pressure variation of these gases in the
cell does not affect appreciably the energy densities
of the photolysis laser beam. The dissociation energy
Fig. 3. Pressure dependence of the cascade fluorescence intensities
Ž
.
Ž .
from Ga 5s state following two-photon excitation of Ga 5p state;
Ž .
a
Ž
.
Ž .
Ž
. Ž .
Ž
.
in H2 ^——^ , D2 B——B ,
The solid lines in
b
in CH4 `——` .
correspond to the variation of the cascade
Ž . Ž .
a
fluorescence intensities calculated from assigning
i
100%, ii
90%, iii 80% and iv 0% of the apparent quenching rate
Ž .
Ž
.
Ž .
constant to kq1 and those in
Ž .
b
correspond to the calculated
Ž .
Ž
.
results from assigning
i
100%, ii 20% and iii 0% of the
quenching rate constant to kq1
.

(
)
536
K. Lee et al.rChemical Physics Letters 288 1998 531–537
Ž
.
of TMGa to generate a bare Ga atom is ;7.44 eV.
Thus, the second-order dependence of the emission
intensities at low energies of the photolysis laser
shown in Fig. 2 is consistent with the energy require-
ment for the dissociation of TMGa. The saturation
effect of the emission intensities observed at higher
pulse energies of the photolysis laser supports that
the concentration of TMGa in the irradiation volume
atoms. The quenching rate constant for Ga 5s atoms
by CH4 measured in this work is essentially the
w x
same as that from Mitchell et al. 6 . Mitchell et al.
Ž
.
have shown that ;30% of the Ga 5s quenching
rate constant by CH4 leads to chemical quenching.
Considering the large apparent quenching rate con-
Ž
.
stant for the Ga 5s and much smaller quenching rate
Ž
.
constant for the Ga 5p atoms, there must be some
Ž .
Ž
.
Ž
.
is a limiting factor. Also, Ga 5p atoms cannot be
generated directly from TMGa by the pump laser
beam, because the power density from the weakly
favorable energy transfer exit channel s for Ga 5s
Ž
.
qCH4, which are closed for the Ga 5p qCH4
case. Since the detailed interaction potential surfaces
for the GaqCH4 system are not known, we cannot
Ž
focused visible pump laser beam 603.2 nm; 5.5
.
w x
Ž
.
Ž .
mJrpulse is not enough to dissociate TMGa 13 . In
fact, no emission from Ga 5s state was observed
without the preceding photolysis laser pulse.
It is well known that efficient quenching of the
explain the intriguing results for the Ga 5s rGa 5p
Ž
.
qCH4 system.
The reactions of excited states of Group-13 ele-
ments with H2 and CH4 in low-temperature matrices
Ž
w
x
excited states of Group-2 and -12 metal atoms Mg,
have been studied by many groups 3–5,17–20 , and
it has been reported that the first excited S and D
2
2
.
Zn, Cd and Hg by H2rD2 gives MH or H–H bond
dissociation 1,14,15 . In spite of the large quenching
w
x
states react with CH4 as well as H2. Since the CH4
quenches Ga 5s atoms very efficiently in the gas
Ž
.
Ž
.
cross-section for the Ga 5p atoms by H2 and D2 ,
chemical quenching for GaHrGaD or GaH2rGaD2
formation is not an important exit channel, and
efficient electronic to vibrational–rotational–transla-
tional energy transfer processes are open for the
Ž
.
phase, there is no doubt that Ga 5s atoms react
readily with CH4. However, the inefficient quench-
ing of Ga 5s atoms by H2 in the gas phase observed
by Mitchell et al. 6 and in this work suggests that
the reactions in the matrices may not be so efficient
Ž
.
w x
Ž
.
Ga 5p qH2rD2 cases. The large apparent quench-
ing cross-sections for Ga 5p atoms by H2 and D2 as
Ž
.
Ž
.
for the Ga 5s with H2.
well as the large collisional branching fractions for
Ž
.
the Ga 5s formation observed in this work could be
explained by the curve crossing mechanism. Mar-
Acknowledgements
w
x
tinez-Magadan et al. 16 reported potentials for the
ground state and low-lying excited states of Ga
interacting with a H2 molecule. Since the potential
This work is financially supported in part by the
Korea Science and Engineering Foundation through
the Center for Molecular Science at KAIST and in
part by the Ministry of Education through the Basic
Ž
.
.
Ž
.
for Ga 5p qH2 Õs0 is less repulsive than that for
Ž
Ž
.
Ž
.
Ž
Ga 5s q H 2 Õ s 0 , the Ga 5s q H 2 Õ s
Ž
.
.
Ž
.
Ž .
Science Research Institute Program BSRI-96-3438 .
1, 2 rD2 Õs2, 3 potentials cross the Ga 5p q
Ž
.
H2 Õs0 potential at about the Van der Waals
˚
Ž
.
distance 2.80 A resulting in efficient quenching.
References
However, there is no appropriate exit channel for the
Ž
.
Ga 5s qH2rD2 collision pairs, and the small ap-
w x
Ž
.
1
H. Breckenridge, H. Umemoto, Adv. Chem. Phys. 50 1982
325.
Ž
.
parent quenching rate constants for the Ga 5s atoms
are consistent with the curve crossing model.
w x
2
A. Fontijn, Gas-Phase Metal Reactions, Elsevier, New York,
1991.
R.D. Lafleur, J.M. Parnis, J. Phys. Chem. 96 1992 2429.
Ž
.
The observed results for the quenching of Ga 5p
atoms by CH4 is very puzzling. Virtually no branch-
ing to the Ga 5s formation might imply that the
measured rate constant is dominated by chemical
quenching, even though we were not able to assign
kq2 and kc1 separately. However, the magnitude of
w x
Ž
.
3
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